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Author: William A. Stein
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'203.252'
************** MAGMA *****************
Host 203.252.48.247 (203.252.48.247)
Time: Sat Dec 31 14:53:23 2005

Input: 
nat:=5;
pairs:=[{i,j}: i in [1..j-1], j in [1..nat]];
G:=PermutationGroup<#pairs |
  [[Index(pairs,p^g): p in pairs]:
    g in [(1,2),(1,2,3),(4,5)]]>;

Rat:=Rationals();
R0:=InvariantRing(G,Rat);

PI:=PrimaryInvariants(R0);
print "*** Primary invariants";
PI;
#PS:=SecondaryInvariants(R0);
#print "*** Secondary invariants";
#PS;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Sat Dec 31 2005 14:53:03 on modular  [Seed = 350336662]
   -------------------------------------


Errors: /bin/sh: line 1: 24073 Alarm clock             nice -n 19 /usr/local/bin/magma


'203.252'
************** MAGMA *****************
Host 203.252.48.247 (203.252.48.247)
Time: Sat Dec 31 14:31:06 2005

Input: 
nat:=5;
pairs:=[{i,j}: i in [1..j-1], j in [1..nat]];
G:=PermutationGroup<#pairs |
  [[Index(pairs,p^g): p in pairs]:
    g in [(1,2),(1,2,3),(4,5)]]>;

Rat:=Rationals();
R0:=InvariantRing(G,Rat);

PI:=PrimaryInvariants(R0);
print "*** Primary invariants";
PI;
PS:=SecondaryInvariants(R0);
print "*** Secondary invariants";
PS;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Sat Dec 31 2005 14:30:45 on modular  [Seed = 4161628035]
   -------------------------------------


Errors: /bin/sh: line 1: 24038 Alarm clock             nice -n 19 /usr/local/bin/magma


'203.252'
************** MAGMA *****************
Host 203.252.48.247 (203.252.48.247)
Time: Sat Dec 31 14:13:07 2005

Input: nat:=4;
pairs:=[{i,j}: i in [1..j-1], j in [1..nat]];
G:=PermutationGroup<#pairs |
  [[Index(pairs,p^g): p in pairs]:
    g in [(1,2),(3,4)]]>;

Rat:=Rationals();
R0:=InvariantRing(G,Rat);

PI:=PrimaryInvariants(R0);
print "*** Primary invariants";
PI;
PS:=SecondaryInvariants(R0);
print "*** Secondary invariants";
PS;


Output: Magma V2.11-10    Sat Dec 31 2005 14:13:07 on modular  [Seed = 3409858710]
   -------------------------------------

*** Primary invariants
[
    x1,
    x2 + x3 + x4 + x5,
    x6,
    x2^2 + x3^2 + x4^2 + x5^2,
    x2*x3 + x4*x5,
    x2*x4 + x3*x5
]
*** Secondary invariants
[
    1,
    x2^3 + x3^3 + x4^3 + x5^3
]

Total time: 0.210 seconds, Total memory usage: 3.43MB


'203.252'
************** MAGMA *****************
Host 203.252.48.247 (203.252.48.247)
Time: Sat Dec 31 14:03:34 2005

Input: nat:=3;
pairs:=[{i,j}: i in [1..j-1], j in [1..nat]];
G:=PermutationGroup<#pairs |
  [[Index(pairs,p^g): p in pairs]:
    g in [(1,2),(1,2,3)]]>;

Rat:=Rationals();
R0:=InvariantRing(G,Rat);

PI:=PrimaryInvariants(R0);
print "*** Primary invariants";
PI;
PS:=SecondaryInvariants(R0);
print "*** Secondary invariants";
PS;


Output: Magma V2.11-10    Sat Dec 31 2005 14:03:33 on modular  [Seed = 3744090820]
   -------------------------------------

*** Primary invariants
[
    x1 + x2 + x3,
    x1^2 + x2^2 + x3^2,
    x1^3 + x2^3 + x3^3
]
*** Secondary invariants
[
    1
]

Total time: 0.200 seconds, Total memory usage: 3.43MB


'212.138'
************** MAGMA *****************
Host 212.138.47.21 (212.138.47.21)
Time: Tue Dec 20 09:25:33 2005

Input: P<x,y,z,u,v>:=PolynomialRing(RationalField(),5); I:=ideal<P |
-x + (y^2+1),
-y + (z^2+1),
-z + (u^2+1),
-u + (v^2+1),
-v + (x^2+1) >;
Radical(I);

Output: Magma V2.11-10    Tue Dec 20 2005 09:25:32 on modular  [Seed = 2940532906]
   -------------------------------------

Ideal of Polynomial ring of rank 5 over Rational Field
Lexicographical Order
Variables: x, y, z, u, v
Dimension 0, Radical
Groebner basis:
[
    x - v^16 - 8*v^14 - 32*v^12 - 80*v^10 - 138*v^8 - 168*v^6 - 144*v^4 - 80*v^2
        - 26,
    y - v^8 - 4*v^6 - 8*v^4 - 8*v^2 - 5,
    z - v^4 - 2*v^2 - 2,
    u - v^2 - 1,
    v^32 + 16*v^30 + 128*v^28 + 672*v^26 + 2580*v^24 + 7664*v^22 + 18208*v^20 + 
        35296*v^18 + 56472*v^16 + 74944*v^14 + 82432*v^12 + 74624*v^10 + 
        54792*v^8 + 31776*v^6 + 13888*v^4 + 4160*v^2 - v + 677
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'212.138'
************** MAGMA *****************
Host 212.138.113.12 (212.138.113.12)
Time: Tue Dec 20 09:24:52 2005

Input: P<x,y,z,u,v>:=PolynomialRing(RationalField(),5); I:=ideal<P |
-x + (y^2+y+1),
-y + (z^2+z+1),
-z + (u^2+u+1),
-u + (v^2+v+1),
-v + (x^2+x+1) >;
Radical(I);

Output: Magma V2.11-10    Tue Dec 20 2005 09:24:51 on modular  [Seed = 2975524571]
   -------------------------------------

Ideal of Polynomial ring of rank 5 over Rational Field
Lexicographical Order
Variables: x, y, z, u, v
Dimension 0, Radical
Groebner basis:
[
    x - v^16 - 8*v^15 - 40*v^14 - 140*v^13 - 390*v^12 - 884*v^11 - 1702*v^10 - 
        2790*v^9 - 3980*v^8 - 4900*v^7 - 5282*v^6 - 4876*v^5 - 3910*v^4 - 
        2580*v^3 - 1440*v^2 - 567*v - 183,
    y - v^8 - 4*v^7 - 12*v^6 - 22*v^5 - 35*v^4 - 38*v^3 - 37*v^2 - 21*v - 13,
    z - v^4 - 2*v^3 - 4*v^2 - 3*v - 3,
    u - v^2 - v - 1,
    v^32 + 16*v^31 + 144*v^30 + 920*v^29 + 4620*v^28 + 19208*v^27 + 68348*v^26 +
        212732*v^25 + 588380*v^24 + 1462760*v^23 + 3297580*v^22 + 6786000*v^21 +
        12814320*v^20 + 22292560*v^19 + 35837420*v^18 + 53355230*v^17 + 
        73679935*v^16 + 94452240*v^15 + 112430520*v^14 + 124216240*v^13 + 
        127251670*v^12 + 120654560*v^11 + 105615510*v^10 + 85034690*v^9 + 
        62677680*v^8 + 42006568*v^7 + 25385078*v^6 + 13653832*v^5 + 6434290*v^4 
        + 2579820*v^3 + 849969*v^2 + 208088*v + 33673
]

Total time: 0.210 seconds, Total memory usage: 3.43MB


'212.138'
************** MAGMA *****************
Host 212.138.47.24 (212.138.47.24)
Time: Tue Dec 20 09:24:05 2005

Input: P<x,y,z,u,v>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x + (y^2+y+1),
-y + (z^2+z+1),
-z + (u^2+u+1),
-u + (v^2+v+1),
-v + (x^2+x+1) >;
Radical(I);

Output: Magma V2.11-10    Tue Dec 20 2005 09:24:05 on modular  [Seed = 3176590049]
   -------------------------------------


>> P<x,y,z,u,v>:=PolynomialRing(RationalField(),3); I:=ideal<P |
    ^
Runtime error in 'AssignNames': Argument 2 should have length at most 3

>> -x + (y^2+y+1),
    ^
User error: Identifier 'x' has not been declared or assigned

>> Radical(I);;
           ^
User error: Identifier 'I' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.47.17 (212.138.47.17)
Time: Tue Dec 20 09:19:52 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x + (y^2+y+1),
-y + (z^2+z+1),
-z + (x^2+x+1) >;
Radical(I);

Output: Magma V2.11-10    Tue Dec 20 2005 09:19:51 on modular  [Seed = 2321668820]
   -------------------------------------

Ideal of Polynomial ring of rank 3 over Rational Field
Lexicographical Order
Variables: x, y, z
Dimension 0, Radical
Groebner basis:
[
    x - z^4 - 2*z^3 - 4*z^2 - 3*z - 3,
    y - z^2 - z - 1,
    z^8 + 4*z^7 + 12*z^6 + 22*z^5 + 35*z^4 + 38*z^3 + 37*z^2 + 20*z + 13
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'212.138'
************** MAGMA *****************
Host 212.138.113.12 (212.138.113.12)
Time: Tue Dec 20 09:18:42 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x + y^2+y+1),
-y + z^2+z+1),
-z + (x^2+x+1) >;
Radical(I);

Output: Magma V2.11-10    Tue Dec 20 2005 09:18:42 on modular  [Seed = 2625096967]
   -------------------------------------


>> -x + y^2+y+1),
               ^
User error: bad syntax

>> -y + z^2+z+1),
               ^
User error: bad syntax

>> -z + (x^2+x+1) >;
                  ^
User error: bad syntax

>> Radical(I);;
           ^
User error: Identifier 'I' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'66.80.2'
************** MAGMA *****************
Host 66.80.213.2 (66.80.213.2)
Time: Mon Dec 19 18:33:57 2005

Input: 123

Output: Magma V2.11-10    Mon Dec 19 2005 18:33:57 on modular  [Seed = 3375221216]
   -------------------------------------

123

Total time: 0.200 seconds, Total memory usage: 3.24MB


'66.80.2'
************** MAGMA *****************
Host 66.80.213.2 (66.80.213.2)
Time: Mon Dec 19 18:33:54 2005

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-10    Mon Dec 19 2005 18:33:54 on modular  [Seed = 3425225954]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.200 seconds, Total memory usage: 3.24MB


'130.83.'
************** MAGMA *****************
Host 130.83.2.27 (130.83.2.27)
Time: Mon Dec 19 09:54:32 2005

Input: F2 := GF(2^163); 
a := 00000000 28194bf9 c17b1b81 9a71b20f 5ef0b51d 67cb6830;
b := 00000009 8e59a5bf 2e0edbab 1487fcce ba428afa 855dfd12;
E := EllipticCurve([1, 0, 0, a, b]); 
time #E; 
FactoredOrder(E);

Output: Magma V2.11-10    Mon Dec 19 2005 09:54:32 on modular  [Seed = 1653074050]
   -------------------------------------


>> a := 00000000 28194bf9 c17b1b81 9a71b20f 5ef0b51d 67cb6830;
                 ^
User error: bad syntax

>> b := 00000009 8e59a5bf 2e0edbab 1487fcce ba428afa 855dfd12;
                 ^
User error: bad syntax

>> E := EllipticCurve([1, 0, 0, a, b]); 
                                ^
User error: Identifier 'a' has not been declared or assigned

>> time #E; 
         ^
User error: Identifier 'E' has not been declared or assigned

>> FactoredOrder(E);;
                 ^
User error: Identifier 'E' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'130.83.'
************** MAGMA *****************
Host 130.83.2.27 (130.83.2.27)
Time: Mon Dec 19 09:53:09 2005

Input: F2 := GF(2^163); 
a := 0000000028194bf9c17b1b819a71b20f5ef0b51d67cb6830;
b := 000000098e59a5bf2e0edbab1487fcceba428afa855dfd12;
E := EllipticCurve([1, 0, 0, a, b]); 
time #E; 
FactoredOrder(E);

Output: Magma V2.11-10    Mon Dec 19 2005 09:53:09 on modular  [Seed = 1820976753]
   -------------------------------------


>> a := 0000000028194bf9c17b1b819a71b20f5ef0b51d67cb6830;
                     ^
User error: bad syntax

>> b := 000000098e59a5bf2e0edbab1487fcceba428afa855dfd12;
                    ^
User error: bad syntax

>> E := EllipticCurve([1, 0, 0, a, b]); 
                                ^
User error: Identifier 'a' has not been declared or assigned

>> time #E; 
         ^
User error: Identifier 'E' has not been declared or assigned

>> FactoredOrder(E);;
                 ^
User error: Identifier 'E' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.24MB


'136.206'
************** MAGMA *****************
Host 136.206.1.20 (136.206.1.20)
Time: Mon Dec 19 08:46:38 2005

Input: 2^123497

Output: Magma V2.11-10    Mon Dec 19 2005 08:46:38 on modular  [Seed = 98631666]
   -------------------------------------

2001587198193684625170316366565213998770374765249539510968102874320528369280493\
8986637440863966655910880436057015983629544805127690562348522105614355084980855\
8100817350081063197408828461733641385699501604461211045438847140673688794520554\
2154078678320893488245862834270199856499880144810356878526556017678836917907254\
1046165766739171527647053135746574000765241140167521092967514930946037638159715\
7324103041307853303707793081576249426290030160858776795634913065666764828870166\
0817659761875008825402341766867988536473966628066571208495055021474203862053389\
5619540415131014622090395555693412034725579822183946548196555711278388954151119\
0335085512829608797342262217110627469824475552779402624494276981138185048459139\
8524065478614504954527189393774015733718549520302500730232792551080567537098078\
8504520403789845365307705116991604735772774428558035953536010649938224410067292\
8726555743983504829486577211989987455967309277828078519623595338742342437569964\
5480459542625040887895090424933868304713939583880575630273834790051610134516840\
6227136764211875488062082160793844857874605530551098666226714806818667434144772\
1063136347457836471378902998209687326426084007814921488032709718444818718797563\
1141813287986845869664517980768746940850528726695163905943110109392108359161327\
1435209214981086265090134155848586057194572973901021662468515412261193920494090\
9274509060742943695708606635951092816028314742513588178522068898450751376914728\
2105774082292189829524094815261817282380214547134492188670089396881892310558668\
1075138822851095257150058382118481180777512842216174253916023460239766019544100\
3440843242728325628214429228738744714732818782903251958599530525220184027857144\
8494766691817545549179063010274278690882471994516169263645095088224017259735556\
5460231370789994586701620182457752827395050864683700385365475052736126239627619\
4565459534267572124445589815767503559146817323763563208395710939760067521823093\
1039478071755774924299386829359477219344654557781020906230508052676142868199375\
8820931570513731276070453033810404956787631704576192896431835499331291546070722\
7190201851621353358192174806118358472970591935359590026199558874379595660861858\
9696012980229179034987320784459133545806797826719157383137889513193005979305814\
9517009315897690318613758217204056551173667110384474025519330720383291584977125\
1501477939505655648279305065857100625251200428822652269455045440687939400145210\
5944109328090321327466102115295188267167908443558655805705652964037232040454723\
3214525907425420448703413811844845355431305416273212490421465116252485072159739\
5832728124959630867540680772887561691838912831388869988133638291883062606868532\
7010553445866529825347265106311408970375411578581162354756181776766855863863910\
3666405469774824822749893808976093004702012502632596092309146114879185980357730\
3861342700363386765252454917887675646729006062822382731919402870677014607812709\
6742863782944785309137485591391473520882675261639169157028134563998259122606414\
1214061808380859475240005407144224706478896212736978049847274888875101819616029\
9966056275586323932325057051732694804116544104519152361253824143726585366108886\
7824403554589285284935611921649878883484648078963332754980560806878465118995176\
8636996763145767446119826236229282709824730386049555511195740119353423233856730\
3003546375862251574339462096898282492902092773335958671071365209990805102574092\
0636142630104451906526838644223997241041911264846371619293496929717047691412369\
1587346265740663090731687558728136079480707562808197369049864379159635030104833\
5462063207330037679739569439800054740440906773030574364446455020404814972154764\
8465659046448645981163111625351420897515029106902997014825073863782367924689987\
3076456293857228619376979994449524671977219099392394476306453997067225647326307\
9651244784572003798516669285898768736293284876231569011061165312951792196750664\
8004754964130050168046555775625521612295094815319045752147740812584490059471702\
9110508498720322371497180824853974807955076774415446379857426101140477331235232\
5282219526154347465870231715669282321911900759173373302053902742843137071740045\
3621167367929877315269281203851500653681929449277541612917321658168275189795276\
2412503712674455797837236292478679948347530840728542976552595796030279570515203\
7940542968833411862734488251943840515303069923090930754867030519999763927008753\
4109278412879725343113493554581197681691396093950913079134280924275077184989217\
1982956692149258192788201462843811643821788250046018873375736899319270437924928\
5540099696779485485716894358744992122125312773996048150216323732658153945679472\
2320977755208176552178482693983039701785708172180465823200429017613355668581316\
9197409885823806913479548221920578462725001628320343226209425531737323271123249\
9727126380340937411653379777029732265276325290672904798107737192524653101768400\
9963726349210748613853596548808286287341587314433611182352932800970657575890482\
9602907447189590499440728343982860489151634746504481128663366540410107769278962\
2181978575636973826070190685730400287078130504620330974191383418411304598280217\
6289175130935471020191822476327340127497769105439927288109432302920619396686207\
5563266955573972135825134090714013167104886818196119505018915027954165916798660\
5640685233817787209455553922776298303907978125459096002683296118532244383049939\
2102581707216392827636621552640316689749473277663821087276462030534324285817090\
1574039834128452828945043423138163615088396652676945031102616772537236027362572\
9093550129291730074222552412449785060754950844397709165842732972161473559312128\
1648177665545877001929057577821788966777334571056138060542028896643985137026462\
8061525933974099968310206635290264404637756991509321664429344972626116684300533\
7861106196797563625824671581750709088611111005393211508348946836662320709164744\
4854402831452730245851694998484779312170342406956127253906007800990005060969124\
2395898623324386522359041849344412397966880334086445922750564087082180538353448\
9634389254021811690315680739893729453852192126826862284872702040996640300451513\
8200522354863683731681011043122873336107797215878814823980958952036686642194726\
3706921381635816998209832545626576977827117750452679746326170192207125326473365\
8497931921864125246498435153832638634428500668609805760957351666370173186152489\
8549196644441257764954206799410775690220693547389493395063894074243026894236255\
6121951407299610469418576123455522867323117795789526865250121923123020730121861\
6624481869097437255443211332437606329843916191606975531157236542756283294761097\
4454018830191740393255424759617907227542814955807285179342469298454284434333124\
2188046685850140650249332877897138070156412249953068010125972434512590631995781\
6632292281816295180543030856988598755698719014935611610497899707334483953087418\
5979872236654381900555278741541091036775020178274565847573095539888643891558305\
0175424376912130256217972415808265422685233550897840075159979797826139100476420\
4214518939826524611784332641689623503135283070093056061865458136633828822285069\
0004425896765346972392541315554962782742115932728784942482810982493570350990537\
5108530943317744846866596119617581606715824753315301552311532186271382016305676\
9063360495161630225801269986315318362731038779141167969552641858086429656721362\
9599772990492455970027177634852018878282322897538817547405848057532086774798145\
5364151801960828568783263237919368509672246292670138632820604703249416046299906\
6309128599020726672129686873000548278929749049292091715882893019593031702086657\
2174198190541394814812140410431243892023851682561822293927876173223740753378627\
4994641265344197339284929991571856502679410265220369215765028835049768624721877\
0121988303345502026704739350854447208331960688620845925110719853167768327430021\
4142932824672056999929554415787065542872881312583864621789852055601802352448366\
9108631443716501593765756505629326189956506734462415837555130395960452986739287\
7660151949506573367420849284827494218187419458582547237607859031878846049644312\
7920103300044594753464102678439477091221172525537648927003459027346572134757383\
1030600313929525796904581198077505596731390132687144156670231248193846340305888\
8787917882570263282367890190436422838181163776957771953426461883287295449828723\
3488289675215560589564372515907540699914660691853939721373454211606692217598553\
6584081788667858602130179979038955672511395920461593442738819291451583509219039\
0618919475111553422287107453358753977381991894543719718939258589010970555112756\
4846282563174724721875722821448159738351297436685228054903187961451796566642003\
8877582017402536367794132418674778384181958606150038938978716935404757178232108\
9544886249853827024538758904911767797137081414281149102511949914183355860551613\
3966655353632315135931193933915921426295256616267943129810039331850010374647879\
5019398749091731961928686112450404317715640599039825046649445559552364442288050\
4878208618632646277400281860369252007926862480622634852930180193126283373580905\
2188932240739236342043990025893410560025923506161687442534685002077189502865770\
8628684577211773410041575281787067835156771184738929787375294329344608955759281\
6377654751461037940825426469015541257395655125850006534845483689697461507641197\
6033519972257906660048537471491539843946831599600103967246479411724790599911674\
1836370606906770341983903573287845621138941743228357128906245733541012474702751\
8453701557805174085939366323849083212393050852348898855243496187309225102337985\
3152423482372965525069167089113730940204405410575250750673485929713480182810589\
8682924721845452017908478942531854379243327576779228936408223207821032121141629\
8026545748202577851026072354880919535700504372738944562621789406059507848845670\
9314010730492365706988794320639036441537104845093729304487948798494150514394443\
3321460335522184092101043554017852228116475405922692692379589150422884131353808\
329
 ** WARNING: Output too long, hence truncated.

'136.206'
************** MAGMA *****************
Host 136.206.1.20 (136.206.1.20)
Time: Mon Dec 19 08:46:24 2005

Input: 2^12349

Output: Magma V2.11-10    Mon Dec 19 2005 08:46:24 on modular  [Seed = 250344695]
   -------------------------------------

2626736171012131461696331866622504022562035768491774100353857649406801506742242\
3084825445525830313237579267060342464266751281652973705149653235374277824190887\
1189531386079630150950885566776783139898209075387224197253278610227046686860285\
2146772936587820191698239338478093635758535173421076624226668386717908021430077\
2575959758867004070058358245154844488213421278411858599405003098389395982774741\
5207523985664026620091887697430049224315869743164135546469569593156053308579763\
4263347484501060259378983778512308193286625242724234283776294831969816375131722\
8936983092780315563728112542813599636673151675373431312055279054784023549919569\
1219311126509583342457083167117071756897339079913318716330389289773213619097648\
5462291545382776372231239190460511893638750161514624836332728442123550337942797\
0107763595947903341784814752544645876919755965073714519271381674895702373091853\
3215436670680437605890497876295398853415101607642404800691586567280726998586113\
3155635070581153975745361022821609701475154342525458848449138355080543080276328\
8562238102868156174523151272995385551848413365281813064332695534895707693916077\
3662839142437371930375144772683967311099712589747556416445072489722773502081757\
3932762811380394736879531383074542888986949490172385899865512107245330358348141\
2002536006877334990455229759352997623012123459286967364906330023656745029008423\
1318591798112344953149789799176371875210520880011310213974786327498190170775194\
0246174540950463559914962203857965870347514848862996573094556026725122248029488\
6275846517739215502335403747057022256585935251030078500156821873918117987513970\
4426698969743209570301505361020908142913826815198427238143354973528877107200224\
1362276706671793015984396682901357490556654981141630717756138713107208664121793\
5964945552831824348164195179552274467535374454989803677496230655131121084486570\
0261226878948470170102082465535705353261735614453198125197698538320433876443585\
5548730497312029569853044174888346610679682782177024305897164452504267762524472\
8942106845930309209375265735037991439661066606147717307209666084147940792076368\
5347488239038281717789732344573987600622333170050711612768838066021919121172723\
7211642627359164577023720988405242216072270697121621110267174598217721659879750\
6359722942347060658884300635157725165894578694825025691943617203907024115252487\
2604789418047694030384602063079611761683791030363420595196990670237588860702010\
6169944921970214471348265581404547669212797420512416967703949848988112509424036\
1134688460311879742839068107057958734150381319733809695520201181756924313844696\
1918204395509649687931010893331484714802246461165949708658831409554486264656020\
2841600039327715319442826732033633872044383688769435144495559623035113598100509\
0075714762536621556465045676759336653654216176823133677119064993039589879343991\
1804372050260066046422880519351824998305832815771105572582031735088076992900746\
8766513825643038069839131037767895599272614757883512126120210656816117647905093\
1080232106668263738912090292701279801420121666281544640796361809598122771169016\
7769682855286385498577015573401574654445955805783975120408618104937011191205360\
0034286567891044077209771318409439621839771975487282097247546270122766333673139\
7818925249813795323067965555218133003053559443872659882156008658054660949373786\
5912057785114351497720960768672901692108186937013204195723476497603434228407112\
0818914716884554084155256682143282018872321808954078627677339016574811674828448\
4545103570576976166155059054557530744414713978466406343423134640612927620214279\
5177691324413778261863862669992600426858077025874394518306583020390601349897083\
3017916526700157169696336864604125724185399555853360649287157768704465038886601\
1190907156678096345969954990068832490888864044127228955581257071464844705313975\
17312

Total time: 0.200 seconds, Total memory usage: 3.24MB


'136.206'
************** MAGMA *****************
Host 136.206.1.20 (136.206.1.20)
Time: Mon Dec 19 08:46:15 2005

Input: 2^1234

Output: Magma V2.11-10    Mon Dec 19 2005 08:46:14 on modular  [Seed = 200208868]
   -------------------------------------

2958112246080986290600446957161035907863396871353729922395562070506573507962389\
2426105383724837805018644364775907095599312082089933038176093702721248284094494\
1362110665443775183495726811929203861182015218323892077355983393191208928867652\
6559936024879031137085494026686245211006117942703402327660993170980488874938090\
23127398253860618772619035009883272941129544640111837184

Total time: 0.190 seconds, Total memory usage: 3.24MB


'136.206'
************** MAGMA *****************
Host 136.206.1.20 (136.206.1.20)
Time: Mon Dec 19 08:46:04 2005

Input: 2^1234324

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Mon Dec 19 2005 08:45:44 on modular  [Seed = 1955696309]
   -------------------------------------


Errors: /bin/sh: line 1:  2621 Alarm clock             nice -n 19 /usr/local/bin/magma


'136.206'
************** MAGMA *****************
Host 136.206.1.20 (136.206.1.20)
Time: Mon Dec 19 08:45:33 2005

Input: 2^123

Output: Magma V2.11-10    Mon Dec 19 2005 08:45:33 on modular  [Seed = 1905560389]
   -------------------------------------

10633823966279326983230456482242756608

Total time: 0.190 seconds, Total memory usage: 3.24MB


'136.206'
************** MAGMA *****************
Host 136.206.1.20 (136.206.1.20)
Time: Mon Dec 19 08:45:26 2005

Input: eval("2^123")

Output: Magma V2.11-10    Mon Dec 19 2005 08:45:26 on modular  [Seed = 2057273413]
   -------------------------------------


>> eval("2^123");
   ^
User error: Identifier 'eval' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'136.206'
************** MAGMA *****************
Host 136.206.1.20 (136.206.1.20)
Time: Mon Dec 19 08:45:09 2005

Input: gap.eval("2^123")

Output: Magma V2.11-10    Mon Dec 19 2005 08:45:08 on modular  [Seed = 1736613194]
   -------------------------------------


>> gap.eval("2^123");
   ^
User error: Identifier 'gap' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.24MB


'82.58.6'
************** MAGMA *****************
Host 82.58.68.160 (82.58.68.160)
Time: Mon Dec 19 08:11:01 2005

Input: 268165538371456392121266295429649186242633

Output: Magma V2.11-10    Mon Dec 19 2005 08:10:58 on modular  [Seed = 2675600823]
   -------------------------------------

268165538371456392121266295429649186242633

Total time: 0.210 seconds, Total memory usage: 3.24MB


'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:10:23 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x2;
x:=Eltseq(x1) cat Eltseq(x2);
M1:=VerticalJoin(all1,circulant(x));
M2:=HorizontalJoin(t,M1);

M2;


Output: Magma V2.11-10    Mon Dec 19 2005 07:10:23 on modular  [Seed = 3425250472]
   -------------------------------------

(0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0)
[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0]
[1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1]
[1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1]
[1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0]
[1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0]
[1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1]
[1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1]
[1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0]
[1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1]
[1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1]
[1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0]
[1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0]
[1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0]
[1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1]
[1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1]
[1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1]
[1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1]
[1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0]
[1 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0]

Total time: 0.220 seconds, Total memory usage: 3.24MB


'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:10:00 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x2;
x:=Eltseq(x1) cat Eltseq(x2);
M1:=VerticalJoin(all1,circulant(x));
M2:=HorizontalJoin(t,M1);

M2;

gen:=HorizontalJoin(ScalarMatrix(n,GF(2)!1),M2);


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:09:51 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x2;
x:=Eltseq(x1) cat Eltseq(x2);
M1:=VerticalJoin(all1,circulant(x));
M2:=HorizontalJoin(t,M1);

M2;

gen:=HorizontalJoin(ScalarMatrix(n,GF(2)!1),M2);
C:=LinearCode(gen);
gen;


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:09:32 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x2;
x:=Eltseq(x1) cat Eltseq(x2);
M1:=VerticalJoin(all1,circulant(x));
M2:=HorizontalJoin(t,M1);

M2;

gen:=HorizontalJoin(ScalarMatrix(n,GF(2)!1),M2);
C:=LinearCode(gen);
IsSelfDual(C);
MinimumWeight(C);

Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:08:52 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x2;
x:=Eltseq(x1) cat Eltseq(x2);
M1:=VerticalJoin(all1,circulant(x));
M2:=HorizontalJoin(t,M1);

M2;



Output: Magma V2.11-10    Mon Dec 19 2005 07:08:52 on modular  [Seed = 667076280]
   -------------------------------------

(0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0)
[0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0]
[1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1]
[1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1]
[1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1]
[1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1]
[1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0]
[1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0]
[1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0]
[1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1]
[1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1]
[1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0]
[1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1]
[1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0]
[1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0]
[1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0]
[1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1]
[1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0]
[1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0]
[1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0]

Total time: 0.200 seconds, Total memory usage: 3.24MB


'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:08:36 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x2;
x:=Eltseq(x1) cat Eltseq(x2);
M1:=VerticalJoin(all1,circulant(x));
M2:=HorizontalJoin(t,M1);
M1;



Output: Magma V2.11-10    Mon Dec 19 2005 07:08:36 on modular  [Seed = 751422883]
   -------------------------------------

(0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0)
[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
[0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0]
[0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1]
[1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0]
[0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0]
[0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0]
[0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1]
[1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1]
[1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1]
[1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1]
[1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0]
[0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0]
[0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0]
[0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0]
[0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1]
[1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0]
[0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0]

Total time: 0.200 seconds, Total memory usage: 3.24MB


'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:08:23 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x2;
x:=Eltseq(x1) cat Eltseq(x2);
M1:=VerticalJoin(all1,circulant(x));
M2:=HorizontalJoin(t,M1);


Output: Magma V2.11-10    Mon Dec 19 2005 07:08:23 on modular  [Seed = 701286613]
   -------------------------------------

(1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0)

Total time: 0.210 seconds, Total memory usage: 3.24MB


'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:08:14 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x2;
x:=Eltseq(x1) cat Eltseq(x2);
M1:=VerticalJoin(all1,circulant(x));
M2:=HorizontalJoin(t,M1);
gen:=HorizontalJoin(ScalarMatrix(n,GF(2)!1),circulant(x));


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:07:57 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x2;
x:=Eltseq(x1) cat Eltseq(x2);
M1:=VerticalJoin(all1,circulant(x));
M2:=HorizontalJoin(t,M1);
gen:=HorizontalJoin(ScalarMatrix(n,GF(2)!1),circulant(x));
C:=LinearCode(gen);
IsSelfDual(C);
MinimumWeight(C);


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:07:37 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x2;


Output: Magma V2.11-10    Mon Dec 19 2005 07:07:37 on modular  [Seed = 519831516]
   -------------------------------------

(1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1)

Total time: 0.210 seconds, Total memory usage: 3.24MB


'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:07:27 2005

Input: n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);

Output: Magma V2.11-10    Mon Dec 19 2005 07:07:26 on modular  [Seed = 469695022]
   -------------------------------------


Total time: 0.230 seconds, Total memory usage: 3.24MB


'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:07:12 2005

Input: 
n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////


Output: Magma V2.11-10    Mon Dec 19 2005 07:07:09 on modular  [Seed = 15065382]
   -------------------------------------


Total time: 0.260 seconds, Total memory usage: 3.24MB


'220.214'
************** MAGMA *****************
Host 220.214.76.207 (220.214.76.207)
Time: Mon Dec 19 07:06:09 2005

Input: 
n:=20;d:=8;

//////////////////////////
circulant:=function(r)
    n:=#r;
    m:=r;
    row:=r;
    for j in [1..n-1] do
       Rotate(~row,1);
       m cat:=row;
    end for;
    return Matrix(Parent(r[1]),n,n,m);
end function;
//////////////////////////
x1:=Vector(GF(2),1,[0]);
x3:=Vector(GF(2),1,[1]);
all1:=Matrix(GF(2),1,n-1,[1 : i in [1..n-1]]);
t:=Transpose(Matrix(GF(2),1,n,Eltseq(x1) cat Eltseq(all1)));
V:=EvenWeightCode(n-2);
x2:=Random(V);
x:=Eltseq(x1) cat Eltseq(x2);
M1:=VerticalJoin(all1,circulant(x));
M2:=HorizontalJoin(t,M1);
gen:=HorizontalJoin(ScalarMatrix(n,GF(2)!1),circulant(x));
C:=LinearCode(gen);
IsSelfDual(C);
MinimumWeight(C);


Output: WARNING: MAGMA command contains unsafe command 'alarm', so it will not be executed.

'60.225.'
************** MAGMA *****************
Host 60.225.128.201 (60.225.128.201)
Time: Mon Dec 19 00:36:02 2005

Input: Factorization(00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000090000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000);

Output: Magma V2.11-10    Mon Dec 19 2005 00:36:02 on modular  [Seed = 3926912878]
   -------------------------------------

[ <2, 94>, <3, 2>, <5, 94> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'60.225.'
************** MAGMA *****************
Host 60.225.128.201 (60.225.128.201)
Time: Mon Dec 19 00:34:19 2005

Input: Factorization(000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000007000000000000000000000000000000000000000000000000000000000000000000000000000000000);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Mon Dec 19 2005 00:33:59 on modular  [Seed = 3758482913]
   -------------------------------------


Errors: /bin/sh: line 1:  1446 Alarm clock             nice -n 19 /usr/local/bin/magma


'60.225.'
************** MAGMA *****************
Host 60.225.128.201 (60.225.128.201)
Time: Mon Dec 19 00:30:20 2005

Input: Factorization(0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000009000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000070000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Mon Dec 19 2005 00:29:59 on modular  [Seed = 3661618379]
   -------------------------------------


Errors: /bin/sh: line 1:  1436 Alarm clock             nice -n 19 /usr/local/bin/magma


'60.225.'
************** MAGMA *****************
Host 60.225.128.201 (60.225.128.201)
Time: Mon Dec 19 00:28:12 2005

Input: Factorization(33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Mon Dec 19 2005 00:27:51 on modular  [Seed = 3543585858]
   -------------------------------------


Errors: /bin/sh: line 1:  1429 Alarm clock             nice -n 19 /usr/local/bin/magma


'82.55.7'
************** MAGMA *****************
Host 82.55.71.167 (82.55.71.167)
Time: Sun Dec 18 17:30:04 2005

Input: 10!

Output: Magma V2.11-10    Sun Dec 18 2005 17:30:04 on modular  [Seed = 3160022383]
   -------------------------------------


>> 10!;
      ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'155.207'
************** MAGMA *****************
Host 155.207.209.176 (155.207.209.176)
Time: Sun Dec 18 16:51:33 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-26*x^2+1;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
u1:=-9842-1526*a-16289/2*(a^2-1)-8036/4*(a^3 +a^2 -a -1);
u2:=651+189*a+1113/2*(a^2-1)+532/4*(a^3 +a^2 -a -1);
u3:=-42+0*a-63/2*(a^2-1)-42/4*(a^3 +a^2 -a -1);
u4:=-63+21*a-161/2*(a^2-1)+56/4*(a^3 +a^2 -a -1);
u5:=994-154*a+2457/2*(a^2-1)-812/4*(a^3 +a^2 -a -1);
UnitEquation(a*u1,-a*u1,2*a*n);
UnitEquation(a*u2,-a*u2,2*a*n);
UnitEquation(a*u3,-a*u3,2*a*n);
UnitEquation(a*u4,-a*u4,2*a*n);
UnitEquation(a*u5,-a*u5,2*a*n);

Output: Magma V2.11-10    Sun Dec 18 2005 16:51:32 on modular  [Seed = 266966483]
   -------------------------------------

[
    1,
    y,
    1/2*(y^2 - 1),
    1/4*(y^3 + y^2 - y - 1)
]
true [
    [-9842, -1526, -16289, -8036],
    [651, 189, 1113, 532],
    [-42, 0, -63, -42],
    [-63, 21, -161, 56],
    [994, -154, 2457, -812]
]
[]
[]
[]
[]
[]

Total time: 1.199 seconds, Total memory usage: 3.72MB


'155.207'
************** MAGMA *****************
Host 155.207.209.176 (155.207.209.176)
Time: Sun Dec 18 16:46:21 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-26*x^2+1;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
u1:=-21-42*a-21/2*(a^2+1)+42/44*(a^3 + 11*a^2 + 43*a + 33);
UnitEquation(a*u1,-a*u1,2*a*n);


Output: Magma V2.11-10    Sun Dec 18 2005 16:46:21 on modular  [Seed = 2958437156]
   -------------------------------------

[
    1,
    y,
    1/2*(y^2 - 1),
    1/4*(y^3 + y^2 - y - 1)
]
true [
    [-9842, -1526, -16289, -8036],
    [651, 189, 1113, 532],
    [-42, 0, -63, -42],
    [-63, 21, -161, 56],
    [994, -154, 2457, -812]
]

>> UnitEquation(a*u1,-a*u1,2*a*n);
               ^
Runtime error in 'UnitEquation': Elements must all be integral

Total time: 0.440 seconds, Total memory usage: 3.60MB


'155.207'
************** MAGMA *****************
Host 155.207.209.124 (155.207.209.124)
Time: Sun Dec 18 16:32:15 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-34*x^2+121;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
u1:=-21-42*a-21/2*(a^2+1)+42/44*(a^3 + 11*a^2 + 43*a + 33);
UnitEquation(a*u1,-a*u1,2*a*n);


Output: Magma V2.11-10    Sun Dec 18 2005 16:32:13 on modular  [Seed = 1269685551]
   -------------------------------------

[
    1,
    y,
    1/2*(y^2 + 1),
    1/44*(y^3 + 11*y^2 + 43*y + 33)
]
true [
    [-21, -42, -21, 42]
]
[
    [[84, 73, 18, -44] [81, 63, 15, -38]],

    [[-40, 73, 26, -44] [-43, 63, 23, -38]],

    [[0, 7, 2, -4] [-3, -3, -1, 2]],

    [[4, 7, 2, -4] [1, -3, -1, 2]],

    [[9, 5, 1, -3] [6, -5, -2, 3]],

    [[-6, 5, 2, -3] [-9, -5, -1, 3]],

    [[-1, 3, 1, -2] [-4, -7, -2, 4]],

    [[3, 3, 1, -2] [0, -7, -2, 4]],

    [[43, -63, -23, 38] [40, -73, -26, 44]],

    [[-81, -63, -15, 38] [-84, -73, -18, 44]]
]

Total time: 1.229 seconds, Total memory usage: 3.72MB


'155.207'
************** MAGMA *****************
Host 155.207.209.124 (155.207.209.124)
Time: Sun Dec 18 16:31:23 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-34*x^2+121;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
u1:=-21-42*a-21/2*(a^2+1)+42/44*(y^3 + 11*y^2 + 43*y + 33);
UnitEquation(a*u1,-a*u1,2*a*n);


Output: Magma V2.11-10    Sun Dec 18 2005 16:31:23 on modular  [Seed = 1421001286]
   -------------------------------------

[
    1,
    y,
    1/2*(y^2 + 1),
    1/44*(y^3 + 11*y^2 + 43*y + 33)
]
true [
    [-21, -42, -21, 42]
]

>> u1:=-21-42*a-21/2*(a^2+1)+42/44*(y^3 + 11*y^2 + 43*y + 33);
                            ^
Runtime error in '+': Arguments are not compatible
Argument types given: FldNumElt, FldNumElt

>> UnitEquation(a*u1,-a*u1,2*a*n);
                  ^
User error: Identifier 'u1' has not been declared or assigned

Total time: 0.350 seconds, Total memory usage: 3.63MB


'155.207'
************** MAGMA *****************
Host 155.207.209.124 (155.207.209.124)
Time: Sun Dec 18 16:28:33 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-34*x^2+121;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
z:=a/2;
u1:=56-105*z-63*z^2+49*z^3;
u2:=14-35*z+7*z^2-7*z^3;
u3:=-21*z+21*z^2+21*z^3;
u4:=14-7*z-77*z^2-35*z^3;
u5:=-56-49*z+217*z^2+105*z^3;
UnitEquation(a*u1,-a*u1,2*a*n);
UnitEquation(a*u2,-a*u2,2*a*n);
UnitEquation(a*u3,-a*u3,2*a*n);
UnitEquation(a*u4,-a*u4,2*a*n);
UnitEquation(a*u5,-a*u5,2*a*n);





Output: Magma V2.11-10    Sun Dec 18 2005 16:28:33 on modular  [Seed = 1589168614]
   -------------------------------------

[
    1,
    y,
    1/2*(y^2 + 1),
    1/44*(y^3 + 11*y^2 + 43*y + 33)
]
true [
    [-21, -42, -21, 42]
]

>> UnitEquation(a*u1,-a*u1,2*a*n);
               ^
Runtime error in 'UnitEquation': Elements must all be integral

>> UnitEquation(a*u2,-a*u2,2*a*n);
               ^
Runtime error in 'UnitEquation': Elements must all be integral

>> UnitEquation(a*u3,-a*u3,2*a*n);
               ^
Runtime error in 'UnitEquation': Elements must all be integral

>> UnitEquation(a*u4,-a*u4,2*a*n);
               ^
Runtime error in 'UnitEquation': Elements must all be integral

>> UnitEquation(a*u5,-a*u5,2*a*n);
               ^
Runtime error in 'UnitEquation': Elements must all be integral

Total time: 0.350 seconds, Total memory usage: 3.63MB


'155.207'
************** MAGMA *****************
Host 155.207.209.221 (155.207.209.221)
Time: Sun Dec 18 14:30:21 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-20*x^2+16;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
z:=a/2;
u1:=56-105*z-63*z^2+49*z^3;
u2:=14-35*z+7*z^2-7*z^3;
u3:=-21*z+21*z^2+21*z^3;
u4:=14-7*z-77*z^2-35*z^3;
u5:=-56-49*z+217*z^2+105*z^3;
UnitEquation(a*u1,-a*u1,2*a*n);
UnitEquation(a*u2,-a*u2,2*a*n);
UnitEquation(a*u3,-a*u3,2*a*n);
UnitEquation(a*u4,-a*u4,2*a*n);
UnitEquation(a*u5,-a*u5,2*a*n);





Output: Magma V2.11-10    Sun Dec 18 2005 14:30:20 on modular  [Seed = 266990835]
   -------------------------------------

[
    1,
    1/2*y,
    1/4*y^2,
    1/8*y^3
]
true [
    [56, -105, -63, 49],
    [14, -35, 7, -7],
    [0, -21, 21, 21],
    [14, -7, -77, -35],
    [-56, -49, 217, 105]
]
[]
[]
[
    [[62, 72, -13, -15] [67, 91, -14, -19]],

    [[5, 0, -1, 0] [10, 19, -2, -4]],

    [[2, -4, -1, 1] [7, 15, -2, -3]],

    [[-7, -15, 2, 3] [-2, 4, 1, -1]],

    [[-10, -19, 2, 4] [-5, 0, 1, 0]],

    [[-67, -91, 14, 19] [-62, -72, 13, 15]]
]
[]
[]

Total time: 1.250 seconds, Total memory usage: 3.70MB


'155.207'
************** MAGMA *****************
Host 155.207.209.221 (155.207.209.221)
Time: Sun Dec 18 14:29:01 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-20*x^2+16;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
z:=a/2;
u1:=56-105*z-63*z^2+49*z^3;
u2:=14-35*z+7*z^2-7*z^3;
u3:=-21*z+21*z^2+21*z^3;
UnitEquation(a*u1,-a*u1,2*a*n);
UnitEquation(a*u2,-a*u2,2*a*n);
UnitEquation(a*u3,-a*u3,2*a*n);




Output: Magma V2.11-10    Sun Dec 18 2005 14:29:00 on modular  [Seed = 166720069]
   -------------------------------------

[
    1,
    1/2*y,
    1/4*y^2,
    1/8*y^3
]
true [
    [56, -105, -63, 49],
    [14, -35, 7, -7],
    [0, -21, 21, 21],
    [14, -7, -77, -35],
    [-56, -49, 217, 105]
]
[]
[]
[
    [[62, 72, -13, -15] [67, 91, -14, -19]],

    [[5, 0, -1, 0] [10, 19, -2, -4]],

    [[2, -4, -1, 1] [7, 15, -2, -3]],

    [[-7, -15, 2, 3] [-2, 4, 1, -1]],

    [[-10, -19, 2, 4] [-5, 0, 1, 0]],

    [[-67, -91, 14, 19] [-62, -72, 13, 15]]
]

Total time: 1.260 seconds, Total memory usage: 3.70MB


'155.207'
************** MAGMA *****************
Host 155.207.209.221 (155.207.209.221)
Time: Sun Dec 18 14:27:53 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-20*x^2+16;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
z:=a/2;
u1:=56-105*z-63*z^2+49*z^3;
u2:=14-35*z+7*z^2-7*z^3;
UnitEquation(a*u1,-a*u1,2*a*n);
UnitEquation(a*u2,-a*u2,2*a*n);



Output: Magma V2.11-10    Sun Dec 18 2005 14:27:53 on modular  [Seed = 81985293]
   -------------------------------------

[
    1,
    1/2*y,
    1/4*y^2,
    1/8*y^3
]
true [
    [56, -105, -63, 49],
    [14, -35, 7, -7],
    [0, -21, 21, 21],
    [14, -7, -77, -35],
    [-56, -49, 217, 105]
]
[]
[]

Total time: 0.420 seconds, Total memory usage: 3.60MB


'155.207'
************** MAGMA *****************
Host 155.207.209.221 (155.207.209.221)
Time: Sun Dec 18 14:27:32 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-20*x^2+16;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
z:=a/2;
u1:=56-105*z-63*z^2+49*z^3;
u2:=14-35*z+7*z^2-7*z^3;
UnitEquation(a*u1,a*u1,2*a*n);
UnitEquation(a*u2,a*u2,2*a*n);



Output: Magma V2.11-10    Sun Dec 18 2005 14:27:31 on modular  [Seed = 536470540]
   -------------------------------------

[
    1,
    1/2*y,
    1/4*y^2,
    1/8*y^3
]
true [
    [56, -105, -63, 49],
    [14, -35, 7, -7],
    [0, -21, 21, 21],
    [14, -7, -77, -35],
    [-56, -49, 217, 105]
]
[]
[]

Total time: 0.430 seconds, Total memory usage: 3.60MB


'155.207'
************** MAGMA *****************
Host 155.207.209.221 (155.207.209.221)
Time: Sun Dec 18 14:26:43 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-20*x^2+16;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
z:=a/2;
u1:=56-105*z-63*z^2+49*z^3;
u1:=56-105*z-63*z^2+49*z^3;
UnitEquation(a*u1,a*u1,2*a*n);

Output: Magma V2.11-10    Sun Dec 18 2005 14:26:42 on modular  [Seed = 452783832]
   -------------------------------------

[
    1,
    1/2*y,
    1/4*y^2,
    1/8*y^3
]
true [
    [56, -105, -63, 49],
    [14, -35, 7, -7],
    [0, -21, 21, 21],
    [14, -7, -77, -35],
    [-56, -49, 217, 105]
]
[]

Total time: 0.430 seconds, Total memory usage: 3.60MB


'155.207'
************** MAGMA *****************
Host 155.207.209.221 (155.207.209.221)
Time: Sun Dec 18 14:26:27 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-20*x^2+16;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
z:=a/2;
u1:=56-105*z-63*z^2+49*z^3;
u1:=56-105*z-63*z^2+49*z^3;
UnitEquation(a*u1,a*u1,2*a*n));

Output: Magma V2.11-10    Sun Dec 18 2005 14:26:27 on modular  [Seed = 368304582]
   -------------------------------------

[
    1,
    1/2*y,
    1/4*y^2,
    1/8*y^3
]
true [
    [56, -105, -63, 49],
    [14, -35, 7, -7],
    [0, -21, 21, 21],
    [14, -7, -77, -35],
    [-56, -49, 217, 105]
]

>> UnitEquation(a*u1,a*u1,2*a*n));;
                                ^
User error: bad syntax

Total time: 0.370 seconds, Total memory usage: 3.60MB


'155.207'
************** MAGMA *****************
Host 155.207.209.221 (155.207.209.221)
Time: Sun Dec 18 14:25:59 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-20*x^2+16;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
n:=p*q;
> >NormEquation(O, 4*n^4);
K<a> := NumberField(f);
z:=a/2;
u1:=56-105*z-63z^2+49*z^3;
u1:=56-105*z-63z^2+49*z^3;
UnitEquation(a*u1,a*u1,2*a*n));

Output: Magma V2.11-10    Sun Dec 18 2005 14:25:58 on modular  [Seed = 284615910]
   -------------------------------------

[
    1,
    1/2*y,
    1/4*y^2,
    1/8*y^3
]
true [
    [56, -105, -63, 49],
    [14, -35, 7, -7],
    [0, -21, 21, 21],
    [14, -7, -77, -35],
    [-56, -49, 217, 105]
]

>> u1:=56-105*z-63z^2+49*z^3;
                  ^
User error: bad syntax

>> u1:=56-105*z-63z^2+49*z^3;
                  ^
User error: bad syntax

>> UnitEquation(a*u1,a*u1,2*a*n));;
                                ^
User error: bad syntax

Total time: 0.420 seconds, Total memory usage: 3.60MB


'155.207'
************** MAGMA *****************
Host 155.207.209.183 (155.207.209.183)
Time: Sun Dec 18 13:14:25 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-20*x^2+16;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=3;
q:=7;
> >NormEquation(O, 4*(p*q)^4);

Output: Magma V2.11-10    Sun Dec 18 2005 13:14:24 on modular  [Seed = 1118086763]
   -------------------------------------

[
    1,
    1/2*y,
    1/4*y^2,
    1/8*y^3
]
true [
    [56, -105, -63, 49],
    [14, -35, 7, -7],
    [0, -21, 21, 21],
    [14, -7, -77, -35],
    [-56, -49, 217, 105]
]

Total time: 0.380 seconds, Total memory usage: 3.60MB


'155.207'
************** MAGMA *****************
Host 155.207.209.81 (155.207.209.81)
Time: Sun Dec 18 13:09:52 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-4*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p:=1;
q:=5;
> >NormEquation(O, 4*(p*q)^4);

Output: Magma V2.11-10    Sun Dec 18 2005 13:09:51 on modular  [Seed = 1286253194]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]
true [
    [0, 0, -5, 0]
]

Total time: 0.330 seconds, Total memory usage: 3.63MB


'155.207'
************** MAGMA *****************
Host 155.207.209.81 (155.207.209.81)
Time: Sun Dec 18 13:09:40 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-4*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
p=1;
q=5;
> >NormEquation(O, 4*(p*q)^4);

Output: Magma V2.11-10    Sun Dec 18 2005 13:09:39 on modular  [Seed = 1236250499]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]

>> p=1;
   ^
User error: Identifier 'p' has not been declared or assigned

>> q=5;
   ^
User error: Identifier 'q' has not been declared or assigned

>>    NormEquation(O, 4*(p*q)^4);;
                         ^
User error: Identifier 'p' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.47.15 (212.138.47.15)
Time: Sun Dec 18 10:08:42 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x + (-6*y^2+7*y+5),
-y + (-6*z^2+7*z+5),
-z^9 + (-6*x^2+7*x+5) >;
Radical(I);

Output: Magma V2.11-10    Sun Dec 18 2005 10:08:41 on modular  [Seed = 1387555329]
   -------------------------------------

Ideal of Polynomial ring of rank 3 over Rational Field
Lexicographical Order
Variables: x, y, z
Dimension 0, Radical
Groebner basis:
[
    x + 216*z^4 - 504*z^3 - 24*z^2 + 371*z + 110,
    y + 6*z^2 - 7*z - 5,
    z^9 + 279936*z^8 - 1306368*z^7 + 1461888*z^6 + 1106784*z^5 - 1953720*z^4 - 
        775656*z^3 + 793998*z^2 + 492317*z + 73365
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'212.138'
************** MAGMA *****************
Host 212.138.47.23 (212.138.47.23)
Time: Sun Dec 18 10:08:04 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x + (-6*y^2+7*y+5),
-y + (-6*z^2+7*z+5),
-z^3 + (-6*x^2+7*x+5) >;
Radical(I);

Output: Magma V2.11-10    Sun Dec 18 2005 10:08:04 on modular  [Seed = 1589143072]
   -------------------------------------

Ideal of Polynomial ring of rank 3 over Rational Field
Lexicographical Order
Variables: x, y, z
Dimension 0, Radical
Groebner basis:
[
    x + 216*z^4 - 504*z^3 - 24*z^2 + 371*z + 110,
    y + 6*z^2 - 7*z - 5,
    z^8 - 14/3*z^7 + 47/9*z^6 + 427/108*z^5 - 335/48*z^4 - 775655/279936*z^3 + 
        44111/15552*z^2 + 492317/279936*z + 24455/93312
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'212.138'
************** MAGMA *****************
Host 212.138.47.29 (212.138.47.29)
Time: Sun Dec 18 10:07:22 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x^3 + (-6*y^2+7*y+5),
-y^3 + (-6*z^2+7*z+5),
-z^3 + (-6*x^2+7*x+5) >;
Radical(I);

Output: Magma V2.11-10    Sun Dec 18 2005 10:07:21 on modular  [Seed = 1151499335]
   -------------------------------------

Ideal of Polynomial ring of rank 3 over Rational Field
Lexicographical Order
Variables: x, y, z
Dimension 0, Radical
Groebner basis:
[
    x - 20670318404676804121590341679907342944438721410236055716516252786259218\
        420711433810584139369555228744398094045155409199104/1393743412806712329\
        99759010297844161860871496969373562963049485474223528276610984064461508\
        093880757021543538634046896781115514291717975*z^26 + 
        52817691742356886370701872211589394258641546772944677761355469155105730\
        384820419602679329873674311460101684589053757063168/1393743412806712329\
        99759010297844161860871496969373562963049485474223528276610984064461508\
        093880757021543538634046896781115514291717975*z^25 + 
        44084189102656559761036896914171515230703918700362814196736477697748482\
        349329165388194181519205694144483399773379046731904/1393743412806712329\
        99759010297844161860871496969373562963049485474223528276610984064461508\
        093880757021543538634046896781115514291717975*z^24 + 
        10282605380629114589617264989256557708549756853994112065698656467656094\
        04406261142299579793912180745541265316913236203077632/13937434128067123\
        29997590102978441618608714969693735629630494854742235282766109840644615\
        08093880757021543538634046896781115514291717975*z^23 - 
        22228881978492193293559859093936405405939009088196569488635554540757211\
        37017756817169737946803181622067694970688957503668224/13937434128067123\
        29997590102978441618608714969693735629630494854742235282766109840644615\
        08093880757021543538634046896781115514291717975*z^22 - 
        17181692219196114429115811806207940681105897576614572215614886254607317\
        41173496080747558758974447442649000940198623520859392/13937434128067123\
        29997590102978441618608714969693735629630494854742235282766109840644615\
        08093880757021543538634046896781115514291717975*z^21 - 
        61640289475596731450679340165759399618431062957953433768199378491567206\
        565511264862842657794696865313209618370001141849358336/1393743412806712\
        32999759010297844161860871496969373562963049485474223528276610984064461\
        508093880757021543538634046896781115514291717975*z^20 - 
        66095752571214459624518529004011368779461729417153411440699393722538310\
        17246088969923789514916084342288456155181781001857089536/13937434128067\
        12329997590102978441618608714969693735629630494854742235282766109840644\
        61508093880757021543538634046896781115514291717975*z^19 + 
        25238028072639823696679503339288656807992425850973474585354246877644706\
        187685801574587471601563331251578311852754405108094443328/1393743412806\
        71232999759010297844161860871496969373562963049485474223528276610984064\
        461508093880757021543538634046896781115514291717975*z^18 + 
        15100774264212872360384730726830227678249159853860787662574702196479871\
        49631337678553773700882486776776263487029256690143371264/13937434128067\
        12329997590102978441618608714969693735629630494854742235282766109840644\
        61508093880757021543538634046896781115514291717975*z^17 + 
        44841353739392875941013024676041792726615548527879166766758623056926826\
        3013268190022444874591316028252564801406550386388655271936/139374341280\
        67123299975901029784416186087149696937356296304948547422352827661098406\
        4461508093880757021543538634046896781115514291717975*z^16 - 
        14801931190140762886015675654974862129502652192610372634978790059234754\
        947512399230178102320439394185071889427571268295241900385632/1393743412\
        80671232999759010297844161860871496969373562963049485474223528276610984\
        064461508093880757021543538634046896781115514291717975*z^15 + 
        64118150688406168899806736311366044438266976175150900955009941229687123\
        359613473660565416868586665235987375007859422298128871370752/1393743412\
        80671232999759010297844161860871496969373562963049485474223528276610984\
        064461508093880757021543538634046896781115514291717975*z^14 - 
        59766235433460852251769712174872729369152399253394915317285117833345339\
        512065855473683081139767348030618064160139820193734351419392/1393743412\
        80671232999759010297844161860871496969373562963049485474223528276610984\
        064461508093880757021543538634046896781115514291717975*z^13 - 
        28951070792768735987119578603040775907790667817768845226622240582260527\
        922476126045937075626141100552572245765618249291256309909688/2787486825\
        61342465999518020595688323721742993938747125926098970948447056553221968\
        12892301618776151404308707726809379356223102858343595*z^12 + 
        76499372079855456323013037441293431543773048046253148902645677881534577\
        4660856190940754360644032963410442949681497376069584715073536/139374341\
        28067123299975901029784416186087149696937356296304948547422352827661098\
        4064461508093880757021543538634046896781115514291717975*z^11 - 
        18265271834715021921507366802108499920741026425191081094680295339668321\
        8637033273500632516798684292743702866140155367781483358671872/139374341\
        28067123299975901029784416186087149696937356296304948547422352827661098\
        4064461508093880757021543538634046896781115514291717975*z^10 + 
        81234711366392755150707194044826385840652588795161583303875060921131616\
        16613798195316541777619380893565306500576380034572591855769816/13937434\
        12806712329997590102978441618608714969693735629630494854742235282766109\
        84064461508093880757021543538634046896781115514291717975*z^9 - 
        76301446847565195312748120513029598866156889065065860133024518164894305\
        3105777355729600924867262813718143714436913502675351522258163712/139374\
        34128067123299975901029784416186087149696937356296304948547422352827661\
        0984064461508093880757021543538634046896781115514291717975*z^8 - 
        82348805467619018020877218869999199242072232530941549101334278979740312\
        08331342268339335248205917407685848265330600950653722177270555648/13937\
        43412806712329997590102978441618608714969693735629630494854742235282766\
        10984064461508093880757021543538634046896781115514291717975*z^7 + 
        84412521960472857160911216066242401851090200344030094679739981190800010\
        375965825632433557714526225507464746855468694951312740791718236002/1393\
        74341280671232999759010297844161860871496969373562963049485474223528276\
        610984064461508093880757021543538634046896781115514291717975*z^6 - 
        19683600898511070798075127987078432887095168620485541000219071579591808\
        6564629037654229865133236791460268215512602009300843346282091915264/139\
        37434128067123299975901029784416186087149696937356296304948547422352827\
        6610984064461508093880757021543538634046896781115514291717975*z^5 + 
        10666103245020463025460572567380480364748019759231156004389783614618856\
        4278509574124073487675029961578117423850555852445478175878833243136/139\
        37434128067123299975901029784416186087149696937356296304948547422352827\
        6610984064461508093880757021543538634046896781115514291717975*z^4 + 
        96184597403301187882098000111345017149388757160701053527995880628846239\
        321327676865418804844922873757179730046636417630135402601301240819/1393\
        74341280671232999759010297844161860871496969373562963049485474223528276\
        610984064461508093880757021543538634046896781115514291717975*z^3 - 
        23484072682953374360602270413978122643907931573358680446186791183604617\
        35064254014182229707643805925968450130018541132374369207378926592/55749\
        73651226849319990360411913766474434859878774942518521979418968941131064\
        439362578460323755230280861741545361875871244620571668719*z^2 - 
        26306871523575483715460693403165967104582376597576450916239167773516248\
        016865114672591341164780430740062095698813097584417659321598050816/1393\
        74341280671232999759010297844161860871496969373562963049485474223528276\
        610984064461508093880757021543538634046896781115514291717975*z - 
        17685951105934495101334685727679688500362705972794161671957590971299254\
        4928960696571368311776218030826201622816796879764966588533652253/278748\
        68256134246599951802059568832372174299393874712592609897094844705655322\
        196812892301618776151404308707726809379356223102858343595,
    y - 52327418222015905902570988536026443305400447176512318167424696241950974\
        64867103815670348284947982736369877307627698015104/13937434128067123299\
        97590102978441618608714969693735629630494854742235282766109840644615080\
        93880757021543538634046896781115514291717975*z^26 + 
        53322713168254937049374753704315866133748322761477018891704908145697222\
        36175698315958165401476066818724050651331474596288/13937434128067123299\
        97590102978441618608714969693735629630494854742235282766109840644615080\
        93880757021543538634046896781115514291717975*z^25 + 
        16200344963969739629738687977305337274986451247440630132666003014205689\
        06154724466997188357122175984508399767599792176664/13937434128067123299\
        97590102978441618608714969693735629630494854742235282766109840644615080\
        93880757021543538634046896781115514291717975*z^24 + 
        24267663491107314919267151607004192719477817031022986301215056432744760\
        4502999413958546800557457229730073541614908067430272/139374341280671232\
        99975901029784416186087149696937356296304948547422352827661098406446150\
        8093880757021543538634046896781115514291717975*z^23 - 
        22941289203469812166392436718685805905743949242949535266547366634353399\
      
 ** WARNING: Output too long, hence truncated.

'212.138'
************** MAGMA *****************
Host 212.138.47.18 (212.138.47.18)
Time: Sun Dec 18 10:06:52 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x^8 + (-6*y^3+7*y+5),
-y^8 + (-6*z^3+7*z+5),
-z^8 + (-6*x^3+7*x+5) >;
Radical(I);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Sun Dec 18 2005 10:06:32 on modular  [Seed = 1084651922]
   -------------------------------------


Errors: /bin/sh: line 1: 26986 Alarm clock             nice -n 19 /usr/local/bin/magma


'212.138'
************** MAGMA *****************
Host 212.138.47.17 (212.138.47.17)
Time: Sun Dec 18 10:05:35 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x^6 + (-6*y^3+7*y+5),
-y^7 + (-6*z^3+7*z+5),
-z^8 + (-6*x^3+7*x+5) >;
Radical(I);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Sun Dec 18 2005 10:05:15 on modular  [Seed = 1219391945]
   -------------------------------------


Errors: /bin/sh: line 1: 26978 Alarm clock             nice -n 19 /usr/local/bin/magma


'212.138'
************** MAGMA *****************
Host 212.138.47.24 (212.138.47.24)
Time: Sun Dec 18 10:04:18 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x^2 + (-6*y^3+7*y+5),
-y^2 + (-6*z^3+7*z+5),
-z^2 + (-6*x^3+7*x+5) >;
Radical(I);

Output: Magma V2.11-10    Sun Dec 18 2005 10:04:17 on modular  [Seed = 1905739818]
   -------------------------------------

Ideal of Polynomial ring of rank 3 over Rational Field
Lexicographical Order
Variables: x, y, z
Dimension 0, Radical
Groebner basis:
[
    x - 607747819788532155708373696835866320181177034137286756794368/1534183140\
        25015422015563440134202740864381613046837395925*z^26 - 
        1644194756182732188695998750143313136448830566796183794089984/767091570\
        125077110077817200671013704321908065234186979625*z^25 + 
        1519370344618022681485678701207219405338713755668400813637632/697355972\
        84097919097983381879183064029264369566744270875*z^24 + 
        5657683761495134333516311523334543610877895279826294418178048/153418314\
        025015422015563440134202740864381613046837395925*z^23 - 
        54919850897379097829474394140593057612213076270900171882102784/76709157\
        0125077110077817200671013704321908065234186979625*z^22 - 
        23749346132955892738971647263493830752398879458430423918444544/15341831\
        4025015422015563440134202740864381613046837395925*z^21 - 
        20700681958857365834122812251195046038933464222145607741997056/76709157\
        0125077110077817200671013704321908065234186979625*z^20 + 
        329797041412983216677707986578040306567545389152753038938669056/7670915\
        70125077110077817200671013704321908065234186979625*z^19 + 
        5743093752282330081008122287919690804163733840955113232662528/153418314\
        025015422015563440134202740864381613046837395925*z^18 - 
        223440592050718037577946396909580575534889719118640118530048/1450078582\
        467064480298331192194732900419485945622281625*z^17 + 
        105410529530167997137721778655638855754188729832104137565487104/3068366\
        2805003084403112688026840548172876322609367479185*z^16 + 
        885277150983208290850600622134945917710089103724880750058029056/7670915\
        70125077110077817200671013704321908065234186979625*z^15 - 
        12228856033159216097966918255958697335709910281377823340045697024/76709\
        1570125077110077817200671013704321908065234186979625*z^14 - 
        2428919581438507999580094225861501397229411784479549789109817344/153418\
        314025015422015563440134202740864381613046837395925*z^13 + 
        19686636770492932197315778634758016279089740344967393996509011968/76709\
        1570125077110077817200671013704321908065234186979625*z^12 + 
        37439000525180257727455377920560461618208300249854315692199601152/76709\
        1570125077110077817200671013704321908065234186979625*z^11 - 
        242567485796071338802342670543220142016253736503063297377912832/1534183\
        14025015422015563440134202740864381613046837395925*z^10 - 
        1851283411800758364534308335130407783249267591238748229467858432/306836\
        62805003084403112688026840548172876322609367479185*z^9 - 
        32281291693399996932626040560041370875138715107061454029379634176/76709\
        1570125077110077817200671013704321908065234186979625*z^8 + 
        15187976308103132481649219442943042891239263040607663202857682752/76709\
        1570125077110077817200671013704321908065234186979625*z^7 + 
        32541311772827410438962148277497379673569947455678018687923473506/76709\
        1570125077110077817200671013704321908065234186979625*z^6 + 
        13913681728440239381658207089017885127837169844456124071384306152/76709\
        1570125077110077817200671013704321908065234186979625*z^5 - 
        5201437434931523590484162612412046914431897286598813426355149518/767091\
        570125077110077817200671013704321908065234186979625*z^4 - 
        8369631173418546797554673043809526207557975516145664666830070596/767091\
        570125077110077817200671013704321908065234186979625*z^3 - 
        367049861123048438708477131899166019080891143075089642030257163/6973559\
        7284097919097983381879183064029264369566744270875*z^2 - 
        952768348549232830699641549698525626444725223809958208866600116/7670915\
        70125077110077817200671013704321908065234186979625*z - 
        18715587866479416200274107374916451473634359600279292058148243/15341831\
        4025015422015563440134202740864381613046837395925,
    y + 8588783796645609270041309550413627734427158955259021244760064/767091570\
        125077110077817200671013704321908065234186979625*z^26 - 
        637476922202747849091768753421039549247886904737543430864896/7670915701\
        25077110077817200671013704321908065234186979625*z^25 - 
        2991662828937587719651268641902300229276057309871396005292802048/767091\
        570125077110077817200671013704321908065234186979625*z^24 - 
        3905324324791053203620496116512887656336880862025760883867648/697355972\
        84097919097983381879183064029264369566744270875*z^23 + 
        27504966074299938066699391828241118157638650281304603241981935616/76709\
        1570125077110077817200671013704321908065234186979625*z^22 + 
        16954503077996297980763933818251459139545426272372724218478723072/76709\
        1570125077110077817200671013704321908065234186979625*z^21 - 
        10148400141775193758023270288734527185830514208009811283475562496/69735\
        597284097919097983381879183064029264369566744270875*z^20 - 
        136748565042632957498398260907316114042218819459638218594974040064/7670\
        91570125077110077817200671013704321908065234186979625*z^19 + 
        218073368412696644786151217621427176878167387891939188253975248896/7670\
        91570125077110077817200671013704321908065234186979625*z^18 + 
        476420567037107074864416424418893515283464984044841541861899829248/7670\
        91570125077110077817200671013704321908065234186979625*z^17 - 
        87911783741774450433038258838115842490336235736309248584654553088/76709\
        1570125077110077817200671013704321908065234186979625*z^16 - 
        865393107630329396744064599190108622066096619174761478073516490752/7670\
        91570125077110077817200671013704321908065234186979625*z^15 - 
        491732366580711670721311407822861406520038434484615375661704249344/7670\
        91570125077110077817200671013704321908065234186979625*z^14 + 
        734818272058152712148400269178951592247749820810396870290521808896/7670\
        91570125077110077817200671013704321908065234186979625*z^13 + 
        1053964300460031535169533803184852097290543328887561757855461595136/767\
        091570125077110077817200671013704321908065234186979625*z^12 + 
        8634030541199246468005771144699878375129632040218392070043614208/153418\
        314025015422015563440134202740864381613046837395925*z^11 - 
        76063092256498361515666815473156851226821587577053074339657521152/69735\
        597284097919097983381879183064029264369566744270875*z^10 - 
        605969915846052348237289545733521947789758114815909673885915143168/7670\
        91570125077110077817200671013704321908065234186979625*z^9 + 
        103462238301384026891084346638351778208358212884489589520021951616/7670\
        91570125077110077817200671013704321908065234186979625*z^8 + 
        206006578234046558080680416999501373559639471746243171719113212/4047976\
        62335133039618900897451722271409977870835982575*z^7 + 
        213087953931560709344296477834302537326554381040028500222583661956/7670\
        91570125077110077817200671013704321908065234186979625*z^6 - 
        1551500011152425928327059620628005368730724758729742956668117102/153418\
        314025015422015563440134202740864381613046837395925*z^5 - 
        14331700909217848590119018556215107062277900112783826180653965517/15341\
        8314025015422015563440134202740864381613046837395925*z^4 - 
        43953099780249835711295595369687919026992869322936517188129514756/76709\
        1570125077110077817200671013704321908065234186979625*z^3 - 
        13801578868727311991345220593097358202836764355928486394382755206/76709\
        1570125077110077817200671013704321908065234186979625*z^2 - 
        2357219767421710505084804774312577449297980257986286253398662112/767091\
        570125077110077817200671013704321908065234186979625*z - 
        35062495528309440485031693067359094546187759778808876771992076/15341831\
        4025015422015563440134202740864381613046837395925,
    z^27 - 21/2*z^25 - 19/3*z^24 + 49*z^23 + 532/9*z^22 - 49939/432*z^21 - 
        6517/27*z^20 + 228487/2592*z^19 + 74759341/139968*z^18 + 
        1224167/5184*z^17 - 86467843/139968*z^16 - 3761045885/5038848*z^15 + 
        290329361/1679616*z^14 + 1419975504253/1632586752*z^13 + 
        13760646589/30233088*z^12 - 131206787713/362797056*z^11 - 
        4113563481113/7346640384*z^10 - 12868110131287/78364164096*z^9 + 
        110838315489477121/609359740010496*z^8 + 
        827650776663089/4231664861184*z^7 + 8940368413909147/152339935002624*z^\
        6 - 652513311785843/25389989167104*z^5 - 
        4957091804726761/152339935002624*z^4 - 
        511975131257783/33853318889472*z^3 - 151452934564537/38084983750656*z^2 
        - 358514838196123/609359740010496*z - 23491990397845/609359740010496
]

Total time: 0.210 seconds, Total memory usage: 3.43MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Sun Dec 18 09:57:59 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
C2:=LinearCode(M2); 
WeightDistribution(C2);
L:=MinimumWords(C2); 
C3:=LinearCode(M);
aut3 := AutomorphismGroup(C3);
Order(aut3);
Generators(aut3); 
aut2 := AutomorphismGroup(C2);
Order(aut2);
Generators(aut2); 

Output: Magma V2.11-10    Sun Dec 18 2005 09:57:58 on modular  [Seed = 954074084]
   -------------------------------------

true
[ <0, 1>, <8, 23>, <10, 175>, <12, 780>, <14, 2227>, <16, 3898>, <18, 4285>, 
<20, 3135>, <22, 1377>, <24, 410>, <26, 64>, <28, 9> ]
7
{
    (1, 5, 2, 6, 3, 7, 4)(8, 12, 9, 13, 10, 22, 11)(14, 23, 15, 24, 16, 25, 
        17)(18, 26, 19, 27, 20, 28, 21)(29, 33, 30, 34, 31, 35, 32)(36, 40, 37, 
        41, 38, 42, 39)(43, 47, 44, 48, 45, 49, 46)(50, 54, 51, 55, 52, 56, 53)
}
1
{}

Total time: 1.330 seconds, Total memory usage: 3.93MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Sun Dec 18 09:56:58 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
C2:=LinearCode(M2); 
WeightDistribution(C2);
L:=MinimumWords(C2); 
C3:=LinearCode(M);
aut3 := AutomorphismGroup(C3);
Order(aut3);
Generators(aut3); 
aut2 := AutomorphismGroup(C2);
Order(aut2);
Generators(aut3); 

Output: Magma V2.11-10    Sun Dec 18 2005 09:56:57 on modular  [Seed = 666967220]
   -------------------------------------

true
[ <0, 1>, <8, 23>, <10, 175>, <12, 780>, <14, 2227>, <16, 3898>, <18, 4285>, 
<20, 3135>, <22, 1377>, <24, 410>, <26, 64>, <28, 9> ]
7
{
    (1, 5, 2, 6, 3, 7, 4)(8, 12, 9, 13, 10, 22, 11)(14, 23, 15, 24, 16, 25, 
        17)(18, 26, 19, 27, 20, 28, 21)(29, 33, 30, 34, 31, 35, 32)(36, 40, 37, 
        41, 38, 42, 39)(43, 47, 44, 48, 45, 49, 46)(50, 54, 51, 55, 52, 56, 53)
}
1
{
    (1, 5, 2, 6, 3, 7, 4)(8, 12, 9, 13, 10, 22, 11)(14, 23, 15, 24, 16, 25, 
        17)(18, 26, 19, 27, 20, 28, 21)(29, 33, 30, 34, 31, 35, 32)(36, 40, 37, 
        41, 38, 42, 39)(43, 47, 44, 48, 45, 49, 46)(50, 54, 51, 55, 52, 56, 53)
}

Total time: 1.320 seconds, Total memory usage: 3.93MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Sun Dec 18 09:51:22 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
C2:=LinearCode(M2); 
WeightDistribution(C2);
L:=MinimumWords(C2); 
C3:=LinearCode(M);
aut3 := AutomorphismGroup(C3);
Order(aut3);
Generators(aut3); 

Output: Magma V2.11-10    Sun Dec 18 2005 09:51:21 on modular  [Seed = 801708908]
   -------------------------------------

true
[ <0, 1>, <8, 23>, <10, 175>, <12, 780>, <14, 2227>, <16, 3898>, <18, 4285>, 
<20, 3135>, <22, 1377>, <24, 410>, <26, 64>, <28, 9> ]
7
{
    (1, 5, 2, 6, 3, 7, 4)(8, 12, 9, 13, 10, 22, 11)(14, 23, 15, 24, 16, 25, 
        17)(18, 26, 19, 27, 20, 28, 21)(29, 33, 30, 34, 31, 35, 32)(36, 40, 37, 
        41, 38, 42, 39)(43, 47, 44, 48, 45, 49, 46)(50, 54, 51, 55, 52, 56, 53)
}

Total time: 1.320 seconds, Total memory usage: 3.93MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Sun Dec 18 09:50:08 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
C2:=LinearCode(M2); 
WeightDistribution(C2);
L:=MinimumWords(C2); 
C3:=LinearCode(M);
aut3 := AutomorphismGroup(C3);
Order(aut3);
Generators(aut3); 

Output: Magma V2.11-10    Sun Dec 18 2005 09:50:08 on modular  [Seed = 3560104159]
   -------------------------------------


>> D := Dual(S);
             ^
User error: Identifier 'S' has not been declared or assigned

>> (D meet S) eq S;
    ^
User error: Identifier 'D' has not been declared or assigned

>> M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
                                   ^
User error: Identifier 'S' has not been declared or assigned

>> M1:=EchelonForm(M);
                   ^
User error: Identifier 'M' has not been declared or assigned

>> M2:=Submatrix(M1,22,22,14,35);
                 ^
User error: Identifier 'M1' has not been declared or assigned

>> C2:=LinearCode(M2); 
                  ^
User error: Identifier 'M2' has not been declared or assigned

>> WeightDistribution(C2);
                      ^
User error: Identifier 'C2' has not been declared or assigned

>> L:=MinimumWords(C2); 
                   ^
User error: Identifier 'C2' has not been declared or assigned

>> C3:=LinearCode(M);
                  ^
User error: Identifier 'M' has not been declared or assigned

>> aut3 := AutomorphismGroup(C3);
                             ^
User error: Identifier 'C3' has not been declared or assigned

>> Order(aut3);
         ^
User error: Identifier 'aut3' has not been declared or assigned

>> Generators(aut3); ;
              ^
User error: Identifier 'aut3' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Sun Dec 18 09:37:24 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;

Output: Magma V2.11-10    Sun Dec 18 2005 09:37:24 on modular  [Seed = 3274044620]
   -------------------------------------


Total time: 0.190 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.47.14 (212.138.47.14)
Time: Sun Dec 18 09:16:17 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x + (-6*y^3+7*y+5),
-y + (-6*z^3+7*z+5),
-z + (-6*x^3+7*x+5) >;
Radical(I);

Output: Magma V2.11-10    Sun Dec 18 2005 09:16:17 on modular  [Seed = 4061454056]
   -------------------------------------

Ideal of Polynomial ring of rank 3 over Rational Field
Lexicographical Order
Variables: x, y, z
Dimension 0, Radical
Groebner basis:
[
    x - 1296*z^9 + 4536*z^7 + 3240*z^6 - 5292*z^5 - 7560*z^4 - 600*z^3 + 
        4410*z^2 + 3101*z + 710,
    y + 6*z^3 - 7*z - 5,
    z^27 - 21/2*z^25 - 15/2*z^24 + 49*z^23 + 70*z^22 - 7811/72*z^21 - 
        1715/6*z^20 + 12985/432*z^19 + 133685/216*z^18 + 14063/32*z^17 - 
        274925/432*z^16 - 8654347/7776*z^15 - 62965/864*z^14 + 
        54259387/46656*z^13 + 88401125/93312*z^12 - 81855529/279936*z^11 - 
        260804915/279936*z^10 - 402754685/839808*z^9 + 224599585/1119744*z^8 + 
        1933044449/5038848*z^7 + 1197004745/6718464*z^6 - 823553731/40310784*z^5
        - 8293758725/120932352*z^4 - 29056568867/725594112*z^3 - 
        3016860665/241864704*z^2 - 781606447/362797056*z - 715820345/4353564672
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'212.138'
************** MAGMA *****************
Host 212.138.47.14 (212.138.47.14)
Time: Sun Dec 18 09:13:54 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-x + (-6*y^2-4*y+5),
-y + (-6*z^2-4*z+5),
-z + (-6*x^2-4*x+5) >;
Radical(I);

Output: Magma V2.11-10    Sun Dec 18 2005 09:13:52 on modular  [Seed = 4279882356]
   -------------------------------------

Ideal of Polynomial ring of rank 3 over Rational Field
Lexicographical Order
Variables: x, y, z
Dimension 0, Radical
Groebner basis:
[
    x + 216*z^4 + 288*z^3 - 288*z^2 - 256*z + 165,
    y + 6*z^2 + 4*z - 5,
    z^8 + 8/3*z^7 - 8/9*z^6 - 160/27*z^5 + 23/162*z^4 + 1262/243*z^3 - 
        458/729*z^2 - 505855/279936*z + 162685/279936
]

Total time: 0.220 seconds, Total memory usage: 3.34MB


'144.137'
************** MAGMA *****************
Host 144.137.185.243 (144.137.185.243)
Time: Sun Dec 18 04:05:26 2005

Input: 2+1 divided by x = 4x

Output: Magma V2.11-10    Sun Dec 18 2005 04:05:26 on modular  [Seed = 3340870312]
   -------------------------------------


>> 2+1 divided by x = 4x;
       ^
User error: bad syntax

Total time: 0.200 seconds, Total memory usage: 3.24MB


'216.239'
************** MAGMA *****************
Host 216.239.167.217 (216.239.167.217)
Time: Sat Dec 17 21:24:05 2005

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-10    Sat Dec 17 2005 21:24:05 on modular  [Seed = 3910034073]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.47.15 (212.138.47.15)
Time: Sat Dec 17 13:59:08 2005

Input: Table[Timing[FullSimplify[{i, Cos[Pi/i], Sin[Pi/i]}]], {i, 1, 22}] 

Output: Magma V2.11-10    Sat Dec 17 2005 13:59:07 on modular  [Seed = 1686337705]
   -------------------------------------


>> Table[Timing[FullSimplify[{i, Cos[Pi/i], Sin[Pi/i]}]], {i, 1, 22}] ;
   ^
User error: Identifier 'Table' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'85.89.1'
************** MAGMA *****************
Host 85.89.168.182 (85.89.168.182)
Time: Sat Dec 17 13:57:50 2005

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-10    Sat Dec 17 2005 13:57:50 on modular  [Seed = 2005953512]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.47.15 (212.138.47.15)
Time: Sat Dec 17 13:52:57 2005

Input: P<t1,t2,t3,t4>:=PolynomialRing(RationalField(),4); I:=ideal<P |
-2 + t2*t3 + t1*t4, 
-2 + t1*t2*t3 + t4*t2*t3 + t1*t3*t4 + t1*t2*t4,
6 +  (t2*t3)^2 + (t1*t4)^2 - t1*t2*t3*t4 - (t1*t2*t3^2 + t4*t3*t2^2 + t1*t3*t4^2 + t1^2*t4*t2),
-6 + t1*t2^2*t3^3/t4   + t1^2*t3*t4^3/t2  +  t1^3*t2*t4^2/t3 + t4*t2^3*t3^2/t1 - 5*(t2*t3 - t1*t4)*(t1*t2*t3 + t4*t2*t3 - t1*t3*t4 - t1*t2*t4)  >;
Radical(I);

Output: Magma V2.11-10    Sat Dec 17 2005 13:52:56 on modular  [Seed = 250155959]
   -------------------------------------


>> P<t1,t2,t3,t4>:=PolynomialRing(RationalField(),4); I:=ideal<P |
                                                              ^
Runtime error in ideal< ... >: Rhs argument 4 is invalid for this constructor

>> Radical(I);;
           ^
User error: Identifier 'I' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.34MB


'212.138'
************** MAGMA *****************
Host 212.138.47.24 (212.138.47.24)
Time: Sat Dec 17 13:50:38 2005

Input: P<m1,m2,m3,m4>:=PolynomialRing(RationalField(),4); I:=ideal<P |
-1 + m1 + m2*m3/(1+m4^2)^(1/2) + (m3 + m3/(1+m4^2)^(1/2))^(1/2),
-4+ m1 + m2*m3/(1+m4^2)^(1/2) - (m3 + m3/(1+m4^2)^(1/2))^(1/2),
-2 + m1 - m2*m3/(1+m4^2)^(1/2) + (m3 - m3/(1+m4^2)^(1/2))^(1/2),
-3+ m1 - m2*m3/(1+m4^2)^(1/2) - (m3 - m3/(1+m4^2)^(1/2))^(1/2)  >;
Radical(I);

Output: Magma V2.11-10    Sat Dec 17 2005 13:50:38 on modular  [Seed = 183309509]
   -------------------------------------


>> -1 + m1 + m2*m3/(1+m4^2)^(1/2) + (m3 + m3/(1+m4^2)^(1/2))^(1/2),
                           ^
Runtime error in '^': Bad argument types
Argument types given: RngMPolElt, RngMPolElt

>> Radical(I);;
           ^
User error: Identifier 'I' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.47.23 (212.138.47.23)
Time: Sat Dec 17 13:50:07 2005

Input: P<m1,m2,m3,m4>:=PolynomialRing(RationalField(),4); I:=ideal<P |
-t1 + m1 + m2*m3/(1+m4^2)^(1/2) + (m3 + m3/(1+m4^2)^(1/2))^(1/2),
-t4+ m1 + m2*m3/(1+m4^2)^(1/2) - (m3 + m3/(1+m4^2)^(1/2))^(1/2),
-t2 + m1 - m2*m3/(1+m4^2)^(1/2) + (m3 - m3/(1+m4^2)^(1/2))^(1/2),
-t3 + m1 - m2*m3/(1+m4^2)^(1/2) - (m3 - m3/(1+m4^2)^(1/2))^(1/2)  >;
Radical(I);

Output: Magma V2.11-10    Sat Dec 17 2005 13:50:06 on modular  [Seed = 132127208]
   -------------------------------------


>> -t1 + m1 + m2*m3/(1+m4^2)^(1/2) + (m3 + m3/(1+m4^2)^(1/2))^(1/2),
    ^
User error: Identifier 't1' has not been declared or assigned

>> Radical(I);;
           ^
User error: Identifier 'I' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.47.15 (212.138.47.15)
Time: Sat Dec 17 13:48:52 2005

Input: P<m1,m2,m3,m4>:=PolynomialRing(RationalField(),4); I:=ideal<P |
1 = m1 + m2*m3/(1+m4^2)^(1/2) + (m3 + m3/(1+m4^2)^(1/2))^(1/2),
4= m1 + m2*m3/(1+m4^2)^(1/2) - (m3 + m3/(1+m4^2)^(1/2))^(1/2),
2 = m1 - m2*m3/(1+m4^2)^(1/2) + (m3 - m3/(1+m4^2)^(1/2))^(1/2),
3 = m1 - m2*m3/(1+m4^2)^(1/2) - (m3 - m3/(1+m4^2)^(1/2))^(1/2)  >;
Radical(I);

Output: Magma V2.11-10    Sat Dec 17 2005 13:48:52 on modular  [Seed = 15146661]
   -------------------------------------


>> 1 = m1 + m2*m3/(1+m4^2)^(1/2) + (m3 + m3/(1+m4^2)^(1/2))^(1/2),
                          ^
Runtime error in '^': Bad argument types
Argument types given: RngMPolElt, RngMPolElt

>> Radical(I);;
           ^
User error: Identifier 'I' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.47.17 (212.138.47.17)
Time: Sat Dec 17 13:48:05 2005

Input: P<m1,m2,m3,m4>:=PolynomialRing(RationalField(),4); I:=ideal<P |
t1 = m1 + m2*m3/(1+m4^2)^(1/2) + (m3 + m3/(1+m4^2)^(1/2))^(1/2),
t4 = m1 + m2*m3/(1+m4^2)^(1/2) - (m3 + m3/(1+m4^2)^(1/2))^(1/2),
t2 = m1 - m2*m3/(1+m4^2)^(1/2) + (m3 - m3/(1+m4^2)^(1/2))^(1/2),
t3 = m1 - m2*m3/(1+m4^2)^(1/2) - (m3 - m3/(1+m4^2)^(1/2))^(1/2)  >;
Radical(I);

Output: Magma V2.11-10    Sat Dec 17 2005 13:48:05 on modular  [Seed = 486212168]
   -------------------------------------


>> t1 = m1 + m2*m3/(1+m4^2)^(1/2) + (m3 + m3/(1+m4^2)^(1/2))^(1/2),
   ^
User error: Identifier 't1' has not been declared or assigned

>> Radical(I);;
           ^
User error: Identifier 'I' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.47.24 (212.138.47.24)
Time: Sat Dec 17 13:45:43 2005

Input: P<y>:=PolynomialRing(RationalField(),1); I:=ideal<P |
y^21 - 12*y^20 + 55*y^19 - 107*y^18 + 17*y^17 + 245*y^16 - 175*y^15 - 535*y^14 + 715*y^13 + 844*y^12 - 2407*y^11 + 1075*y^10 + 1459*y^9 - 503*y^8 - 2999*y^7 + 4018*y^6 - 2002*y^5 + 37*y^4 + 489*y^3 - 311*y^2 + 86*y-13  >;
Radical(I);

Output: Magma V2.11-10    Sat Dec 17 2005 13:45:42 on modular  [Seed = 351472627]
   -------------------------------------

Ideal of Polynomial ring of rank 1 over Rational Field
Lexicographical Order
Variables: y
Dimension 0, Radical
Groebner basis:
[
    y^21 - 12*y^20 + 55*y^19 - 107*y^18 + 17*y^17 + 245*y^16 - 175*y^15 - 
        535*y^14 + 715*y^13 + 844*y^12 - 2407*y^11 + 1075*y^10 + 1459*y^9 - 
        503*y^8 - 2999*y^7 + 4018*y^6 - 2002*y^5 + 37*y^4 + 489*y^3 - 311*y^2 + 
        86*y - 13
]

Total time: 0.200 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.113.12 (212.138.113.12)
Time: Sat Dec 17 13:44:41 2005

Input: P<x>:=PolynomialRing(RationalField(),1); I:=ideal<P |
x^7 - 2*x^6 - x^5 + x^4 + x^3 + x^2 - x - 1  >;
Radical(I);

Output: Magma V2.11-10    Sat Dec 17 2005 13:44:41 on modular  [Seed = 301338297]
   -------------------------------------

Ideal of Polynomial ring of rank 1 over Rational Field
Lexicographical Order
Variables: x
Dimension 0, Radical
Groebner basis:
[
    x^7 - 2*x^6 - x^5 + x^4 + x^3 + x^2 - x - 1
]

Total time: 0.200 seconds, Total memory usage: 3.24MB


'83.26.1'
************** MAGMA *****************
Host 83.26.157.172 (83.26.157.172)
Time: Sat Dec 17 10:35:39 2005

Input: pi(51)




Output: Magma V2.11-10    Sat Dec 17 2005 10:35:39 on modular  [Seed = 301359720]
   -------------------------------------


>> pi(51)
   ^
User error: Identifier 'pi' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'83.26.1'
************** MAGMA *****************
Host 83.26.157.172 (83.26.157.172)
Time: Sat Dec 17 10:35:28 2005

Input: piprime(51)




Output: Magma V2.11-10    Sat Dec 17 2005 10:35:28 on modular  [Seed = 751525726]
   -------------------------------------


>> piprime(51)
   ^
User error: Identifier 'piprime' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'83.26.1'
************** MAGMA *****************
Host 83.26.157.172 (83.26.157.172)
Time: Sat Dec 17 10:29:43 2005

Input: prime(51)



Output: Magma V2.11-10    Sat Dec 17 2005 10:29:43 on modular  [Seed = 3442122777]
   -------------------------------------


>> prime(51)
   ^
User error: Identifier 'prime' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'83.26.1'
************** MAGMA *****************
Host 83.26.157.172 (83.26.157.172)
Time: Sat Dec 17 10:28:07 2005

Input: pi(100)


Output: Magma V2.11-10    Sat Dec 17 2005 10:28:07 on modular  [Seed = 3257249654]
   -------------------------------------


>> pi(100)
   ^
User error: Identifier 'pi' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.24MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 17 03:18:15 2005

Input: G:=DirichletGroup(432);G;
X :=Elements(G);X;
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;
qEigenform(D[1],99);


Output: Magma V2.11-10    Sat Dec 17 2005 03:18:13 on modular  [Seed = 684237507]
   -------------------------------------

Group of Dirichlet characters of modulus 432 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.3,
    $.1*$.3,
    $.2*$.3,
    $.1*$.2*$.3
]
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.3,
    $.1*$.3,
    $.2*$.3,
    $.1*$.2*$.3
]
1
1
[
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field
]
q - 5*q^7 - 7*q^13 + q^19 - 5*q^25 + 4*q^31 - q^37 - 8*q^43 + 18*q^49 - 13*q^61 
    - 11*q^67 + 17*q^73 + 13*q^79 + 35*q^91 + 5*q^97 + O(q^99)

Total time: 1.399 seconds, Total memory usage: 6.08MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 17 03:15:53 2005

Input: G: =DirichletGroup(432);G;
X :=Elements(G);X;
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;
qEigenform(D[1],99);


Output: Magma V2.11-10    Sat Dec 17 2005 03:15:52 on modular  [Seed = 3509672902]
   -------------------------------------


>> G: =DirichletGroup(432);G;
      ^
User error: bad syntax

>> X :=Elements(G);X;
                ^
User error: Identifier 'G' has not been declared or assigned

>> X :=Elements(G);X;
                   ^
User error: Identifier 'X' has not been declared or assigned

>> X;
   ^
User error: Identifier 'X' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
       ^
User error: Identifier 'X' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
                       ^
User error: Identifier 'Y' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
                                 ^
User error: Identifier 'Y' has not been declared or assigned

>> M := ModularSymbols(Y, 2, 1);
                       ^
User error: Identifier 'Y' has not been declared or assigned

>> D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
                                                          ^
User error: Identifier 'M' has not been declared or assigned

>> D;
   ^
User error: Identifier 'D' has not been declared or assigned

>> qEigenform(D[1],99);
              ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.24MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 17 03:15:32 2005

Input: G: = DirichletGroup(432);G;
X :=Elements(G);X;
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;
qEigenform(D[1],99);


Output: Magma V2.11-10    Sat Dec 17 2005 03:15:32 on modular  [Seed = 3593886941]
   -------------------------------------


>> G: = DirichletGroup(432);G;
      ^
User error: bad syntax

>> X :=Elements(G);X;
                ^
User error: Identifier 'G' has not been declared or assigned

>> X :=Elements(G);X;
                   ^
User error: Identifier 'X' has not been declared or assigned

>> X;
   ^
User error: Identifier 'X' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
       ^
User error: Identifier 'X' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
                       ^
User error: Identifier 'Y' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
                                 ^
User error: Identifier 'Y' has not been declared or assigned

>> M := ModularSymbols(Y, 2, 1);
                       ^
User error: Identifier 'Y' has not been declared or assigned

>> D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
                                                          ^
User error: Identifier 'M' has not been declared or assigned

>> D;
   ^
User error: Identifier 'D' has not been declared or assigned

>> qEigenform(D[1],99);
              ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 17 03:15:27 2005

Input: G: =DirichletGroup(432);G;
X :=Elements(G);X;
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;
qEigenform(D[1],99);


Output: Magma V2.11-10    Sat Dec 17 2005 03:15:27 on modular  [Seed = 3678097899]
   -------------------------------------


>> G: =DirichletGroup(432);G;
      ^
User error: bad syntax

>> X :=Elements(G);X;
                ^
User error: Identifier 'G' has not been declared or assigned

>> X :=Elements(G);X;
                   ^
User error: Identifier 'X' has not been declared or assigned

>> X;
   ^
User error: Identifier 'X' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
       ^
User error: Identifier 'X' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
                       ^
User error: Identifier 'Y' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
                                 ^
User error: Identifier 'Y' has not been declared or assigned

>> M := ModularSymbols(Y, 2, 1);
                       ^
User error: Identifier 'Y' has not been declared or assigned

>> D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
                                                          ^
User error: Identifier 'M' has not been declared or assigned

>> D;
   ^
User error: Identifier 'D' has not been declared or assigned

>> qEigenform(D[1],99);
              ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.24MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 17 03:15:16 2005

Input: G:=DirichletGroup(432);G;
X :=Elements(G);X;
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;
qEigenform(D[1],99);


Output: Magma V2.11-10    Sat Dec 17 2005 03:15:14 on modular  [Seed = 3223341821]
   -------------------------------------

Group of Dirichlet characters of modulus 432 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.3,
    $.1*$.3,
    $.2*$.3,
    $.1*$.2*$.3
]
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.3,
    $.1*$.3,
    $.2*$.3,
    $.1*$.2*$.3
]
1
1
[
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field
]
q + 4*q^5 + 3*q^7 - 4*q^11 + q^13 - 4*q^17 + q^19 - 4*q^23 + 11*q^25 + 4*q^31 + 
    12*q^35 - 9*q^37 + 8*q^43 + 12*q^47 + 2*q^49 - 8*q^53 - 16*q^55 - 4*q^59 - 
    5*q^61 + 4*q^65 - 11*q^67 - 8*q^71 + q^73 - 12*q^77 + 5*q^79 - 8*q^83 - 
    16*q^85 + 12*q^89 + 3*q^91 + 4*q^95 + 5*q^97 + O(q^99)

Total time: 1.409 seconds, Total memory usage: 6.10MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 17 03:15:02 2005

Input: G: =DirichletGroup(432);G;
X :=Elements(G);X;
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;
qEigenform(D[1],99);


Output: Magma V2.11-10    Sat Dec 17 2005 03:15:02 on modular  [Seed = 3307556844]
   -------------------------------------


>> G: =DirichletGroup(432);G;
      ^
User error: bad syntax

>> X :=Elements(G);X;
                ^
User error: Identifier 'G' has not been declared or assigned

>> X :=Elements(G);X;
                   ^
User error: Identifier 'X' has not been declared or assigned

>> X;
   ^
User error: Identifier 'X' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
       ^
User error: Identifier 'X' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
                       ^
User error: Identifier 'Y' has not been declared or assigned

>> Y :=X[1]; Conductor(Y); Order(Y);
                                 ^
User error: Identifier 'Y' has not been declared or assigned

>> M := ModularSymbols(Y, 2, 1);
                       ^
User error: Identifier 'Y' has not been declared or assigned

>> D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
                                                          ^
User error: Identifier 'M' has not been declared or assigned

>> D;
   ^
User error: Identifier 'D' has not been declared or assigned

>> qEigenform(D[1],99);
              ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.24MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 17 03:14:49 2005

Input: G:=DirichletGroup(432);G;
X :=Elements(G);X;
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;
qEigenform(D[1],99);


Output: Magma V2.11-10    Sat Dec 17 2005 03:14:48 on modular  [Seed = 3391766813]
   -------------------------------------

Group of Dirichlet characters of modulus 432 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.3,
    $.1*$.3,
    $.2*$.3,
    $.1*$.2*$.3
]
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.3,
    $.1*$.3,
    $.2*$.3,
    $.1*$.2*$.3
]
1
1
[
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field
]
q + 3*q^5 + q^7 + 3*q^11 - 4*q^13 - 2*q^19 + 6*q^23 + 4*q^25 + 6*q^29 - 5*q^31 +
    3*q^35 + 2*q^37 - 6*q^41 + 10*q^43 - 6*q^47 - 6*q^49 + 9*q^53 + 9*q^55 - 
    12*q^59 + 8*q^61 - 12*q^65 - 14*q^67 - 7*q^73 + 3*q^77 - 8*q^79 + 3*q^83 - 
    18*q^89 - 4*q^91 - 6*q^95 - q^97 + O(q^99)

Total time: 1.429 seconds, Total memory usage: 6.00MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 17 03:12:34 2005

Input: G :=DirichletGroup(432);
G;
X :=Elements(G);
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;
qEigenform(D[1],99);


Output: Magma V2.11-10    Sat Dec 17 2005 03:12:32 on modular  [Seed = 4027612079]
   -------------------------------------

Group of Dirichlet characters of modulus 432 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.3,
    $.1*$.3,
    $.2*$.3,
    $.1*$.2*$.3
]
1
1
[
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field
]
q - 5*q^7 - 7*q^13 + q^19 - 5*q^25 + 4*q^31 - q^37 - 8*q^43 + 18*q^49 - 13*q^61 
    - 11*q^67 + 17*q^73 + 13*q^79 + 35*q^91 + 5*q^97 + O(q^99)

Total time: 1.399 seconds, Total memory usage: 6.00MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 17 03:11:15 2005

Input: G :=DirichletGroup(432);
G;
X :=Elements(G);
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;

Output: Magma V2.11-10    Sat Dec 17 2005 03:11:14 on modular  [Seed = 4111826680]
   -------------------------------------

Group of Dirichlet characters of modulus 432 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.3,
    $.1*$.3,
    $.2*$.3,
    $.1*$.2*$.3
]
1
1
[
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field,
    Modular symbols space for Gamma_0(432) of weight 2 and dimension 1 over 
    Rational Field
]

Total time: 1.379 seconds, Total memory usage: 6.00MB


'200.177'
************** MAGMA *****************
Host 200.177.28.205 (200.177.28.205)
Time: Fri Dec 16 21:51:05 2005

Input: 0^0;

Output: Magma V2.11-10    Fri Dec 16 2005 21:51:04 on modular  [Seed = 2153823931]
   -------------------------------------

1

Total time: 0.190 seconds, Total memory usage: 3.24MB


'212.138'
************** MAGMA *****************
Host 212.138.47.14 (212.138.47.14)
Time: Fri Dec 16 21:08:24 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3); I:=ideal<P |
-100 + (-6*y^2-144*y*z+27*z^2),
-1 + (-18/5*z^2-27/4*y*z-12*x*z-45/16*y^2-9*x*y-6*x^2),
-10 + (-1215/112*z^2-81/4*y*z-567/20*x*z-81/10*y^2-81/4*x*y-45/4*x^2) >;
Radical(I);

Output: Magma V2.11-10    Fri Dec 16 2005 21:08:23 on modular  [Seed = 1437951329]
   -------------------------------------

Ideal of Polynomial ring of rank 3 over Rational Field
Lexicographical Order
Variables: x, y, z
Dimension 0, Radical
Groebner basis:
[
    x + 24021947384028469294199051557281326175896046567/88390501855296726402302\
        4091659442585600000000*z^7 - 499887372604618086734751651977842907689699\
        89/6313607275378337600164457797567447040000000*z^5 - 
        3578323456874350741013274769517430940050603/450971948241309828583175556\
        96910336000000*z^3 - 7781918205774041731639575981199074243/257698256137\
        8913306189574611252019200*z,
    y - 463586742170926250485324993944801190173/1287206326036293892078321948672\
        0000000*z^7 + 1085903501599971128651516196294585591/9194330900259242086\
        2737282048000000*z^5 + 9873044499317982446687031775259151/9381970306386\
        9817206874777600000*z^3 + 128601565742559180668707869379/11258364367664\
        3780648249733120*z,
    z^8 - 36195915798000255920/96199778220194782809*z^6 - 
        22658347845807961565600/7792182035835777407529*z^4 + 
        432194167813940000000/4125272842501293921633*z^2 + 
        16295122460522500000000/631166744902697970009849
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'155.207'
************** MAGMA *****************
Host 155.207.209.210 (155.207.209.210)
Time: Fri Dec 16 19:36:19 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-4*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
> >NormEquation(O,5^4);

Output: Magma V2.11-10    Fri Dec 16 2005 19:36:18 on modular  [Seed = 3476017489]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]
true [
    [5, 0, 0, 0]
]

Total time: 0.320 seconds, Total memory usage: 3.63MB


'155.207'
************** MAGMA *****************
Host 155.207.209.210 (155.207.209.210)
Time: Fri Dec 16 19:35:13 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-4*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
> >NormEquation(O,2*5^4);

Output: Magma V2.11-10    Fri Dec 16 2005 19:35:13 on modular  [Seed = 3526544527]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]
true [
    [0, -5, 0, 0]
]

Total time: 0.330 seconds, Total memory usage: 3.63MB


'155.207'
************** MAGMA *****************
Host 155.207.209.210 (155.207.209.210)
Time: Fri Dec 16 19:35:00 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-4*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
> >NormEquation(O,5);

Output: Magma V2.11-10    Fri Dec 16 2005 19:35:00 on modular  [Seed = 3577072637]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]
false

Total time: 0.310 seconds, Total memory usage: 3.63MB


'155.207'
************** MAGMA *****************
Host 155.207.209.210 (155.207.209.210)
Time: Fri Dec 16 19:32:52 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-4*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
> >NormEquation(O, 5^4);

Output: Magma V2.11-10    Fri Dec 16 2005 19:32:51 on modular  [Seed = 3745497200]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]
true [
    [5, 0, 0, 0]
]

Total time: 0.320 seconds, Total memory usage: 3.63MB


'66.14.9'
************** MAGMA *****************
Host 66.14.95.197 (66.14.95.197)
Time: Fri Dec 16 18:40:23 2005

Input: sin(3.141549);

Output: Magma V2.11-10    Fri Dec 16 2005 18:40:23 on modular  [Seed = 2659093989]
   -------------------------------------


>> sin(3.141549);;
   ^
User error: Identifier 'sin' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'66.14.9'
************** MAGMA *****************
Host 66.14.95.197 (66.14.95.197)
Time: Fri Dec 16 18:39:33 2005

Input: sin(pi);

Output: Magma V2.11-10    Fri Dec 16 2005 18:39:33 on modular  [Seed = 2040097360]
   -------------------------------------


>> sin(pi);;
       ^
User error: Identifier 'pi' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'66.14.9'
************** MAGMA *****************
Host 66.14.95.197 (66.14.95.197)
Time: Fri Dec 16 18:38:29 2005

Input: 5!

Output: Magma V2.11-10    Fri Dec 16 2005 18:38:29 on modular  [Seed = 1071592406]
   -------------------------------------


>> 5!;
     ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'155.207'
************** MAGMA *****************
Host 155.207.209.110 (155.207.209.110)
Time: Fri Dec 16 18:36:14 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-4*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
> >NormEquation(O, 4*5^4);


Output: Magma V2.11-10    Fri Dec 16 2005 18:36:12 on modular  [Seed = 14683248]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]
true [
    [0, 0, -5, 0]
]

Total time: 0.330 seconds, Total memory usage: 3.63MB


'128.138'
************** MAGMA *****************
Host 128.138.240.175 (128.138.240.175)
Time: Fri Dec 16 16:41:06 2005

Input: 1234123412341234341111/2714351253451253424

Output: Magma V2.11-10    Fri Dec 16 2005 16:41:06 on modular  [Seed = 3459168674]
   -------------------------------------

411374470780411447037/904783751150417808

Total time: 0.180 seconds, Total memory usage: 3.24MB


'131.156'
************** MAGMA *****************
Host 131.156.3.93 (131.156.3.93)
Time: Fri Dec 16 16:09:01 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3);  I:=ideal<P |
-100 + (-6*y^2-144*y*z+27*z^2),
 -1  + (-18/5*z^2-27/4*y*z-12*x*z-45/16*y^2-9*x*y-6*x^2),
-10+(-1215/112*z^2-81/4*y*z-567/20*x*z-81/10*y^2-81/4*x*y-45/4*x^2)>;
Radical(I);

Output: Magma V2.11-10    Fri Dec 16 2005 16:09:01 on modular  [Seed = 2040075914]
   -------------------------------------

Ideal of Polynomial ring of rank 3 over Rational Field
Lexicographical Order
Variables: x, y, z
Dimension 0, Radical
Groebner basis:
[
    x + 24021947384028469294199051557281326175896046567/88390501855296726402302\
        4091659442585600000000*z^7 - 499887372604618086734751651977842907689699\
        89/6313607275378337600164457797567447040000000*z^5 - 
        3578323456874350741013274769517430940050603/450971948241309828583175556\
        96910336000000*z^3 - 7781918205774041731639575981199074243/257698256137\
        8913306189574611252019200*z,
    y - 463586742170926250485324993944801190173/1287206326036293892078321948672\
        0000000*z^7 + 1085903501599971128651516196294585591/9194330900259242086\
        2737282048000000*z^5 + 9873044499317982446687031775259151/9381970306386\
        9817206874777600000*z^3 + 128601565742559180668707869379/11258364367664\
        3780648249733120*z,
    z^8 - 36195915798000255920/96199778220194782809*z^6 - 
        22658347845807961565600/7792182035835777407529*z^4 + 
        432194167813940000000/4125272842501293921633*z^2 + 
        16295122460522500000000/631166744902697970009849
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'131.156'
************** MAGMA *****************
Host 131.156.3.93 (131.156.3.93)
Time: Fri Dec 16 16:06:07 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3);  I:=ideal<P |
-100 + (-6*y^2-144*y*z+27*z^2),
 -1  + (-18/5*z^2-27/4*y*z-12*x*z-45/16*y^2-9*x*y-6*x^2),
-10+(-1215/112*z^2-81/4*y*z-567/20*x*z-81/10*y^2-81/4*x*y-45/4*x^2)>;
GroebnerBasis(I);

Output: Magma V2.11-10    Fri Dec 16 2005 16:06:07 on modular  [Seed = 2124288351]
   -------------------------------------

[
    x + 24021947384028469294199051557281326175896046567/88390501855296726402302\
        4091659442585600000000*z^7 - 499887372604618086734751651977842907689699\
        89/6313607275378337600164457797567447040000000*z^5 - 
        3578323456874350741013274769517430940050603/450971948241309828583175556\
        96910336000000*z^3 - 7781918205774041731639575981199074243/257698256137\
        8913306189574611252019200*z,
    y - 463586742170926250485324993944801190173/1287206326036293892078321948672\
        0000000*z^7 + 1085903501599971128651516196294585591/9194330900259242086\
        2737282048000000*z^5 + 9873044499317982446687031775259151/9381970306386\
        9817206874777600000*z^3 + 128601565742559180668707869379/11258364367664\
        3780648249733120*z,
    z^8 - 36195915798000255920/96199778220194782809*z^6 - 
        22658347845807961565600/7792182035835777407529*z^4 + 
        432194167813940000000/4125272842501293921633*z^2 + 
        16295122460522500000000/631166744902697970009849
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'131.156'
************** MAGMA *****************
Host 131.156.3.93 (131.156.3.93)
Time: Fri Dec 16 16:02:52 2005

Input: P<x,y,z>:=PolynomialRing(RationalField(),3);  I:=ideal<P |
-100 + (-6*y^2-144*y*z+27*z^2),
 -1  + (-18/5*z^2-27/4*y*z-12*x*z-45/16*y^2-9*x*y-6*x^2),
-10+(-1215/112*z^2-81/4*y*z-567/20*x*z-81/10*y^2-81/4*x*y-45/4*x^2)>;
GroebnerBasis(I);

Output: Magma V2.11-10    Fri Dec 16 2005 16:02:48 on modular  [Seed = 1168452898]
   -------------------------------------

[
    x + 24021947384028469294199051557281326175896046567/88390501855296726402302\
        4091659442585600000000*z^7 - 499887372604618086734751651977842907689699\
        89/6313607275378337600164457797567447040000000*z^5 - 
        3578323456874350741013274769517430940050603/450971948241309828583175556\
        96910336000000*z^3 - 7781918205774041731639575981199074243/257698256137\
        8913306189574611252019200*z,
    y - 463586742170926250485324993944801190173/1287206326036293892078321948672\
        0000000*z^7 + 1085903501599971128651516196294585591/9194330900259242086\
        2737282048000000*z^5 + 9873044499317982446687031775259151/9381970306386\
        9817206874777600000*z^3 + 128601565742559180668707869379/11258364367664\
        3780648249733120*z,
    z^8 - 36195915798000255920/96199778220194782809*z^6 - 
        22658347845807961565600/7792182035835777407529*z^4 + 
        432194167813940000000/4125272842501293921633*z^2 + 
        16295122460522500000000/631166744902697970009849
]

Total time: 0.230 seconds, Total memory usage: 3.34MB


'222.124'
************** MAGMA *****************
Host 222.124.19.133 (222.124.19.133)
Time: Fri Dec 16 14:01:39 2005

Input: if ver eq 1 then
M := Matrix(8,8,[
  [2,   0,   0,   0,   0,   0,   0,   0], 
  [0, 396,-214,-386,  36,  25,-144, 426],
  [1,-205, -34,-196, 230,  83,-662,  19],
  [1,-305, 528,-358,-250,  73,  38, 277],
  [1,  38, -45,-282, 584, 122, -24,-476],
  [0, 127, 131, 119, 369,-633, 152,-275],
  [0, 436, -54,-138,-442, 330,-312,-350],
  [1,  82, 757, 102, 372, 111,-248, 258]]);
else
M := Matrix(8,8,[
  [ 2,  0,   0,   0,   0,   0,   0,   0],
  [ 0, 36, 221,   5, -64,  23, -32, 352],
  [ 0,129,-108,-193,-285,  97, 146,-178],
  [ 0, 46, -89,-166,  66, -46,-374,-241],
  [ 0,274, -85, 254, 212, 175, 166,  36],
  [ 1, 99,-185, 145, 145,-400, -19,  98],
  [ 1, 82,-367, 197, -42, 197,-191,  80],
  [ 0, 23,  40, 218,-182,-214,-224,-330]]);
end if;


Output: Magma V2.11-10    Fri Dec 16 2005 14:01:35 on modular  [Seed = 2170670481]
   -------------------------------------


>> if ver eq 1 then
      ^
User error: Identifier 'ver' has not been declared or assigned

Total time: 0.230 seconds, Total memory usage: 3.24MB


'144.122'
************** MAGMA *****************
Host 144.122.137.67 (144.122.137.67)
Time: Fri Dec 16 07:55:33 2005

Input: F:=GF(2^4);
DefiningPolynomial(F); 
P<x> := PolynomialRing(F);
f := x^3+3*x+1;
Order($.1);

Output: Magma V2.11-10    Fri Dec 16 2005 07:55:32 on modular  [Seed = 2124383264]
   -------------------------------------

$.1^4 + $.1 + 1

>> Order($.1);;
         ^
Runtime error: Bad dollar structure

Total time: 0.200 seconds, Total memory usage: 3.34MB


'144.122'
************** MAGMA *****************
Host 144.122.137.67 (144.122.137.67)
Time: Fri Dec 16 07:55:15 2005

Input: F:=GF(2^4);
DefiningPolynomial(F); 
P<x> := PolynomialRing(F);
f := x^3+3*x+1;
Order(f);

Output: Magma V2.11-10    Fri Dec 16 2005 07:55:15 on modular  [Seed = 2073723219]
   -------------------------------------

$.1^4 + $.1 + 1

>> Order(f);;
        ^
Runtime error in 'Order': Bad argument types
Argument types given: RngUPolElt[FldFin]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'144.122'
************** MAGMA *****************
Host 144.122.137.67 (144.122.137.67)
Time: Fri Dec 16 07:52:31 2005

Input: F:=GF(2^4);
P<x> := PolynomialRing(F);
f := x^3+3*x+1;
Order(f);

Output: Magma V2.11-10    Fri Dec 16 2005 07:52:31 on modular  [Seed = 1252766174]
   -------------------------------------


>> Order(f);;
        ^
Runtime error in 'Order': Bad argument types
Argument types given: RngUPolElt[FldFin]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'144.122'
************** MAGMA *****************
Host 144.122.137.67 (144.122.137.67)
Time: Fri Dec 16 07:52:16 2005

Input: F:=GF(2^4);
P<x> := PolynomialRing(F);
f := x^3+3*x+1;
Exponent(f);

Output: Magma V2.11-10    Fri Dec 16 2005 07:52:15 on modular  [Seed = 1471589427]
   -------------------------------------


>> Exponent(f);;
           ^
Runtime error in 'Exponent': Bad argument types
Argument types given: RngUPolElt[FldFin]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'144.122'
************** MAGMA *****************
Host 144.122.137.67 (144.122.137.67)
Time: Fri Dec 16 07:52:08 2005

Input: F:=GF(2^4);
P<x> := PolynomialRing(F);
f := x^3+3*x+1;
Exponenet(f);

Output: Magma V2.11-10    Fri Dec 16 2005 07:52:08 on modular  [Seed = 1555932991]
   -------------------------------------


>> Exponenet(f);;
   ^
User error: Identifier 'Exponenet' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'144.122'
************** MAGMA *****************
Host 144.122.137.67 (144.122.137.67)
Time: Fri Dec 16 07:51:51 2005

Input: F:=GF(2^4);
P<x> := PolynomialRing(F);
f := x^3+3*x+1;
2*f;

Output: Magma V2.11-10    Fri Dec 16 2005 07:51:50 on modular  [Seed = 1505272356]
   -------------------------------------

0

Total time: 0.190 seconds, Total memory usage: 3.34MB


'144.122'
************** MAGMA *****************
Host 144.122.137.67 (144.122.137.67)
Time: Fri Dec 16 07:51:29 2005

Input: F:=GF(2^4);
P<x> := PolynomialRing(F);
f := x^3+3*x+1;
3*f;

Output: Magma V2.11-10    Fri Dec 16 2005 07:51:29 on modular  [Seed = 650632556]
   -------------------------------------

x^3 + x + 1

Total time: 0.190 seconds, Total memory usage: 3.34MB


'144.122'
************** MAGMA *****************
Host 144.122.137.67 (144.122.137.67)
Time: Fri Dec 16 07:51:18 2005

Input: F:=GF(2^4);
P<x> := PolynomialRing(F);
f := x^3+3*x+1;
3*f;

Output: Magma V2.11-10    Fri Dec 16 2005 07:51:17 on modular  [Seed = 599971965]
   -------------------------------------

x^3 + x + 1

Total time: 0.190 seconds, Total memory usage: 3.34MB


'144.122'
************** MAGMA *****************
Host 144.122.137.67 (144.122.137.67)
Time: Fri Dec 16 07:51:09 2005

Input: F:=GF(2^4);
P<x> := PolynomialRing(F);
f := x^3+3*x+1;
f;

Output: Magma V2.11-10    Fri Dec 16 2005 07:51:04 on modular  [Seed = 684315403]
   -------------------------------------

x^3 + x + 1

Total time: 0.260 seconds, Total memory usage: 3.34MB


'213.84.'
************** MAGMA *****************
Host 213.84.213.14 (213.84.213.14)
Time: Fri Dec 16 02:41:40 2005

Input: 
FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;

p := 140853945410621700611366248656986006762214430713643;
s := 941728572;
FindGroupOrder2(p, s);

Output: Magma V2.11-10    Fri Dec 16 2005 02:41:38 on modular  [Seed = 920066706]
   -------------------------------------

[ <2, 2>, <3, 1>, <5, 1>, <137, 1>, <251, 1>, <317, 1>, <331, 1>, <7307, 1>, 
<13339, 1>, <15667, 1>, <29209, 1>, <137209, 1>, <332933, 1>, <393571, 1>, 
<811351, 1> ]

Total time: 2.390 seconds, Total memory usage: 5.31MB


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Fri Dec 16 02:29:36 2005

Input: Factorization(00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001);

Output: Magma V2.11-10    Fri Dec 16 2005 02:29:36 on modular  [Seed = 3994009881]
   -------------------------------------

[]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Fri Dec 16 02:29:14 2005

Input: Factorization(0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000);

Output: Magma V2.11-10    Fri Dec 16 2005 02:29:14 on modular  [Seed = 3808611390]
   -------------------------------------


>> Factorization(0000000000000000000000000000000000000000000000000000000000000
                ^
Runtime error in 'Factorization': Argument 1 is not non-zero

Total time: 0.190 seconds, Total memory usage: 3.24MB


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Fri Dec 16 00:56:30 2005

Input: Factorization(50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000);

Output: Magma V2.11-10    Fri Dec 16 2005 00:56:30 on modular  [Seed = 616902717]
   -------------------------------------

[ <2, 832>, <5, 833> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Fri Dec 16 00:55:25 2005

Input: Factorization(500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012355);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Fri Dec 16 2005 00:55:05 on modular  [Seed = 970468503]
   -------------------------------------


Errors: /bin/sh: line 1: 21550 Alarm clock             nice -n 19 /usr/local/bin/magma


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Fri Dec 16 00:53:55 2005

Input: Factorization(50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000005678901234567890);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Fri Dec 16 2005 00:53:34 on modular  [Seed = 852699003]
   -------------------------------------


Errors: /bin/sh: line 1: 21541 Alarm clock             nice -n 19 /usr/local/bin/magma


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Fri Dec 16 00:06:55 2005

Input: Factorization(4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000);

Output: Magma V2.11-10    Fri Dec 16 2005 00:06:55 on modular  [Seed = 2090693635]
   -------------------------------------

[ <2, 2351>, <5, 2349> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Fri Dec 16 00:06:08 2005

Input: Factorization(0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004);

Output: Magma V2.11-10    Fri Dec 16 2005 00:06:07 on modular  [Seed = 1437883770]
   -------------------------------------

[ <2, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Fri Dec 16 00:05:06 2005

Input: Factorization(0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000);

Output: Magma V2.11-10    Fri Dec 16 2005 00:05:05 on modular  [Seed = 48433683]
   -------------------------------------


>> Factorization(0000000000000000000000000000000000000000000000000000000000000
                ^
Runtime error in 'Factorization': Argument 1 is not non-zero

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 19:21:11 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);
L:=MinimumWords(C2); 
C3:=LinearCode<K, 35 |L>; 
C3;

Output: Magma V2.11-10    Thu Dec 15 2005 19:21:11 on modular  [Seed = 3576995498]
   -------------------------------------

true
[1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 23>, <10, 175>, <12, 780>, <14, 2227>, <16, 3898>, <18, 4285>, 
<20, 3135>, <22, 1377>, <24, 410>, <26, 64>, <28, 9> ]
[35, 14, 8] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 19:20:21 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);
L:=MinimumWords(C2); 
C3:=LinearCode<K, 35 |L>; 
L;

Output: Magma V2.11-10    Thu Dec 15 2005 19:20:21 on modular  [Seed = 3745420434]
   -------------------------------------

true
[1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 23>, <10, 175>, <12, 780>, <14, 2227>, <16, 3898>, <18, 4285>, 
<20, 3135>, <22, 1377>, <24, 410>, <26, 64>, <28, 9> ]
{
    (1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0),
    (1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0),
    (0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0),
    (0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0),
    (0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1),
    (0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1),
    (0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1),
    (0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0),
    (0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0),
    (0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1),
    (0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0),
    (0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1),
    (0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0),
    (1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0),
    (0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0)
}

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 19:17:48 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);
L:=MinimumWords(C2); 
C3:=LinearCode(L); 
L;

Output: Magma V2.11-10    Thu Dec 15 2005 19:17:47 on modular  [Seed = 3644366202]
   -------------------------------------

true
[1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 23>, <10, 175>, <12, 780>, <14, 2227>, <16, 3898>, <18, 4285>, 
<20, 3135>, <22, 1377>, <24, 410>, <26, 64>, <28, 9> ]

>> C3:=LinearCode(L); 
                 ^
Runtime error in 'LinearCode': Bad argument types
Argument types given: SetEnum[ModTupFldElt]
{
    (1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0),
    (1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0),
    (0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0),
    (0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0),
    (0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1),
    (0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1),
    (0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1),
    (0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0),
    (0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0),
    (0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1),
    (0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0),
    (0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1),
    (0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0),
    (1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0),
    (0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0)
}

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 18:58:17 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);
MinimumWords(C2); 

Output: Magma V2.11-10    Thu Dec 15 2005 18:58:17 on modular  [Seed = 3193962159]
   -------------------------------------

true
[1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 23>, <10, 175>, <12, 780>, <14, 2227>, <16, 3898>, <18, 4285>, 
<20, 3135>, <22, 1377>, <24, 410>, <26, 64>, <28, 9> ]
{
    (1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0),
    (0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0),
    (1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0),
    (0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0),
    (0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0),
    (0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1),
    (0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1),
    (0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1),
    (0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0),
    (0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0),
    (0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1),
    (0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0),
    (0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1),
    (0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0),
    (1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0),
    (0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0)
}

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 18:56:30 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);

Output: Magma V2.11-10    Thu Dec 15 2005 18:56:30 on modular  [Seed = 3092904222]
   -------------------------------------

true
[1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 23>, <10, 175>, <12, 780>, <14, 2227>, <16, 3898>, <18, 4285>, 
<20, 3135>, <22, 1377>, <24, 410>, <26, 64>, <28, 9> ]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 18:55:19 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
M2;


Output: Magma V2.11-10    Thu Dec 15 2005 18:55:19 on modular  [Seed = 2739069644]
   -------------------------------------

true
[1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 18:54:58 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>:
S, f := StandardForm(C);
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M2:=Submatrix(M1,22,22,14,35);
M2;


Output: Magma V2.11-10    Thu Dec 15 2005 18:54:58 on modular  [Seed = 2924474356]
   -------------------------------------


>> 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>:
                                                            ^
User error: bad syntax

>> S, f := StandardForm(C);
                        ^
User error: Identifier 'C' has not been declared or assigned

>> D := Dual(S);
             ^
User error: Identifier 'S' has not been declared or assigned

>> (D meet S) eq S;
    ^
User error: Identifier 'D' has not been declared or assigned

>> M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
                                   ^
User error: Identifier 'S' has not been declared or assigned

>> M1:=EchelonForm(M);
                   ^
User error: Identifier 'M' has not been declared or assigned

>> M2:=Submatrix(M1,22,22,14,35);
                 ^
User error: Identifier 'M1' has not been declared or assigned

>> M2;
   ^
User error: Identifier 'M2' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 18:53:27 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
S;
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M1;
M2:=Submatrix(M1,22,22,14,35);
M2;


Output: Magma V2.11-10    Thu Dec 15 2005 18:53:27 on modular  [Seed = 2823416407]
   -------------------------------------

[56, 21] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0
    0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1
    0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
    1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1
    1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1
    0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0
    0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0
    1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0
    0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1
    0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1
    1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1
    0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1
    1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1
    0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0
    1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0
    0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0
    0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1
    1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1
    0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0
    0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1
    0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1]
true
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1
    0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0
    1 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1
    0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0
    1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0
    1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1
    0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1
    0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1
    0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0
    1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1
    0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0
    0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0
    1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0
    0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1
    1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1
    1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0
    1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0
    1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1
    1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1
    1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0
    1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1
    1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0
    1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1
    1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0
    0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1
    0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1
    0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1
    1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1
    1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0
    0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1
    1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1
    0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1
    1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0
 ** WARNING: Output too long, hence truncated.

'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 18:47:10 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
S;
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(D));
M1:=EchelonForm(M);
M1;


Output: Magma V2.11-10    Thu Dec 15 2005 18:47:10 on modular  [Seed = 2675891433]
   -------------------------------------

[56, 21] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0
    0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1
    0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
    1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1
    1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1
    0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0
    0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0
    1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0
    0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1
    0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1
    1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1
    0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1
    1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1
    0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0
    1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0
    0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0
    0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1
    1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1
    0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0
    0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1
    0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1]
true
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1
    0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0
    1 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1
    0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0
    1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0
    1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1
    0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1
    0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1
    0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0
    1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1
    0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0
    0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0
    1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0
    0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1
    1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1
    1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0
    1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0
    1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1
    1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1
    1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0
    1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1
    1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0
    1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1
    1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0
    0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1
    0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1
    0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1
    1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1
    1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0
    0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1
    1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1
    0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1
    1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 18:45:08 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
S;
D := Dual(S);
(D meet S) eq S;
M:=VerticalJoin(GeneratorMatrix(S), GeneratorMatrix(S));
M1:=EchelonForm(M);
M1;


Output: Magma V2.11-10    Thu Dec 15 2005 18:45:08 on modular  [Seed = 2591807894]
   -------------------------------------

[56, 21] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0
    0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1
    0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
    1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1
    1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1
    0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0
    0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0
    1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0
    0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1
    0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1
    1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1
    0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1
    1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1
    0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0
    1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0
    0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0
    0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1
    1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1
    0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0
    0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1
    0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1]
true
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0
    0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1
    0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
    1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1
    1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1
    0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0
    0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0
    1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0
    0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1
    0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1
    1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1
    0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1
    1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1
    0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0
    1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0
    0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0
    0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1
    1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1
    0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0
    0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1
    0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

Total time: 0.180 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 18:05:15 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
S;
D := Dual(S);
(D meet S) eq S;

Output: Magma V2.11-10    Thu Dec 15 2005 18:05:14 on modular  [Seed = 1538911993]
   -------------------------------------

[56, 21] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0
    0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1
    0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
    1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1
    1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1
    0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0
    0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0
    1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0
    0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1
    0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1
    1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1
    0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1
    1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1
    0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0
    1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0
    0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0
    0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1
    1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1
    0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0
    0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1
    0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1]
true

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec 15 18:03:40 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
S;
D := Dual(S);


Output: Magma V2.11-10    Thu Dec 15 2005 18:03:40 on modular  [Seed = 1168633857]
   -------------------------------------

[56, 21] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0
    0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1
    0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
    1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1
    1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1
    0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0
    0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0
    1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0
    0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1
    0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1
    1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1
    0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1
    1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1
    0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0
    1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0
    0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0
    0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1
    1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1
    0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0
    0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1
    0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'152.6.1'
************** MAGMA *****************
Host 152.6.19.192 (152.6.19.192)
Time: Thu Dec 15 12:35:48 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
IsSelfOrthogonal(C);
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
WeightDistribution(C);

Output: Magma V2.11-10    Thu Dec 15 2005 12:35:48 on modular  [Seed = 3177142192]
   -------------------------------------

false
7
[ <7, 1> ]
    G
    |  Cyclic(7)
    1
{
    (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14)(15, 16, 17, 18, 19, 20, 
        21)(22, 23, 24, 25, 26, 27, 28)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 
        39, 40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)
}
[ <0, 1>, <16, 5082>, <20, 91168>, <24, 507045>, <28, 890560>, <32, 507045>, 
<36, 91168>, <40, 5082>, <56, 1> ]

Total time: 0.310 seconds, Total memory usage: 5.51MB


'199.89.'
************** MAGMA *****************
Host 199.89.64.177 (199.89.64.177)
Time: Thu Dec 15 11:15:37 2005

Input: FindGroupOrder2 := function (p, s)
   K := GF(p);
   v := K ! (4*s);
   u := K ! (s^2-5);
   x := u^3;
   b := 4*x*v;
   a := (v-u)^3*(3*u+v);
   A := a/b-2;
   x := x/v^3;
   b := x^3 + A*x^2 + x;
   E := EllipticCurve([0,b*A,0,b^2,0]);
   return FactoredOrder(E);
end function;

p := 140853945410621700611366248656986006762214430713643;
s := 941728572;
FindGroupOrder2(p, s);

Output: Magma V2.11-10    Thu Dec 15 2005 11:15:30 on modular  [Seed = 1636021435]
   -------------------------------------

[ <2, 2>, <3, 1>, <5, 1>, <137, 1>, <251, 1>, <317, 1>, <331, 1>, <7307, 1>, 
<13339, 1>, <15667, 1>, <29209, 1>, <137209, 1>, <332933, 1>, <393571, 1>, 
<811351, 1> ]

Total time: 2.439 seconds, Total memory usage: 5.31MB


'129.13.'
************** MAGMA *****************
Host 129.13.186.1 (129.13.186.1)
Time: Thu Dec 15 05:37:39 2005

Input: 9+100000000000000000000000000000

Output: Magma V2.11-10    Thu Dec 15 2005 05:37:39 on modular  [Seed = 2338951053]
   -------------------------------------

100000000000000000000000000009

Total time: 0.180 seconds, Total memory usage: 3.24MB


'148.87.'
************** MAGMA *****************
Host 148.87.1.172 (148.87.1.172)
Time: Thu Dec 15 00:38:27 2005

Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", "))

Output: Magma V2.11-10    Thu Dec 15 2005 00:38:27 on modular  [Seed = 1669407046]
   -------------------------------------


>> for(x=1,50,print1("d(",x,")=",numdiv(x),", "));
      ^
User error: bad syntax

Total time: 0.200 seconds, Total memory usage: 3.24MB


'159.18.'
************** MAGMA *****************
Host 159.18.221.196 (159.18.221.196)
Time: Wed Dec 14 17:22:35 2005

Input: 3^-1%0xF5DD146F31C94C0F7BF8CE66A63E86D47FB68E7C3F00BFB2232B848ECCBB0AF5

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

'159.18.'
************** MAGMA *****************
Host 159.18.221.196 (159.18.221.196)
Time: Wed Dec 14 17:22:14 2005

Input: 3^-1mod0xF5DD146F31C94C0F7BF8CE66A63E86D47FB68E7C3F00BFB2232B848ECCBB0AF5

Output: Magma V2.11-10    Wed Dec 14 2005 17:22:14 on modular  [Seed = 3143132098]
   -------------------------------------


>> 3^-1mod0xF5DD146F31C94C0F7BF8CE66A63E86D47FB68E7C3F00BFB2232B848ECCBB0AF5;
       ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'159.18.'
************** MAGMA *****************
Host 159.18.221.196 (159.18.221.196)
Time: Wed Dec 14 17:22:06 2005

Input: 3^-1%0xF5DD146F31C94C0F7BF8CE66A63E86D47FB68E7C3F00BFB2232B848ECCBB0AF5

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

'159.18.'
************** MAGMA *****************
Host 159.18.221.196 (159.18.221.196)
Time: Wed Dec 14 17:21:51 2005

Input: 3^-1

Output: Magma V2.11-10    Wed Dec 14 2005 17:21:51 on modular  [Seed = 2738911795]
   -------------------------------------

1/3

Total time: 0.190 seconds, Total memory usage: 3.24MB


'159.18.'
************** MAGMA *****************
Host 159.18.221.196 (159.18.221.196)
Time: Wed Dec 14 17:21:26 2005

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-10    Wed Dec 14 2005 17:21:25 on modular  [Seed = 2823516450]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.200 seconds, Total memory usage: 3.24MB


'147.96.'
************** MAGMA *****************
Host 147.96.20.233 (147.96.20.233)
Time: Wed Dec 14 14:00:13 2005

Input: P<[x]>:=PolynomialRing(GF(2),3,"grevlex");

g1:=x[1]*x[3]+x[2]*x[3]+x[3];
g2:=x[1]*x[2]+x[1]*x[3]+x[2]*x[3]+x[1];
g3:=x[2]^2+x[2]*x[3]+x[3]^2+1;
g4:=x[2]+x[3]+1;
g5:=x[3]^2+x[3];

pol:=x[2]*x[3]*g4;

g:=[g1,g2,g3,g4,g5];


I:=ideal<P|[g1,g2,g3]>;

T1:=ideal<P|0>;
T2:=ideal<P|x[1]*x[3]>;
T3:=ideal<P|[x[1]*x[3],x[1]*x[2]]>;
T4:=ideal<P|[x[1],x[2]]>;
T5:=ideal<P|[x[2],x[3]]>;

T:=[T1,T2,T3,T4,T5];

deg:=1;


equis:=x cat [1];

Mons:={a:a in x} join {1};

for j in [2..deg] do
	Mons:={mon*vble:vble in equis, mon in Mons};
end for;

Mons2:=Mons;

for i in [1,2] do

Mons2:={mon*vble:vble in equis, mon in Mons2};

end for;

Mons2:=[mon:mon in Mons2];


polinomios:=[mon*g[i]: i in [1..5], mon in Mons | not(mon in T[i])];

dim1:=#polinomios+1;
dim2:=#Mons2+1;

//G<alpha>:=GF(2,dim1+1);
//AssertAttribute(G,"PowerPrinting",false);

M:=RMatrixSpace(P,dim1,dim2);
Mat:=M!0;

for i in [1..dim1-1] do
	lista:=Monomials(polinomios[i]);
	for j in [1..dim2-1] do
		if Mons2[j] in lista then
			Mat[i,j]:=1;
		end if;
	end for;
end for;


lista:=Monomials(pol);
for j in [1..dim2-1] do
	if Mons2[j] in lista then
		Mat[dim1,j]:=1;
	end if;
end for;
Mat[dim1,dim2]:=1;
//Mat[dim1,dim2]:=1;




B:=EchelonForm(Mat);



//newpol:=&+[Mons2[j]*B[dim1,j]:j in [1..dim2-1]];


	



Output: Magma V2.11-10    Wed Dec 14 2005 14:00:12 on modular  [Seed = 2356126809]
   -------------------------------------


>> B:=EchelonForm(Mat);
                 ^
Runtime error in 'EchelonForm': Argument 1 has no echelon algorithm

Total time: 0.190 seconds, Total memory usage: 3.24MB


'66.50.2'
************** MAGMA *****************
Host 66.50.2.109 (66.50.2.109)
Time: Wed Dec 14 11:20:13 2005

Input: 7102277187569652249869562285153253710645556161842592536300347670222640516361186363486317189963554176580264215037288238394086254424175854090684343545452440

Output: Magma V2.11-10    Wed Dec 14 2005 11:20:12 on modular  [Seed = 3728595848]
   -------------------------------------

7102277187569652249869562285153253710645556161842592536300347670222640516361186\
363486317189963554176580264215037288238394086254424175854090684343545452440

Total time: 0.190 seconds, Total memory usage: 3.24MB


'129.20.'
************** MAGMA *****************
Host 129.20.36.132 (129.20.36.132)
Time: Wed Dec 14 10:32:34 2005

Input: K:=CyclotomicField(13);
G,phi:=UnitGroup(K);
G;

Output: Magma V2.11-10    Wed Dec 14 2005 10:32:33 on modular  [Seed = 301099370]
   -------------------------------------

Abelian Group isomorphic to Z/26 + Z (5 copies)
Defined on 6 generators
Relations:
    26*G.1 = 0

Total time: 1.260 seconds, Total memory usage: 3.82MB


'67.62.1'
************** MAGMA *****************
Host 67.62.112.123 (67.62.112.123)
Time: Wed Dec 14 07:16:04 2005

Input: a:=1;
a:

Output: Magma V2.11-10    Wed Dec 14 2005 07:16:03 on modular  [Seed = 3442377647]
   -------------------------------------


>> a:;
     ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'83.250.'
************** MAGMA *****************
Host 83.250.129.152 (83.250.129.152)
Time: Wed Dec 14 06:40:51 2005

Input: 5*5

Output: Magma V2.11-10    Wed Dec 14 2005 06:40:49 on modular  [Seed = 717843850]
   -------------------------------------

25

Total time: 0.260 seconds, Total memory usage: 3.24MB


'217.24.'
************** MAGMA *****************
Host 217.24.144.35 (217.24.144.35)
Time: Wed Dec 14 06:30:58 2005

Input: jnbkjnlml

Output: Magma V2.11-10    Wed Dec 14 2005 06:30:57 on modular  [Seed = 1972778086]
   -------------------------------------


>> jnbkjnlml;
   ^
User error: Identifier 'jnbkjnlml' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 22:39:18 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M1:=EchelonForm(M); 
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);
C2;
L:=MinimumWords(C2); 
C3:= LinearCode<K, 35 | (L)>;  
C3;
C4:=EvenWeightCode(15);
WeightDistribution(C4); 

Output: Magma V2.11-10    Tue Dec 13 2005 22:39:17 on modular  [Seed = 670824447]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 14>, <10, 182>, <12, 805>, <14, 2200>, <16, 3885>, <18, 4340>, 
<20, 3066>, <22, 1400>, <24, 420>, <26, 70>, <28, 1> ]
[35, 14, 8] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[35, 10, 8] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1]
[0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1]
[0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1]
[0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0]
[0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1]
[0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <2, 105>, <4, 1365>, <6, 5005>, <8, 6435>, <10, 3003>, <12, 455>, <14,
15> ]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 22:23:21 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M1:=EchelonForm(M); 
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);
C2;
L:=MinimumWords(C2); 
C3:= LinearCode<K, 35 | (L)>;  
C3;

Output: Magma V2.11-10    Tue Dec 13 2005 22:23:21 on modular  [Seed = 1038216745]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 14>, <10, 182>, <12, 805>, <14, 2200>, <16, 3885>, <18, 4340>, 
<20, 3066>, <22, 1400>, <24, 420>, <26, 70>, <28, 1> ]
[35, 14, 8] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[35, 10, 8] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1]
[0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1]
[0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1]
[0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0]
[0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1]
[0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 22:20:16 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M1:=EchelonForm(M); 
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);
C2;
L:=MinimumWords(C2); 
C3:= LinearCode<K, 11 |  
(L)>;  
C3;

Output: Magma V2.11-10    Tue Dec 13 2005 22:20:16 on modular  [Seed = 3323595400]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 14>, <10, 182>, <12, 805>, <14, 2200>, <16, 3885>, <18, 4340>, 
<20, 3066>, <22, 1400>, <24, 420>, <26, 70>, <28, 1> ]
[35, 14, 8] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]

>> C3:= LinearCode<K, 11 |  
                  ^
Runtime error in LinearCode< ... >: Rhs argument 1 is invalid for this 
constructor

>> C3;;
   ^
User error: Identifier 'C3' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.46.74 (200.177.46.74)
Time: Tue Dec 13 22:05:47 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
rho := (p - n)^2;
"rho =", rho;
"rho^6 mod n =", rho^6 mod n;

H := rho*G;
"H =", H;
zeta := H[1];
"zeta =", zeta;
"zeta^3 =", zeta^3;

lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    return g + t + s;
end function;

trace6 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; // g^(p^6)
    return g + t;
end function;

conj4 := function(g)
    s := Eltseq(g);
    s[4] := -s[4];
    s[5] := -s[5];
    s[6] := -s[6];
    return Seqelt(s, Fp12);
end function;

t40 := trace4(g);
t41 := conj4(t40);
"trace4(g)   =", Eltseq(t40);
"trace4(g)'  =", Eltseq(t41);
"sum4 =", t40 + t41;
"prod4 =", t40*t41;


Output: Magma V2.11-10    Tue Dec 13 2005 22:05:46 on modular  [Seed = 4246811337]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
rho = 1461501624493534334825397658811989710051820598436
rho^6 mod n = 1
H = (1627965160026674480212199743920457792 : 2 : 1)
zeta = 1627965160026674480212199743920457792
zeta^3 = 1
lambda = 2
mu = i + 1
Gt = (8 : 816263181872116351510202985179226587277470764815*i + 
    295865244505705705023665406736615173923424579851 : 1)
g = (1113252570408097904801784205204725186435037650621*i + 
    828892838102560531997994710291403383901103286823)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (1334693519950620886403708174450030523556565932446*i + 
    65995713479010101585078190425689016349129829691)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (1167306608241793402349182741773283684304074553579*i + 
    813404015744428633410120092529896632595508931142)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
trace4(g)   = [
    939709461715339668293863546426995422914672052984*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    1081077310858282128920227343508520583235180015700*i + 
        197987140437030304755234571277067049047389489073,
    0,
    0
]
trace4(g)'  = [
    939709461715339668293863546426995422914672052984*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    380424313638508136225221246412264910482078875119*i + 
        1263514484059759960390214018643718444669869401746,
    0,
    0
]
sum4 = 417917298933889071442278502933205352112085215149*i + 
    1022991499774629604152735929191636691013539358387
prod4 = 1290910566114678872655078479583819895277125832347*i + 
    1222447203379043640445950747036893708432248781076

Total time: 0.870 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.46.74 (200.177.46.74)
Time: Tue Dec 13 22:02:17 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
rho := (p - n)^2;
"rho =", rho;
"rho^6 mod n =", rho^6 mod n;

H := rho*G;
"H =", H;
zeta := H[1];
"zeta =", zeta;
"zeta^3 =", zeta^3;

lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    return g + t + s;
end function;

trace6 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; // g^(p^6)
    return g + t;
end function;

conj6 := function(g)
    s := Eltseq(g);
    s[4] := -s[4];
    s[5] := -s[5];
    s[6] := -s[6];
    return Seqelt(s, Fp12);
end function;

t40 := trace4(g);
t41 := t40^p;
t42 := t41^p;
"trace4(g)   =", Eltseq(t40);
"trace4(g)'  =", Eltseq(t41);
"trace4(g)'' =", Eltseq(t42);
"sum4 =", t40 + t41 + t42;
"prod4 =", t40*t41*t42;
t60 := trace6(g);
t61 := conj6(t60);
"trace6(g)   =", t60;
"trace6(g)'  =", t61;
"sum6 =", t60 + t61;
"prod6 =", t60*t61;


Output: Magma V2.11-10    Tue Dec 13 2005 22:02:16 on modular  [Seed = 2204060549]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
rho = 1461501624493534334825397658811989710051820598436
rho^6 mod n = 1
H = (1627965160026674480212199743920457792 : 2 : 1)
zeta = 1627965160026674480212199743920457792
zeta^3 = 1
lambda = 2
mu = i + 1
Gt = (8 : 816263181872116351510202985179226587277470764815*i + 
    295865244505705705023665406736615173923424579851 : 1)
g = (1113252570408097904801784205204725186435037650621*i + 
    828892838102560531997994710291403383901103286823)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (1334693519950620886403708174450030523556565932446*i + 
    65995713479010101585078190425689016349129829691)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (1167306608241793402349182741773283684304074553579*i + 
    813404015744428633410120092529896632595508931142)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
trace4(g)   = [
    939709461715339668293863546426995422914672052984*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    1081077310858282128920227343508520583235180015700*i + 
        197987140437030304755234571277067049047389489073,
    0,
    0
]
trace4(g)'  = [
    521792162781450596851585043493790070802586837835*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    600370227937686771113197478282678333920097663482*i + 
        1221575564612301174446849985825970354859774772881,
    0,
    0
]
trace4(g)'' = [
    939709461715339668293863546426995422914672052984*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    380424313638508136225221246412264910482078875119*i + 
        1263514484059759960390214018643718444669869401746,
    0,
    0
]
sum4 = (600370227937686771113197478282678333920097663482*i + 
    1221575564612301174446849985825970354859774772881)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    803736437413549273656379598827062289661679592171
prod4 = (351960067217720226471026218912124823215388842998*i + 
    636471885525581132299463326642541502123540418918)*z^3 + 
    1073254876702081306986584990089982603797367449521*i + 
    1088939299807643406655341764511290451420861288604
trace6(g)   = (156577465902024414247303474719686770606206859232*i + 
    1382078665443524484841423079394787904516185203317)*z^4 + 
    (841515242395890270530857306215275633514884532655*i + 
    1201508585068810609093824954696108083012473692827)*z^2 + 
    139305766311296357147426167644401784037361738383*i + 
    340997166591543201384245309730545563671179786129
trace6(g)'  = (1304924158594765850898145115201098723111052031587*i + 
    79422959053265780304025510525997589201073687502)*z^4 + 
    (841515242395890270530857306215275633514884532655*i + 
    1201508585068810609093824954696108083012473692827)*z^2 + 
    139305766311296357147426167644401784037361738383*i + 
    340997166591543201384245309730545563671179786129
sum6 = (221528860294990275916266022509765773312510174491*i + 
    941515545640830953042201319471430672307688494835)*z^2 + 
    278611532622592714294852335288803568074723476766*i + 
    681994333183086402768490619461091127342359572258
prod6 = (1199217906511468853397684229168281220558780854227*i + 
    1030765899693116805073366946226732872257120333608)*z^4 + 
    (378575975826376771203186488360822049552104323606*i + 
    472503248255084275151742862775344953200669638852)*z^2 + 
    230957764124266000451333381176639619321109453643*i + 
    684491156455614923026389854551594178711792858992

Total time: 1.100 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:59:13 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y, w> := AffineAlgebra<F, x, y, w | w^5+w-x*t*(1/t^17*w^100 + (4*t^4 + 4)/t^17*w^80 + 4/t^13*w^76 + (t^8 + 2*t^4 + 1)/t^17*w^60
    + (2*t^4 + 2)/t^13*w^56 + 1/t^9*w^52 + (4*t^12 + 2*t^8 + 2*t^4 + 
    4)/t^17*w^40 + (2*t^8 + 4*t^4 + 2)/t^13*w^36 + (2*t^4 + 2)/t^9*w^32 + 
    4/t^5*w^28 + (t^16 + 4*t^12 + t^8 + 4*t^4 + 1)/t^17*w^20 + (4*t^12 + 2*t^8 +
    2*t^4 + 4)/t^13*w^16 + (t^8 + 2*t^4 + 1)/t^9*w^12 + (4*t^4 + 4)/t^5*w^8 + 
    1/t*w^4 + 1/t), x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(w);


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Tue Dec 13 2005 21:58:53 on modular  [Seed = 1134529040]
   -------------------------------------


Errors: /bin/sh: line 1: 32125 Alarm clock             nice -n 19 /usr/local/bin/magma


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:58:26 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y, w> := AffineAlgebra<F, x, y, w | w^5+w-x*t, x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:58:25 on modular  [Seed = 1184534313]
   -------------------------------------

1/t^17*w^100 + (4*t^4 + 4)/t^17*w^80 + 4/t^13*w^76 + (t^8 + 2*t^4 + 1)/t^17*w^60
    + (2*t^4 + 2)/t^13*w^56 + 1/t^9*w^52 + (4*t^12 + 2*t^8 + 2*t^4 + 
    4)/t^17*w^40 + (2*t^8 + 4*t^4 + 2)/t^13*w^36 + (2*t^4 + 2)/t^9*w^32 + 
    4/t^5*w^28 + (t^16 + 4*t^12 + t^8 + 4*t^4 + 1)/t^17*w^20 + (4*t^12 + 2*t^8 +
    2*t^4 + 4)/t^13*w^16 + (t^8 + 2*t^4 + 1)/t^9*w^12 + (4*t^4 + 4)/t^5*w^8 + 
    1/t*w^4 + 1/t
z^125 + (t^20 + t^16 + 1)*z^25 + (2*t^20 + t^16)*z^5 + t^20*z + 4*t^21

Total time: 0.200 seconds, Total memory usage: 3.72MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:58:12 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y, w> := AffineAlgebra<F, x, y, w | w^5+w-x*y, x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(w);


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Tue Dec 13 2005 21:57:52 on modular  [Seed = 1284539714]
   -------------------------------------


Errors: /bin/sh: line 1: 32114 Alarm clock             nice -n 19 /usr/local/bin/magma


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:56:51 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y, w> := AffineAlgebra<F, x, y, w | w^5+w-x*t, x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:56:51 on modular  [Seed = 1401919902]
   -------------------------------------

1/t^17*w^100 + (4*t^4 + 4)/t^17*w^80 + 4/t^13*w^76 + (t^8 + 2*t^4 + 1)/t^17*w^60
    + (2*t^4 + 2)/t^13*w^56 + 1/t^9*w^52 + (4*t^12 + 2*t^8 + 2*t^4 + 
    4)/t^17*w^40 + (2*t^8 + 4*t^4 + 2)/t^13*w^36 + (2*t^4 + 2)/t^9*w^32 + 
    4/t^5*w^28 + (t^16 + 4*t^12 + t^8 + 4*t^4 + 1)/t^17*w^20 + (4*t^12 + 2*t^8 +
    2*t^4 + 4)/t^13*w^16 + (t^8 + 2*t^4 + 1)/t^9*w^12 + (4*t^4 + 4)/t^5*w^8 + 
    1/t*w^4 + 1/t
z^125 + (t^20 + t^16 + 1)*z^25 + (2*t^20 + t^16)*z^5 + t^20*z + 4*t^21

Total time: 0.210 seconds, Total memory usage: 3.72MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:56:42 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y, w> := AffineAlgebra<F, x, y, w | w^5+w-x, x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:56:42 on modular  [Seed = 1451924610]
   -------------------------------------

t^3*w^100 + 3*t^3*w^80 + 4*t^3*w^76 + 4*t^3*w^60 + 4*t^3*w^56 + t^3*w^52 + 
    2*t^3*w^40 + 3*t^3*w^36 + 4*t^3*w^32 + 4*t^3*w^28 + t^3*w^20 + 2*t^3*w^16 + 
    4*t^3*w^12 + 3*t^3*w^8 + t^3*w^4 + 1/t
z^125 + (2*t^4 + 1)/t^4*z^25 + (t^4 + 2)/t^4*z^5 + 1/t^4*z + 4/t^4

Total time: 0.200 seconds, Total memory usage: 3.82MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:56:18 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y, w> := AffineAlgebra<F, x, y, w | w^5+w-x, x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x);


Output: Magma V2.11-10    Tue Dec 13 2005 21:56:18 on modular  [Seed = 1568774065]
   -------------------------------------

t^3*w^100 + 3*t^3*w^80 + 4*t^3*w^76 + 4*t^3*w^60 + 4*t^3*w^56 + t^3*w^52 + 
    2*t^3*w^40 + 3*t^3*w^36 + 4*t^3*w^32 + 4*t^3*w^28 + t^3*w^20 + 2*t^3*w^16 + 
    4*t^3*w^12 + 3*t^3*w^8 + t^3*w^4 + 1/t
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + 4/t^4

Total time: 0.200 seconds, Total memory usage: 3.53MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:56:15 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y, w> := AffineAlgebra<F, x, y, w | w^5+w-x, x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x);


Output: Magma V2.11-10    Tue Dec 13 2005 21:56:15 on modular  [Seed = 1622977169]
   -------------------------------------

t^3*w^100 + 3*t^3*w^80 + 4*t^3*w^76 + 4*t^3*w^60 + 4*t^3*w^56 + t^3*w^52 + 
    2*t^3*w^40 + 3*t^3*w^36 + 4*t^3*w^32 + 4*t^3*w^28 + t^3*w^20 + 2*t^3*w^16 + 
    4*t^3*w^12 + 3*t^3*w^8 + t^3*w^4 + 1/t
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + 4/t^4

Total time: 0.200 seconds, Total memory usage: 3.53MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:56:01 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y, w> := AffineAlgebra<F, x, y, w | w^5-t, x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x);


Output: Magma V2.11-10    Tue Dec 13 2005 21:56:00 on modular  [Seed = 1740352921]
   -------------------------------------

1/t*y^4 + 1/t
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + 4/t^4

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:55:53 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y, w> := AffineAlgebra<F, x, y | w^5-t, x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x);


Output: Magma V2.11-10    Tue Dec 13 2005 21:55:52 on modular  [Seed = 1790353644]
   -------------------------------------


>> A<x, y, w> := AffineAlgebra<F, x, y | w^5-t, x^5+x - y/t, y^5+y - t>;
                                         ^
User error: Identifier 'w' has not been declared or assigned

>> y^-1;
   ^
User error: Identifier 'y' has not been declared or assigned

>>   MinimalPolynomial(x);
                       ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.46.74 (200.177.46.74)
Time: Tue Dec 13 21:53:18 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
rho := (p - n)^2;
"rho =", rho;
"rho^6 mod n =", rho^6 mod n;

H := rho*G;
"H =", H;
zeta := H[1];
"zeta =", zeta;
"zeta^3 =", zeta^3;

lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    return g + t + s;
end function;

trace6 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; // g^(p^6)
    return g + t;
end function;

t40 := trace4(g);
t41 := t40^p;
t42 := t41^p;
"trace4(g)   =", t40;
"trace4(g)   =", Eltseq(t40);
"trace4(g)'  =", Eltseq(t41);
"trace4(g)'' =", Eltseq(t42);
"sum4 =", t40 + t41 + t42;
"prod4 =", t40*t41*t42;
t60 := trace6(g);
t61 := t60^p;
"trace6(g)   =", Eltseq(t60);
"trace6(g)'  =", Eltseq(t61);
"sum6 =", t60 + t61;
"prod6 =", t60*t61;


Output: Magma V2.11-10    Tue Dec 13 2005 21:53:17 on modular  [Seed = 1907211090]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
rho = 1461501624493534334825397658811989710051820598436
rho^6 mod n = 1
H = (1627965160026674480212199743920457792 : 2 : 1)
zeta = 1627965160026674480212199743920457792
zeta^3 = 1
lambda = 2
mu = i + 1
Gt = (8 : 816263181872116351510202985179226587277470764815*i + 
    295865244505705705023665406736615173923424579851 : 1)
g = (1113252570408097904801784205204725186435037650621*i + 
    828892838102560531997994710291403383901103286823)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (1334693519950620886403708174450030523556565932446*i + 
    65995713479010101585078190425689016349129829691)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (1167306608241793402349182741773283684304074553579*i + 
    813404015744428633410120092529896632595508931142)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
trace4(g)   = (1081077310858282128920227343508520583235180015700*i + 
    197987140437030304755234571277067049047389489073)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)   = [
    939709461715339668293863546426995422914672052984*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    1081077310858282128920227343508520583235180015700*i + 
        197987140437030304755234571277067049047389489073,
    0,
    0
]
trace4(g)'  = [
    521792162781450596851585043493790070802586837835*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    600370227937686771113197478282678333920097663482*i + 
        1221575564612301174446849985825970354859774772881,
    0,
    0
]
trace4(g)'' = [
    939709461715339668293863546426995422914672052984*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    380424313638508136225221246412264910482078875119*i + 
        1263514484059759960390214018643718444669869401746,
    0,
    0
]
sum4 = (600370227937686771113197478282678333920097663482*i + 
    1221575564612301174446849985825970354859774772881)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    803736437413549273656379598827062289661679592171
prod4 = (351960067217720226471026218912124823215388842998*i + 
    636471885525581132299463326642541502123540418918)*z^3 + 
    1073254876702081306986584990089982603797367449521*i + 
    1088939299807643406655341764511290451420861288604
trace6(g)   = [
    139305766311296357147426167644401784037361738383*i + 
        340997166591543201384245309730545563671179786129,
    0,
    841515242395890270530857306215275633514884532655*i + 
        1201508585068810609093824954696108083012473692827,
    0,
    156577465902024414247303474719686770606206859232*i + 
        1382078665443524484841423079394787904516185203317,
    0
]
trace6(g)'  = [
    1322195858185493907998022422276383709679897152436*i + 
        340997166591543201384245309730545563671179786129,
    0,
    96267089637067702603160574155571500808560497740*i + 
        198193976097141083414977909683245959979351734515,
    0,
    39750298548322008993974458110694835814573932369*i + 
        170269780948936534327757016306807241564764251208,
    0
]
sum6 = (196327764450346423241277932830381606420780791601*i + 
    90846821895670754023731505780809652363690563706)*z^4 + 
    (937782332032957973134017880370847134323445030395*i + 
    1399702561165951692508802864379354042991825427342)*z^2 + 
    681994333183086402768490619461091127342359572258
prod6 = (403224252430258213018808164592556921112551430842*i + 
    1072501587439756383839928276680242651041055479001)*z^4 + 
    (515192785473442154214411326985372045692209216551*i + 
    1264811833155190234052567165579767753345088245117)*z^2 + 
    933753153541436149967745700541145775019625660786*i + 
    579210675113629004884943196866573303442263067154

Total time: 1.080 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:46:47 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
Q<w> := PolynomialRing(A);
B<w> := ext<Q | w^5+w-x*t/y>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:46:47 on modular  [Seed = 2074591186]
   -------------------------------------


>> B<w> := ext<Q | w^5+w-x*t/y>;
              ^
Runtime error: No constructor provided for this type of object
1/t*y^4 + 1/t

>>   MinimalPolynomial(x+y+w);
                      ^
Runtime error in 'MinimalPolynomial': Bad argument types
Argument types given: RngUPolElt[RngMPolRes]

Total time: 0.290 seconds, Total memory usage: 7.84MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:46:34 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
Q<w> := PolynomialRing(A);
B<w> := ext<A | w^5+w-x*t/y>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:46:33 on modular  [Seed = 2124593865]
   -------------------------------------


>> B<w> := ext<A | w^5+w-x*t/y>;
              ^
Runtime error: No constructor provided for this type of object
1/t*y^4 + 1/t

>>   MinimalPolynomial(x+y+w);
                      ^
Runtime error in 'MinimalPolynomial': Bad argument types
Argument types given: RngUPolElt[RngMPolRes]

Total time: 0.300 seconds, Total memory usage: 7.84MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:45:47 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<w> := ext<A | w^5+w-x*t/y>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:45:47 on modular  [Seed = 98156896]
   -------------------------------------


>> B<w> := ext<A | w^5+w-x*t/y>;
                   ^
User error: Identifier 'w' has not been declared or assigned
1/t*y^4 + 1/t

>>   MinimalPolynomial(x+y+w);
                           ^
User error: Identifier 'w' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:45:13 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<w> := ext<A, w | w^5+w-x*t/y>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:45:13 on modular  [Seed = 148163599]
   -------------------------------------


>> B<w> := ext<A, w | w^5+w-x*t/y>;
                      ^
User error: bad syntax
1/t*y^4 + 1/t

>>   MinimalPolynomial(x+y+w);
                           ^
User error: Identifier 'w' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:44:54 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<w> := Ext<A, w | w^5+w-x*t/y>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:44:54 on modular  [Seed = 248695318]
   -------------------------------------


>> B<w> := Ext<A, w | w^5+w-x*t/y>;
              ^
User error: bad syntax
1/t*y^4 + 1/t

>>   MinimalPolynomial(x+y+w);
                           ^
User error: Identifier 'w' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:44:44 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := Ext<A, w | w^5+w-x*t/y>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:44:44 on modular  [Seed = 365547831]
   -------------------------------------


>> B<x,y,w> := Ext<A, w | w^5+w-x*t/y>;
                  ^
User error: bad syntax
1/t*y^4 + 1/t

>>   MinimalPolynomial(x+y+w);
                           ^
User error: Identifier 'w' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:43:39 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<F, x, y, w | w^5+w-x*y^4-x, x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Tue Dec 13 2005 21:43:19 on modular  [Seed = 415555041]
   -------------------------------------


Errors: /bin/sh: line 1: 32038 Alarm clock             nice -n 19 /usr/local/bin/magma


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:42:55 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<F, x, y, w | w^5+w-x*y^4+x, x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Tue Dec 13 2005 21:42:35 on modular  [Seed = 516086715]
   -------------------------------------


Errors: /bin/sh: line 1: 32032 Alarm clock             nice -n 19 /usr/local/bin/magma


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:41:57 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<F, x, y, w | w^5+w-x*(y^4+1), x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Tue Dec 13 2005 21:41:36 on modular  [Seed = 637132923]
   -------------------------------------


Errors: /bin/sh: line 1: 32027 Alarm clock             nice -n 19 /usr/local/bin/magma


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:40:43 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<F, x, y, w | w^5+w-x*t*(y^-1), x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:40:43 on modular  [Seed = 687140157]
   -------------------------------------


>> B<x,y,w> := AffineAlgebra<F, x, y, w | w^5+w-x*t*(y^-1), x^5+x - y/t, y^5+y
                                                      ^
Runtime error in '^': Argument 2 (-1) should be >= 0
1/t*y^4 + 1/t

>>   MinimalPolynomial(x+y+w);
                           ^
User error: Identifier 'w' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:40:31 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<F, x, y | w^5+w-x*t*(y^-1), x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:40:31 on modular  [Seed = 804514318]
   -------------------------------------


>> B<x,y,w> := AffineAlgebra<F, x, y | w^5+w-x*t*(y^-1), x^5+x - y/t, y^5+y - 
                                       ^
User error: Identifier 'w' has not been declared or assigned
1/t*y^4 + 1/t

>>   MinimalPolynomial(x+y+w);
                           ^
User error: Identifier 'w' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:39:31 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<A<x,y>, w | w^5+w-x*t/y>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:39:31 on modular  [Seed = 854521071]
   -------------------------------------


>> B<x,y,w> := AffineAlgebra<A<x,y>, w | w^5+w-x*t/y>;
                              ^
User error: bad syntax
1/t*y^4 + 1/t

>>   MinimalPolynomial(x+y+w);
                           ^
User error: Identifier 'w' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:39:13 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<A, w | w^5+w-x*t/y>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:39:13 on modular  [Seed = 971374550]
   -------------------------------------


>> B<x,y,w> := AffineAlgebra<A, w | w^5+w-x*t/y>;
    ^
Runtime error in 'AssignNames': Argument 2 should have length at most 1
1/t*y^4 + 1/t

>>   MinimalPolynomial(x+y+w);
                           ^
User error: Identifier 'w' has not been declared or assigned

Total time: 0.300 seconds, Total memory usage: 7.84MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:38:49 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<w> := AffineAlgebra<A, w | w^5+w-x*t/y>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x+y+w);


Output: Magma V2.11-10    Tue Dec 13 2005 21:38:48 on modular  [Seed = 3373600590]
   -------------------------------------

1/t*y^4 + 1/t
$.1^5 + $.1 + 4*x*y^4 + 4*x + 4/t*y + 4*t

Total time: 0.300 seconds, Total memory usage: 7.84MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:37:38 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<w> := AffineAlgebra<A, w | w^5+w-x*t/y>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x-y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:37:37 on modular  [Seed = 3574141851]
   -------------------------------------

1/t*y^4 + 1/t
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + (t^9 + t + 4)/t^4

Total time: 0.300 seconds, Total memory usage: 7.84MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:37:22 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<w> := AffineAlgebra<A, w | w^5+w-x*t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x-y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:37:21 on modular  [Seed = 3657833604]
   -------------------------------------

1/t*y^4 + 1/t
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + (t^9 + t + 4)/t^4

Total time: 0.300 seconds, Total memory usage: 7.84MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:36:38 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<F, x, y, w | w^5+w-x*t , x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
y^-1;

> MinimalPolynomial(x-y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:36:38 on modular  [Seed = 3741522390]
   -------------------------------------

1/t^17*w^100 + (4*t^4 + 4)/t^17*w^80 + 4/t^13*w^76 + (t^8 + 2*t^4 + 1)/t^17*w^60
    + (2*t^4 + 2)/t^13*w^56 + 1/t^9*w^52 + (4*t^12 + 2*t^8 + 2*t^4 + 
    4)/t^17*w^40 + (2*t^8 + 4*t^4 + 2)/t^13*w^36 + (2*t^4 + 2)/t^9*w^32 + 
    4/t^5*w^28 + (t^16 + 4*t^12 + t^8 + 4*t^4 + 1)/t^17*w^20 + (4*t^12 + 2*t^8 +
    2*t^4 + 4)/t^13*w^16 + (t^8 + 2*t^4 + 1)/t^9*w^12 + (4*t^4 + 4)/t^5*w^8 + 
    1/t*w^4 + 1/t
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + (t^9 + t + 4)/t^4

Total time: 0.250 seconds, Total memory usage: 3.63MB


'200.177'
************** MAGMA *****************
Host 200.177.7.38 (200.177.7.38)
Time: Tue Dec 13 21:36:30 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
rho := (p - n)^2;
"rho =", rho;
"rho^6 mod n =", rho^6 mod n;

H := rho*G;
"H =", H;
zeta := H[1];
"zeta =", zeta;
"zeta^3 =", zeta^3;

lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    return g + t + s;
end function;

trace6 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; // g^(p^6)
    return g + t;
end function;

t40 := trace4(g);
t41 := t40^p;
t42 := t41^p;
"trace4(g)   =", Eltseq(t40);
"trace4(g)'  =", Eltseq(t41);
"trace4(g)'' =", Eltseq(t42);
"sum4 =", t40 + t41 + t42;
"prod4 =", t40*t41*t42;
t60 := trace6(g);
t61 := t60^p;
"trace6(g)   =", Eltseq(t60);
"trace6(g)'  =", Eltseq(t61);
"sum6 =", t60 + t61;
"prod6 =", t60*t61;


Output: Magma V2.11-10    Tue Dec 13 2005 21:36:29 on modular  [Seed = 3845727223]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
rho = 1461501624493534334825397658811989710051820598436
rho^6 mod n = 1
H = (1627965160026674480212199743920457792 : 2 : 1)
zeta = 1627965160026674480212199743920457792
zeta^3 = 1
lambda = 2
mu = i + 1
Gt = (8 : 816263181872116351510202985179226587277470764815*i + 
    295865244505705705023665406736615173923424579851 : 1)
g = (1113252570408097904801784205204725186435037650621*i + 
    828892838102560531997994710291403383901103286823)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (1334693519950620886403708174450030523556565932446*i + 
    65995713479010101585078190425689016349129829691)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (1167306608241793402349182741773283684304074553579*i + 
    813404015744428633410120092529896632595508931142)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
trace4(g)   = [
    939709461715339668293863546426995422914672052984*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    1081077310858282128920227343508520583235180015700*i + 
        197987140437030304755234571277067049047389489073,
    0,
    0
]
trace4(g)'  = [
    521792162781450596851585043493790070802586837835*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    600370227937686771113197478282678333920097663482*i + 
        1221575564612301174446849985825970354859774772881,
    0,
    0
]
trace4(g)'' = [
    939709461715339668293863546426995422914672052984*i + 
        1242246562135709934649092259556211092365399124603,
    0,
    0,
    380424313638508136225221246412264910482078875119*i + 
        1263514484059759960390214018643718444669869401746,
    0,
    0
]
sum4 = (600370227937686771113197478282678333920097663482*i + 
    1221575564612301174446849985825970354859774772881)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    803736437413549273656379598827062289661679592171
prod4 = (351960067217720226471026218912124823215388842998*i + 
    636471885525581132299463326642541502123540418918)*z^3 + 
    1073254876702081306986584990089982603797367449521*i + 
    1088939299807643406655341764511290451420861288604
trace6(g)   = [
    139305766311296357147426167644401784037361738383*i + 
        340997166591543201384245309730545563671179786129,
    0,
    841515242395890270530857306215275633514884532655*i + 
        1201508585068810609093824954696108083012473692827,
    0,
    156577465902024414247303474719686770606206859232*i + 
        1382078665443524484841423079394787904516185203317,
    0
]
trace6(g)'  = [
    1322195858185493907998022422276383709679897152436*i + 
        340997166591543201384245309730545563671179786129,
    0,
    96267089637067702603160574155571500808560497740*i + 
        198193976097141083414977909683245959979351734515,
    0,
    39750298548322008993974458110694835814573932369*i + 
        170269780948936534327757016306807241564764251208,
    0
]
sum6 = (196327764450346423241277932830381606420780791601*i + 
    90846821895670754023731505780809652363690563706)*z^4 + 
    (937782332032957973134017880370847134323445030395*i + 
    1399702561165951692508802864379354042991825427342)*z^2 + 
    681994333183086402768490619461091127342359572258
prod6 = (403224252430258213018808164592556921112551430842*i + 
    1072501587439756383839928276680242651041055479001)*z^4 + 
    (515192785473442154214411326985372045692209216551*i + 
    1264811833155190234052567165579767753345088245117)*z^2 + 
    933753153541436149967745700541145775019625660786*i + 
    579210675113629004884943196866573303442263067154

Total time: 1.070 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:36:22 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<F, x, y, w | w^5+w-x*t , x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x-y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:36:22 on modular  [Seed = 3946262002]
   -------------------------------------

1/t^20*w^120 + 4/t^20*w^116 + 1/t^20*w^112 + 4/t^20*w^108 + 1/t^20*w^104 + 
    4/t^20*w^100 + 1/t^20*w^96 + 4/t^20*w^92 + 1/t^20*w^88 + 4/t^20*w^84 + 
    1/t^20*w^80 + 4/t^20*w^76 + 1/t^20*w^72 + 4/t^20*w^68 + 1/t^20*w^64 + 
    4/t^20*w^60 + 1/t^20*w^56 + 4/t^20*w^52 + 1/t^20*w^48 + 4/t^20*w^44 + 
    1/t^20*w^40 + 4/t^20*w^36 + 1/t^20*w^32 + 4/t^20*w^28 + 1/t^20*w^24 + (t^4 +
    1)/t^4*w^20 + (4*t^4 + 4)/t^4*w^16 + (t^4 + 1)/t^4*w^12 + (4*t^4 + 
    4)/t^4*w^8 + (t^4 + 1)/t^4*w^4 + 1
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + (t^9 + t + 4)/t^4

Total time: 0.240 seconds, Total memory usage: 3.53MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:35:19 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<F, x, y, w | w^5+w-x*t/y , x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x-y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:35:19 on modular  [Seed = 4029429544]
   -------------------------------------


>> B<x,y,w> := AffineAlgebra<F, x, y, w | w^5+w-x*t/y , x^5+x - y/t, y^5+y - t
                            ^
Runtime error in AffineAlgebra< ... >: Rhs argument 1 is invalid for this 
constructor
x^4*y^4 + x^4 + y^4 + 1
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + (t^9 + t + 4)/t^4

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:34:52 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
B<x,y,w> := AffineAlgebra<F,x,y,w | w^5+w-x*t/y , x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x-y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:34:52 on modular  [Seed = 4113117702]
   -------------------------------------


>> B<x,y,w> := AffineAlgebra<F,x,y,w | w^5+w-x*t/y , x^5+x - y/t, y^5+y - t>;
                            ^
Runtime error in AffineAlgebra< ... >: Rhs argument 1 is invalid for this 
constructor
x^4*y^4 + x^4 + y^4 + 1
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + (t^9 + t + 4)/t^4

Total time: 0.200 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.7.38 (200.177.7.38)
Time: Tue Dec 13 21:20:51 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
rho := (p - n)^2;
"rho =", rho;
"rho^6 mod n =", rho^6 mod n;

H := rho*G;
"H =", H;
zeta := H[1];
"zeta =", zeta;
"zeta^3 =", zeta^3;

lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    return g + t + s;
end function;

trace6 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; // g^(p^6)
    return g + t;
end function;

t40 := trace4(g);
t41 := t40^p;
t42 := t41^p;
"trace4(g)   =", t40;
"trace4(g)'  =", t41;
"trace4(g)'' =", t42;
"sum4 =", t40 + t41 + t42;
"prod4 =", t40*t41*t42;
t60 := trace6(g);
t61 := t60^p;
"trace6(g)   =", t60;
"trace6(g)'  =", t61;
"sum6 =", t60 + t61;
"prod6 =", t60*t61;


Output: Magma V2.11-10    Tue Dec 13 2005 21:20:50 on modular  [Seed = 2170372924]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
rho = 1461501624493534334825397658811989710051820598436
rho^6 mod n = 1
H = (1627965160026674480212199743920457792 : 2 : 1)
zeta = 1627965160026674480212199743920457792
zeta^3 = 1
lambda = 2
mu = i + 1
Gt = (8 : 645238442624673913635245604741558906439788126004*i + 
    1165636379991084560121783183184170319793834310968 : 1)
g = (348249054088692360343664384716060307282221240198*i + 
    632608786394229733147453879629382109816155603996)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (126808104546169378741740415470754970160692958373*i + 
    1395505911017780163560370399495096477368129061128)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (294195016254996862796265848147501809413184337240*i + 
    648097608752361631735328497390888861121749959677)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
trace4(g)   = (380424313638508136225221246412264910482078875119*i + 
    1263514484059759960390214018643718444669869401746)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)'  = (861131396559103494032251111638107159797161227337*i + 
    239926059884489090698598604094815138857484117938)*z^3 + 
    521792162781450596851585043493790070802586837835*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)'' = (1081077310858282128920227343508520583235180015700*i + 
    197987140437030304755234571277067049047389489073)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
sum4 = (861131396559103494032251111638107159797161227337*i + 
    239926059884489090698598604094815138857484117938)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    803736437413549273656379598827062289661679592171
prod4 = (1109541557279070038674422371008660670501870047821*i + 
    825029738971209132845985263278243991593718471901)*z^3 + 
    1073254876702081306986584990089982603797367449521*i + 
    1088939299807643406655341764511290451420861288604
trace6(g)   = (156577465902024414247303474719686770606206859232*i + 
    1382078665443524484841423079394787904516185203317)*z^4 + 
    (841515242395890270530857306215275633514884532655*i + 
    1201508585068810609093824954696108083012473692827)*z^2 + 
    139305766311296357147426167644401784037361738383*i + 
    340997166591543201384245309730545563671179786129
trace6(g)'  = (39750298548322008993974458110694835814573932369*i + 
    170269780948936534327757016306807241564764251208)*z^4 + 
    (96267089637067702603160574155571500808560497740*i + 
    198193976097141083414977909683245959979351734515)*z^2 + 
    1322195858185493907998022422276383709679897152436*i + 
    340997166591543201384245309730545563671179786129
sum6 = (196327764450346423241277932830381606420780791601*i + 
    90846821895670754023731505780809652363690563706)*z^4 + 
    (937782332032957973134017880370847134323445030395*i + 
    1399702561165951692508802864379354042991825427342)*z^2 + 
    681994333183086402768490619461091127342359572258
prod6 = (403224252430258213018808164592556921112551430842*i + 
    1072501587439756383839928276680242651041055479001)*z^4 + 
    (515192785473442154214411326985372045692209216551*i + 
    1264811833155190234052567165579767753345088245117)*z^2 + 
    933753153541436149967745700541145775019625660786*i + 
    579210675113629004884943196866573303442263067154

Total time: 1.080 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.7.38 (200.177.7.38)
Time: Tue Dec 13 21:15:15 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
rho := (p - n)^2;
"rho =", rho;
"rho^3 mod n =", rho^3 mod n;

H := rho*G;
"H =", H;
zeta := H[1];
"zeta =", zeta;
"zeta^3 =", zeta^3;

lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    return g + t + s;
end function;

trace6 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; // g^(p^6)
    return g + t;
end function;

t40 := trace4(g);
t41 := t40^p;
t42 := t41^p;
"trace4(g)   =", t40;
"trace4(g)'  =", t41;
"trace4(g)'' =", t42;
"sum4 =", t40 + t41 + t42;
"prod4 =", t40*t41*t42;
t60 := trace6(g);
t61 := t60^p;
"trace6(g)   =", t60;
"trace6(g)'  =", t61;
"sum6 =", t60 + t61;
"prod6 =", t60*t61;


Output: Magma V2.11-10    Tue Dec 13 2005 21:15:14 on modular  [Seed = 2387758467]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
rho = 1461501624493534334825397658811989710051820598436
rho^3 mod n = 1461501624496790265145447380994971188499300027612
H = (1627965160026674480212199743920457792 : 2 : 1)
zeta = 1627965160026674480212199743920457792
zeta^3 = 1
lambda = 2
mu = i + 1
Gt = (8 : 645238442624673913635245604741558906439788126004*i + 
    1165636379991084560121783183184170319793834310968 : 1)
g = (348249054088692360343664384716060307282221240198*i + 
    632608786394229733147453879629382109816155603996)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (126808104546169378741740415470754970160692958373*i + 
    1395505911017780163560370399495096477368129061128)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (294195016254996862796265848147501809413184337240*i + 
    648097608752361631735328497390888861121749959677)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
trace4(g)   = (380424313638508136225221246412264910482078875119*i + 
    1263514484059759960390214018643718444669869401746)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)'  = (861131396559103494032251111638107159797161227337*i + 
    239926059884489090698598604094815138857484117938)*z^3 + 
    521792162781450596851585043493790070802586837835*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)'' = (1081077310858282128920227343508520583235180015700*i + 
    197987140437030304755234571277067049047389489073)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
sum4 = (861131396559103494032251111638107159797161227337*i + 
    239926059884489090698598604094815138857484117938)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    803736437413549273656379598827062289661679592171
prod4 = (1109541557279070038674422371008660670501870047821*i + 
    825029738971209132845985263278243991593718471901)*z^3 + 
    1073254876702081306986584990089982603797367449521*i + 
    1088939299807643406655341764511290451420861288604
trace6(g)   = (156577465902024414247303474719686770606206859232*i + 
    1382078665443524484841423079394787904516185203317)*z^4 + 
    (841515242395890270530857306215275633514884532655*i + 
    1201508585068810609093824954696108083012473692827)*z^2 + 
    139305766311296357147426167644401784037361738383*i + 
    340997166591543201384245309730545563671179786129
trace6(g)'  = (39750298548322008993974458110694835814573932369*i + 
    170269780948936534327757016306807241564764251208)*z^4 + 
    (96267089637067702603160574155571500808560497740*i + 
    198193976097141083414977909683245959979351734515)*z^2 + 
    1322195858185493907998022422276383709679897152436*i + 
    340997166591543201384245309730545563671179786129
sum6 = (196327764450346423241277932830381606420780791601*i + 
    90846821895670754023731505780809652363690563706)*z^4 + 
    (937782332032957973134017880370847134323445030395*i + 
    1399702561165951692508802864379354042991825427342)*z^2 + 
    681994333183086402768490619461091127342359572258
prod6 = (403224252430258213018808164592556921112551430842*i + 
    1072501587439756383839928276680242651041055479001)*z^4 + 
    (515192785473442154214411326985372045692209216551*i + 
    1264811833155190234052567165579767753345088245117)*z^2 + 
    933753153541436149967745700541145775019625660786*i + 
    579210675113629004884943196866573303442263067154

Total time: 1.070 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:14:51 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x-y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:14:50 on modular  [Seed = 2471448758]
   -------------------------------------

x^4*y^4 + x^4 + y^4 + 1
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + (t^9 + t + 4)/t^4

Total time: 0.190 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.7.38 (200.177.7.38)
Time: Tue Dec 13 21:14:43 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
rho := (p - n)^2;
"rho =", rho;
"rho^3 mod n =", rho^3 mod n;

H := rho*G;
"H =", H;
zeta := H[1];
"zeta =", zeta;
"zeta^3 mod p =", zeta^3 mod p;

lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    return g + t + s;
end function;

trace6 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; // g^(p^6)
    return g + t;
end function;

t40 := trace4(g);
t41 := t40^p;
t42 := t41^p;
"trace4(g)   =", t40;
"trace4(g)'  =", t41;
"trace4(g)'' =", t42;
"sum4 =", t40 + t41 + t42;
"prod4 =", t40*t41*t42;
t60 := trace6(g);
t61 := t60^p;
"trace6(g)   =", t60;
"trace6(g)'  =", t61;
"sum6 =", t60 + t61;
"prod6 =", t60*t61;


Output: Magma V2.11-10    Tue Dec 13 2005 21:14:42 on modular  [Seed = 2554616757]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
rho = 1461501624493534334825397658811989710051820598436
rho^3 mod n = 1461501624496790265145447380994971188499300027612
H = (1627965160026674480212199743920457792 : 2 : 1)
zeta = 1627965160026674480212199743920457792

>> "zeta^3 mod p =", zeta^3 mod p;
                            ^
Runtime error in 'mod': Bad argument types
Argument types given: FldFinElt, FldFinElt
lambda = 2
mu = i + 1
Gt = (8 : 645238442624673913635245604741558906439788126004*i + 
    1165636379991084560121783183184170319793834310968 : 1)
g = (348249054088692360343664384716060307282221240198*i + 
    632608786394229733147453879629382109816155603996)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (126808104546169378741740415470754970160692958373*i + 
    1395505911017780163560370399495096477368129061128)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (294195016254996862796265848147501809413184337240*i + 
    648097608752361631735328497390888861121749959677)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
trace4(g)   = (380424313638508136225221246412264910482078875119*i + 
    1263514484059759960390214018643718444669869401746)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)'  = (861131396559103494032251111638107159797161227337*i + 
    239926059884489090698598604094815138857484117938)*z^3 + 
    521792162781450596851585043493790070802586837835*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)'' = (1081077310858282128920227343508520583235180015700*i + 
    197987140437030304755234571277067049047389489073)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
sum4 = (861131396559103494032251111638107159797161227337*i + 
    239926059884489090698598604094815138857484117938)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    803736437413549273656379598827062289661679592171
prod4 = (1109541557279070038674422371008660670501870047821*i + 
    825029738971209132845985263278243991593718471901)*z^3 + 
    1073254876702081306986584990089982603797367449521*i + 
    1088939299807643406655341764511290451420861288604
trace6(g)   = (156577465902024414247303474719686770606206859232*i + 
    1382078665443524484841423079394787904516185203317)*z^4 + 
    (841515242395890270530857306215275633514884532655*i + 
    1201508585068810609093824954696108083012473692827)*z^2 + 
    139305766311296357147426167644401784037361738383*i + 
    340997166591543201384245309730545563671179786129
trace6(g)'  = (39750298548322008993974458110694835814573932369*i + 
    170269780948936534327757016306807241564764251208)*z^4 + 
    (96267089637067702603160574155571500808560497740*i + 
    198193976097141083414977909683245959979351734515)*z^2 + 
    1322195858185493907998022422276383709679897152436*i + 
    340997166591543201384245309730545563671179786129
sum6 = (196327764450346423241277932830381606420780791601*i + 
    90846821895670754023731505780809652363690563706)*z^4 + 
    (937782332032957973134017880370847134323445030395*i + 
    1399702561165951692508802864379354042991825427342)*z^2 + 
    681994333183086402768490619461091127342359572258
prod6 = (403224252430258213018808164592556921112551430842*i + 
    1072501587439756383839928276680242651041055479001)*z^4 + 
    (515192785473442154214411326985372045692209216551*i + 
    1264811833155190234052567165579767753345088245117)*z^2 + 
    933753153541436149967745700541145775019625660786*i + 
    579210675113629004884943196866573303442263067154

Total time: 1.100 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.7.38 (200.177.7.38)
Time: Tue Dec 13 21:07:56 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    return g + t + s;
end function;

trace6 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; // g^(p^6)
    return g + t;
end function;

t40 := trace4(g);
t41 := t40^p;
t42 := t41^p;
"trace4(g)   =", t40;
"trace4(g)'  =", t41;
"trace4(g)'' =", t42;
"sum4 =", t40 + t41 + t42;
"prod4 =", t40*t41*t42;
t60 := trace6(g);
t61 := t60^p;
"trace6(g)   =", t60;
"trace6(g)'  =", t61;
"sum6 =", t60 + t61;
"prod6 =", t60*t61;


Output: Magma V2.11-10    Tue Dec 13 2005 21:07:54 on modular  [Seed = 2909901032]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
lambda = 2
mu = i + 1
Gt = (8 : 645238442624673913635245604741558906439788126004*i + 
    1165636379991084560121783183184170319793834310968 : 1)
g = (348249054088692360343664384716060307282221240198*i + 
    632608786394229733147453879629382109816155603996)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (126808104546169378741740415470754970160692958373*i + 
    1395505911017780163560370399495096477368129061128)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (294195016254996862796265848147501809413184337240*i + 
    648097608752361631735328497390888861121749959677)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
trace4(g)   = (380424313638508136225221246412264910482078875119*i + 
    1263514484059759960390214018643718444669869401746)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)'  = (861131396559103494032251111638107159797161227337*i + 
    239926059884489090698598604094815138857484117938)*z^3 + 
    521792162781450596851585043493790070802586837835*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)'' = (1081077310858282128920227343508520583235180015700*i + 
    197987140437030304755234571277067049047389489073)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
sum4 = (861131396559103494032251111638107159797161227337*i + 
    239926059884489090698598604094815138857484117938)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    803736437413549273656379598827062289661679592171
prod4 = (1109541557279070038674422371008660670501870047821*i + 
    825029738971209132845985263278243991593718471901)*z^3 + 
    1073254876702081306986584990089982603797367449521*i + 
    1088939299807643406655341764511290451420861288604
trace6(g)   = (156577465902024414247303474719686770606206859232*i + 
    1382078665443524484841423079394787904516185203317)*z^4 + 
    (841515242395890270530857306215275633514884532655*i + 
    1201508585068810609093824954696108083012473692827)*z^2 + 
    139305766311296357147426167644401784037361738383*i + 
    340997166591543201384245309730545563671179786129
trace6(g)'  = (39750298548322008993974458110694835814573932369*i + 
    170269780948936534327757016306807241564764251208)*z^4 + 
    (96267089637067702603160574155571500808560497740*i + 
    198193976097141083414977909683245959979351734515)*z^2 + 
    1322195858185493907998022422276383709679897152436*i + 
    340997166591543201384245309730545563671179786129
sum6 = (196327764450346423241277932830381606420780791601*i + 
    90846821895670754023731505780809652363690563706)*z^4 + 
    (937782332032957973134017880370847134323445030395*i + 
    1399702561165951692508802864379354042991825427342)*z^2 + 
    681994333183086402768490619461091127342359572258
prod6 = (403224252430258213018808164592556921112551430842*i + 
    1072501587439756383839928276680242651041055479001)*z^4 + 
    (515192785473442154214411326985372045692209216551*i + 
    1264811833155190234052567165579767753345088245117)*z^2 + 
    933753153541436149967745700541145775019625660786*i + 
    579210675113629004884943196866573303442263067154

Total time: 1.060 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:07:15 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x+y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:07:15 on modular  [Seed = 2993590238]
   -------------------------------------

x^4*y^4 + x^4 + y^4 + 1
z^25 + (t^4 + 1)/t^4*z^5 + 1/t^4*z + (4*t^9 + 4*t + 4)/t^4

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:06:43 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | x^5+x - y/t, y^5+y - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x+t^(-3)*y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:06:43 on modular  [Seed = 3077278395]
   -------------------------------------

x^4*y^4 + x^4 + y^4 + 1
z^25 + (t^60 + t^56 + 4*t^54 + t^52 + 4*t^50 + t^48 + t^42 + 3*t^40 + 3*t^38 + 
    t^36 + t^28 + 2*t^26 + t^24 + t^14 + t^12 + 1)/t^60*z^5 + (t^56 + 4*t^54 + 
    t^52 + 4*t^50 + t^48 + t^42 + 3*t^40 + 3*t^38 + t^36 + t^28 + 2*t^26 + t^24 
    + t^14 + t^12 + 1)/t^60*z + (4*t^66 + 4*t^56 + 4*t^52 + t^50 + 4*t^48 + t^46
    + 4*t^44 + 4*t^38 + 2*t^36 + 2*t^34 + 4*t^32 + 4*t^24 + 3*t^22 + 4*t^20 + 
    4*t^10 + 4*t^8 + 4)/t^70

Total time: 0.220 seconds, Total memory usage: 3.43MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:05:48 2005

Input: F<t> := FunctionField(GF(5,2));
A<x, y> := AffineAlgebra<F, x, y | t*x^2 - y^2 + t + 1, y^3 - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x+t^(-3)*y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:05:48 on modular  [Seed = 3160441471]
   -------------------------------------

(4*t^2 + 4*t)/(t^3 + 2*t^2 + 3*t + 1)*x*y^2 + 4*t^2/(t^3 + 2*t^2 + 3*t + 1)*x*y 
    + (4*t^3 + 3*t^2 + 4*t)/(t^3 + 2*t^2 + 3*t + 1)*x
z^6 + (3*t + 3)/t*z^4 + (4*t^5 + 3)/t^8*z^3 + (3*t^2 + t + 3)/t^2*z^2 + (4*t^6 +
    4*t^5 + t + 1)/t^9*z + (t^16 + 2*t^15 + 3*t^14 + t^13 + 3*t^10 + 2*t^5 + 
    1)/t^16

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:04:26 2005

Input: F<t> := FunctionField(IntegerRing());
A<x, y> := AffineAlgebra<F, x, y | t*x^2 - y^2 + t + 1, y^3 - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x+t^(-3)*y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:04:26 on modular  [Seed = 1100840916]
   -------------------------------------

(-t^2 - t)/(t^3 + 2*t^2 + 3*t + 1)*x*y^2 - t^2/(t^3 + 2*t^2 + 3*t + 1)*x*y + 
    (-t^3 - 2*t^2 - t)/(t^3 + 2*t^2 + 3*t + 1)*x
z^6 + (3*t + 3)/t*z^4 + (-6*t^5 - 2)/t^8*z^3 + (3*t^2 + 6*t + 3)/t^2*z^2 + 
    (-6*t^6 - 6*t^5 + 6*t + 6)/t^9*z + (t^16 + 2*t^15 + 3*t^14 + t^13 + 3*t^10 -
    3*t^5 + 1)/t^16

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:04:09 2005

Input: F<t> := FunctionField(IntegerRing());
A<x, y> := AffineAlgebra<F, x, y | t*x^2 - y^2 + t + 1, y^3 - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x+t^3*y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:04:09 on modular  [Seed = 1184528608]
   -------------------------------------

(-t^2 - t)/(t^3 + 2*t^2 + 3*t + 1)*x*y^2 - t^2/(t^3 + 2*t^2 + 3*t + 1)*x*y + 
    (-t^3 - 2*t^2 - t)/(t^3 + 2*t^2 + 3*t + 1)*x
z^6 + (3*t + 3)/t*z^4 + (-2*t^10 - 6*t^3)*z^3 + (3*t^2 + 6*t + 3)/t^2*z^2 + 
    (6*t^10 + 6*t^9 - 6*t^3 - 6*t^2)*z + (t^23 - 3*t^16 + 3*t^9 + t^3 + 2*t^2 + 
    3*t + 1)/t^3

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:03:46 2005

Input: F<t> := FunctionField(IntegerRing());
A<x, y> := AffineAlgebra<F, x, y | t*x^2 - y^2 + t + 1, y^3 - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x+y);


Output: Magma V2.11-10    Tue Dec 13 2005 21:03:46 on modular  [Seed = 1268217334]
   -------------------------------------

(-t^2 - t)/(t^3 + 2*t^2 + 3*t + 1)*x*y^2 - t^2/(t^3 + 2*t^2 + 3*t + 1)*x*y + 
    (-t^3 - 2*t^2 - t)/(t^3 + 2*t^2 + 3*t + 1)*x
z^6 + (3*t + 3)/t*z^4 + (-2*t - 6)*z^3 + (3*t^2 + 6*t + 3)/t^2*z^2 + (6*t^2 - 
    6)/t*z + (t^5 - 3*t^4 + 4*t^3 + 2*t^2 + 3*t + 1)/t^3

Total time: 0.190 seconds, Total memory usage: 3.24MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 21:01:59 2005

Input: F<t> := FunctionField(IntegerRing());
A<x, y> := AffineAlgebra<F, x, y | t*x^2 - y^2 + t + 1, y^3 - t>;
P<z> := PolynomialRing(F);
x^-1;

> MinimalPolynomial(x);


Output: Magma V2.11-10    Tue Dec 13 2005 21:01:59 on modular  [Seed = 1368223609]
   -------------------------------------

(-t^2 - t)/(t^3 + 2*t^2 + 3*t + 1)*x*y^2 - t^2/(t^3 + 2*t^2 + 3*t + 1)*x*y + 
    (-t^3 - 2*t^2 - t)/(t^3 + 2*t^2 + 3*t + 1)*x
z^6 + (3*t + 3)/t*z^4 + (3*t^2 + 6*t + 3)/t^2*z^2 + (t^3 + 2*t^2 + 3*t + 1)/t^3

Total time: 0.190 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.38 (200.177.7.38)
Time: Tue Dec 13 20:57:39 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    return g + t + s;
end function;

trace6 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; t ^:= p; // g^(p^6)
    return g + t;
end function;

t4 := trace4(g);
"trace4(g)   =", t4;
"trace4(g)'  =", t4^p;
"trace4(g)'' =", t4^(p^2);
t6 := trace6(g);
"trace6(g)   =", t6;
"trace6(g)'  =", t6^p;


Output: Magma V2.11-10    Tue Dec 13 2005 20:57:38 on modular  [Seed = 1485072245]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
lambda = 2
mu = i + 1
Gt = (8 : 645238442624673913635245604741558906439788126004*i + 
    1165636379991084560121783183184170319793834310968 : 1)
g = (348249054088692360343664384716060307282221240198*i + 
    632608786394229733147453879629382109816155603996)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (126808104546169378741740415470754970160692958373*i + 
    1395505911017780163560370399495096477368129061128)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (294195016254996862796265848147501809413184337240*i + 
    648097608752361631735328497390888861121749959677)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
trace4(g)   = (380424313638508136225221246412264910482078875119*i + 
    1263514484059759960390214018643718444669869401746)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)'  = (861131396559103494032251111638107159797161227337*i + 
    239926059884489090698598604094815138857484117938)*z^3 + 
    521792162781450596851585043493790070802586837835*i + 
    1242246562135709934649092259556211092365399124603
trace4(g)'' = (1081077310858282128920227343508520583235180015700*i + 
    197987140437030304755234571277067049047389489073)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603
trace6(g)   = (156577465902024414247303474719686770606206859232*i + 
    1382078665443524484841423079394787904516185203317)*z^4 + 
    (841515242395890270530857306215275633514884532655*i + 
    1201508585068810609093824954696108083012473692827)*z^2 + 
    139305766311296357147426167644401784037361738383*i + 
    340997166591543201384245309730545563671179786129
trace6(g)'  = (39750298548322008993974458110694835814573932369*i + 
    170269780948936534327757016306807241564764251208)*z^4 + 
    (96267089637067702603160574155571500808560497740*i + 
    198193976097141083414977909683245959979351734515)*z^2 + 
    1322195858185493907998022422276383709679897152436*i + 
    340997166591543201384245309730545563671179786129

Total time: 1.080 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:42:28 2005

Input: R<x> := FunctionField(GF(5,2));
P<y> := PolynomialRing(R);
F<alpha> := ext< R | y^5+y - x >;
F;
Q<z> := PolynomialRing(P);
Q;
G<beta> := ext<F | z^5+z - y/x>;
G;

Output: Magma V2.11-10    Tue Dec 13 2005 20:42:27 on modular  [Seed = 1673484511]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5^2) by
y^5 + y + 4*x
Univariate Polynomial Ring in z over Univariate Polynomial Ring in y over 
Univariate rational function field over GF(5^2)
Algebraic function field defined over F by
$.1^5 + $.1 + 4/x*alpha

Total time: 0.310 seconds, Total memory usage: 7.89MB


'200.177'
************** MAGMA *****************
Host 200.177.7.38 (200.177.7.38)
Time: Tue Dec 13 20:40:50 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    return g + t + s;
end function;

"trace4(g) =", trace4(g);


Output: Magma V2.11-10    Tue Dec 13 2005 20:40:49 on modular  [Seed = 1756648310]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
lambda = 2
mu = i + 1
Gt = (8 : 645238442624673913635245604741558906439788126004*i + 
    1165636379991084560121783183184170319793834310968 : 1)
g = (348249054088692360343664384716060307282221240198*i + 
    632608786394229733147453879629382109816155603996)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (126808104546169378741740415470754970160692958373*i + 
    1395505911017780163560370399495096477368129061128)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (294195016254996862796265848147501809413184337240*i + 
    648097608752361631735328497390888861121749959677)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
trace4(g) = (380424313638508136225221246412264910482078875119*i + 
    1263514484059759960390214018643718444669869401746)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603

Total time: 0.900 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:40:47 2005

Input: R<x> := FunctionField(GF(5,2));
P<y> := PolynomialRing(R);
F<alpha> := ext< R | y^5+y - x >;
F;
Q<z> := PolynomialRing(P);
G<beta> := ext<F | z^5+z - y/x>;
G;

Output: Magma V2.11-10    Tue Dec 13 2005 20:40:47 on modular  [Seed = 1823496012]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5^2) by
y^5 + y + 4*x
Algebraic function field defined over F by
$.1^5 + $.1 + 4/x*alpha

Total time: 0.310 seconds, Total memory usage: 7.89MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:40:29 2005

Input: R<x> := FunctionField(GF(5,2));
P<y> := PolynomialRing(R);
F<alpha> := ext< R | y^5+y - x >;
F;
Q<z> := PolynomialRing(P);
G<beta> := ext<F | z^5+z - alpha/x>;
G;

Output: Magma V2.11-10    Tue Dec 13 2005 20:40:29 on modular  [Seed = 1924024640]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5^2) by
y^5 + y + 4*x

>> G<beta> := ext<F | z^5+z - alpha/x>;
                            ^
Runtime error in '-': Bad argument types
Argument types given: RngUPolElt[RngUPol[FldFunRat]], FldFunElt

>> G;;
   ^
User error: Identifier 'G' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:40:12 2005

Input: R<x> := FunctionField(GF(5,2));
P<y> := PolynomialRing(R);
F<alpha> := ext< R | y^5+y - x >;
F;
Q<z> := PolynomialRing(P);
G<beta> := ext<F | z^5+z^1-alpha/x>;
G;

Output: Magma V2.11-10    Tue Dec 13 2005 20:40:12 on modular  [Seed = 2040876474]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5^2) by
y^5 + y + 4*x

>> G<beta> := ext<F | z^5+z^1-alpha/x>;
                             ^
Runtime error in '-': Bad argument types
Argument types given: RngUPolElt[RngUPol[FldFunRat]], FldFunElt

>> G;;
   ^
User error: Identifier 'G' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.7.38 (200.177.7.38)
Time: Tue Dec 13 20:40:03 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
"g[1] =", g[1];
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/

trace4 := function(g)
    t := g^p; t ^:= p; t ^:= p; t ^:= p; // g^(p^4)
    s := t^p; s ^:= p; s ^:= p; s ^:= p; // g^(p^8)
    g + t + s;
end function;

"trace4(g) =", trace4(g);


Output: Magma V2.11-10    Tue Dec 13 2005 20:40:02 on modular  [Seed = 2124565171]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
lambda = 2
mu = i + 1
Gt = (8 : 645238442624673913635245604741558906439788126004*i + 
    1165636379991084560121783183184170319793834310968 : 1)
g = (348249054088692360343664384716060307282221240198*i + 
    632608786394229733147453879629382109816155603996)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (126808104546169378741740415470754970160692958373*i + 
    1395505911017780163560370399495096477368129061128)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (294195016254996862796265848147501809413184337240*i + 
    648097608752361631735328497390888861121749959677)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474

>> "g[1] =", g[1];
              ^
Runtime error in '[]': Bad argument types
(380424313638508136225221246412264910482078875119*i + 
    1263514484059759960390214018643718444669869401746)*z^3 + 
    939709461715339668293863546426995422914672052984*i + 
    1242246562135709934649092259556211092365399124603

>> "trace4(g) =", trace4(g);
                        ^
Runtime error: No return statement executed in user-defined function

Total time: 0.860 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:39:56 2005

Input: R<x> := FunctionField(GF(5,2));
P<y> := PolynomialRing(R);
F<alpha> := ext< R | y^5+y - x >;
F;
Q<z> := PolynomialRing(P);
G<beta> := ext<F | z^5+z-alpha/x>;
G;

Output: Magma V2.11-10    Tue Dec 13 2005 20:39:56 on modular  [Seed = 64960464]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5^2) by
y^5 + y + 4*x

>> G<beta> := ext<F | z^5+z-alpha/x>;
                           ^
Runtime error in '-': Bad argument types
Argument types given: RngUPolElt[RngUPol[FldFunRat]], FldFunElt

>> G;;
   ^
User error: Identifier 'G' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:38:46 2005

Input: R<x> := FunctionField(GF(5));
P<y> := PolynomialRing(R);
F<alpha> := ext< R | y^2 - 1/x >;
F;
Q<z> := PolynomialRing(P);
G<beta> := ext<F | z^3-y-x>;
G;

Output: Magma V2.11-10    Tue Dec 13 2005 20:38:46 on modular  [Seed = 348659853]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5) by
y^2 + 4/x
Algebraic function field defined over F by
$.1^3 + 4*alpha + 4*x

Total time: 0.290 seconds, Total memory usage: 7.85MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:37:32 2005

Input: R<x> := FunctionField(GF(5));
P<y> := PolynomialRing(R);
F<alpha> := ext< R | y^2 - 1/x >;
F;


Output: Magma V2.11-10    Tue Dec 13 2005 20:37:32 on modular  [Seed = 482355327]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5) by
y^2 + 4/x

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:37:26 2005

Input: R<x> := FunctionField(GF(5));

F<alpha> := ext< R | y^2 - 1/x >;
F;


Output: Magma V2.11-10    Tue Dec 13 2005 20:37:26 on modular  [Seed = 570234184]
   -------------------------------------


>> F<alpha> := ext< R | y^2 - 1/x >;
                        ^
User error: Identifier 'y' has not been declared or assigned

>> F;
   ^
User error: Identifier 'F' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:37:09 2005

Input: R<x> := FunctionField(GF(5));
P<y> := PolynomialRing(R);
F<alpha> := ext< R | y^2 - 1/x >;
F;


Output: Magma V2.11-10    Tue Dec 13 2005 20:37:09 on modular  [Seed = 653922908]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5) by
y^2 + 4/x

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:35:29 2005

Input: R<x> := FunctionField(GF(5,2));
P<y> := PolynomialRing(R);
F<z> := FunctionField(y^5+y - x);
F;



Output: Magma V2.11-10    Tue Dec 13 2005 20:35:28 on modular  [Seed = 737615604]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5^2) by
y^5 + y + 4*x

Total time: 0.180 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:34:56 2005

Input: R<x> := FunctionField(GF(5,2));
P<y> := PolynomialRing(R);
F<alpha> := FunctionField(y^2 - 1/x);
F;



Output: Magma V2.11-10    Tue Dec 13 2005 20:34:56 on modular  [Seed = 820774351]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5^2) by
y^2 + 4/x

Total time: 0.190 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:34:10 2005

Input: R<x> := FunctionField(GF(5));
P<y> := PolynomialRing(R);
F<alpha> := FunctionField(y^2 - 1/x);
F;



Output: Magma V2.11-10    Tue Dec 13 2005 20:34:09 on modular  [Seed = 904462491]
   -------------------------------------

Algebraic function field defined over Univariate rational function field over 
GF(5) by
y^2 + 4/x

Total time: 0.190 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 20:27:47 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
"g[1] =", g[1];
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/

/*
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";
*/


Output: Magma V2.11-10    Tue Dec 13 2005 20:27:46 on modular  [Seed = 1021315601]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
lambda = 2
mu = i + 1
Gt = (8 : 816263181872116351510202985179226587277470764815*i + 
    295865244505705705023665406736615173923424579851 : 1)
g = (1113252570408097904801784205204725186435037650621*i + 
    828892838102560531997994710291403383901103286823)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (1334693519950620886403708174450030523556565932446*i + 
    65995713479010101585078190425689016349129829691)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (1167306608241793402349182741773283684304074553579*i + 
    813404015744428633410120092529896632595508931142)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474

>> "g[1] =", g[1];
              ^
Runtime error in '[]': Bad argument types

Total time: 0.610 seconds, Total memory usage: 3.34MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:26:47 2005

Input: FunctionField(FiniteField(11))



Output: Magma V2.11-10    Tue Dec 13 2005 20:26:46 on modular  [Seed = 3323654440]
   -------------------------------------

Univariate rational function field over GF(11)
Variables: $.1

Total time: 0.180 seconds, Total memory usage: 3.24MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:25:00 2005

Input: FunctionField(Integers())



Output: Magma V2.11-10    Tue Dec 13 2005 20:25:00 on modular  [Seed = 3239966357]
   -------------------------------------

Univariate rational function field over Integer Ring
Variables: $.1

Total time: 0.190 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 20:20:26 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    /*
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
    */
    if U eq V then
        m := 3*U[1]^2;
        s := 2*U[2];
    else
        m := V[2] - U[2];
        s := V[1] - U[1];
    end if;
    return m*(Q[1] - U[1]) + s*(U[2] - Q[2]);
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Tue Dec 13 2005 20:20:06 on modular  [Seed = 3373660599]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
lambda = 2
mu = i + 1
Gt = (8 : 816263181872116351510202985179226587277470764815*i + 
    295865244505705705023665406736615173923424579851 : 1)
g = (1113252570408097904801784205204725186435037650621*i + 
    828892838102560531997994710291403383901103286823)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (1334693519950620886403708174450030523556565932446*i + 
    65995713479010101585078190425689016349129829691)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (1167306608241793402349182741773283684304074553579*i + 
    813404015744428633410120092529896632595508931142)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
-- 1
-- 2
-- 3
-- 4
-- 5
-- 6
-- 7
-- 8
-- 9
-- 10
-- 11
-- 12
-- 13
-- 14
-- 15
-- 16
-- 17
-- 18
-- 19
-- 20
-- 21
-- 22
-- 23
-- 24
-- 25
-- 26
-- 27
-- 28
-- 29
-- 30
-- 31
-- 32
-- 33
-- 34
-- 35
-- 36
-- 37
-- 38
-- 39
-- 40
-- 41
-- 42
-- 43
-- 44
-- 45
-- 46
-- 47
-- 48

Errors: /bin/sh: line 1: 31729 Alarm clock             nice -n 19 /usr/local/bin/magma


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 20:15:58 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    "--", j;
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Tue Dec 13 2005 20:15:38 on modular  [Seed = 3490505170]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
lambda = 2
mu = i + 1
Gt = (8 : 645238442624673913635245604741558906439788126004*i + 
    1165636379991084560121783183184170319793834310968 : 1)
g = (348249054088692360343664384716060307282221240198*i + 
    632608786394229733147453879629382109816155603996)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (126808104546169378741740415470754970160692958373*i + 
    1395505911017780163560370399495096477368129061128)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (294195016254996862796265848147501809413184337240*i + 
    648097608752361631735328497390888861121749959677)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474
-- 1
-- 2
-- 3
-- 4
-- 5
-- 6
-- 7
-- 8
-- 9
-- 10
-- 11
-- 12
-- 13
-- 14
-- 15
-- 16
-- 17
-- 18
-- 19
-- 20
-- 21
-- 22
-- 23
-- 24
-- 25
-- 26
-- 27
-- 28
-- 29
-- 30
-- 31
-- 32
-- 33
-- 34
-- 35
-- 36
-- 37
-- 38
-- 39
-- 40
-- 41
-- 42
-- 43
-- 44
-- 45
-- 46
-- 47
-- 48

Errors: /bin/sh: line 1: 31720 Alarm clock             nice -n 19 /usr/local/bin/magma


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 20:14:45 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(n, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Tue Dec 13 2005 20:14:25 on modular  [Seed = 3674728722]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
lambda = 2
mu = i + 1
Gt = (8 : 816263181872116351510202985179226587277470764815*i + 
    295865244505705705023665406736615173923424579851 : 1)
g = (1113252570408097904801784205204725186435037650621*i + 
    828892838102560531997994710291403383901103286823)*z^5 + 
    (78288732951012207123651737359843385303103429616*i + 
    1421790144970157374993435834657786699116722047068)*z^4 + 
    (1334693519950620886403708174450030523556565932446*i + 
    65995713479010101585078190425689016349129829691)*z^3 + 
    (1151508433446340267838152948068030563616071711737*i + 
    1331505104782800437119636772308446788364866291823)*z^2 + 
    (1167306608241793402349182741773283684304074553579*i + 
    813404015744428633410120092529896632595508931142)*z + 
    800403695404043311146437378782593638877310314601*i + 
    901249395544166733264846949825665528694219338474

Errors: /bin/sh: line 1: 31715 Alarm clock             nice -n 19 /usr/local/bin/magma


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 20:13:26 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(n) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 20:13:25 on modular  [Seed = 3862615147]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
lambda = 2
mu = i + 1
Gt = (8 : 816263181872116351510202985179226587277470764815*i + 
    295865244505705705023665406736615173923424579851 : 1)

>>         if bit(r, i) eq 1 then
                  ^
User error: Identifier 'r' has not been declared or assigned

>> g := tate(G, Gt);
        ^
User error: Identifier 'tate' has not been declared or assigned
g = function(U, V, Q) ... end function

>>     w := tate(u*G, v*Gt);
            ^
User error: Identifier 'tate' has not been declared or assigned
Success!

Total time: 0.260 seconds, Total memory usage: 3.34MB


'70.172.'
************** MAGMA *****************
Host 70.172.216.115 (70.172.216.115)
Time: Tue Dec 13 20:13:13 2005

Input: factor 74037563479561712828046796097429573142593188889231
28908493623263897276503402826627689199641962511784
39958943305021275853701189680982867331732731089309
00552505116877063299072396380786710086096962537934
650563796359

Output: Magma V2.11-10    Tue Dec 13 2005 20:13:13 on modular  [Seed = 3778925424]
   -------------------------------------


>> factor 74037563479561712828046796097429573142593188889231
          ^
User error: bad syntax

>> 39958943305021275853701189680982867331732731089309
   ^
User error: bad syntax

>> 650563796359;
   ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'70.172.'
************** MAGMA *****************
Host 70.172.216.115 (70.172.216.115)
Time: Tue Dec 13 20:12:56 2005

Input: fac 74037563479561712828046796097429573142593188889231
28908493623263897276503402826627689199641962511784
39958943305021275853701189680982867331732731089309
00552505116877063299072396380786710086096962537934
650563796359

Output: Magma V2.11-10    Tue Dec 13 2005 20:12:56 on modular  [Seed = 3946305867]
   -------------------------------------


>> fac 74037563479561712828046796097429573142593188889231
       ^
User error: bad syntax

>> 39958943305021275853701189680982867331732731089309
   ^
User error: bad syntax

>> 650563796359;
   ^
User error: bad syntax

Total time: 0.180 seconds, Total memory usage: 3.24MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Tue Dec 13 20:12:28 2005

Input: K<w> := GF(16)




Output: Magma V2.11-10    Tue Dec 13 2005 20:12:28 on modular  [Seed = 4096313008]
   -------------------------------------


Total time: 0.180 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 20:12:24 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    f := 1; A := P;
    for i := length(r) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 20:12:24 on modular  [Seed = 4029465264]
   -------------------------------------

b = 3
G = (1 : 1461501624496790265145448589920785493717258890817 : 1)
lambda = 2
mu = i + 1
Gt = (8 : 816263181872116351510202985179226587277470764815*i + 
    295865244505705705023665406736615173923424579851 : 1)

>>     for i := length(r) - 2 to 0 by -1 do
                       ^
User error: Identifier 'r' has not been declared or assigned

>> g := tate(G, Gt);
        ^
User error: Identifier 'tate' has not been declared or assigned
g = function(U, V, Q) ... end function

>>     w := tate(u*G, v*Gt);
            ^
User error: Identifier 'tate' has not been declared or assigned
Success!

Total time: 0.230 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 20:10:50 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
/*
for u in [1..n-1] do
    w := tate(u*G, Gt);
    //s := g^((u*v) mod n);
    s := tate(G, u*Gt);
    h := g^u;
    if w ne s or w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "e(u*P, Q) = " * Sprint(w);
        print "e(P, u*Q) = " * Sprint(s);
        print "e(P, Q)^u = " * Sprint(h);
        quit;
    end if;
end for;
*/
for j in [1..100] do
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 20:10:50 on modular  [Seed = 4213688793]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (76*i + 99)*z^5 + (3*i + 57)*z^4 + (24*i + 88)*z^3 + (78*i + 63)*z^2 + (58*i
    + 84)*z + 23*i + 29
Success!

Total time: 0.220 seconds, Total memory usage: 3.53MB


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 20:09:33 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
/*
for u in [1..n-1] do
    w := tate(u*G, Gt);
    //s := g^((u*v) mod n);
    s := tate(G, u*Gt);
    h := g^u;
    if w ne s or w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "e(u*P, Q) = " * Sprint(w);
        print "e(P, u*Q) = " * Sprint(s);
        print "e(P, Q)^u = " * Sprint(h);
        quit;
    end if;
end for;
*/
for j in [1..100] do
    u := Random(n-1);
    v := Random(n-1);
    w := tate(u*G, v*Gt);
    h := g^((u*v) mod n);
    if w ne s or w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P, v*Q)   = " * Sprint(w);
        print "e(P, Q)^(u*v) = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 20:09:32 on modular  [Seed = 2254091634]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (76*i + 99)*z^5 + (3*i + 57)*z^4 + (24*i + 88)*z^3 + (78*i + 63)*z^2 + (58*i
    + 84)*z + 23*i + 29

>>     if w ne s or w ne h then
               ^
User error: Identifier 's' has not been declared or assigned
Success!

Total time: 0.190 seconds, Total memory usage: 3.53MB


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 20:01:22 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for u in [1..n-1] do
    w := tate(u*G, Gt);
    //s := g^((u*v) mod n);
    s := tate(G, u*Gt);
    h := g^u;
    if w ne s or w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "e(u*P, Q) = " * Sprint(w);
        print "e(P, u*Q) = " * Sprint(s);
        print "e(P, Q)^u = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 20:01:22 on modular  [Seed = 3077282413]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (76*i + 99)*z^5 + (3*i + 57)*z^4 + (24*i + 88)*z^3 + (78*i + 63)*z^2 + (58*i
    + 84)*z + 23*i + 29
Success!

Total time: 0.240 seconds, Total memory usage: 3.53MB


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 20:00:15 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 2 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            "***", i;
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for u in [1..n-1] do
    w := tate(u*G, Gt);
    //s := g^((u*v) mod n);
    s := tate(G, u*Gt);
    h := g^u;
    if w ne s or w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "e(u*P, Q) = " * Sprint(w);
        print "e(P, u*Q) = " * Sprint(s);
        print "e(P, Q)^u = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 20:00:15 on modular  [Seed = 2993594133]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
*** 5
*** 0
g = (76*i + 99)*z^5 + (3*i + 57)*z^4 + (24*i + 88)*z^3 + (78*i + 63)*z^2 + (58*i
    + 84)*z + 23*i + 29
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
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*** 0
*** 5
*** 0
*** 5
*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
*** 5
*** 0
*** 5
*** 0
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*** 0
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*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
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*** 0
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*** 0
*** 5
*** 0
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*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
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*** 0
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*** 0
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*** 0
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*** 0
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*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
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*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
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*** 0
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*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
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*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
*** 5
*** 0
Success!

Total time: 0.250 seconds, Total memory usage: 3.53MB


'200.177'
************** MAGMA *****************
Host 200.177.26.116 (200.177.26.116)
Time: Tue Dec 13 19:53:53 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            "***", i;
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for u in [1..n-1] do
    w := tate(u*G, Gt);
    //s := g^((u*v) mod n);
    s := tate(G, u*Gt);
    h := g^u;
    if w ne s or w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "e(u*P, Q) = " * Sprint(w);
        print "e(P, u*Q) = " * Sprint(s);
        print "e(P, Q)^u = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 19:53:53 on modular  [Seed = 2090881637]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
*** 6
*** 5
*** 0
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
*** 6
*** 5
*** 0
*** 6
*** 5
*** 0
*** 6
*** 5
*** 0
*** 6
*** 5
*** 0
Failure!
u = 2
e(u*P, Q) = (38*i + 16)*z^5 + (101*i + 58)*z^4 + (43*i + 45)*z^3 + (102*i + 
83)*z^2 + (61*i + 73)*z + 20*i + 35
e(P, u*Q) = (100*i + 19)*z^5 + (89*i + 82)*z^4 + (74*i + 97)*z^3 + (74*i + 
77)*z^2 + (92*i + 40)*z + 92*i + 48
e(P, Q)^u = (48*i + 96)*z^5 + (98*i + 69)*z^4 + (91*i + 98)*z^3 + (100*i + 
11)*z^2 + (48*i + 67)*z + 29*i + 33

Total time: 0.190 seconds, Total memory usage: 3.53MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 19:16:04 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M1:=EchelonForm(M); 
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);
C2;
L:=MinimumWords(C2); 
C3:=LinearCode(L); 
C3;

Output: Magma V2.11-10    Tue Dec 13 2005 19:16:04 on modular  [Seed = 587072862]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 14>, <10, 182>, <12, 805>, <14, 2200>, <16, 3885>, <18, 4340>, 
<20, 3066>, <22, 1400>, <24, 420>, <26, 70>, <28, 1> ]
[35, 14, 8] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]

>> C3:=LinearCode(L); 
                 ^
Runtime error in 'LinearCode': Bad argument types
Argument types given: SetEnum[ModTupFldElt]

>> C3;;
   ^
User error: Identifier 'C3' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 19:11:47 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M1:=EchelonForm(M); 
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);
C2;
MinimumWords(C2); 

Output: Magma V2.11-10    Tue Dec 13 2005 19:11:47 on modular  [Seed = 753929303]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 14>, <10, 182>, <12, 805>, <14, 2200>, <16, 3885>, <18, 4340>, 
<20, 3066>, <22, 1400>, <24, 420>, <26, 70>, <28, 1> ]
[35, 14, 8] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
{
    (0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0),
    (0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0),
    (1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0),
    (0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0),
    (0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1),
    (0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0),
    (0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0),
    (1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0)
}

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:52:22 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M1:=EchelonForm(M); 
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);
C2;

Output: Magma V2.11-10    Tue Dec 13 2005 18:52:22 on modular  [Seed = 3256803149]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 14>, <10, 182>, <12, 805>, <14, 2200>, <16, 3885>, <18, 4340>, 
<20, 3066>, <22, 1400>, <24, 420>, <26, 70>, <28, 1> ]
[35, 14, 8] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:46:56 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M1:=EchelonForm(M); 
M2:=Submatrix(M1,22,22,14,35);
M2;
C2:=LinearCode(M2); 
WeightDistribution(C2);

Output: Magma V2.11-10    Tue Dec 13 2005 18:46:55 on modular  [Seed = 3423654554]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[ <0, 1>, <8, 14>, <10, 182>, <12, 805>, <14, 2200>, <16, 3885>, <18, 4340>, 
<20, 3066>, <22, 1400>, <24, 420>, <26, 70>, <28, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:42:13 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M1:=EchelonForm(M); 
M2:=Submatrix(M1,22,22,14,35);
M2;

Output: Magma V2.11-10    Tue Dec 13 2005 18:42:12 on modular  [Seed = 3591031227]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:38:53 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M:=EchelonForm(M); 
M2:=Submatrix(M,22,22,14,35);
M2;

Output: Magma V2.11-10    Tue Dec 13 2005 18:38:53 on modular  [Seed = 3879468883]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:37:30 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M:=EchelonForm(M); 
M2:=Submatrix(M,22,22,35,14);
M2;

Output: Magma V2.11-10    Tue Dec 13 2005 18:37:30 on modular  [Seed = 4013160428]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 1 0 0 1]
[0 1 0 0 0 0 0 0 0 0 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1]
[0 0 0 1 0 0 0 0 0 0 1 1 0 0]
[0 0 0 0 1 0 0 0 0 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 1 0 0 0 1 1 1 1]
[0 0 0 0 0 0 0 1 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:37:09 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M:=EchelonForm(M); 
M2:=Submathrix(M,22,22,35,14);
M2;

Output: Magma V2.11-10    Tue Dec 13 2005 18:37:08 on modular  [Seed = 3895783669]
   -------------------------------------


>> M2:=Submathrix(M,22,22,35,14);
       ^
User error: Identifier 'Submathrix' has not been declared or assigned

>> M2;;
   ^
User error: Identifier 'M2' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:32:27 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M:=EchelonForm(M); 
M;

Output: Magma V2.11-10    Tue Dec 13 2005 18:32:26 on modular  [Seed = 4063161281]
   -------------------------------------

[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1
    0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0
    1 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1
    0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0
    1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0
    1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1
    0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1
    0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1
    0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0
    1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1
    0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0
    0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0
    1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0
    0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0
    1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1
    1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1
    1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0
    1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0
    1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1
    1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0
    0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1
    0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1
    1 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1
    1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0
    1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1
    1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1
    0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1
    1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1
    1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0
    0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1
    1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1
    0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1
    1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:30:17 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   

[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0

,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0

,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0

,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1

,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0

,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1

,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1

,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0

,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1

,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0

,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0

,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0

,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1

,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M:=EchelonForm(M); 

Output: Magma V2.11-10    Tue Dec 13 2005 18:30:17 on modular  [Seed = 4280542543]
   -------------------------------------


Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:27:47 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
EchelonForm(M); 

Output: Magma V2.11-10    Tue Dec 13 2005 18:27:47 on modular  [Seed = 2170395211]
   -------------------------------------

[1 0 0 0 0 1 1 1]
[0 1 0 0 0 1 0 1]
[0 0 1 0 0 0 1 1]
[0 0 0 1 0 0 0 0]
[0 0 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:15:06 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
C := LinearCode(M);
GeneratorMatrix(C);

Output: Magma V2.11-10    Tue Dec 13 2005 18:15:06 on modular  [Seed = 2504622934]
   -------------------------------------

[1 0 0 0 0 1 1 1]
[0 1 0 0 0 1 0 1]
[0 0 1 0 0 0 1 1]
[0 0 0 1 0 0 0 0]
[0 0 0 0 1 1 1 0]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:11:56 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));
M;

Output: Magma V2.11-10    Tue Dec 13 2005 18:11:56 on modular  [Seed = 2672003482]
   -------------------------------------

[1 0 0 0 0 1 1 1]
[0 1 0 0 1 0 1 1]
[0 0 1 0 1 1 0 1]
[0 0 0 1 1 1 1 0]
[1 0 0 0 0 1 1 1]
[0 1 0 0 1 0 1 1]
[0 0 1 0 1 1 0 1]
[0 0 0 1 1 1 1 0]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:11:38 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
M:=VerticalJoin(GeneratorMatrix(C), ParityCheckMatrix(C));

Output: Magma V2.11-10    Tue Dec 13 2005 18:11:37 on modular  [Seed = 2554629768]
   -------------------------------------


Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:06:45 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
GeneratorMatrix(C);
ParityCheckMatrix(C);

Output: Magma V2.11-10    Tue Dec 13 2005 18:06:44 on modular  [Seed = 3026756489]
   -------------------------------------

[1 0 0 0 0 1 1 1]
[0 1 0 0 1 0 1 1]
[0 0 1 0 1 1 0 1]
[0 0 0 1 1 1 1 0]
[1 0 0 0 0 1 1 1]
[0 1 0 0 1 0 1 1]
[0 0 1 0 1 1 0 1]
[0 0 0 1 1 1 1 0]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:06:09 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
GeneratorMatrix(C);

Output: Magma V2.11-10    Tue Dec 13 2005 18:06:09 on modular  [Seed = 2976751977]
   -------------------------------------

[1 0 0 0 0 1 1 1]
[0 1 0 0 1 0 1 1]
[0 0 1 0 1 1 0 1]
[0 0 0 1 1 1 1 0]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 18:05:35 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
C;

Output: Magma V2.11-10    Tue Dec 13 2005 18:05:35 on modular  [Seed = 3127290428]
   -------------------------------------

[8, 4, 4] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 1 1 1]
[0 1 0 0 1 0 1 1]
[0 0 1 0 1 1 0 1]
[0 0 0 1 1 1 1 0]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 17:53:01 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   

[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0

,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0

,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0

,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1

,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0

,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1

,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1

,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0

,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1

,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0

,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0

,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0

,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1

,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
S;


Output: Magma V2.11-10    Tue Dec 13 2005 17:53:01 on modular  [Seed = 64950519]
   -------------------------------------

[56, 21] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0
    0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1
    0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
    1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1
    1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1
    0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0
    0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0
    1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0
    0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1
    0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1
    1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1
    0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1
    1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1
    0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0
    1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0
    0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0
    0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1
    1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1
    0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0
    0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1
    0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1]

Total time: 0.180 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:55:57 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for u in [1..n-1] do
    w := tate(u*G, Gt);
    //s := g^((u*v) mod n);
    s := tate(G, u*Gt);
    h := g^u;
    if w ne s or w ne h then
        "Failure!";
        print "u = " * Sprint(u);
        print "e(u*P, Q) = " * Sprint(w);
        print "e(P, u*Q) = " * Sprint(s);
        print "e(P, Q)^u = " * Sprint(h);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:55:57 on modular  [Seed = 1807159056]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
Failure!
u = 2
e(u*P, Q) = (38*i + 16)*z^5 + (101*i + 58)*z^4 + (43*i + 45)*z^3 + (102*i + 
83)*z^2 + (61*i + 73)*z + 20*i + 35
e(P, u*Q) = (100*i + 19)*z^5 + (89*i + 82)*z^4 + (74*i + 97)*z^3 + (74*i + 
77)*z^2 + (92*i + 40)*z + 92*i + 48
e(P, Q)^u = (48*i + 96)*z^5 + (98*i + 69)*z^4 + (91*i + 98)*z^3 + (100*i + 
11)*z^2 + (48*i + 67)*z + 29*i + 33

Total time: 0.200 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:55:01 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for u in [1..n-1] do
    w := tate(u*G, Gt);
    //s := g^((u*v) mod n);
    s := tate(G, u*Gt);
    if w ne s then
        "Failure!";
        print "u = " * Sprint(u);
        print "e(u*P, Q) = " * Sprint(w);
        print "e(P, u*Q) = " * Sprint(s);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:55:01 on modular  [Seed = 1857161805]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
Failure!
u = 2
e(u*P, Q) = (38*i + 16)*z^5 + (101*i + 58)*z^4 + (43*i + 45)*z^3 + (102*i + 
83)*z^2 + (61*i + 73)*z + 20*i + 35
e(P, u*Q) = (100*i + 19)*z^5 + (89*i + 82)*z^4 + (74*i + 97)*z^3 + (74*i + 
77)*z^2 + (92*i + 40)*z + 92*i + 48

Total time: 0.190 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:52:25 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
v := 1;
for u in [1..n-1] do
    w := tate(u*G, v*Gt);
    s := g^((u*v) mod n);
    if w ne s then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P,v*Q)  = " * Sprint(w);
        print "e(P,Q)^(uv) = " * Sprint(s);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:52:24 on modular  [Seed = 2024021302]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
Failure!
u = 2
v = 1
e(u*P,v*Q)  = (38*i + 16)*z^5 + (101*i + 58)*z^4 + (43*i + 45)*z^3 + (102*i + 
83)*z^2 + (61*i + 73)*z + 20*i + 35
e(P,Q)^(uv) = (48*i + 96)*z^5 + (98*i + 69)*z^4 + (91*i + 98)*z^3 + (100*i + 
11)*z^2 + (48*i + 67)*z + 29*i + 33

Total time: 0.200 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:51:09 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for v, u in [1..n-1] do
    w := tate(u*G, v*Gt);
    s := g^((u*v) mod n);
    if w ne s then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P,v*Q)  = " * Sprint(w);
        print "e(P,Q)^(uv) = " * Sprint(s);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:51:08 on modular  [Seed = 1907168363]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
Failure!
u = 2
v = 1
e(u*P,v*Q)  = (38*i + 16)*z^5 + (101*i + 58)*z^4 + (43*i + 45)*z^3 + (102*i + 
83)*z^2 + (61*i + 73)*z + 20*i + 35
e(P,Q)^(uv) = (48*i + 96)*z^5 + (98*i + 69)*z^4 + (91*i + 98)*z^3 + (100*i + 
11)*z^2 + (48*i + 67)*z + 29*i + 33

Total time: 0.200 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:49:25 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for u, v in [1..n-1] do
    w := tate(u*G, v*Gt);
    s := g^((u*v) mod n);
    if w ne s then
        "Failure!";
        print "u = " * Sprint(u);
        print "v = " * Sprint(v);
        print "e(u*P,v*Q)  = " * Sprint(w);
        print "e(P,Q)^(uv) = " * Sprint(s);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:49:25 on modular  [Seed = 1957171847]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
Failure!
u = 1
v = 2
e(u*P,v*Q)  = (100*i + 19)*z^5 + (89*i + 82)*z^4 + (74*i + 97)*z^3 + (74*i + 
77)*z^2 + (92*i + 40)*z + 92*i + 48
e(P,Q)^(uv) = (48*i + 96)*z^5 + (98*i + 69)*z^4 + (91*i + 98)*z^3 + (100*i + 
11)*z^2 + (48*i + 67)*z + 29*i + 33

Total time: 0.200 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:48:24 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for u in [1..n-1] do
    for v in [1..n-1] do
        w := tate(u*G, v*Gt);
        s := g^((u*v) mod n);
        if w ne s then
            "Failure!";
            print "u = " * Sprint(u);
            print "v = " * Sprint(v);
            print "e(u*P,v*Q)  = " * Sprint(w);
            print "e(P,Q)^(uv) = " * Sprint(s);
            quit;
        end if;
    end for;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:48:23 on modular  [Seed = 198667706]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
Failure!
u = 1
v = 2
e(u*P,v*Q)  = (100*i + 19)*z^5 + (89*i + 82)*z^4 + (74*i + 97)*z^3 + (74*i + 
77)*z^2 + (92*i + 40)*z + 92*i + 48
e(P,Q)^(uv) = (48*i + 96)*z^5 + (98*i + 69)*z^4 + (91*i + 98)*z^3 + (100*i + 
11)*z^2 + (48*i + 67)*z + 29*i + 33

Total time: 0.200 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:46:16 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for u in [1..n-1] do
    for v in [1..n-1] do
        w := tate(u*G, v*Gt);
        if w ne g^((u*v) mod n) then
            "Failure: u =", u, ", v =", v, ", e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
            quit;
        end if;
    end for;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:46:16 on modular  [Seed = 31287103]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
Failure: u = 1 , v = 2 , e(u*P,v*Q) = (100*i + 19)*z^5 + (89*i + 82)*z^4 + (74*i
    + 97)*z^3 + (74*i + 77)*z^2 + (92*i + 40)*z + 92*i + 48
, e(P,Q)^(uv) = (48*i + 96)*z^5 + (98*i + 69)*z^4 + (91*i + 98)*z^3 + (100*i + 
    11)*z^2 + (48*i + 67)*z + 29*i + 33

Total time: 0.190 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:45:31 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for u in [0..n-1] do
    for v in [0..n-1] do
        w := tate(u*G, v*Gt);
        if w ne g^((u*v) mod n) then
            "Failure: u =", u, ", v =", v, ", e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
            quit;
        end if;
    end for;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:45:30 on modular  [Seed = 81290216]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56

tate(
    P: (0 : 1 : 0),
    Qt: (0 : 1 : 0)
)
>>     Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
              ^
Runtime error in '!': Illegal coercion
Success!

Total time: 0.190 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:44:16 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
Fp := GF(p);
b := Fp!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([Fp | 0, b]);
    G := E![1, y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := Fp!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
Et := EllipticCurve([Fp2 | 0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;

k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([Fp12 | 0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n - 1);
    v := Random(n - 1);
    w := tate(u*G, v*Gt);
    if w ne g^((u*v) mod n) then
        "Failure: u =", u, ", v =", v, ", e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:44:16 on modular  [Seed = 466058429]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2
Gt = (4 : 44*i + 6 : 1)
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
Failure: u = 88 , v = 67 , e(u*P,v*Q) = (100*i + 78)*z^5 + (36*i + 83)*z^4 + 
    (30*i + 95)*z^3 + (93*i + 66)*z^2 + (21*i + 39)*z + 74*i + 33
, e(P,Q)^(uv) = (28*i + 78)*z^5 + (62*i + 21)*z^4 + (82*i + 32)*z^3 + (36*i + 
    57)*z^2 + (69*i + 26)*z + 95*i + 78

Total time: 0.190 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:39:51 2005

Input: p := 103;//1461501624496790265145448589920785493717258890819;
n :=  97;//1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := Fp!2;
mu := 2 + i;//1 + i;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!12;//Fp!3;
y0 := Fp!61;//Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
"G  =", G;
Et := EllipticCurve([0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
"Gt =", Gt;
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n - 1);
    v := Random(n - 1);
    w := tate(u*G, v*Gt);
    if w ne g^((u*v) mod n) then
        "Failure: u =", u, ", v =", v, ", e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:39:51 on modular  [Seed = 298676640]
   -------------------------------------

G  = (1 : 61 : 1)
Gt = (4 : 44*i + 6 : 1)
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
Failure: u = 2 , v = 18 , e(u*P,v*Q) = (50*i + 27)*z^5 + (94*i + 26)*z^4 + (96*i
    + 54)*z^3 + (19*i + 50)*z^2 + (61*i + 86)*z + 74*i + 83
, e(P,Q)^(uv) = (85*i + 97)*z^5 + (46*i + 29)*z^4 + (25*i + 30)*z^3 + (5*i + 
    40)*z^2 + (59*i + 45)*z + 71*i + 56

Total time: 0.190 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:39:14 2005

Input: p := 103;//1461501624496790265145448589920785493717258890819;
n :=  97;//1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := Fp!2;
mu := 2 + i;//1 + i;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!12;//Fp!3;
y0 := Fp!61;//Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n - 1);
    v := Random(n - 1);
    w := tate(u*G, v*Gt);
    if w ne g^((u*v) mod n) then
        "Failure: u =", u, ", v =", v, ", e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:39:14 on modular  [Seed = 348681280]
   -------------------------------------

xt = 4
g = (4*i + 70)*z^5 + (i + 79)*z^4 + (78*i + 73)*z^3 + (24*i + 89)*z^2 + (95*i + 
    55)*z + 71*i + 56
Failure: u = 77 , v = 45 , e(u*P,v*Q) = (99*i + 33)*z^5 + (i + 79)*z^4 + (25*i +
    30)*z^3 + (24*i + 89)*z^2 + (8*i + 48)*z + 71*i + 56
, e(P,Q)^(uv) = (45*i + 90)*z^5 + (29*i + 53)*z^4 + (91*i + 98)*z^3 + (68*i + 
    94)*z^2 + (10*i + 44)*z + 29*i + 33

Total time: 0.200 seconds, Total memory usage: 3.53MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:37:09 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := Fp!2;
mu := 1 + i;
xi := 1/(lambda^2*mu^3);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
//xt := i + 2;
xt := 8;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n - 1);
    v := Random(n - 1);
    w := tate(u*G, v*Gt);
    if w ne g^((u*v) mod n) then
        "Failure: u =", u, ", v =", v, ", e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:37:08 on modular  [Seed = 1005017833]
   -------------------------------------

g = (788575332791159297943382330888091507234373160984*i + 
    1058591418264462827430151667682426387205715653646)*z^5 + 
    (1322305885575807535232020102800928943661744848278*i + 
    1409518745655936467893014453594650508665852052962)*z^4 + 
    (92691491674328017873297655882559873492848083281*i + 
    833387513557317502960994534404369304220347785370)*z^3 + 
    (494268977073817690135764886501032821621331118299*i + 
    1229571523737605236254885852230274558531837523170)*z^2 + 
    (808544033252198825980179735588413753558824714098*i + 
    1078734709554906413376551726137377859976359534003)*z + 
    901493422496026382770929617713581877034333521597*i + 
    179130707045747991601837568997307929180024496359
Failure: u = 946857947927091542053549758428905646280859693128 , v = 
466000635125302880497731311434509156520464968357 , e(u*P,v*Q) = 
    (1200099635135265526944287342088491944694417283646*i + 
    1014718590403343121885833198299782572285854256079)*z^5 + 
    (471917906168926683696779282454416809308080942623*i + 
    812644610572628849110985110390868588547305952867)*z^4 + 
    (1324320698252798975422880297923770527123745467545*i + 
    1369801539108789273837312698785305468703191114557)*z^3 + 
    (912504363855611966661376277297362740269326191111*i + 
    1380551513148965958602464026524016649810176191967)*z^2 + 
    (1105893840184059270391354805924659396077920064041*i + 
    1288971271799831078521824062316836734081548434254)*z + 
    597889428879138809242066013037790879345607008490*i + 
    1169462561227871511533990611160523461698537007163
, e(P,Q)^(uv) = (1279762112918260549426510071012241774233201710837*i + 
    1038569981133317417069888654877080847608690012705)*z^5 + 
    (1209071413845908584505709653556653498685569554252*i + 
    367978315180861868580674923069718724352829282487)*z^4 + 
    (1092679439520606553629045996698544887309903354323*i + 
    1432439429241915293719430050078044125231284711989)*z^3 + 
    (720945178705548260866392701230718571277060392582*i + 
    965355359457859959621310893985759282425870986789)*z^2 + 
    (237204670011952913218038313811081503208054984454*i + 
    1073500538414130670572005779575000303603195535920)*z + 
    37244205619087872590547375873385141388703250234*i + 
    1082282633627808574389817278679504033474868288016

Total time: 1.050 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:36:11 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
K := GF(p);
b := K!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([K|0,b]);
    G := E![1,y];
until IsZero(n*G);
"b =", b;
"G =", G;
lambda := K!2;
while IsPower(lambda, 3) do
    lambda +:= 1;
end while;
"lambda =", lambda;
K2<i> := ExtensionField<K, i | i^2 + 1>;
mu := i + 1;
while IsSquare(mu) do
    mu +:= 1;
end while;
"mu =", mu;


Output: Magma V2.11-10    Tue Dec 13 2005 14:36:10 on modular  [Seed = 1055023010]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)
lambda = 2
mu = i + 2

Total time: 0.190 seconds, Total memory usage: 3.43MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:32:16 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
K := GF(p);
b := K!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([K|0,b]);
    G := E![1,y];
until IsZero(n*G);
"b =", b;
"G =", G;


Output: Magma V2.11-10    Tue Dec 13 2005 14:32:15 on modular  [Seed = 887641789]
   -------------------------------------

u = 1
p = 103
n = 97
b = 12
G = (1 : 61 : 1)

Total time: 0.180 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:32:00 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;
K := GF(p);
b := K!0;
repeat
    repeat
        b := b + 1;   
    until IsSquare(b + 1);
    y := Root(b + 1, 2);
    E := EllipticCurve([k|0,b]);
    G := E![1,y];
until IsZero(n*G);
"b =", b;
"G =", G;


Output: Magma V2.11-10    Tue Dec 13 2005 14:32:00 on modular  [Seed = 3390482509]
   -------------------------------------

u = 1
p = 103
n = 97

>>     E := EllipticCurve([k|0,b]);
                           ^
User error: Identifier 'k' has not been declared or assigned
b = 0

>> "G =", G;
          ^
User error: Identifier 'G' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:30:09 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if p mod 4 eq 3 and p mod 9 eq 4 and IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;


Output: Magma V2.11-10    Tue Dec 13 2005 14:30:08 on modular  [Seed = 3474173368]
   -------------------------------------

u = 1
p = 103
n = 97

Total time: 0.190 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:28:50 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
v := 0;
while true do
    v +:= 1;
    t := 6*v^2 + 1;
    u := -v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
    u :=  v;
    p := Evaluate(P, u);
    n := p + 1 - t;
    if IsProbablePrime(p) and IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;


Output: Magma V2.11-10    Tue Dec 13 2005 14:28:49 on modular  [Seed = 3289949954]
   -------------------------------------

u = -1
p = 19
n = 13

Total time: 0.190 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:25:25 2005

Input: Zz<z> := PolynomialRing(Integers());
P := 36*z^4 + 36*z^3 + 24*z^2 + 6*z + 1;
u := 0;
while true do
    u +:= 1;
    t := 6*u^2 + 1;
    p := Evaluate(P, -u);
    if not IsProbablePrime(p) then
        continue;
    end if;
    n := p + 1 - t;
    if IsProbablePrime(n) then
        break;
    end if;
    p := Evaluate(P, u);
    if not IsProbablePrime(p) then
        continue;
    end if;
    n := p + 1 - t;
    if IsProbablePrime(n) then
        break;
    end if;
end while;
"u =", u;
"p =", p;
"n =", n;


Output: Magma V2.11-10    Tue Dec 13 2005 14:25:24 on modular  [Seed = 3657873865]
   -------------------------------------

u = 1
p = 19
n = 13

Total time: 0.190 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:17:13 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
//xt := i + 2;
xt := 8;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[2]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n - 1);
    v := Random(n - 1);
    w := tate(u*G, v*Gt);
    if w ne g^((u*v) mod n) then
        "Failure: u =", u, ", v =", v, ", e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:17:12 on modular  [Seed = 4113148154]
   -------------------------------------

g = (672926291705630967202066259032693986482885729835*i + 
    402910206232327437715296922238359106511543237173)*z^5 + 
    (1322305885575807535232020102800928943661744848278*i + 
    1409518745655936467893014453594650508665852052962)*z^4 + 
    (1368810132822462247272150934038225620224410807538*i + 
    628114110939472762184454055516416189496911105449)*z^3 + 
    (494268977073817690135764886501032821621331118299*i + 
    1229571523737605236254885852230274558531837523170)*z^2 + 
    (652957591244591439165268854332371740158434176721*i + 
    382766914941883851768896863783407633740899356816)*z + 
    901493422496026382770929617713581877034333521597*i + 
    179130707045747991601837568997307929180024496359
Failure: u = 787544600137698273840913483523578412686940791799 , v = 
633390288056570917236749546569673252543054620654 , e(u*P,v*Q) = 
    (1230799145370778246341173515929335566649536643006*i + 
    480750625874954609025504843133359714744867086605)*z^5 + 
    (1042350571388618446487630159957378489367482972903*i + 
    603997525618261102690174964818300174247773796868)*z^4 + 
    (372555237390881172830113633133348948005361857273*i + 
    795790796595629198651221834435852032328843762695)*z^3 + 
    (294507650957009594258002783265863173832662354454*i + 
    608683974417992602158011087154420253986790025605)*z^2 + 
    (7609910714021721107059555931969091666598777225*i + 
    945198760430716673304112293252204618143489684435)*z + 
    147738933904891503161234155216849327398150311466*i + 
    11975084496371106465181782342706929746861740417
, e(P,Q)^(uv) = (436069547787440145692125043594555141196201225212*i + 
    104917863794017341921655052505855786976213992405)*z^5 + 
    (1273611771612726823696618599863708218222654331128*i + 
    58016250495606580058214502460360819634176535723)*z^4 + 
    (650807760957229285905208902992656562655973656443*i + 
    522387035783265890583694065207579752375558876825)*z^3 + 
    (935118843989569600386157522041707999880163319815*i + 
    769360049790716169376779087226867932064575695394)*z^2 + 
    (1137422255938782465848831089043436888213998499734*i + 
    255708389714534001533432868391992802173796862328)*z + 
    61611046909036180490590110705335451925853639750*i + 
    146857281263717838984053265699458256927236573517

Total time: 1.100 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:15:53 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
//xt := i + 2;
xt := 8;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    x_U := U[0];
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n - 1);
    v := Random(n - 1);
    w := tate(u*G, v*Gt);
    if w ne g^((u*v) mod n) then
        "Failure: u =", u, ", v =", v, ", e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:15:53 on modular  [Seed = 2370949971]
   -------------------------------------


tate(
    P: (1 : 2 : 1),
    Qt: (8 : 645238442624673913635245604741558906439788126004*i + 11...
)
miller(
    r: 1461501624496790265145447380994971188499300027613,
    P: (1 : 2 : 1),
    Q: (8*z^2 : (645238442624673913635245604741558906439788126004*i...
)
g(
    U: (1 : 2 : 1),
    V: (1 : 2 : 1),
    Q: (8*z^2 : (645238442624673913635245604741558906439788126004*i...
)
>>     x_U := U[0];
               ^
Runtime error in '[]': Argument 2 (0) should be in the range [1 .. 3]
g = function(U, V, Q) ... end function

tate(
    P: (1168716806992048472600575426428280493482442262392 : 9145640...,
    Qt: (1398335284650143722212829649205089955966390414241*i + 51796...
)
miller(
    r: 1461501624496790265145447380994971188499300027613,
    P: (1168716806992048472600575426428280493482442262392 : 9145640...,
    Q: ((1398335284650143722212829649205089955966390414241*i + 5179...
)
g(
    U: (1168716806992048472600575426428280493482442262392 : 9145640...,
    V: (1168716806992048472600575426428280493482442262392 : 9145640...,
    Q: ((1398335284650143722212829649205089955966390414241*i + 5179...
)
>>     x_U := U[0];
               ^
Runtime error in '[]': Argument 2 (0) should be in the range [1 .. 3]
Success!

Total time: 0.230 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:14:47 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
//xt := i + 2;
xt := 8;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[2] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n - 1);
    v := Random(n - 1);
    w := tate(u*G, v*Gt);
    if w ne g^((u*v) mod n) then
        "Failure: u =", u, ", v =", v, ", e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:14:46 on modular  [Seed = 2187254803]
   -------------------------------------

g = (1294412285019402306363363178405640025835588490573*i + 
    110083851862711115164294604712404064123786212316)*z^5 + 
    (1461000921493363626807176655087143303615070519998*i + 
    179329319464877725831768652574235563708218294754)*z^4 + 
    (1380159870452351478229999574688122314163279894835*i + 
    608853380181358438321396844362562256927503461575)*z^3 + 
    (1096834514295262897057490471840451625632598605569*i + 
    556024354574832251790797618637935038587303588339)*z^2 + 
    (1312769194087813280589806690561007885216498370207*i + 
    585387117445278704678873601298024025030517986150)*z + 
    737166616423533515609953322860296363171325419696*i + 
    327478258348140990171576024019950781712369617012
Failure: u = 1125474438691666154889619531753276137514054616092 , v = 
74355561060828237152603481423932850628604339121 , e(u*P,v*Q) = 
    (429751061675843899340369203815082176545408527718*i + 
    909427573279119657754805669761900114071342873652)*z^5 + 
    (1247734288733857748021692265553075464695937579208*i + 
    743816016218828928608456547179207548076982979307)*z^4 + 
    (487557256047992095318968005263397437474936254189*i + 
    37857860423732375651447446890944269006478056096)*z^3 + 
    (1163989855974890736075862642655486087920170035473*i + 
    203749602481885254344251451474004759409452749236)*z^2 + 
    (1030453876983867035177297133699795873715007249920*i + 
    660735836157490264065099937197471719042581607777)*z + 
    81803167227496355034247834271195469737156426272*i + 
    956207628639205541360074132469925387897212870999
, e(P,Q)^(uv) = (456387365657668154214383519085672897734254356213*i + 
    901464030134534466212711635931829911205601723280)*z^5 + 
    (1457502911931788790996440618804285616966470935812*i + 
    167907066249828659721266469744918999176634507737)*z^4 + 
    (1117081125135662063752403398732529743718000625159*i + 
    1166482808557132720766303763649223676515724544694)*z^3 + 
    (45409092783112768705197353118716020133117497726*i + 
    1140195580893668606687433084773043246385384621649)*z^2 + 
    (797400106022357958571873126411052707015877860255*i + 
    1144849651621705114749107513915197993111731626826)*z + 
    398139448757274963177977906845541386205679308934*i + 
    1011464188230029570370071800294314999300195638774

Total time: 1.080 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 14:13:45 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
//xt := i + 2;
xt := 8;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    assert U[3] eq 1;
    assert V[3] eq 1;
    assert Q[3] eq 1;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n - 1);
    v := Random(n - 1);
    w := tate(u*G, v*Gt);
    if w ne g^((u*v) mod n) then
        "Failure: u =", u, ", v =", v, ", e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 14:13:44 on modular  [Seed = 2270943704]
   -------------------------------------

g = (1414620835193373657646613880233559577407734609545*i + 
    352489175314961464607671418528001817189092256541)*z^5 + 
    (904802261065103105936668720505067133656667597074*i + 
    1343248922269291340494538393490943353845819222256)*z^4 + 
    (1025700017505207783921241027028089077317301724291*i + 
    1267567142236668396047190065512596226428512971416)*z^3 + 
    (283587609846347412879109527640610607003328134432*i + 
    250487955904041646310509260856358041239663937723)*z^2 + 
    (110054808378578108265445578093874268052578876998*i + 
    202041545854984388890408940644851972139794936772)*z + 
    257093848091331658607960702914357017287219708568*i + 
    652950073647454119068347296682657355787566777234
Failure: u = 658677412291089462095414946131774452312281593714 , v = 
1216437558465192851244742711765770083951252389636 , e(u*P,v*Q) = 
    (1399072020171236105190679320673870340346132836857*i + 
    557339706670292369068837859617582039559121726559)*z^5 + 
    (87632175260928283896022294886624356298791691273*i + 
    353631789820014829475382783849498669504077254473)*z^4 + 
    (1167181401062038608632643315708112439190409866068*i + 
    1201319255475829211069929657476285565774671872992)*z^3 + 
    (1314520118761252810746572930401672772734452109507*i + 
    692190026558869491946574975355715885291753444864)*z^2 + 
    (30302970564993022126258376903270909561081118427*i + 
    981711504087328555212568427163427828202637031781)*z + 
    650156321266501086248612693725874390933511156097*i + 
    86504195952951481401572117229146789328835422166
, e(P,Q)^(uv) = (213093635849167276598922493416793532239780363365*i + 
    176954146803611932474107371546291585496100314567)*z^5 + 
    (423996100507151792116824541957513700044018239694*i + 
    83422655284377911844489375762414059048084741713)*z^4 + 
    (1422886585162015559920092658102846713850101330779*i + 
    458574078442061740914292994408151093044898187067)*z^3 + 
    (273126339780048501849982943960562129337069997055*i + 
    1303685246506966196047520334746858504911291400698)*z^2 + 
    (1304770219556858465763105537968022378874250386356*i + 
    416455068376200642044392053732047037130013150572)*z + 
    398741370625816481193912713678168496900587107922*i + 
    581927151108935829460509086487928349289055788193

Total time: 1.060 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 13:05:57 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   

[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0

,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0

,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0

,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1

,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0

,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1

,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1

,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0

,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1

,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0

,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0

,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0

,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1

,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
Submatrix(S, 1, 22, 21, 35);


Output: Magma V2.11-10    Tue Dec 13 2005 13:05:57 on modular  [Seed = 804479389]
   -------------------------------------


>> Submatrix(S, 1, 22, 21, 35);
            ^
Runtime error in 'Submatrix': Bad argument types
Argument types given: CodeLinFld, RngIntElt, RngIntElt, RngIntElt, RngIntElt

Total time: 0.200 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 13:03:43 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   

[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0

,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0

,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0

,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1

,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0

,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1

,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1

,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0

,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1

,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0

,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0

,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0

,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1

,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
ExtractBlock(S, 1, 22, 21, 35);


Output: Magma V2.11-10    Tue Dec 13 2005 13:03:42 on modular  [Seed = 653945327]
   -------------------------------------


>> ExtractBlock(S, 1, 22, 21, 35);
               ^
Runtime error in 'ExtractBlock': Bad argument types
Argument types given: CodeLinFld, RngIntElt, RngIntElt, RngIntElt, RngIntElt

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 13:01:22 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   

[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0

,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0

,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0

,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1

,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0

,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1

,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1

,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0

,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1

,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0

,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0

,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0

,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1

,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
S;

Output: Magma V2.11-10    Tue Dec 13 2005 13:01:22 on modular  [Seed = 1021342585]
   -------------------------------------

[56, 21] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0
    0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1
    0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
    1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1
    1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1
    0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0
    0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0
    1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0
    0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1
    0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1
    1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1
    0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1
    1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1
    0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0
    1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0
    0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0
    0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1
    1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1
    0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0
    0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1
    0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 13:00:59 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   

[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0

,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0

,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0

,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0

,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1

,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0

,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1

,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1

,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1

,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0

,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1

,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0

,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0

,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0

,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1

,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1

,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);

Output: Magma V2.11-10    Tue Dec 13 2005 13:00:59 on modular  [Seed = 837647965]
   -------------------------------------


Total time: 0.190 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 12:41:53 2005

Input: M:=[1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1];
Transpose(M);

Output: Magma V2.11-10    Tue Dec 13 2005 12:41:53 on modular  [Seed = 3624180745]
   -------------------------------------


>> M:=[1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
         ^
User error: bad syntax

>> [1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
      ^
User error: bad syntax

>> [1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
      ^
User error: bad syntax

>> [1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
      ^
User error: bad syntax

>> [1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
      ^
User error: bad syntax

>> [1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
      ^
User error: bad syntax

>> [1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
      ^
User error: bad syntax

>> [1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
      ^
User error: bad syntax

>> [1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
      ^
User error: bad syntax

>> [1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
      ^
User error: bad syntax

>> [1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
      ^
User error: bad syntax

>> [1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
      ^
User error: bad syntax

>> [1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
      ^
User error: bad syntax

>> [0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
      ^
User error: bad syntax

>> [0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
      ^
User error: bad syntax

>> [0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
      ^
User error: bad syntax

>> [0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
      ^
User error: bad syntax

>> [0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
      ^
User error: bad syntax

>> [0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
      ^
User error: bad syntax

>> [0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
      ^
User error: bad syntax

>> [0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1];
      ^
User error: bad syntax

>> Transpose(M);;
             ^
User error: Identifier 'M' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'146.6.1'
************** MAGMA *****************
Host 146.6.139.217 (146.6.139.217)
Time: Tue Dec 13 12:10:52 2005

Input: count:=0;
m:=5;
q:=2^m;
F1:=GF(q);
F2:=GF(q^2);
Trace0:={@[email protected]};

for i:=1 to q-1 do
dd:=F1.1^i;
if Trace(dd) eq 0 then
Trace0:=Trace0 join {@[email protected]};
end if;
end for;

d:=0;

for i:=1 to q-1 do
a:=F1.1^i;

        for j:=1 to #Trace0 do
            b:=Trace0[j];

            P<x>:=PolynomialRing(F1);
                C:=HyperellipticCurve(a*x^5+b*x^3+x,x);
                N1:=#C; //over Fq

            R<z>:=PolynomialRing(F2);
                CC:=HyperellipticCurve(a*z^5+b*z^3+z,z);
                N2:=#CC; //over Fq^2;

                a1:=N1-q-1;
                a2:=(N2-1-q^2+a1^2)/2;

        if not IsSquare(a1^2-4*a2+8*q) then
                        if IsDivisibleBy(a2, 2^Ceiling(m/2)) then
                            delta:=(a2+2*q)^2-4*q*a1^2;
                            V:=0;
                            if delta ne 0 then
                            V:=Valuation(delta,2);
                            end if;
                            B:=delta/(2^V);

                            if IsOdd(V) or (B-1 mod 8 ne 0) then
                      //      count:=count+1;
                       //         print C,"(a1,a2)= (", a1 ,",", a2,")";
                    //print "(",a1, a2,")";
                            end if;
                        end if;
      //  end if;

J:=q^2+a1*q+a1+a2+1;
Rat:=#RationalPoints(C);
Jac:=Jacobian(C);
R:=RingOfIntegers();
if R!J mod 8 eq 0 then

for ii:=1 to Floor(J) do
DP:=Points(Jac)[ii];
if HasOrder(DP,8) then
for jj:=1 to Floor(J) do
DQ:=Points(Jac)[jj];
if HasOrder(DQ,8) then
WeilPairing(DP,DQ,8);
end if;
end for;

//print DD, "has order 8, a=", a," b= ", b;
end if;
end for;
count;

end if;
count:=0;
end if;
end for;
end for;

print "done";


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Tue Dec 13 2005 12:10:32 on modular  [Seed = 2893082388]
   -------------------------------------

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

Errors: /bin/sh: line 1: 29596 Alarm clock             nice -n 19 /usr/local/bin/magma


'146.6.1'
************** MAGMA *****************
Host 146.6.139.217 (146.6.139.217)
Time: Tue Dec 13 12:08:28 2005

Input: count:=0;
m:=5;
q:=2^m;
F1:=GF(q);
F2:=GF(q^2);
Trace0:={@[email protected]};

for i:=1 to q-1 do
dd:=F1.1^i;
if Trace(dd) eq 0 then
Trace0:=Trace0 join {@[email protected]};
end if;
end for;

d:=0;

for i:=1 to q-1 do
a:=F1.1^i;

        for j:=1 to #Trace0 do
            b:=Trace0[j];

            P<x>:=PolynomialRing(F1);
                C:=HyperellipticCurve(a*x^5+b*x^3+x,x);
                N1:=#C; //over Fq

            R<z>:=PolynomialRing(F2);
                CC:=HyperellipticCurve(a*z^5+b*z^3+z,z);
                N2:=#CC; //over Fq^2;

                a1:=N1-q-1;
                a2:=(N2-1-q^2+a1^2)/2;

        if not IsSquare(a1^2-4*a2+8*q) then
                        if IsDivisibleBy(a2, 2^Ceiling(m/2)) then
                            delta:=(a2+2*q)^2-4*q*a1^2;
                            V:=0;
                            if delta ne 0 then
                            V:=Valuation(delta,2);
                            end if;
                            B:=delta/(2^V);

                            if IsOdd(V) or (B-1 mod 8 ne 0) then
                      //      count:=count+1;
                       //         print C,"(a1,a2)= (", a1 ,",", a2,")";
                    //print "(",a1, a2,")";
                            end if;
                        end if;
      //  end if;

J:=q^2+a1*q+a1+a2+1;
Rat:=#RationalPoints(C);
Jac:=Jacobian(C);
R:=RingOfIntegers();
if R!J mod 8 eq 0 then

for ii:=1 to Floor(J) do
DP:=Points(Jac)[ii];
if HasOrder(DP,8) then
for jj:=1 to Floor(J) do
DQ:=Points(Jac)[jj];
if HasOrder(DQ,8) then
WeilPairing(DP,DQ,3);
end if;
end for;

//print DD, "has order 8, a=", a," b= ", b;
end if;
end for;
count;

end if;
count:=0;
end if;
end for;
end for;

print "done";


Output: Magma V2.11-10    Tue Dec 13 2005 12:08:27 on modular  [Seed = 3127310721]
   -------------------------------------


>> WeilPairing(DP,DQ,3);
              ^
Runtime error in 'WeilPairing': divisors must be m-torsion elements
done

Total time: 0.780 seconds, Total memory usage: 3.72MB


'146.6.1'
************** MAGMA *****************
Host 146.6.139.217 (146.6.139.217)
Time: Tue Dec 13 12:08:14 2005

Input: m:=5;
q:=2^m;
F1:=GF(q);
F2:=GF(q^2);
Trace0:={@[email protected]};

for i:=1 to q-1 do
dd:=F1.1^i;
if Trace(dd) eq 0 then
Trace0:=Trace0 join {@[email protected]};
end if;
end for;

d:=0;

for i:=1 to q-1 do
a:=F1.1^i;

        for j:=1 to #Trace0 do
            b:=Trace0[j];

            P<x>:=PolynomialRing(F1);
                C:=HyperellipticCurve(a*x^5+b*x^3+x,x);
                N1:=#C; //over Fq

            R<z>:=PolynomialRing(F2);
                CC:=HyperellipticCurve(a*z^5+b*z^3+z,z);
                N2:=#CC; //over Fq^2;

                a1:=N1-q-1;
                a2:=(N2-1-q^2+a1^2)/2;

        if not IsSquare(a1^2-4*a2+8*q) then
                        if IsDivisibleBy(a2, 2^Ceiling(m/2)) then
                            delta:=(a2+2*q)^2-4*q*a1^2;
                            V:=0;
                            if delta ne 0 then
                            V:=Valuation(delta,2);
                            end if;
                            B:=delta/(2^V);

                            if IsOdd(V) or (B-1 mod 8 ne 0) then
                      //      count:=count+1;
                       //         print C,"(a1,a2)= (", a1 ,",", a2,")";
                    //print "(",a1, a2,")";
                            end if;
                        end if;
      //  end if;

J:=q^2+a1*q+a1+a2+1;
Rat:=#RationalPoints(C);
Jac:=Jacobian(C);
R:=RingOfIntegers();
if R!J mod 8 eq 0 then

for ii:=1 to Floor(J) do
DP:=Points(Jac)[ii];
if HasOrder(DP,8) then
for jj:=1 to Floor(J) do
DQ:=Points(Jac)[jj];
if HasOrder(DQ,8) then
WeilPairing(DP,DQ,3);
end if;
end for;

//print DD, "has order 8, a=", a," b= ", b;
end if;
end for;
count;

end if;
count:=0;
end if;
end for;
end for;

print "done";


Output: Magma V2.11-10    Tue Dec 13 2005 12:08:14 on modular  [Seed = 3043494267]
   -------------------------------------


>> count;
   ^
User error: Identifier 'count' has not been declared or assigned
done

Total time: 0.190 seconds, Total memory usage: 3.34MB


'146.6.1'
************** MAGMA *****************
Host 146.6.139.217 (146.6.139.217)
Time: Tue Dec 13 12:07:59 2005

Input: m:=5;
q:=2^m;
F1:=GF(q);
F2:=GF(q^2);
Trace0:={@[email protected]};

for i:=1 to q-1 do
dd:=F1.1^i;
if Trace(dd) eq 0 then
Trace0:=Trace0 join {@[email protected]};
end if;
end for;

d:=0;

for i:=1 to q-1 do
a:=F1.1^i;

        for j:=1 to #Trace0 do
            b:=Trace0[j];

            P<x>:=PolynomialRing(F1);
                C:=HyperellipticCurve(a*x^5+b*x^3+x,x);
                N1:=#C; //over Fq

            R<z>:=PolynomialRing(F2);
                CC:=HyperellipticCurve(a*z^5+b*z^3+z,z);
                N2:=#CC; //over Fq^2;

                a1:=N1-q-1;
                a2:=(N2-1-q^2+a1^2)/2;

        if not IsSquare(a1^2-4*a2+8*q) then
                        if IsDivisibleBy(a2, 2^Ceiling(m/2)) then
                            delta:=(a2+2*q)^2-4*q*a1^2;
                            V:=0;
                            if delta ne 0 then
                            V:=Valuation(delta,2);
                            end if;
                            B:=delta/(2^V);

                            if IsOdd(V) or (B-1 mod 8 ne 0) then
                      //      count:=count+1;
                       //         print C,"(a1,a2)= (", a1 ,",", a2,")";
                    //print "(",a1, a2,")";
                            end if;
                        end if;
      //  end if;

J:=q^2+a1*q+a1+a2+1;
Rat:=#RationalPoints(C);
Jac:=Jacobian(C);
R:=RingOfIntegers();
if R!J mod 8 eq 0 then

for ii:=1 to Floor(J) do
DP:=Points(Jac)[ii];
if HasOrder(DP,8) then
for jj:=1 to Floor(J) do
DQ:=Points(Jac)[jj];
if HasOrder(DQ,8) then
WeilPairing(DP,DQ,3);
end if
end for

//print DD, "has order 8, a=", a," b= ", b;
end if;
end for;
count;

end if;
count:=0;
end if;
end for;
end for;

print "done";


Output: Magma V2.11-10    Tue Dec 13 2005 12:07:58 on modular  [Seed = 1318318736]
   -------------------------------------


>> end for
   ^
User error: bad syntax

>> end if;
   ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

>> count;
   ^
User error: Identifier 'count' has not been declared or assigned

>> end if;
   ^
User error: bad syntax

>> end if;
   ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax
done

Total time: 0.180 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 11:58:23 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   

[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
S, f := StandardForm(C);
S;

Output: Magma V2.11-10    Tue Dec 13 2005 11:58:22 on modular  [Seed = 449291396]
   -------------------------------------

[56, 21] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0
    0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1
    0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
    1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1
    1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1
    0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0
    0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0
    1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0
    0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1
    0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1
    1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1
    0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1
    1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1
    0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0
    1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0
    0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0
    0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1
    1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1
    0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0
    0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1
    0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 11:39:59 2005

Input: R<x>:=PolynomialRing(GF(2));
f:=x^155+x^62+1;
K<a>:=ext<GF(2)|f>;

I:=ideal<GF(2)|f>;

Output: Magma V2.11-10    Tue Dec 13 2005 11:39:59 on modular  [Seed = 804427072]
   -------------------------------------


>> I:=ideal<GF(2)|f>;;
           ^
Runtime error: No constructor provided for this type of object

Total time: 0.190 seconds, Total memory usage: 3.24MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 11:38:59 2005

Input: R<x>:=PolynomialRing(GF(2));
f:=x^155+x^62+1;
K<a>:=ext<GF(2)|f>;

I:=Ideal<GF(2)|f>;

Output: Magma V2.11-10    Tue Dec 13 2005 11:38:59 on modular  [Seed = 1055097901]
   -------------------------------------


>> I:=Ideal<GF(2)|f>;;
           ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 11:37:27 2005

Input: R<x>:=PolynomialRing(GF(2));
f:=x^155+x^62+1;
K<a>:=ext<GF(2)|f>;

Decomposition(K);

Output: Magma V2.11-10    Tue Dec 13 2005 11:37:27 on modular  [Seed = 921406913]
   -------------------------------------


>> Decomposition(K);;
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: FldFin

Total time: 0.180 seconds, Total memory usage: 3.24MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 11:36:34 2005

Input: R<x>:=PolynomialRing(GF(2));
f:=x^155+x^62+1;
K<a>:=ext<GF(2)|f>;

Decomposition(K,f);

Output: Magma V2.11-10    Tue Dec 13 2005 11:36:33 on modular  [Seed = 837585552]
   -------------------------------------


>> Decomposition(K,f);;
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: FldFin, RngUPolElt[FldFin]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 11:34:06 2005

Input: R<x>:=PolynomialRing(GF(2));
f:=x^155+x^62+1;
K<a>:=ext<GF(2)|f>;

Decomposition(K,f);

Output: Magma V2.11-10    Tue Dec 13 2005 11:34:05 on modular  [Seed = 3440408833]
   -------------------------------------


>> Decomposition(K,f);;
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: FldFin, RngUPolElt[FldFin]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 11:32:13 2005

Input: R<x>:=PolynomialRing(GF(2));
f:=x^155+x^62+1;
K<a>:=ext<GF(2)|f>;

Decomposition(f);

Output: Magma V2.11-10    Tue Dec 13 2005 11:32:13 on modular  [Seed = 3340399483]
   -------------------------------------


>> Decomposition(f);;
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: RngUPolElt[FldFin]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 11:31:11 2005

Input: R<x>:=PolynomialRing(GF(2));
f:=x^155+x^62+1;
K<a>:=ext<GF(2)|definingPolynomial>;

Decomposition(f);

Output: Magma V2.11-10    Tue Dec 13 2005 11:31:11 on modular  [Seed = 3223155902]
   -------------------------------------


>> K<a>:=ext<GF(2)|definingPolynomial>;
                   ^
User error: Identifier 'definingPolynomial' has not been declared or assigned

>> Decomposition(f);;
                ^
Runtime error in 'Decomposition': Bad argument types
Argument types given: RngUPolElt[FldFin]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 11:29:51 2005

Input: R<x>:=PolynomialRing(GF(2));
definingPolynomial:=x^155+x^62+1;
K<a>:=ext<GF(2)|definingPolynomial>;

Decomposition(f);

Output: Magma V2.11-10    Tue Dec 13 2005 11:29:51 on modular  [Seed = 3540936221]
   -------------------------------------


>> Decomposition(f);;
                 ^
User error: Identifier 'f' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 11:26:17 2005

Input: > K := FiniteField(2);
> E := LinearCode<K, 16 | 
[1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0]>;
> WeightDistribution(E);


Output: Magma V2.11-10    Tue Dec 13 2005 11:26:17 on modular  [Seed = 3979368693]
   -------------------------------------

[ <0, 1>, <2, 105>, <4, 1365>, <6, 5005>, <8, 6435>, <10, 3003>, <12, 455>, <14,
15> ]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 10:54:53 2005

Input: > K := FiniteField(2);
> C := LinearCode<K, 56 | 
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
> D:=Dual(C);
> (D meet C) eq C;



Output: Magma V2.11-10    Tue Dec 13 2005 10:54:53 on modular  [Seed = 2354127216]
   -------------------------------------

true

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 10:52:23 2005

Input: > K := FiniteField(2);
> C := LinearCode<K, 56 | 
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
> D:=Dual(C);
> (d meet C) eq C;



Output: Magma V2.11-10    Tue Dec 13 2005 10:52:22 on modular  [Seed = 2220435843]
   -------------------------------------


>>   (d meet C) eq C;
      ^
User error: Identifier 'd' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 10:40:50 2005

Input: > K := FiniteField(2);
> K56 := VectorSpace(K, 56);
> C := LinearCode(sub<K56 |  
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>);
> D:=Hull(C);
> WeightDistribution(D);


Output: Magma V2.11-10    Tue Dec 13 2005 10:40:50 on modular  [Seed = 2671916844]
   -------------------------------------


>>   D:=Hull(C);
        ^
User error: Identifier 'Hull' has not been declared or assigned

>>   WeightDistribution(D);
                        ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 10:35:53 2005

Input: > K := FiniteField(2);
> K56 := VectorSpace(K, 56);
> C := LinearCode(sub<K56 |  
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
> D:=Hull(C);
> WeightDistribution(D);


Output: Magma V2.11-10    Tue Dec 13 2005 10:35:53 on modular  [Seed = 2876637891]
   -------------------------------------


>> 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
                                                              ^
User error: bad syntax

>>   D:=Hull(C);
             ^
User error: Identifier 'C' has not been declared or assigned

>>   WeightDistribution(D);
                        ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 10:25:19 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |  
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
> D:=Hull(C);
> WeightDistribution(D);


Output: Magma V2.11-10    Tue Dec 13 2005 10:25:19 on modular  [Seed = 2726233676]
   -------------------------------------


>>   D:=Hull(C);
        ^
User error: Identifier 'Hull' has not been declared or assigned

>>   WeightDistribution(D);
                        ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 10:23:39 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |  
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
D:=Hull(C);
WeightDistribution(D);


Output: Magma V2.11-10    Tue Dec 13 2005 10:23:39 on modular  [Seed = 3210877941]
   -------------------------------------


>> D:=Hull(C);
      ^
User error: Identifier 'Hull' has not been declared or assigned

>> WeightDistribution(D);
                      ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.210 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 10:20:00 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |  
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
C;
WeightDistribution(C);


Output: Magma V2.11-10    Tue Dec 13 2005 10:19:57 on modular  [Seed = 820876674]
   -------------------------------------

[56, 21] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0
    0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1
    0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1
    1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1
    0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1
    1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1
    0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1]
[0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0
    0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0
    1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0
    0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1
    0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1
    1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1
    0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1
    1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1
    0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0
    1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0
    0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0
    0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1
    1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1
    0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0
    0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1
    0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1]
[ <0, 1>, <16, 5082>, <20, 91168>, <24, 507045>, <28, 890560>, <32, 507045>, 
<36, 91168>, <40, 5082>, <56, 1> ]

Total time: 0.240 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 10:16:57 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |  
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
E := Hull(C);
E;
WeightDistribution(E);


Output: Magma V2.11-10    Tue Dec 13 2005 10:16:56 on modular  [Seed = 2671917382]
   -------------------------------------


>> E := Hull(C);
        ^
User error: Identifier 'Hull' has not been declared or assigned

>> E;
   ^
User error: Identifier 'E' has not been declared or assigned

>> WeightDistribution(E);
                      ^
User error: Identifier 'E' has not been declared or assigned

Total time: 0.220 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 10:01:43 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |  
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
D := Dual(C);
WeightDistribution(C);
time WeightDistribution(D);

Output: Magma V2.11-10    Tue Dec 13 2005 10:01:42 on modular  [Seed = 4096349653]
   -------------------------------------

[ <0, 1>, <16, 5082>, <20, 91168>, <24, 507045>, <28, 890560>, <32, 507045>, 
<36, 91168>, <40, 5082>, <56, 1> ]
[ <0, 1>, <8, 1155>, <10, 34496>, <12, 539280>, <14, 5480640>, <16, 40029297>, 
<18, 200963840>, <20, 755023808>, <22, 2027262720>, <24, 4185896715>, <26, 
6289084032>, <28, 7351106400>, <30, 6289084032>, <32, 4185896715>, <34, 
2027262720>, <36, 755023808>, <38, 200963840>, <40, 40029297>, <42, 5480640>, 
<44, 539280>, <46, 34496>, <48, 1155>, <56, 1> ]
Time: 0.020

Total time: 0.250 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 10:00:16 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
//xt := i + 2;
xt := 8;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n - 1);
    v := Random(n - 1);
    w := tate(u*G, v*Gt);
    if w ne g^((u*v) mod n) then
        "Failure: u =", u, ", v =", v, "e(u*P,v*Q) =", w, ", e(P,Q)^(uv) =", g^((u*v) mod n);
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 10:00:15 on modular  [Seed = 164932481]
   -------------------------------------

g = (1414620835193373657646613880233559577407734609545*i + 
    352489175314961464607671418528001817189092256541)*z^5 + 
    (904802261065103105936668720505067133656667597074*i + 
    1343248922269291340494538393490943353845819222256)*z^4 + 
    (1025700017505207783921241027028089077317301724291*i + 
    1267567142236668396047190065512596226428512971416)*z^3 + 
    (283587609846347412879109527640610607003328134432*i + 
    250487955904041646310509260856358041239663937723)*z^2 + 
    (110054808378578108265445578093874268052578876998*i + 
    202041545854984388890408940644851972139794936772)*z + 
    257093848091331658607960702914357017287219708568*i + 
    652950073647454119068347296682657355787566777234
Failure: u = 505653466152672793617695632599288515920022369214 , v = 
813309314074995504442616266927015985129671509525 e(u*P,v*Q) = 
    (229450318520897930832122824950759136162186600899*i + 
    171458666541069865322322784204702213676643928600)*z^5 + 
    (1123336210201860974010594496403076935746616156201*i + 
    382509869157557354897123314935302020523067652238)*z^4 + 
    (195956015357740925670293015392589736976005190419*i + 
    1201060680146586880867752998079193262658782520318)*z^3 + 
    (1400183652328377308210652428671451994834327508147*i + 
    885783581485769151127555190406908658009200060139)*z^2 + 
    (241990578305321134124934647372233092586143696750*i + 
    353283743758609339844557914979526193600469875967)*z + 
    69301698278701722581645298580459933625029213350*i + 
    522130179428839937361552509967162010658032702262
, e(P,Q)^(uv) = (1233480993554786834008498621906536758921898377565*i + 
    1190015354691216118850119495146059439731677746380)*z^5 + 
    (921756594327110983814290309172804473768320708717*i + 
    738420790495346685113640877223616173148157182434)*z^4 + 
    (1448167631698704692933635090700677473693607566307*i + 
    467911266345108570245537574526004995346892189176)*z^3 + 
    (819222557435172257255808600604347664799809662153*i + 
    691163176033377731593142083640280484981447850039)*z^2 + 
    (1178974401966800441343583985193986104164302821005*i + 
    276511259554730579432106796424120788700936371162)*z + 
    646813776638959146887930847368281873288578357077*i + 
    1043047602020859885512585427844085790318024216544

Total time: 1.080 seconds, Total memory usage: 3.34MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 09:47:58 2005

Input: K := FiniteField(2);
> D := LinearCode<K, 56 |  
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
> aut := AutomorphismGroup(D);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(D);

Output: Magma V2.11-10    Tue Dec 13 2005 09:47:57 on modular  [Seed = 1552007222]
   -------------------------------------

7
[ <7, 1> ]
    G
    |  Cyclic(7)
    1
{
    (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14)(15, 16, 17, 18, 19, 20, 
        21)(22, 23, 24, 25, 26, 27, 28)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 
        39, 40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)
}
false

Total time: 0.280 seconds, Total memory usage: 5.51MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 09:47:01 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |  
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);

Output: Magma V2.11-10    Tue Dec 13 2005 09:47:01 on modular  [Seed = 1385156544]
   -------------------------------------

7
[ <7, 1> ]
    G
    |  Cyclic(7)
    1
{
    (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14)(15, 16, 17, 18, 19, 20, 
        21)(22, 23, 24, 25, 26, 27, 28)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 
        39, 40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)
}
false

Total time: 0.250 seconds, Total memory usage: 5.51MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Tue Dec 13 09:43:19 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);

Output: Magma V2.11-10    Tue Dec 13 2005 09:43:18 on modular  [Seed = 1468713510]
   -------------------------------------

1344
[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
{
    (3, 4)(7, 8),
    (4, 6)(5, 7),
    (4, 7)(5, 6),
    (1, 2)(5, 6),
    (2, 4, 3)(6, 8, 7)
}
true

Total time: 0.200 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 09:41:20 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
//xt := i + 2;
xt := 8;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
/*
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;
*/
for j in [1..100] do
    u := Random(n - 1);
    v := Random(n - 1);
    if tate(u*G, v*Gt) ne g^((u*v) mod n) then
        "Failure: u =", u, ", v =", v;
        quit;
    end if;
end for;
"Success!";


Output: Magma V2.11-10    Tue Dec 13 2005 09:41:19 on modular  [Seed = 1840313237]
   -------------------------------------

g = (46880789303416607498834709687225916309524281274*i + 
    1109012449181828800537777171392783676528166634278)*z^5 + 
    (904802261065103105936668720505067133656667597074*i + 
    1343248922269291340494538393490943353845819222256)*z^4 + 
    (435801606991582481224207562892696416399957166528*i + 
    193934482260121869098258524408189267288745919403)*z^3 + 
    (283587609846347412879109527640610607003328134432*i + 
    250487955904041646310509260856358041239663937723)*z^2 + 
    (1351446816118212156880003011826911225664680013821*i + 
    1259460078641805876255039649275933521577463954047)*z + 
    257093848091331658607960702914357017287219708568*i + 
    652950073647454119068347296682657355787566777234
Failure: u = 1026132414533535312271167998032452174431467642015 , v = 
607317891842996534038173466812558720729177303044

Total time: 1.060 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 09:30:18 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
//xt := i + 2;
xt := 8;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    /*
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    */
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^12-1) eq 1);
"g^n =", g^n;


Output: Magma V2.11-10    Tue Dec 13 2005 09:30:15 on modular  [Seed = 1924131826]
   -------------------------------------

g = (1414620835193373657646613880233559577407734609545*i + 
    352489175314961464607671418528001817189092256541)*z^5 + 
    (904802261065103105936668720505067133656667597074*i + 
    1343248922269291340494538393490943353845819222256)*z^4 + 
    (1025700017505207783921241027028089077317301724291*i + 
    1267567142236668396047190065512596226428512971416)*z^3 + 
    (283587609846347412879109527640610607003328134432*i + 
    250487955904041646310509260856358041239663937723)*z^2 + 
    (110054808378578108265445578093874268052578876998*i + 
    202041545854984388890408940644851972139794936772)*z + 
    257093848091331658607960702914357017287219708568*i + 
    652950073647454119068347296682657355787566777234
g^(p^1-1): true
g^(p^2-1): true
g^(p^3-1): true
g^(p^4-1): true
g^(p^5-1): true
g^(p^6-1): true
g^(p^7-1): true
g^(p^8-1): true
g^(p^9-1): true
g^(p^10-1): true
g^(p^11-1): true
g^(p^12-1): true
g^n = 1

Total time: 2.600 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 09:28:11 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := i + 2;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
for j in [1..12] do
    print "g^(p^" * Sprint(j) * "-1) = " * Sprint(g^(p^j-1));
end for;
"g^n =", g^n;


Output: Magma V2.11-10    Tue Dec 13 2005 09:28:08 on modular  [Seed = 2655192982]
   -------------------------------------

P  = (1 : 2 : 1)
Q' = (i + 2 : 1097950022558348869462494891919937327680507168109*i + 
    1374283222983568961963002763601919595127481124512 : 1)
Q  = ((i + 2)*z^2 : (1097950022558348869462494891919937327680507168109*i + 
    1374283222983568961963002763601919595127481124512)*z^3 : 1)
g = (123909007522715632304234432926990441159731420430*i + 
    637508010256500182107280699368993348477341084485)*z^5 + 
    (688703507104756931070001853914995131005373541312*i + 
    1002621352581475249329708955843984496240073153982)*z^4 + 
    (608846424657090324998119234825851616974125548764*i + 
    771482020725020581050629871627202529613821639823)*z^3 + 
    (1392434018234511176428044389335844610478592711217*i + 
    473331107538064635840791020785366158595476919127)*z^2 + 
    (73970378918706542820629598671516884756426271661*i + 
    365943832704743787495421878796345795274953421973)*z + 
    616166846676061100095127430332774495441755394581*i + 
    889255287756560160849573452496040306572455585395
g^(p^1-1) = (748100618927567348520741622873551546451532782022*i + 
1428699130224630511049471936323405187567302837671)*z^5 + 
(1202680812184493569478300721391313577308119778263*i + 
313447253330080409810020430322639687095227202514)*z^4 + 
(896962745306077156991764130250048502701811544250*i + 
75030114724933747382754664337864814318468370719)*z^3 + 
(333682831282116263631143017468030399561367002231*i + 
518405572876237815324490177632651602018332790765)*z^2 + 
(1112317314850298844232882970368687655422664826708*i + 
560782544915172117676888817418082341837354667733)*z + 
1202838306203487510142528951450976199443662125144*i + 
795069427093050539880893267448617311116978407546
g^(p^2-1) = (1122685762559073106420486640172303029900241318667*i + 
1206761843969459490842516022375418025481873864298)*z^5 + 
(3817024364748341053470651752544249413211110060*i + 
92074379894423550543412574098909660792084933016)*z^4 + 
(608846424657090324998119234825851616974125548764*i + 
771482020725020581050629871627202529613821639823)*z^3 + 
(477186809706685400548284839616627303398814604581*i + 
1353293254655497653064288440912729947389627707084)*z^2 + 
(708592972296574786248902668360725858769675156568*i + 
566475776092548476468859447971519767492233615991)*z + 
616166846676061100095127430332774495441755394581*i + 
889255287756560160849573452496040306572455585395
g^(p^3-1) = (1357106999709464496564779036298599057498303412530*i + 
1345682320959266667240129620417040749623418914188)*z^5 + 
(936139532752018606210117538341071166608350863727*i + 
1112461501477852426997296904293113682769958766774)*z^4 + 
(1445405172445096850777244515807849246142141374340*i + 
396466674385106777111606626855996450744375790171)*z^3 + 
(1461250712521757914096163977919390965791567384854*i + 
244970246429598896709919226014995935882868586820)*z^2 + 
(542551411651261070353031322827794497138348015296*i + 
429807684156175367374279713695611598069895859239)*z + 
70531838254713320311910681453696149021611168678*i + 
1398834529239549175114023695374662216300177982250
g^(p^4-1) = (1221509504491967374311557208672867933832795980673*i + 
200467472176772056987212698380766546792219162971)*z^5 + 
(208862746409985936264596906005246300650626057668*i + 
565357618624448102009812399714319141941210262495)*z^4 + 
(865756177282313545985213216550036708550476280949*i + 
475475525215527373084617709122508974760880884335)*z^3 + 
(102466015727909809069678183573961098275241875184*i + 
940151235303014027110245043307168921216332322768)*z^2 + 
(928922738858698562216100850689154274539784497877*i + 
382002999584106301024558712410303674095683347609)*z + 
1220974658126123565670019751888593761044993991185*i + 
211811947018249923223576976718524137383767937965
g^(p^5-1) = (594480147410955283734684832159447099240412938228*i + 
1007447468906095875580426526654019572773339214368)*z^5 + 
(1152066755303591353030630678326466707035079216340*i + 
651594961867943713451573799740600135483141099859)*z^4 + 
(49501392213291562027375381267081647404991522810*i + 
820710015151236425244004586118888126082585441078)*z^3 + 
(42188653754860119450135480418886642353674596443*i + 
562408702302581793941475002165818938687417258094)*z^2 + 
(1091572228871275931758790486093603710299273846570*i + 
577436592715763274817514347647367029829638669007)*z + 
1168565180281449525586662304102209555431570678308*i + 
503582600681258840386198926408111711693060441073
g^(p^6-1) = (205768684348313624077451572794465353568914781421*i + 
613950226393615708182994901900063381875511405659)*z^5 + 
(1428633672987200370786940114820930632812523417902*i + 
395314511348759603485431448487808080038157695517)*z^4 + 
(881979103651631189249974992863662825116960349537*i + 
1044381106242866386024323569275011144406191731131)*z^3 + 
(377475555156278737030694625815440794829353520650*i + 
60549325767510300874857944491779135450365424950)*z^2 + 
(904476028311783023806480875092919429317592811440*i + 
654508681633842315960851796564179216185709460867)*z + 
826543425518806376820411130172467469135354246707*i + 
546674685375929320723432354108401487302836191956
g^(p^7-1) = (334999190429734450302032977239633601705995714949*i + 
285499081478684180346094108130235958500726170807)*z^5 + 
(1357641212310828158490838523101409841505272979404*i + 
678284707222532143244512307089503927268688656266)*z^4 + 
(447713965858424633050352197649395842462816234715*i + 
523942895907349573254753909344390113077006213603)*z^3 + 
(395448289533461064020784297720245760316432679996*i + 
256449527939203012159253238775693631557658125017)*z^2 + 
(825189319832069956822612513847208165005287290855*i + 
333752408118167725005777483986738208826843204644)*z + 
292936444215340739558786285818575938285688212511*i + 
503582600681258840386198926408111711693060441073
g^(p^8-1) = (128794472520144390825537958245889556576532668457*i + 
682817146795319322173041394863892996788054910205)*z^5 + 
(712683874015386917422759238642315687393680373361*i + 
1227924079489556276578945161248737876531470377844)*z^4 + 
(595745447214476719160235373370748785166782609870*i + 
986026099281262892060830880798276518956378006484)*z^3 + 
(375673708125247397107051660343678979770619117775*i + 
114357758639702456761704170918133809768845643944)*z^2 + 
(1411889287093050769181126017526789790323252735684*i + 
1105315081259072298561198519568055599119405178147)*z + 
1220974658126123565670019751888593761044993991185*i + 
211811947018249923223576976718524137383767937965
g^(p^9-1) = (1223692038621048430153872436913389348975101235031*i + 
474621643755870221635939468034787852720049039479)*z^5 + 
(936139532752018606210117538341071166608350863727*i + 
349040123018937838148151685627671810947300124045)*z^4 + 
(1376144652516737512570670115379753945711985528623*i + 
1373311158685001552683394130170484212465308688527)*z^3 + 
(244970246429598896709919226014995935882868586820*i + 
1461250712521757914096163977919390965791567384854)*z^2 + 
(51496949206574234593005076323843447627546727734*i + 
22372145650816023655116449432656061648752517842)*z + 
1390969786242076944833537908467089344695647722141*i + 
1398834529239549175114023695374662216300177982250
g^(p^10-1) = (214906854415001526420727516821492022657286151722*i + 
1078733394767620857341100458097159613475302832855)*z^5 + 
(768981093027284993021976084253246113298674239447*i + 
366805892020891465272327059977891336685100803821)*z^4 + 
(608846424657090324998119234825851616974125548764*i + 
771482020725020581050629871627202529613821639823)*z^3 + 
(1053382421052383953314567950889099073557110465840*i + 
1096378886800018241385817718143474881449413155427)*z^2 + 
(678938273281508936075916322888542750191157462590*i + 
529082015699498001181167263152919930950071852855)*z + 
616166846676061100095127430332774495441755394581*i + 
889255287756560160849573452496040306572455585395
g^(p^11-1) = (548580783601665930616001142054617430470218498646*i + 
1451628029083941079148995842838738809076287723525)*z^5 + 
(2545939521711331370283095426719602351824833799*i + 
1344046085896870808486244472445559740184244945852)*z^4 + 
(837618043175865668846772504097006035270479350279*i + 
786494693152924360802801900817858926731509706423)*z^3 + 
(1402153388011088316650991466733555001741554598260*i + 
247983074468381684089738348912296989265022486477)*z^2 + 
(1185906070039435994832468343291972442612922376685*i + 
305123309751637633980829646230021828644012617207)*z + 
258663318293302755002919638469809294273596765675*i + 
795069427093050539880893267448617311116978407546
g^(p^12-1) = 1
g^n = 1

Total time: 2.589 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 09:25:43 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
//xt := i + 2;
xt := 8;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    //"P  =", P; "Q' =", Qt; "Q  =", Q;
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
for j in [1..11] do
    print "g^(p^" * Sprint(j) * "-1): " * Sprint(g^(p^j-1) ne 1);
end for;
print "g^(p^12-1): " * Sprint(g^(p^j-1) eq 1);
"g^n =", g^n;


Output: Magma V2.11-10    Tue Dec 13 2005 09:25:40 on modular  [Seed = 2538212611]
   -------------------------------------

g = (46880789303416607498834709687225916309524281274*i + 
    1109012449181828800537777171392783676528166634278)*z^5 + 
    (904802261065103105936668720505067133656667597074*i + 
    1343248922269291340494538393490943353845819222256)*z^4 + 
    (435801606991582481224207562892696416399957166528*i + 
    193934482260121869098258524408189267288745919403)*z^3 + 
    (283587609846347412879109527640610607003328134432*i + 
    250487955904041646310509260856358041239663937723)*z^2 + 
    (1351446816118212156880003011826911225664680013821*i + 
    1259460078641805876255039649275933521577463954047)*z + 
    257093848091331658607960702914357017287219708568*i + 
    652950073647454119068347296682657355787566777234
g^(p^1-1): true
g^(p^2-1): true
g^(p^3-1): true
g^(p^4-1): true
g^(p^5-1): true
g^(p^6-1): true
g^(p^7-1): true
g^(p^8-1): true
g^(p^9-1): true
g^(p^10-1): true
g^(p^11-1): true

>> print "g^(p^12-1): " * Sprint(g^(p^j-1) eq 1);
                                      ^
User error: Identifier 'j' has not been declared or assigned
g^n = 1

Total time: 2.640 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 09:21:25 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := i + 2;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    return miller(n, P, Q)^chi;
end function;

g := tate(G, Gt);
"g =", g;
for j in [1..12] do
    print "g^(p^" * Sprint(j) * "-1) = " * Sprint(g^(p^j-1));
end for;
"g^n =", g^n;


Output: Magma V2.11-10    Tue Dec 13 2005 09:21:17 on modular  [Seed = 2943497218]
   -------------------------------------

P  = (1 : 2 : 1)
Q' = (i + 2 : 363551601938441395682953698000848166036751722710*i + 
    87218401513221303182445826318865898589777766307 : 1)
Q  = ((i + 2)*z^2 : (363551601938441395682953698000848166036751722710*i + 
    87218401513221303182445826318865898589777766307)*z^3 : 1)
g = (1337592616974074632841214156993795052557527470389*i + 
    823993614240290083038167890551792145239917806334)*z^5 + 
    (688703507104756931070001853914995131005373541312*i + 
    1002621352581475249329708955843984496240073153982)*z^4 + 
    (852655199839699940147329355094933876743133342055*i + 
    690019603771769684094818718293582964103437250996)*z^3 + 
    (1392434018234511176428044389335844610478592711217*i + 
    473331107538064635840791020785366158595476919127)*z^2 + 
    (1387531245578083722324818991249268608960832619158*i + 
    1095557791792046477650026711124439698442305468846)*z + 
    616166846676061100095127430332774495441755394581*i + 
    889255287756560160849573452496040306572455585395
g^(p^1-1) = (713401005569222916624706967047233947265726108797*i + 
32802494272159754095976653597380306149956053148)*z^5 + 
(1202680812184493569478300721391313577308119778263*i + 
313447253330080409810020430322639687095227202514)*z^4 + 
(564538879190713108153684459670736991015447346569*i + 
1386471509771856517762693925582920679398790520100)*z^3 + 
(333682831282116263631143017468030399561367002231*i + 
518405572876237815324490177632651602018332790765)*z^2 + 
(349184309646491420912565619552097838294594064111*i + 
900719079581618147468559772502703151879904223086)*z + 
1202838306203487510142528951450976199443662125144*i + 
795069427093050539880893267448617311116978407546
g^(p^2-1) = (338815861937717158724961949748482463817017572152*i + 
254739780527330774302932567545367468235385026521)*z^5 + 
(3817024364748341053470651752544249413211110060*i + 
92074379894423550543412574098909660792084933016)*z^4 + 
(852655199839699940147329355094933876743133342055*i + 
690019603771769684094818718293582964103437250996)*z^3 + 
(477186809706685400548284839616627303398814604581*i + 
1353293254655497653064288440912729947389627707084)*z^2 + 
(752908652200215478896545921560059634947583734251*i + 
895025848404241788676589141949265726225025274828)*z + 
616166846676061100095127430332774495441755394581*i + 
889255287756560160849573452496040306572455585395
g^(p^3-1) = (104394624787325768580669553622186436218955478289*i + 
115819303537523597905318969503744744093839976631)*z^5 + 
(936139532752018606210117538341071166608350863727*i + 
1112461501477852426997296904293113682769958766774)*z^4 + 
(16096452051693414368204074112936247575117516479*i + 
1065034950111683488033841963064789042972883100648)*z^3 + 
(1461250712521757914096163977919390965791567384854*i + 
244970246429598896709919226014995935882868586820)*z^2 + 
(918950212845529194792417267092990996578910875523*i + 
1031693940340614897771168876225173895647363031580)*z + 
70531838254713320311910681453696149021611168678*i + 
1398834529239549175114023695374662216300177982250
g^(p^4-1) = (239992120004822890833891381247917559884462910146*i + 
1261034152320018208158235891540018946925039727848)*z^5 + 
(208862746409985936264596906005246300650626057668*i + 
565357618624448102009812399714319141941210262495)*z^4 + 
(595745447214476719160235373370748785166782609870*i + 
986026099281262892060830880798276518956378006484)*z^3 + 
(102466015727909809069678183573961098275241875184*i + 
940151235303014027110245043307168921216332322768)*z^2 + 
(532578885638091702929347739231631219177474392942*i + 
1079498624912683964120889877510481819621575543210)*z + 
1220974658126123565670019751888593761044993991185*i + 
211811947018249923223576976718524137383767937965
g^(p^5-1) = (867021477085834981410763757761338394476845952591*i + 
454054155590694389565022063266765920943919676451)*z^5 + 
(1152066755303591353030630678326466707035079216340*i + 
651594961867943713451573799740600135483141099859)*z^4 + 
(1412000232283498703118073208653703846312267368009*i + 
640791609345553839901444003801897367634673449741)*z^3 + 
(42188653754860119450135480418886642353674596443*i + 
562408702302581793941475002165818938687417258094)*z^2 + 
(369929395625514333386658103827181783417985044249*i + 
884065031781026990327934242273418463887620221812)*z + 
1168565180281449525586662304102209555431570678308*i + 
503582600681258840386198926408111711693060441073
g^(p^6-1) = (1255732940148476641067997017126320140148344109398*i + 
847551398103174556962453688020722111841747485160)*z^5 + 
(1428633672987200370786940114820930632812523417902*i + 
395314511348759603485431448487808080038157695517)*z^4 + 
(579522520845159075895473597057122668600298541282*i + 
417120518253923879121125020645774349311067159688)*z^3 + 
(377475555156278737030694625815440794829353520650*i + 
60549325767510300874857944491779135450365424950)*z^2 + 
(557025596185007241338967714827866064399666079379*i + 
806992942862947949184596793356606277531549429952)*z + 
826543425518806376820411130172467469135354246707*i + 
546674685375929320723432354108401487302836191956
g^(p^7-1) = (1126502434067055814843415612681151892011263175870*i + 
1176002543018106084799354481790549535216532720012)*z^5 + 
(1357641212310828158490838523101409841505272979404*i + 
678284707222532143244512307089503927268688656266)*z^4 + 
(1013787658638365632095096392271389651254442656104*i + 
937558728589440691890694680576395380640252677216)*z^3 + 
(395448289533461064020784297720245760316432679996*i + 
256449527939203012159253238775693631557658125017)*z^2 + 
(636312304664720308322836076073577328711971599964*i + 
1127749216378622540139671105934047284890415686175)*z + 
292936444215340739558786285818575938285688212511*i + 
503582600681258840386198926408111711693060441073
g^(p^8-1) = (1332707151976645874319910631674895937140726222362*i + 
778684477701470942972407195056892496929203980614)*z^5 + 
(712683874015386917422759238642315687393680373361*i + 
1227924079489556276578945161248737876531470377844)*z^4 + 
(865756177282313545985213216550036708550476280949*i + 
475475525215527373084617709122508974760880884335)*z^3 + 
(375673708125247397107051660343678979770619117775*i + 
114357758639702456761704170918133809768845643944)*z^2 + 
(49612337403739495964322572393995703394006155135*i + 
356186543237717966584250070352729894597853712672)*z + 
1220974658126123565670019751888593761044993991185*i + 
211811947018249923223576976718524137383767937965
g^(p^9-1) = (237809585875741834991576153007396144742157655788*i + 
986879980740920043509509121885997640997209851340)*z^5 + 
(936139532752018606210117538341071166608350863727*i + 
349040123018937838148151685627671810947300124045)*z^4 + 
(85356971980052752574778474541031548005273362196*i + 
88190465811788712462054459750301281251950202292)*z^3 + 
(244970246429598896709919226014995935882868586820*i + 
1461250712521757914096163977919390965791567384854)*z^2 + 
(1410004675290216030552443513596942046089712163085*i + 
1439129478845974241490332140488129432068506372977)*z + 
1390969786242076944833537908467089344695647722141*i + 
1398834529239549175114023695374662216300177982250
g^(p^10-1) = (1246594770081788738724721073099293471059972739097*i + 
382768229729169407804348131823625880241956057964)*z^5 + 
(768981093027284993021976084253246113298674239447*i + 
366805892020891465272327059977891336685100803821)*z^4 + 
(852655199839699940147329355094933876743133342055*i + 
690019603771769684094818718293582964103437250996)*z^3 + 
(1053382421052383953314567950889099073557110465840*i + 
1096378886800018241385817718143474881449413155427)*z^2 + 
(782563351215281329069532267032242743526101428229*i + 
932419608797292263964281326767865562767187037964)*z + 
616166846676061100095127430332774495441755394581*i + 
889255287756560160849573452496040306572455585395
g^(p^11-1) = (912920840895124334529447447866168063247040392173*i + 
9873595412849185996452747082046684640971167294)*z^5 + 
(2545939521711331370283095426719602351824833799*i + 
1344046085896870808486244472445559740184244945852)*z^4 + 
(623883581320924596298676085823779458446779540540*i + 
675006931343865904342646689102926566985749184396)*z^3 + 
(1402153388011088316650991466733555001741554598260*i + 
247983074468381684089738348912296989265022486477)*z^2 + 
(275595554457354270312980246628813051104336514134*i + 
1156378314745152631164618943690763665073246273612)*z + 
258663318293302755002919638469809294273596765675*i + 
795069427093050539880893267448617311116978407546
g^(p^12-1) = 1
g^n = 1

Total time: 2.680 seconds, Total memory usage: 3.34MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 09:09:16 2005

Input: R<x>:=PolynomialRing(GF(2));
definingPolynomial:=x^155+x^62+1;
K<a>:=ext<GF(2)|definingPolynomial>;

CompositionFactors(155);

Output: Magma V2.11-10    Tue Dec 13 2005 09:09:15 on modular  [Seed = 3010340552]
   -------------------------------------


>> CompositionFactors(155);;
                     ^
Runtime error in 'CompositionFactors': Bad argument types
Argument types given: RngIntElt

Total time: 0.190 seconds, Total memory usage: 3.24MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 09:07:43 2005

Input: R<x>:=PolynomialRing(GF(2));
definingPolynomial:=x^155+x^62+1;
K<a>:=ext<GF(2)|definingPolynomial>;

CompositionFactors(definingPolynomial);

Output: Magma V2.11-10    Tue Dec 13 2005 09:07:43 on modular  [Seed = 3741468928]
   -------------------------------------


>> CompositionFactors(definingPolynomial);;
                     ^
Runtime error in 'CompositionFactors': Bad argument types
Argument types given: RngUPolElt[FldFin]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 09:04:55 2005

Input: R<x>:=PolynomialRing(GF(2));
definingPolynomial:=x^155+x^62+1;
K<a>:=ext<GF(2)|definingPolynomial>;

Output: Magma V2.11-10    Tue Dec 13 2005 09:04:55 on modular  [Seed = 3657911469]
   -------------------------------------


Total time: 0.190 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 09:03:36 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := i + 2;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
chi := (p^k - 1) div n;
Ek := EllipticCurve([0, Fp12!b]);

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Qt)
    Q := Ek![Qt[1]*z^2, Qt[2]*z^3];
    "P  =", P;
    "Q' =", Qt;
    "Q  =", Q;
    return miller(n, P, Q)^chi;
end function;

"miller =", miller(n, G, Gt);
"tate =", tate(G, Gt);


Output: Magma V2.11-10    Tue Dec 13 2005 09:03:36 on modular  [Seed = 3574088221]
   -------------------------------------

miller = 162471042542776450109546911262159626540194874282*i + 
    1254993595675210729223411613343751283964425868707
P  = (1 : 2 : 1)
Q' = (i + 2 : 363551601938441395682953698000848166036751722710*i + 
    87218401513221303182445826318865898589777766307 : 1)
Q  = ((i + 2)*z^2 : (363551601938441395682953698000848166036751722710*i + 
    87218401513221303182445826318865898589777766307)*z^3 : 1)
tate = (1337592616974074632841214156993795052557527470389*i + 
    823993614240290083038167890551792145239917806334)*z^5 + 
    (688703507104756931070001853914995131005373541312*i + 
    1002621352581475249329708955843984496240073153982)*z^4 + 
    (852655199839699940147329355094933876743133342055*i + 
    690019603771769684094818718293582964103437250996)*z^3 + 
    (1392434018234511176428044389335844610478592711217*i + 
    473331107538064635840791020785366158595476919127)*z^2 + 
    (1387531245578083722324818991249268608960832619158*i + 
    1095557791792046477650026711124439698442305468846)*z + 
    616166846676061100095127430332774495441755394581*i + 
    889255287756560160849573452496040306572455585395

Total time: 0.630 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:59:32 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := i + 2;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
z := (p^k - 1) div n;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Q)
    return miller(n, P, Q)^z;
end function;

"P =", G;
"Q =", Gt;
"miller =", miller(n, G, Gt);
"tate =", tate(G, Gt);


Output: Magma V2.11-10    Tue Dec 13 2005 08:59:31 on modular  [Seed = 4013064028]
   -------------------------------------

P = (1 : 2 : 1)
Q = (i + 2 : 363551601938441395682953698000848166036751722710*i + 
    87218401513221303182445826318865898589777766307 : 1)
miller = 162471042542776450109546911262159626540194874282*i + 
    1254993595675210729223411613343751283964425868707
tate = 1

Total time: 0.260 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:58:31 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := i + 2;
/*
xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
z := (p^k - 1) div n;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Q)
    return miller(n, P, Q)^z;
end function;

"miller =", miller(n, G, Gt);
"tate =", tate(G, Gt);


Output: Magma V2.11-10    Tue Dec 13 2005 08:58:31 on modular  [Seed = 3929504285]
   -------------------------------------

miller = 694976144959185627384757159853755106109815530714*i + 
    1311958513305109301215342597778813598163540723157
tate = 1

Total time: 0.250 seconds, Total memory usage: 3.34MB


'84.56.2'
************** MAGMA *****************
Host 84.56.209.34 (84.56.209.34)
Time: Tue Dec 13 08:58:30 2005

Input: R<x>:=PolynomialRing(GF(2));

Output: Magma V2.11-10    Tue Dec 13 2005 08:58:23 on modular  [Seed = 3845682666]
   -------------------------------------


Total time: 0.210 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:50:40 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := lambda^3;
/*
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
z := (p^k - 1) div n;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Q)
    return miller(n, P, Q)^z;
end function;

"miller =", miller(n, G, Gt);
"tate =", tate(G, Gt);

Roots(24+25*i, 3);

xt := i;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;


Output: Magma V2.11-10    Tue Dec 13 2005 08:50:18 on modular  [Seed = 4179913490]
   -------------------------------------

miller = 34978940859506703873739429950455443570933508707*i + 
    411686203016070577518067565293188378259628682113
tate = 1

>> Roots(24+25*i, 3);
        ^
Runtime error in 'Roots': Bad argument types
Argument types given: FldFinElt, RngIntElt
xt = i + 2

Total time: 0.300 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:42:17 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := lambda^3;
/*
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];
k := 12;
assert (p^k - 1) mod n eq 0;
z := (p^k - 1) div n;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(P, Q)
    return miller(n, P, Q)^z;
end function;

"miller =", miller(n, P, Q);
"tate =", tate(G, Gt);


Output: Magma V2.11-10    Tue Dec 13 2005 08:42:01 on modular  [Seed = 4046224683]
   -------------------------------------


>> "miller =", miller(n, P, Q);
                         ^
User error: Identifier 'P' has not been declared or assigned
tate = 1

Total time: 0.270 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:37:54 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := lambda^3;
/*
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    // assert (q^k - 1) mod r eq 0;
    z := (q^k - 1) div r;
    return miller(r, P, Q)^z;
end function;

tate(n, p, 12, G, Gt);


Output: Magma V2.11-10    Tue Dec 13 2005 08:37:53 on modular  [Seed = 516133855]
   -------------------------------------

1

Total time: 0.240 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:36:36 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := lambda^3;
/*
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    m := miller(r, P, Q);
    assert (q^k - 1) mod r eq 0;
    z := (q^k - 1) div r;
    return m^z;
end function;

tate(n, p, 12, G, Gt);


Output: Magma V2.11-10    Tue Dec 13 2005 08:36:33 on modular  [Seed = 415601929]
   -------------------------------------

1

Total time: 0.260 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:34:42 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := lambda^3;
/*
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) eq 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;

tate(n, p, 12, G, Gt);


Output: Magma V2.11-10    Tue Dec 13 2005 08:34:23 on modular  [Seed = 332307842]
   -------------------------------------


tate(
    r: 1461501624496790265145447380994971188499300027613,
    q: 1461501624496790265145448589920785493717258890819,
    k: 12,
    P: (1 : 2 : 1),
    Q: (8 : 645238442624673913635245604741558906439788126004*i + 11...
)
>>     return miller(r, P, Q)^((q^k - 1)/r);
                             ^
Runtime error in '^': Bad argument types
Argument types given: FldFinElt, FldFinElt

Total time: 0.290 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:32:15 2005

Input: p := 1461501624496790265145448589920785493717258890819;
n := 1461501624496790265145447380994971188499300027613;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := lambda^3;
/*
xt := 1;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
*/
yt := Sqrt(xt^3 + b/xi);
Gt := Et![xt, yt];

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;

tate(n, p, 12, G, Gt);


Output: Magma V2.11-10    Tue Dec 13 2005 08:31:57 on modular  [Seed = 770745107]
   -------------------------------------


tate(
    r: 1461501624496790265145447380994971188499300027613,
    q: 1461501624496790265145448589920785493717258890819,
    k: 12,
    P: (1 : 2 : 1),
    Q: (8 : 816263181872116351510202985179226587277470764815*i + 29...
)
miller(
    r: 1461501624496790265145447380994971188499300027613,
    P: (1 : 2 : 1),
    Q: (8 : 816263181872116351510202985179226587277470764815*i + 29...
)
>>         if bit(r, i) = 1 then
           ^
Runtime error in if: Logical expected

Total time: 0.319 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:19:36 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
xt := 2;
while not IsSquare(xt^3 + b/xi) do
    xt +:= 1;
end while;
"xt =", xt;
Gt := Et![xt, Sqrt(xt^3 + b/xi)];
Gt;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:19:24 on modular  [Seed = 620342536]
   -------------------------------------

xt = 8
(8 : 816263181872116351510202985179226587277470764815*i + 
    295865244505705705023665406736615173923424579851 : 1)

Total time: 0.260 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:17:14 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
Gt := Et![1, Sqrt(1 + b/xi)];
Gt;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:17:11 on modular  [Seed = 1038137242]
   -------------------------------------


>> Gt := Et![1, Sqrt(1 + b/xi)];
                    ^
Runtime error in 'Sqrt': Argument has no square root

>> Gt;
   ^
User error: Identifier 'Gt' has not been declared or assigned

Total time: 0.240 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:15:08 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
Et := EllipticCurve([0, b/xi]);
Et;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:15:05 on modular  [Seed = 871282970]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + (24*i + 
    1461501624496790265145448589920785493717258890795) over 
GF(1461501624496790265145448589920785493717258890819^2)

Total time: 0.230 seconds, Total memory usage: 3.34MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:14:46 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
G;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:14:43 on modular  [Seed = 1318306941]
   -------------------------------------

(1 : 2 : 1)

Total time: 0.230 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:13:39 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
y0 := Fp!2; // -Sqrt(1 + b);
E := EllipticCurve([0, b]);
G := E![1, y0];
G;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:13:35 on modular  [Seed = 1234485958]
   -------------------------------------

(1 : 2 : 1)

Total time: 0.220 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:12:47 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
E := EllipticCurve([0, b]);
y0 := -Sqrt(1 + b);
G := E![1, y0];
G;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:12:44 on modular  [Seed = 1552013280]
   -------------------------------------

(1 : 2 : 1)

Total time: 0.220 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:12:00 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
E := EllipticCurve([0, b]);
y0 := -Sqrt(1 + b);
E;
y0;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:11:57 on modular  [Seed = 1468718266]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 3 over 
GF(1461501624496790265145448589920785493717258890819)
2

Total time: 0.240 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:11:47 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
E := EllipticCurve([0, b]);
y0 := p - Sqrt(1 + b);
E;
y0;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:11:44 on modular  [Seed = 1385159090]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 3 over 
GF(1461501624496790265145448589920785493717258890819)
2

Total time: 0.230 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:11:19 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := Fp!3;
E := EllipticCurve([0, b]);
y0 := Sqrt(1 + b);
E;
y0;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:11:16 on modular  [Seed = 1840309865]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 3 over 
GF(1461501624496790265145448589920785493717258890819)
1461501624496790265145448589920785493717258890817

Total time: 0.240 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:10:59 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;
b := 3;
E := EllipticCurve([0, b]);
y0 := Sqrt(1 + b);
E;
y0;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:10:55 on modular  [Seed = 1756750663]
   -------------------------------------

Elliptic Curve defined by y^2 = x^3 + 3 over Rational Field
2.00000000000000000000000000000000000000

Total time: 0.250 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:08:18 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := length(r) - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;

for r in [0..64] do
    r, ":", length(r);
end for;


Output: Magma V2.11-10    Tue Dec 13 2005 08:08:11 on modular  [Seed = 2007692220]
   -------------------------------------

0 : 0
1 : 1
2 : 2
3 : 2
4 : 3
5 : 3
6 : 3
7 : 3
8 : 4
9 : 4
10 : 4
11 : 4
12 : 4
13 : 4
14 : 4
15 : 4
16 : 5
17 : 5
18 : 5
19 : 5
20 : 5
21 : 5
22 : 5
23 : 5
24 : 5
25 : 5
26 : 5
27 : 5
28 : 5
29 : 5
30 : 5
31 : 5
32 : 6
33 : 6
34 : 6
35 : 6
36 : 6
37 : 6
38 : 6
39 : 6
40 : 6
41 : 6
42 : 6
43 : 6
44 : 6
45 : 6
46 : 6
47 : 6
48 : 6
49 : 6
50 : 6
51 : 6
52 : 6
53 : 6
54 : 6
55 : 6
56 : 6
57 : 6
58 : 6
59 : 6
60 : 6
61 : 6
62 : 6
63 : 6
64 : 7

Total time: 0.220 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:06:55 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

length := function(r)
    n := 0; v := 1;
    while v le r do
        n +:= 1; v +:= v;
    end while;
    return n;
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := t - 1 to 0 by -1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;

tate := function(r, q, k, P, Q)
    return miller(r, P, Q)^((q^k - 1)/r);
end function;

for r in [0..64] do
    r, ":", length(r);
end for;


Output: Magma V2.11-10    Tue Dec 13 2005 08:06:48 on modular  [Seed = 2387806870]
   -------------------------------------


>>     for i := t - 1 to 0 by -1 do
                ^
User error: Identifier 't' has not been declared or assigned

>>     return miller(r, P, Q)^((q^k - 1)/r);
              ^
User error: Identifier 'miller' has not been declared or assigned
0 : 0
1 : 1
2 : 2
3 : 2
4 : 3
5 : 3
6 : 3
7 : 3
8 : 4
9 : 4
10 : 4
11 : 4
12 : 4
13 : 4
14 : 4
15 : 4
16 : 5
17 : 5
18 : 5
19 : 5
20 : 5
21 : 5
22 : 5
23 : 5
24 : 5
25 : 5
26 : 5
27 : 5
28 : 5
29 : 5
30 : 5
31 : 5
32 : 6
33 : 6
34 : 6
35 : 6
36 : 6
37 : 6
38 : 6
39 : 6
40 : 6
41 : 6
42 : 6
43 : 6
44 : 6
45 : 6
46 : 6
47 : 6
48 : 6
49 : 6
50 : 6
51 : 6
52 : 6
53 : 6
54 : 6
55 : 6
56 : 6
57 : 6
58 : 6
59 : 6
60 : 6
61 : 6
62 : 6
63 : 6
64 : 7

Total time: 0.240 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Tue Dec 13 08:03:03 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;

bit := function(r, i)
    return (r div 2^i) mod 2;
end function;

miller := function(r, P, Q)
    f := 1; A := P;
    for i := t � 1 to 0 by �1 do
        f := f^2*g(A, A, Q); A := 2*A;
        if bit(r, i) = 1 then
            f *:= g(A, P, Q); A +:= P;
        end if;
    end for;
    return f;
end function;


Output: Magma V2.11-10    Tue Dec 13 2005 08:02:46 on modular  [Seed = 2287275406]
   -------------------------------------


>>     for i := t ^� 1 to 0 by ^�1 do
                  ^
User error: Unknown character (ASCII value 150)

>>         f := f^2*g(A, A, Q); A := 2*A;
                ^
User error: Identifier 'f' has not been declared or assigned

>>         f := f^2*g(A, A, Q); A := 2*A;
                                       ^
User error: Identifier 'A' has not been declared or assigned

>>         if bit(r, i) = 1 then
                  ^
User error: Identifier 'r' has not been declared or assigned

>>     end for;
       ^
User error: bad syntax

>>     return f;
       ^
User error: A 'return' can only be used inside a procedure or function

>> end function;
   ^
User error: bad syntax

Total time: 0.270 seconds, Total memory usage: 3.24MB


'213.78.'
************** MAGMA *****************
Host 213.78.42.15 (213.78.42.15)
Time: Tue Dec 13 06:18:14 2005

Input: 10!

Output: Magma V2.11-10    Tue Dec 13 2005 06:18:13 on modular  [Seed = 298647435]
   -------------------------------------


>> 10!;
      ^
User error: bad syntax

Total time: 0.220 seconds, Total memory usage: 3.24MB


'130.83.'
************** MAGMA *****************
Host 130.83.244.131 (130.83.244.131)
Time: Tue Dec 13 06:14:16 2005

Input: F2 := FiniteField(2);
P<x> := PolynomialRing(F2);
p := x^230 + x^50 + x^33 + x^32 + 1;
F<z> := ext< F2 | p >;
a := z;
E := EllipticCurve([1, 0, 0, 0, a]);
time #E;
FactoredOrder(E);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Tue Dec 13 2005 06:13:32 on modular  [Seed = 1234478843]
   -------------------------------------

1725436586697640946858688965569256371777165413914956878562009594085376
Time: 0.170

Errors: /bin/sh: line 1: 11302 Alarm clock             nice -n 19 /usr/local/bin/magma


'159.149'
************** MAGMA *****************
Host 159.149.2.252 (159.149.2.252)
Time: Tue Dec 13 04:03:09 2005

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-10    Tue Dec 13 2005 04:02:39 on modular  [Seed = 2420989386]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.370 seconds, Total memory usage: 3.24MB


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Mon Dec 12 18:17:50 2005

Input: Factorization(100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Mon Dec 12 2005 18:17:30 on modular  [Seed = 1890399814]
   -------------------------------------


Errors: /bin/sh: line 1: 32588 Alarm clock             nice -n 19 /usr/local/bin/magma


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Mon Dec 12 18:16:29 2005

Input: Factorization(10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000);

Output: Magma V2.11-10    Mon Dec 12 2005 18:16:28 on modular  [Seed = 2141337743]
   -------------------------------------

[ <2, 709>, <5, 709> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'80.201.'
************** MAGMA *****************
Host 80.201.74.36 (80.201.74.36)
Time: Mon Dec 12 15:19:29 2005

Input: factor(111111111111111111111111111111111)



Output: Magma V2.11-10    Mon Dec 12 2005 15:19:29 on modular  [Seed = 2170493422]
   -------------------------------------


>> factor(111111111111111111111111111111111)
   ^
User error: Identifier 'factor' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Mon Dec 12 14:29:29 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (U eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;


Output: Magma V2.11-10    Mon Dec 12 2005 14:29:29 on modular  [Seed = 1418385651]
   -------------------------------------


Total time: 0.200 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Mon Dec 12 14:29:20 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;

g := function(U, V, Q)
    if IsZero(U) or IsZero(V) or (u eq -V) or IsZero(Q) then
        return Fp12!1;
    end if;
    m := (U eq V) select 3*U[1]^2/(2*U[1]) else (V[2] - U[2])/(V[1] - U[1]);
    return m*(Q[1] - U[1]) + U[1] - Q[2];
end function;


Output: Magma V2.11-10    Mon Dec 12 2005 14:29:20 on modular  [Seed = 1535498229]
   -------------------------------------


>>     if IsZero(U) or IsZero(V) or (u eq -V) or IsZero(Q) then
                                     ^
User error: Identifier 'u' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Mon Dec 12 14:06:22 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ExtensionField<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ExtensionField<Fp2, z | z^6 - xi>;


Output: Magma V2.11-10    Mon Dec 12 2005 14:06:21 on modular  [Seed = 2057630569]
   -------------------------------------


Total time: 0.200 seconds, Total memory usage: 3.24MB


'143.107'
************** MAGMA *****************
Host 143.107.111.59 (143.107.111.59)
Time: Mon Dec 12 14:04:05 2005

Input: p := 1461501624496790265145448589920785493717258890819;
Fp := GF(p);
Fp2<i> := ext<Fp, i | i^2 + 1>;
lambda := 2;
mu := 1 + i;
xi := 1/(-8 + 8*i);
Fp12<z> := ext<Fp2, z | z^6 - xi>;


Output: Magma V2.11-10    Mon Dec 12 2005 14:04:05 on modular  [Seed = 14584475]
   -------------------------------------


>> Fp2<i> := ext<Fp, i | i^2 + 1>;
                         ^
User error: bad syntax

>> mu := 1 + i;
             ^
User error: Identifier 'i' has not been declared or assigned

>> xi := 1/(-8 + 8*i);
                   ^
User error: Identifier 'i' has not been declared or assigned

>> Fp12<z> := ext<Fp2, z | z^6 - xi>;
                           ^
User error: bad syntax

Total time: 0.200 seconds, Total memory usage: 3.24MB


'131.188'
************** MAGMA *****************
Host 131.188.166.152 (131.188.166.152)
Time: Mon Dec 12 11:58:49 2005

Input: 1+2;

Output: Magma V2.11-10    Mon Dec 12 2005 11:58:49 on modular  [Seed = 248570239]
   -------------------------------------

3

Total time: 0.190 seconds, Total memory usage: 3.24MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Mon Dec 12 07:14:00 2005

Input: G :=DirichletGroup(15);
G;
X :=Elements(G);
X;
Y :=X[4]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 3, 1);
D := 
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[1],80);Parent($1);

Output: Magma V2.11-10    Mon Dec 12 2005 07:14:00 on modular  [Seed = 586942663]
   -------------------------------------

Group of Dirichlet characters of modulus 15 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2
]
15
2
[
    Modular symbols space of level 15, weight 3, character $.1*$.2, and 
    dimension 1 over Rational Field,
    Modular symbols space of level 15, weight 3, character $.1*$.2, and 
    dimension 1 over Rational Field
]
q + q^2 - 3*q^3 - 3*q^4 + 5*q^5 - 3*q^6 - 7*q^8 + 9*q^9 + 5*q^10 + 9*q^12 - 
    15*q^15 + 5*q^16 - 14*q^17 + 9*q^18 - 22*q^19 - 15*q^20 + 34*q^23 + 21*q^24 
    + 25*q^25 - 27*q^27 - 15*q^30 + 2*q^31 + 33*q^32 - 14*q^34 - 27*q^36 - 
    22*q^38 - 35*q^40 + 45*q^45 + 34*q^46 - 14*q^47 - 15*q^48 + 49*q^49 + 
    25*q^50 + 42*q^51 - 86*q^53 - 27*q^54 + 66*q^57 + 45*q^60 - 118*q^61 + 
    2*q^62 + 13*q^64 + 42*q^68 - 102*q^69 - 63*q^72 - 75*q^75 + 66*q^76 + 
    98*q^79 + O(q^80)
Power series ring in q over Rational Field

Total time: 0.280 seconds, Total memory usage: 4.81MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Mon Dec 12 07:13:46 2005

Input: G :=DirichletGroup(15);
G;
X :=Elements(G);
X;
Y :=X[4]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 3, 1);
D := 
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[12],80);Parent($1);

Output: Magma V2.11-10    Mon Dec 12 2005 07:13:42 on modular  [Seed = 670633276]
   -------------------------------------

Group of Dirichlet characters of modulus 15 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2
]
15
2
[
    Modular symbols space of level 15, weight 3, character $.1*$.2, and 
    dimension 1 over Rational Field,
    Modular symbols space of level 15, weight 3, character $.1*$.2, and 
    dimension 1 over Rational Field
]

>> qEigenform(D[12],80);Parent($1);;
               ^
Runtime error in '[]': Sequence element 12 not defined
Set of sequences over Power Structure of ModSym

Total time: 0.300 seconds, Total memory usage: 4.42MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Mon Dec 12 06:27:07 2005

Input: G :=DirichletGroup(75,CyclotomicField(4));
G;
X :=Elements(G);
X;
Y :=X[8]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := 
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[2],80);Parent($1);

Output: Magma V2.11-10    Mon Dec 12 2005 06:27:06 on modular  [Seed = 1054876634]
   -------------------------------------

Group of Dirichlet characters of modulus 75 over Cyclotomic Field of order 4 and
degree 2
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.2^2,
    $.1*$.2^2,
    $.2^3,
    $.1*$.2^3
]
15
4
[
    Modular symbols space of level 75, weight 2, character $.1*$.2^3, and 
    dimension 2 over Cyclotomic Field of order 4 and degree 2,
    Modular symbols space of level 75, weight 2, character $.1*$.2^3, and 
    dimension 2 over Cyclotomic Field of order 4 and degree 2
]
q + a*q^2 + zeta_4*a*q^3 + zeta_4*q^4 - 3*q^6 - zeta_4*a*q^8 - 3*zeta_4*q^9 - 
    a*q^12 + 5*q^16 - 4*a*q^17 - 3*zeta_4*a*q^18 + 4*zeta_4*q^19 + 
    2*zeta_4*a*q^23 + 3*zeta_4*q^24 + 3*a*q^27 - 8*q^31 + 3*a*q^32 - 
    12*zeta_4*q^34 + 3*q^36 + 4*zeta_4*a*q^38 - 6*q^46 + 6*a*q^47 + 
    5*zeta_4*a*q^48 + 7*zeta_4*q^49 + 12*q^51 - 8*zeta_4*a*q^53 + 9*zeta_4*q^54 
    - 4*a*q^57 + 2*q^61 - 8*a*q^62 - zeta_4*q^64 - 4*zeta_4*a*q^68 - 
    6*zeta_4*q^69 - 3*a*q^72 - 4*q^76 - 16*zeta_4*q^79 + O(q^80)
Power series ring in q over Univariate Quotient Polynomial Algebra in a over 
Cyclotomic Field of order 4 and degree 2
with modulus a^2 - 3*zeta_4

Total time: 0.380 seconds, Total memory usage: 5.04MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Mon Dec 12 06:26:16 2005

Input: G :=DirichletGroup(75,CyclotomicField(4));
G;
X :=Elements(G);
X;
Y :=X[8]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := 
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[1],80);Parent($1);

Output: Magma V2.11-10    Mon Dec 12 2005 06:26:16 on modular  [Seed = 620378386]
   -------------------------------------

Group of Dirichlet characters of modulus 75 over Cyclotomic Field of order 4 and
degree 2
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.2^2,
    $.1*$.2^2,
    $.2^3,
    $.1*$.2^3
]
15
4
[
    Modular symbols space of level 75, weight 2, character $.1*$.2^3, and 
    dimension 2 over Cyclotomic Field of order 4 and degree 2,
    Modular symbols space of level 75, weight 2, character $.1*$.2^3, and 
    dimension 2 over Cyclotomic Field of order 4 and degree 2
]
q - zeta_4*a*q^3 - 2*zeta_4*q^4 + a*q^7 + 3*zeta_4*q^9 - 2*a*q^12 + 
    3*zeta_4*a*q^13 - 4*q^16 + zeta_4*q^19 - 3*q^21 + 3*a*q^27 - 2*zeta_4*a*q^28
    + 7*q^31 + 6*q^36 - 4*a*q^37 - 9*zeta_4*q^39 - 7*zeta_4*a*q^43 + 
    4*zeta_4*a*q^48 + 4*zeta_4*q^49 + 6*a*q^52 + a*q^57 - 13*q^61 + 
    3*zeta_4*a*q^63 + 8*zeta_4*q^64 - 9*a*q^67 + 8*zeta_4*a*q^73 + 2*q^76 - 
    4*zeta_4*q^79 + O(q^80)
Power series ring in q over Univariate Quotient Polynomial Algebra in a over 
Cyclotomic Field of order 4 and degree 2
with modulus a^2 + 3*zeta_4

Total time: 0.400 seconds, Total memory usage: 5.04MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Mon Dec 12 06:23:10 2005

Input: G :=DirichletGroup(45,CyclotomicField(4));
G;
X :=Elements(G);
X;
Y :=X[8]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := 
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[1],80);Parent($1);

Output: Magma V2.11-10    Mon Dec 12 2005 06:23:10 on modular  [Seed = 1940745603]
   -------------------------------------

Group of Dirichlet characters of modulus 45 over Cyclotomic Field of order 4 and
degree 2
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.2^2,
    $.1*$.2^2,
    $.2^3,
    $.1*$.2^3
]
15
4
[
    Modular symbols space of level 45, weight 2, character $.1*$.2^3, and 
    dimension 2 over Cyclotomic Field of order 4 and degree 2
]
q + a*q^2 - zeta_4*q^4 + (2*zeta_4 - 1)*a*q^5 + (2*zeta_4 - 2)*q^7 - 
    3*zeta_4*a*q^8 + (-zeta_4 - 2)*q^10 + (-2*zeta_4 - 2)*a*q^11 + (zeta_4 + 
    1)*q^13 + (2*zeta_4 - 2)*a*q^14 + q^16 + 4*a*q^17 + (zeta_4 + 2)*a*q^20 + 
    (-2*zeta_4 + 2)*q^22 + 4*zeta_4*a*q^23 + (-3*zeta_4 + 4)*q^25 + (zeta_4 + 
    1)*a*q^26 + (2*zeta_4 + 2)*q^28 + (-3*zeta_4 + 3)*a*q^29 - 4*q^31 - 5*a*q^32
    + 4*zeta_4*q^34 + (-6*zeta_4 - 2)*a*q^35 + (-zeta_4 + 1)*q^37 + (6*zeta_4 - 
    3)*q^40 + (zeta_4 + 1)*a*q^41 + (-8*zeta_4 - 8)*q^43 + (2*zeta_4 - 2)*a*q^44
    - 4*q^46 - 8*a*q^47 - zeta_4*q^49 + (-3*zeta_4 + 4)*a*q^50 + (-zeta_4 + 
    1)*q^52 + 4*zeta_4*a*q^53 + (6*zeta_4 + 2)*q^55 + (6*zeta_4 + 6)*a*q^56 + 
    (3*zeta_4 + 3)*q^58 + (-6*zeta_4 + 6)*a*q^59 + 8*q^61 - 4*a*q^62 - 
    7*zeta_4*q^64 + (zeta_4 - 3)*a*q^65 + (-4*zeta_4 + 4)*q^67 - 4*zeta_4*a*q^68
    + (-2*zeta_4 + 6)*q^70 + (4*zeta_4 + 4)*a*q^71 + (zeta_4 + 1)*q^73 + 
    (-zeta_4 + 1)*a*q^74 + 8*a*q^77 + 12*zeta_4*q^79 + O(q^80)
Power series ring in q over Univariate Quotient Polynomial Algebra in a over 
Cyclotomic Field of order 4 and degree 2
with modulus a^2 - zeta_4

Total time: 0.340 seconds, Total memory usage: 4.98MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Mon Dec 12 06:21:51 2005

Input: G :=DirichletGroup(45,CyclotomicField(4));
G;
X :=Elements(G);
X;
Y :=X[8]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := 
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[1],300);

Output: Magma V2.11-10    Mon Dec 12 2005 06:21:50 on modular  [Seed = 2024171096]
   -------------------------------------

Group of Dirichlet characters of modulus 45 over Cyclotomic Field of order 4 and
degree 2
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.2^2,
    $.1*$.2^2,
    $.2^3,
    $.1*$.2^3
]
15
4
[
    Modular symbols space of level 45, weight 2, character $.1*$.2^3, and 
    dimension 2 over Cyclotomic Field of order 4 and degree 2
]
q + a*q^2 - zeta_4*q^4 + (2*zeta_4 - 1)*a*q^5 + (2*zeta_4 - 2)*q^7 - 
    3*zeta_4*a*q^8 + (-zeta_4 - 2)*q^10 + (-2*zeta_4 - 2)*a*q^11 + (zeta_4 + 
    1)*q^13 + (2*zeta_4 - 2)*a*q^14 + q^16 + 4*a*q^17 + (zeta_4 + 2)*a*q^20 + 
    (-2*zeta_4 + 2)*q^22 + 4*zeta_4*a*q^23 + (-3*zeta_4 + 4)*q^25 + (zeta_4 + 
    1)*a*q^26 + (2*zeta_4 + 2)*q^28 + (-3*zeta_4 + 3)*a*q^29 - 4*q^31 - 5*a*q^32
    + 4*zeta_4*q^34 + (-6*zeta_4 - 2)*a*q^35 + (-zeta_4 + 1)*q^37 + (6*zeta_4 - 
    3)*q^40 + (zeta_4 + 1)*a*q^41 + (-8*zeta_4 - 8)*q^43 + (2*zeta_4 - 2)*a*q^44
    - 4*q^46 - 8*a*q^47 - zeta_4*q^49 + (-3*zeta_4 + 4)*a*q^50 + (-zeta_4 + 
    1)*q^52 + 4*zeta_4*a*q^53 + (6*zeta_4 + 2)*q^55 + (6*zeta_4 + 6)*a*q^56 + 
    (3*zeta_4 + 3)*q^58 + (-6*zeta_4 + 6)*a*q^59 + 8*q^61 - 4*a*q^62 - 
    7*zeta_4*q^64 + (zeta_4 - 3)*a*q^65 + (-4*zeta_4 + 4)*q^67 - 4*zeta_4*a*q^68
    + (-2*zeta_4 + 6)*q^70 + (4*zeta_4 + 4)*a*q^71 + (zeta_4 + 1)*q^73 + 
    (-zeta_4 + 1)*a*q^74 + 8*a*q^77 + 12*zeta_4*q^79 + (2*zeta_4 - 1)*a*q^80 + 
    (zeta_4 - 1)*q^82 + 4*zeta_4*a*q^83 + (-4*zeta_4 - 8)*q^85 + (-8*zeta_4 - 
    8)*a*q^86 + (-6*zeta_4 - 6)*q^88 + (9*zeta_4 - 9)*a*q^89 - 4*q^91 + 4*a*q^92
    - 8*zeta_4*q^94 + (11*zeta_4 - 11)*q^97 - zeta_4*a*q^98 + (-4*zeta_4 - 
    3)*q^100 + (-11*zeta_4 - 11)*a*q^101 + (10*zeta_4 + 10)*q^103 + (-3*zeta_4 +
    3)*a*q^104 - 4*q^106 + 4*a*q^107 + (6*zeta_4 + 2)*a*q^110 + (2*zeta_4 - 
    2)*q^112 - 14*zeta_4*a*q^113 + (-8*zeta_4 + 4)*q^115 + (-3*zeta_4 - 
    3)*a*q^116 + (6*zeta_4 + 6)*q^118 + (8*zeta_4 - 8)*a*q^119 + 3*q^121 + 
    8*a*q^122 + 4*zeta_4*q^124 + (11*zeta_4 + 2)*a*q^125 + (-10*zeta_4 + 
    10)*q^127 + 3*zeta_4*a*q^128 + (-3*zeta_4 - 1)*q^130 + (10*zeta_4 + 
    10)*a*q^131 + (-4*zeta_4 + 4)*a*q^134 + 12*q^136 + 10*a*q^137 - 
    12*zeta_4*q^139 + (2*zeta_4 - 6)*a*q^140 + (4*zeta_4 - 4)*q^142 - 
    4*zeta_4*a*q^143 + (3*zeta_4 - 9)*q^145 + (zeta_4 + 1)*a*q^146 + (-zeta_4 - 
    1)*q^148 + (3*zeta_4 - 3)*a*q^149 + 8*q^151 + 8*zeta_4*q^154 + (-8*zeta_4 + 
    4)*a*q^155 + (5*zeta_4 - 5)*q^157 + 12*zeta_4*a*q^158 + (5*zeta_4 + 
    10)*q^160 + (-8*zeta_4 - 8)*a*q^161 + (-8*zeta_4 - 8)*q^163 + (-zeta_4 + 
    1)*a*q^164 - 4*q^166 - 20*a*q^167 - 11*zeta_4*q^169 + (-4*zeta_4 - 
    8)*a*q^170 + (8*zeta_4 - 8)*q^172 - 14*zeta_4*a*q^173 + (14*zeta_4 - 
    2)*q^175 + (-2*zeta_4 - 2)*a*q^176 + (-9*zeta_4 - 9)*q^178 + (-18*zeta_4 + 
    18)*a*q^179 - 16*q^181 - 4*a*q^182 + 12*zeta_4*q^184 + (3*zeta_4 + 
    1)*a*q^185 + (-8*zeta_4 + 8)*q^187 + 8*zeta_4*a*q^188 + (16*zeta_4 + 
    16)*a*q^191 + (zeta_4 + 1)*q^193 + (11*zeta_4 - 11)*a*q^194 - q^196 - 
    14*a*q^197 + (-12*zeta_4 - 9)*a*q^200 + (-11*zeta_4 + 11)*q^202 + 
    12*zeta_4*a*q^203 + (-3*zeta_4 - 1)*q^205 + (10*zeta_4 + 10)*a*q^206 + 
    (zeta_4 + 1)*q^208 - 4*q^211 + 4*a*q^212 + 4*zeta_4*q^214 + (-8*zeta_4 + 
    24)*a*q^215 + (-8*zeta_4 + 8)*q^217 + (-2*zeta_4 + 6)*q^220 + (4*zeta_4 + 
    4)*a*q^221 + (10*zeta_4 + 10)*q^223 + (-10*zeta_4 + 10)*a*q^224 + 14*q^226 -
    8*a*q^227 + 6*zeta_4*q^229 + (-8*zeta_4 + 4)*a*q^230 + (-9*zeta_4 + 9)*q^232
    + 4*zeta_4*a*q^233 + (8*zeta_4 + 16)*q^235 + (-6*zeta_4 - 6)*a*q^236 + 
    (-8*zeta_4 - 8)*q^238 + (12*zeta_4 - 12)*a*q^239 - 10*q^241 + 3*a*q^242 - 
    8*zeta_4*q^244 + (zeta_4 + 2)*a*q^245 + 12*zeta_4*a*q^248 + (2*zeta_4 - 
    11)*q^250 + (-14*zeta_4 - 14)*a*q^251 + (8*zeta_4 + 8)*q^253 + (-10*zeta_4 +
    10)*a*q^254 - 17*q^256 - 2*a*q^257 + 4*zeta_4*q^259 + (3*zeta_4 + 1)*a*q^260
    + (10*zeta_4 - 10)*q^262 + 4*zeta_4*a*q^263 + (-8*zeta_4 + 4)*q^265 + 
    (-4*zeta_4 - 4)*q^268 + (9*zeta_4 - 9)*a*q^269 - 16*q^271 + 4*a*q^272 + 
    10*zeta_4*q^274 + (-2*zeta_4 - 14)*a*q^275 + (11*zeta_4 - 11)*q^277 - 
    12*zeta_4*a*q^278 + (-18*zeta_4 - 6)*q^280 + (7*zeta_4 + 7)*a*q^281 + 
    (-8*zeta_4 - 8)*q^283 + (-4*zeta_4 + 4)*a*q^284 + 4*q^286 - 4*a*q^287 - 
    zeta_4*q^289 + (3*zeta_4 - 9)*a*q^290 + (-zeta_4 + 1)*q^292 - 
    14*zeta_4*a*q^293 + (6*zeta_4 - 18)*q^295 + (-3*zeta_4 - 3)*a*q^296 + 
    (-3*zeta_4 - 3)*q^298 + (4*zeta_4 - 4)*a*q^299 + O(q^300)

Total time: 0.550 seconds, Total memory usage: 7.41MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Mon Dec 12 06:21:37 2005

Input: G :=DirichletGroup(45,CyclotomicField(4));
G;
X :=Elements(G);
X;
Y :=X[16]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D := 
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[1],300);

Output: Magma V2.11-10    Mon Dec 12 2005 06:21:36 on modular  [Seed = 2141282641]
   -------------------------------------

Group of Dirichlet characters of modulus 45 over Cyclotomic Field of order 4 and
degree 2
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.2^2,
    $.1*$.2^2,
    $.2^3,
    $.1*$.2^3
]

>> Y :=X[16]; Conductor(Y); Order(Y);
        ^
Runtime error in '[]': Sequence element 16 not defined

>> Y :=X[16]; Conductor(Y); Order(Y);
                        ^
User error: Identifier 'Y' has not been declared or assigned

>> Y :=X[16]; Conductor(Y); Order(Y);
                                  ^
User error: Identifier 'Y' has not been declared or assigned

>> M := ModularSymbols(Y, 2, 1);
                       ^
User error: Identifier 'Y' has not been declared or assigned

>> SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
                                                                       ^
User error: Identifier 'M' has not been declared or assigned

>> D;
   ^
User error: Identifier 'D' has not been declared or assigned

>> qEigenform(D[1],300);;
              ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.34MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Mon Dec 12 06:02:56 2005

Input: G :=DirichletGroup(15);
G;
X :=Elements(G);
X;
Y :=X[4]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 3, 1);
D := 
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[1],300);

Output: Magma V2.11-10    Mon Dec 12 2005 06:02:55 on modular  [Seed = 3026890500]
   -------------------------------------

Group of Dirichlet characters of modulus 15 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2
]
15
2
[
    Modular symbols space of level 15, weight 3, character $.1*$.2, and 
    dimension 1 over Rational Field,
    Modular symbols space of level 15, weight 3, character $.1*$.2, and 
    dimension 1 over Rational Field
]
q + q^2 - 3*q^3 - 3*q^4 + 5*q^5 - 3*q^6 - 7*q^8 + 9*q^9 + 5*q^10 + 9*q^12 - 
    15*q^15 + 5*q^16 - 14*q^17 + 9*q^18 - 22*q^19 - 15*q^20 + 34*q^23 + 21*q^24 
    + 25*q^25 - 27*q^27 - 15*q^30 + 2*q^31 + 33*q^32 - 14*q^34 - 27*q^36 - 
    22*q^38 - 35*q^40 + 45*q^45 + 34*q^46 - 14*q^47 - 15*q^48 + 49*q^49 + 
    25*q^50 + 42*q^51 - 86*q^53 - 27*q^54 + 66*q^57 + 45*q^60 - 118*q^61 + 
    2*q^62 + 13*q^64 + 42*q^68 - 102*q^69 - 63*q^72 - 75*q^75 + 66*q^76 + 
    98*q^79 + 25*q^80 + 81*q^81 + 154*q^83 - 70*q^85 + 45*q^90 - 102*q^92 - 
    6*q^93 - 14*q^94 - 110*q^95 - 99*q^96 + 49*q^98 - 75*q^100 + 42*q^102 - 
    86*q^106 + 106*q^107 + 81*q^108 - 22*q^109 - 206*q^113 + 66*q^114 + 
    170*q^115 + 105*q^120 + 121*q^121 - 118*q^122 - 6*q^124 + 125*q^125 - 
    119*q^128 - 135*q^135 + 98*q^136 + 226*q^137 - 102*q^138 - 262*q^139 + 
    42*q^141 + 45*q^144 - 147*q^147 - 75*q^150 - 238*q^151 + 154*q^152 - 
    126*q^153 + 10*q^155 + 98*q^158 + 258*q^159 + 165*q^160 + 81*q^162 + 
    154*q^166 - 254*q^167 + 169*q^169 - 70*q^170 - 198*q^171 + 154*q^173 - 
    135*q^180 + 122*q^181 + 354*q^183 - 238*q^184 - 6*q^186 + 42*q^188 - 
    110*q^190 - 39*q^192 - 147*q^196 - 374*q^197 - 142*q^199 - 175*q^200 - 
    126*q^204 + 306*q^207 + 362*q^211 + 258*q^212 + 106*q^214 + 189*q^216 - 
    22*q^218 + 225*q^225 - 206*q^226 - 134*q^227 - 198*q^228 + 218*q^229 + 
    170*q^230 + 34*q^233 - 70*q^235 - 294*q^237 - 75*q^240 - 478*q^241 + 
    121*q^242 - 243*q^243 + 354*q^244 + 245*q^245 - 14*q^248 - 462*q^249 + 
    125*q^250 + 210*q^255 - 171*q^256 + 466*q^257 - 446*q^263 - 430*q^265 - 
    135*q^270 + 482*q^271 - 70*q^272 + 226*q^274 + 306*q^276 - 262*q^278 + 
    18*q^279 + 42*q^282 + 330*q^285 + 297*q^288 - 93*q^289 + 394*q^293 - 
    147*q^294 + O(q^300)

Total time: 0.500 seconds, Total memory usage: 7.23MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Mon Dec 12 06:02:39 2005

Input: G :=DirichletGroup(15);
G;
X :=Elements(G);
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 3, 1);
D := 
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[1],300);

Output: Magma V2.11-10    Mon Dec 12 2005 06:02:39 on modular  [Seed = 3110576665]
   -------------------------------------

Group of Dirichlet characters of modulus 15 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2
]
1
1
[]

>> qEigenform(D[1],300);;
               ^
Runtime error in '[]': Sequence element 1 not defined

Total time: 0.230 seconds, Total memory usage: 4.59MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Mon Dec 12 06:02:30 2005

Input: G :=DirichletGroup(15);
G;
X :=Elements(G);
X;
Y :=X[16]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 3, 1);
D := 
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[1],300);

Output: Magma V2.11-10    Mon Dec 12 2005 06:02:30 on modular  [Seed = 3194004759]
   -------------------------------------

Group of Dirichlet characters of modulus 15 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2
]

>> Y :=X[16]; Conductor(Y); Order(Y);
        ^
Runtime error in '[]': Sequence element 16 not defined

>> Y :=X[16]; Conductor(Y); Order(Y);
                        ^
User error: Identifier 'Y' has not been declared or assigned

>> Y :=X[16]; Conductor(Y); Order(Y);
                                  ^
User error: Identifier 'Y' has not been declared or assigned

>> M := ModularSymbols(Y, 3, 1);
                       ^
User error: Identifier 'Y' has not been declared or assigned

>> SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
                                                                       ^
User error: Identifier 'M' has not been declared or assigned

>> D;
   ^
User error: Identifier 'D' has not been declared or assigned

>> qEigenform(D[1],300);;
              ^
User error: Identifier 'D' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.34MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:20:10 2005

Input: Factorization(40^2+40+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:20:10 on modular  [Seed = 1401770230]
   -------------------------------------

[ <41, 2> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:19:59 2005

Input: Factorization(41^2+41+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:19:59 on modular  [Seed = 1485200264]
   -------------------------------------

[ <41, 1>, <43, 1> ]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:19:51 2005

Input: Factorization(40^2+40+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:19:50 on modular  [Seed = 1568890500]
   -------------------------------------

[ <41, 2> ]

Total time: 0.180 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:19:42 2005

Input: Factorization(39^2+39+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:19:42 on modular  [Seed = 1117536643]
   -------------------------------------

[ <1601, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:19:34 2005

Input: Factorization(31^2+31+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:19:34 on modular  [Seed = 1201226894]
   -------------------------------------

[ <1033, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:19:23 2005

Input: Factorization(26^2+26+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:19:23 on modular  [Seed = 1284657080]
   -------------------------------------

[ <743, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:19:15 2005

Input: Factorization(19^2+19+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:19:15 on modular  [Seed = 1907323533]
   -------------------------------------

[ <421, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:19:10 2005

Input: Factorization(9^2+9+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:19:09 on modular  [Seed = 1990751636]
   -------------------------------------

[ <131, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:19:03 2005

Input: Factorization(4^2+4+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:19:03 on modular  [Seed = 2074441875]
   -------------------------------------

[ <61, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:18:55 2005

Input: Factorization(3^2+3+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:18:55 on modular  [Seed = 1623090032]
   -------------------------------------

[ <53, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:18:47 2005

Input: Factorization(2^2+2+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:18:47 on modular  [Seed = 1706780285]
   -------------------------------------

[ <47, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:18:40 2005

Input: Factorization(1^2+1+41);

Output: Magma V2.11-10    Mon Dec 12 2005 04:18:40 on modular  [Seed = 1790208373]
   -------------------------------------

[ <43, 1> ]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:18:31 2005

Input: 1^2+1+41

Output: Magma V2.11-10    Mon Dec 12 2005 04:18:31 on modular  [Seed = 1873898599]
   -------------------------------------

43

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:12:46 2005

Input: e^(Pi 163^(1/2))

Output: Magma V2.11-10    Mon Dec 12 2005 04:12:46 on modular  [Seed = 2671895545]
   -------------------------------------


>> e^(Pi 163^(1/2));
         ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'64.229.'
************** MAGMA *****************
Host 64.229.200.59 (64.229.200.59)
Time: Mon Dec 12 04:12:36 2005

Input: e^(pi 163^(1/2))

Output: Magma V2.11-10    Mon Dec 12 2005 04:12:35 on modular  [Seed = 2220554472]
   -------------------------------------


>> e^(pi 163^(1/2));
         ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'70.228.'
************** MAGMA *****************
Host 70.228.67.16 (70.228.67.16)
Time: Mon Dec 12 02:46:25 2005

Input: A := Matrix(2,2,[1,2,3,4])
SmithForm(A)

Output: Magma V2.11-10    Mon Dec 12 2005 02:46:25 on modular  [Seed = 1150955005]
   -------------------------------------


>> SmithForm(A);
   ^
User error: bad syntax

Total time: 0.180 seconds, Total memory usage: 3.24MB


'70.228.'
************** MAGMA *****************
Host 70.228.67.16 (70.228.67.16)
Time: Mon Dec 12 02:45:59 2005

Input:  A := Matrix(2,2,[1,2,3,4])

Output: Magma V2.11-10    Mon Dec 12 2005 02:45:59 on modular  [Seed = 1334912656]
   -------------------------------------


Total time: 0.180 seconds, Total memory usage: 3.24MB


'70.228.'
************** MAGMA *****************
Host 70.228.67.16 (70.228.67.16)
Time: Mon Dec 12 02:45:28 2005

Input:  A := Matrix(2,2,[1,2,3,4])

Output: Magma V2.11-10    Mon Dec 12 2005 02:45:28 on modular  [Seed = 1251222458]
   -------------------------------------


Total time: 0.180 seconds, Total memory usage: 3.24MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sun Dec 11 15:31:08 2005

Input: G :=DirichletGroup(1155);
G;
X :=Elements(G);
X;


Output: Magma V2.11-10    Sun Dec 11 2005 15:31:07 on modular  [Seed = 3026942808]
   -------------------------------------

Group of Dirichlet characters of modulus 1155 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.3,
    $.1*$.3,
    $.2*$.3,
    $.1*$.2*$.3,
    $.4,
    $.1*$.4,
    $.2*$.4,
    $.1*$.2*$.4,
    $.3*$.4,
    $.1*$.3*$.4,
    $.2*$.3*$.4,
    $.1*$.2*$.3*$.4
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'155.207'
************** MAGMA *****************
Host 155.207.209.204 (155.207.209.204)
Time: Sun Dec 11 13:10:04 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-2*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
> >NormEquation(O, 4*5^4);

Output: Magma V2.11-10    Sun Dec 11 2005 13:10:03 on modular  [Seed = 1251304016]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]
true [
    [8, 0, -9, 4],
    [4, -8, -1, 2],
    [-8, 0, 7, 0],
    [4, 8, -1, -2],
    [8, 0, -9, -4],
    [4, -8, -3, 6],
    [0, 0, 5, 0],
    [4, 8, -3, -6],
    [8, 0, -1, 0]
]

Total time: 0.400 seconds, Total memory usage: 3.72MB


'155.207'
************** MAGMA *****************
Host 155.207.209.204 (155.207.209.204)
Time: Sun Dec 11 13:09:51 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-2*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
> >NormEquation(O, 4);

Output: Magma V2.11-10    Sun Dec 11 2005 13:09:51 on modular  [Seed = 2007523193]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]
true [
    [0, 0, 1, 0]
]

Total time: 0.340 seconds, Total memory usage: 3.72MB


'155.207'
************** MAGMA *****************
Host 155.207.209.204 (155.207.209.204)
Time: Sun Dec 11 13:08:48 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-2*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
> >NormEquation(O, 4*5^4);

Output: Magma V2.11-10    Sun Dec 11 2005 13:08:48 on modular  [Seed = 2554835146]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]
true [
    [8, 0, -9, 4],
    [4, -8, -1, 2],
    [-8, 0, 7, 0],
    [4, 8, -1, -2],
    [8, 0, -9, -4],
    [4, -8, -3, 6],
    [0, 0, 5, 0],
    [4, 8, -3, -6],
    [8, 0, -1, 0]
]

Total time: 0.400 seconds, Total memory usage: 3.72MB


'155.207'
************** MAGMA *****************
Host 155.207.209.204 (155.207.209.204)
Time: Sun Dec 11 13:08:33 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^4-2*x^2+2;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
> >NormEquation(O, 3);

Output: Magma V2.11-10    Sun Dec 11 2005 13:08:33 on modular  [Seed = 2521415381]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3
]
false

Total time: 0.310 seconds, Total memory usage: 3.72MB


'155.207'
************** MAGMA *****************
Host 155.207.209.204 (155.207.209.204)
Time: Sun Dec 11 13:08:13 2005

Input: R<x> := PolynomialRing(Integers());
> > f :=x^8 - 20*x^6 + 98*x^4 - 76*x^2 + 1;
> > K<y> := NumberField(f);
> > O := MaximalOrder(K);
> > I := IntegralBasis(K);
> > print I;
> >NormEquation(O, 3);

Output: Magma V2.11-10    Sun Dec 11 2005 13:08:12 on modular  [Seed = 2371003875]
   -------------------------------------

[
    1,
    y,
    y^2,
    y^3,
    1/8*(y^4 + 4*y^3 + 6*y^2 + 4*y + 7),
    1/8*(y^5 + 6*y^3 + 4*y^2 + 7*y + 4),
    1/56*(y^6 + 28*y^3 + 35*y^2 + 28*y + 22),
    1/112*(y^7 + y^6 + 7*y^5 + 7*y^4 + 21*y^3 + 77*y^2 + 71*y + 15)
]
false

Total time: 0.520 seconds, Total memory usage: 3.90MB


'84.167.'
************** MAGMA *****************
Host 84.167.225.156 (84.167.225.156)
Time: Sun Dec 11 10:16:20 2005

Input: F2 := FiniteField(2);
P<x> := PolynomialRing(F2);
p := x^120 + x^41 + x^35 + x^32 + 1;
F<z> := ext< F2 | p >;
a := z;
E := EllipticCurve([1, 0, 0, 0, a]);
time #E;
FactoredOrder(E);

Output: Magma V2.11-10    Sun Dec 11 2005 10:16:19 on modular  [Seed = 3707952194]
   -------------------------------------

1329227995784915872847313096830369792
Time: 0.290
[ <2, 14>, <26113, 1>, <368539681, 1>, <8430212384348387921, 1> ]

Total time: 0.620 seconds, Total memory usage: 3.82MB


'85.226.'
************** MAGMA *****************
Host 85.226.120.223 (85.226.120.223)
Time: Sun Dec 11 09:41:05 2005

Input: R<x> := PolynomialRing(RationalField(),1);
I := ideal< R | (x - 1)^2*x>;
S := R/I;
S;
IsNilpotent((x-1)^2);

Output: Magma V2.11-10    Sun Dec 11 2005 09:41:04 on modular  [Seed = 1468542603]
   -------------------------------------

Affine Algebra of rank 1 over Rational Field
Lexicographical Order
Variables: x
Quotient relations:
[
    x^3 - 2*x^2 + x
]


Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
    to [email protected]
Version: 2.11-10
Link date: Thu Nov 4 20:39:55 EST 2004
Machine type: x86_64-linux
Initial seed: 1468542603
Time to this point: 0.19
Memory usage: 3.24MB
Internal error in glue_ring_elt_is_nilpotent() at ring/elt_glue.c, line 367

Total time: 0.190 seconds, Total memory usage: 3.24MB


'85.226.'
************** MAGMA *****************
Host 85.226.120.223 (85.226.120.223)
Time: Sun Dec 11 09:40:50 2005

Input: R<x> := PolynomialRing(RationalField(),1);
I := ideal< R | (x - 1)^2*x>;
S := R/I;
S;

Output: Magma V2.11-10    Sun Dec 11 2005 09:40:49 on modular  [Seed = 1518674807]
   -------------------------------------

Affine Algebra of rank 1 over Rational Field
Lexicographical Order
Variables: x
Quotient relations:
[
    x^3 - 2*x^2 + x
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'85.226.'
************** MAGMA *****************
Host 85.226.120.223 (85.226.120.223)
Time: Sun Dec 11 09:40:43 2005

Input: R<x> := PolynomialRing(RationalField(),1);
I := ideal< R | (x - 1)^2*x>;
S := R/I;

Output: Magma V2.11-10    Sun Dec 11 2005 09:40:42 on modular  [Seed = 1568810091]
   -------------------------------------


Total time: 0.190 seconds, Total memory usage: 3.24MB


'85.226.'
************** MAGMA *****************
Host 85.226.120.223 (85.226.120.223)
Time: Sun Dec 11 09:40:14 2005

Input: R<x> := PolyonialRing(RationalField(),1);
I := ideal< R | (x - 1)^2*x>;
S := R/I;

Output: Magma V2.11-10    Sun Dec 11 2005 09:40:13 on modular  [Seed = 2793004982]
   -------------------------------------


>> R<x> := PolyonialRing(RationalField(),1);
           ^
User error: Identifier 'PolyonialRing' has not been declared or assigned

>> I := ideal< R | (x - 1)^2*x>;
               ^
User error: Identifier 'R' has not been declared or assigned

>> S := R/I;;
        ^
User error: Identifier 'R' has not been declared or assigned

Total time: 0.200 seconds, Total memory usage: 3.24MB


'67.62.1'
************** MAGMA *****************
Host 67.62.112.123 (67.62.112.123)
Time: Sun Dec 11 07:14:56 2005

Input: c:=10;
e:=180;
r:=c*e;
r;


Output: Magma V2.11-10    Sun Dec 11 2005 07:14:55 on modular  [Seed = 3390411179]
   -------------------------------------

1800

Total time: 0.190 seconds, Total memory usage: 3.24MB


'67.62.1'
************** MAGMA *****************
Host 67.62.112.123 (67.62.112.123)
Time: Sun Dec 11 06:40:38 2005

Input: t:=11111111111;
y:=11111111111;
g:=t*y;
g;


Output: Magma V2.11-10    Sun Dec 11 2005 06:40:37 on modular  [Seed = 2220611561]
   -------------------------------------

123456790120987654321

Total time: 0.240 seconds, Total memory usage: 3.24MB


'67.62.1'
************** MAGMA *****************
Host 67.62.112.123 (67.62.112.123)
Time: Sun Dec 11 06:34:58 2005

Input: c:=11;
e:=18;
r:=c*e;
r;


Output: Magma V2.11-10    Sun Dec 11 2005 06:34:58 on modular  [Seed = 2421153066]
   -------------------------------------

198

Total time: 0.200 seconds, Total memory usage: 3.24MB


'67.62.1'
************** MAGMA *****************
Host 67.62.112.123 (67.62.112.123)
Time: Sun Dec 11 06:34:47 2005

Input: c:=11;
e:=11;
r:=c*e;
r;


Output: Magma V2.11-10    Sun Dec 11 2005 06:34:47 on modular  [Seed = 2604979732]
   -------------------------------------

121

Total time: 0.200 seconds, Total memory usage: 3.24MB


'217.24.'
************** MAGMA *****************
Host 217.24.144.35 (217.24.144.35)
Time: Sun Dec 11 06:33:09 2005

Input: c:=11;
e:=11;
r:=c*e;
r;


Output: Magma V2.11-10    Sun Dec 11 2005 06:33:09 on modular  [Seed = 3778981068]
   -------------------------------------

121

Total time: 0.200 seconds, Total memory usage: 3.24MB


'217.24.'
************** MAGMA *****************
Host 217.24.144.35 (217.24.144.35)
Time: Sun Dec 11 06:27:13 2005

Input: c:=123;
e:=11;
r:=c*e;
r;


Output: Magma V2.11-10    Sun Dec 11 2005 06:27:11 on modular  [Seed = 3657798797]
   -------------------------------------

1353

Total time: 0.190 seconds, Total memory usage: 3.24MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sun Dec 11 04:38:47 2005

Input: 
G :=DirichletGroup(175,CyclotomicField(4));G;
X :=Elements(G);X;
Y :=X[6]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 2, 1);
D :=
SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(M))));
D;
qEigenform(D[1],104);Parent($1);

Output: Magma V2.11-10    Sun Dec 11 2005 04:38:47 on modular  [Seed = 921601736]
   -------------------------------------

Group of Dirichlet characters of modulus 175 over Cyclotomic Field of order 4 
and degree 2
[
    1,
    $.1,
    $.1^2,
    $.1^3,
    $.2,
    $.1*$.2,
    $.1^2*$.2,
    $.1^3*$.2
]
35
4
[
    Modular symbols space of level 175, weight 2, character $.1*$.2, and 
    dimension 2 over Cyclotomic Field of order 4 and degree 2,
    Modular symbols space of level 175, weight 2, character $.1*$.2, and 
    dimension 2 over Cyclotomic Field of order 4 and degree 2,
    Modular symbols space of level 175, weight 2, character $.1*$.2, and 
    dimension 2 over Cyclotomic Field of order 4 and degree 2,
    Modular symbols space of level 175, weight 2, character $.1*$.2, and 
    dimension 4 over Cyclotomic Field of order 4 and degree 2
]
q - 1/3*a*q^3 - 2*zeta_4*q^4 + 1/3*zeta_4*a*q^7 + 4*zeta_4*q^9 - 3*q^11 + 
    2/3*zeta_4*a*q^12 - 1/3*a*q^13 - 4*q^16 - zeta_4*a*q^17 + 7*q^21 - 
    1/3*zeta_4*a*q^27 + 2/3*a*q^28 - 9*zeta_4*q^29 + a*q^33 + 8*q^36 + 
    7*zeta_4*q^39 + 6*zeta_4*q^44 - zeta_4*a*q^47 + 4/3*a*q^48 - 7*zeta_4*q^49 -
    21*q^51 + 2/3*zeta_4*a*q^52 - 4/3*a*q^63 + 8*zeta_4*q^64 - 2*a*q^68 + 
    12*q^71 + 4/3*a*q^73 - zeta_4*a*q^77 + zeta_4*q^79 + 5*q^81 - 2*a*q^83 - 
    14*zeta_4*q^84 + 3*zeta_4*a*q^87 + 7*q^91 + 7/3*zeta_4*a*q^97 - 
    12*zeta_4*q^99 - 1/3*a*q^103 + O(q^104)
Power series ring in q over Univariate Quotient Polynomial Algebra in a over 
Cyclotomic Field of order 4 and degree 2
with modulus a^2 - 63*zeta_4

Total time: 0.530 seconds, Total memory usage: 5.46MB


'83.194.'
************** MAGMA *****************
Host 83.194.162.38 (83.194.162.38)
Time: Sun Dec 11 03:35:56 2005

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-10    Sun Dec 11 2005 03:35:55 on modular  [Seed = 4147073094]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.190 seconds, Total memory usage: 3.24MB


'72.19.1'
************** MAGMA *****************
Host 72.19.126.33 (72.19.126.33)
Time: Sat Dec 10 16:55:59 2005

Input: Q:=GaloisField(35098201); P<x,y>:=PolynomialRing(Q,2);
   I:=ideal<P| y + (1+x^5+x^10), x^34 +1 >; Groebner(I); I; 

Output: Magma V2.11-10    Sat Dec 10 2005 16:55:56 on modular  [Seed = 3290220920]
   -------------------------------------

Ideal of Polynomial ring of rank 2 over GF(35098201)
Lexicographical Order
Variables: x, y
Dimension 0
Groebner basis:
[
    x + 33784728*y^33 + 15744019*y^32 + 14466235*y^31 + 14937582*y^30 + 
        9988153*y^29 + 24849537*y^28 + 13827463*y^27 + 10851940*y^26 + 
        25333828*y^25 + 29238403*y^24 + 35087366*y^23 + 3185785*y^22 + 
        12125255*y^21 + 11305600*y^20 + 713800*y^19 + 11882241*y^18 + 
        23388419*y^17 + 12677392*y^16 + 20159861*y^15 + 31143912*y^14 + 
        33062327*y^13 + 11580434*y^12 + 10629964*y^11 + 14094725*y^10 + 
        30606411*y^9 + 20913610*y^8 + 23355486*y^7 + 32139384*y^6 + 35026862*y^5
        + 11038274*y^4 + 26690476*y^3 + 752845*y^2 + 9514380*y + 16409093,
    y^34 + 34*y^33 + 561*y^32 + 5984*y^31 + 46376*y^30 + 278256*y^29 + 
        1344904*y^28 + 5379616*y^27 + 18156204*y^26 + 17353055*y^25 + 
        25833537*y^24 + 5312152*y^23 + 21881025*y^22 + 15430534*y^21 + 
        23145801*y^20 + 30861068*y^19 + 27872968*y^18 + 17124952*y^17 + 
        27873223*y^16 + 30858484*y^15 + 23140973*y^14 + 15452362*y^13 + 
        21951303*y^12 + 5362540*y^11 + 25762851*y^10 + 17184126*y^9 + 
        18014271*y^8 + 5332492*y^7 + 1358334*y^6 + 297330*y^5 + 54824*y^4 + 
        7259*y^3 + 714*y^2 + 34*y + 1
]

Total time: 0.240 seconds, Total memory usage: 3.43MB


'84.59.7'
************** MAGMA *****************
Host 84.59.79.231 (84.59.79.231)
Time: Sat Dec 10 11:35:50 2005

Input: factor(1111111111111)

Output: Magma V2.11-10    Sat Dec 10 2005 11:35:50 on modular  [Seed = 3895502914]
   -------------------------------------


>> factor(1111111111111);
   ^
User error: Identifier 'factor' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'86.138.'
************** MAGMA *****************
Host 86.138.172.89 (86.138.172.89)
Time: Sat Dec 10 11:04:37 2005

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-10    Sat Dec 10 2005 11:04:37 on modular  [Seed = 654285311]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.200 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:31:44 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl*Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
            assert (Vh ne 0) or (Uh eq 0 and Vh eq 0 and Vh eq -2*Qh);
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
            assert (Vl ne 0) or (Uh eq -Ql and Vh eq 0 and Vl eq -2*Ql);
        end if;
        assert (Vl eq 0 and Uh eq 0) or (Vh eq 0);
    end for;
    assert Vl*Vh eq 0;
    //assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    assert Uh*Vl eq 0;
    return Uh, Vl;
end function;

for i, j in [1..10] do
    i, ":", Lucas(j, i);
end for;


Output: Magma V2.11-10    Sat Dec 10 2005 10:31:43 on modular  [Seed = 1940571360]
   -------------------------------------

1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
2 : 0 -2
2 : 0 -4
2 : 0 -6
2 : 0 -8
2 : 0 -10
2 : 0 -12
2 : 0 -14
2 : 0 -16
2 : 0 -18
2 : 0 -20
3 : -1 0
3 : -2 0
3 : -3 0
3 : -4 0
3 : -5 0
3 : -6 0
3 : -7 0
3 : -8 0
3 : -9 0
3 : -10 0
4 : 0 2
4 : 0 8
4 : 0 18
4 : 0 32
4 : 0 50
4 : 0 72
4 : 0 98
4 : 0 128
4 : 0 162
4 : 0 200
5 : 1 0
5 : 4 0
5 : 9 0
5 : 16 0
5 : 25 0
5 : 36 0
5 : 49 0
5 : 64 0
5 : 81 0
5 : 100 0
6 : 0 -2
6 : 0 -16
6 : 0 -54
6 : 0 -128
6 : 0 -250
6 : 0 -432
6 : 0 -686
6 : 0 -1024
6 : 0 -1458
6 : 0 -2000
7 : -1 0
7 : -8 0
7 : -27 0
7 : -64 0
7 : -125 0
7 : -216 0
7 : -343 0
7 : -512 0
7 : -729 0
7 : -1000 0
8 : 0 2
8 : 0 32
8 : 0 162
8 : 0 512
8 : 0 1250
8 : 0 2592
8 : 0 4802
8 : 0 8192
8 : 0 13122
8 : 0 20000
9 : 1 0
9 : 16 0
9 : 81 0
9 : 256 0
9 : 625 0
9 : 1296 0
9 : 2401 0
9 : 4096 0
9 : 6561 0
9 : 10000 0
10 : 0 -2
10 : 0 -64
10 : 0 -486
10 : 0 -2048
10 : 0 -6250
10 : 0 -15552
10 : 0 -33614
10 : 0 -65536
10 : 0 -118098
10 : 0 -200000

Total time: 0.200 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:28:35 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl*Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
        assert (Vl eq 0 and Uh eq 0) or (Vh eq 0);
    end for;
    assert Vl*Vh eq 0;
    //assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    assert Uh*Vl eq 0;
    return Uh, Vl;
end function;

for i, j in [1..10] do
    i, ":", Lucas(j, i);
end for;


Output: Magma V2.11-10    Sat Dec 10 2005 10:28:34 on modular  [Seed = 2141636625]
   -------------------------------------

1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
1 : 1 0
2 : 0 -2
2 : 0 -4
2 : 0 -6
2 : 0 -8
2 : 0 -10
2 : 0 -12
2 : 0 -14
2 : 0 -16
2 : 0 -18
2 : 0 -20
3 : -1 0
3 : -2 0
3 : -3 0
3 : -4 0
3 : -5 0
3 : -6 0
3 : -7 0
3 : -8 0
3 : -9 0
3 : -10 0
4 : 0 2
4 : 0 8
4 : 0 18
4 : 0 32
4 : 0 50
4 : 0 72
4 : 0 98
4 : 0 128
4 : 0 162
4 : 0 200
5 : 1 0
5 : 4 0
5 : 9 0
5 : 16 0
5 : 25 0
5 : 36 0
5 : 49 0
5 : 64 0
5 : 81 0
5 : 100 0
6 : 0 -2
6 : 0 -16
6 : 0 -54
6 : 0 -128
6 : 0 -250
6 : 0 -432
6 : 0 -686
6 : 0 -1024
6 : 0 -1458
6 : 0 -2000
7 : -1 0
7 : -8 0
7 : -27 0
7 : -64 0
7 : -125 0
7 : -216 0
7 : -343 0
7 : -512 0
7 : -729 0
7 : -1000 0
8 : 0 2
8 : 0 32
8 : 0 162
8 : 0 512
8 : 0 1250
8 : 0 2592
8 : 0 4802
8 : 0 8192
8 : 0 13122
8 : 0 20000
9 : 1 0
9 : 16 0
9 : 81 0
9 : 256 0
9 : 625 0
9 : 1296 0
9 : 2401 0
9 : 4096 0
9 : 6561 0
9 : 10000 0
10 : 0 -2
10 : 0 -64
10 : 0 -486
10 : 0 -2048
10 : 0 -6250
10 : 0 -15552
10 : 0 -33614
10 : 0 -65536
10 : 0 -118098
10 : 0 -200000

Total time: 0.190 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:27:19 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl*Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
        assert (Vl eq 0 and Uh eq 0) or (Vh eq 0);
    end for;
    assert Vl*Vh eq 0;
    //assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    assert Uh*Vl eq 0;
    return Uh, Vl;
end function;

for i in [1..100] do
    i, ":", Lucas(5, i);
end for;


Output: Magma V2.11-10    Sat Dec 10 2005 10:27:18 on modular  [Seed = 1639502331]
   -------------------------------------

1 : 1 0
2 : 0 -10
3 : -5 0
4 : 0 50
5 : 25 0
6 : 0 -250
7 : -125 0
8 : 0 1250
9 : 625 0
10 : 0 -6250
11 : -3125 0
12 : 0 31250
13 : 15625 0
14 : 0 -156250
15 : -78125 0
16 : 0 781250
17 : 390625 0
18 : 0 -3906250
19 : -1953125 0
20 : 0 19531250
21 : 9765625 0
22 : 0 -97656250
23 : -48828125 0
24 : 0 488281250
25 : 244140625 0
26 : 0 -2441406250
27 : -1220703125 0
28 : 0 12207031250
29 : 6103515625 0
30 : 0 -61035156250
31 : -30517578125 0
32 : 0 305175781250
33 : 152587890625 0
34 : 0 -1525878906250
35 : -762939453125 0
36 : 0 7629394531250
37 : 3814697265625 0
38 : 0 -38146972656250
39 : -19073486328125 0
40 : 0 190734863281250
41 : 95367431640625 0
42 : 0 -953674316406250
43 : -476837158203125 0
44 : 0 4768371582031250
45 : 2384185791015625 0
46 : 0 -23841857910156250
47 : -11920928955078125 0
48 : 0 119209289550781250
49 : 59604644775390625 0
50 : 0 -596046447753906250
51 : -298023223876953125 0
52 : 0 2980232238769531250
53 : 1490116119384765625 0
54 : 0 -14901161193847656250
55 : -7450580596923828125 0
56 : 0 74505805969238281250
57 : 37252902984619140625 0
58 : 0 -372529029846191406250
59 : -186264514923095703125 0
60 : 0 1862645149230957031250
61 : 931322574615478515625 0
62 : 0 -9313225746154785156250
63 : -4656612873077392578125 0
64 : 0 46566128730773925781250
65 : 23283064365386962890625 0
66 : 0 -232830643653869628906250
67 : -116415321826934814453125 0
68 : 0 1164153218269348144531250
69 : 582076609134674072265625 0
70 : 0 -5820766091346740722656250
71 : -2910383045673370361328125 0
72 : 0 29103830456733703613281250
73 : 14551915228366851806640625 0
74 : 0 -145519152283668518066406250
75 : -72759576141834259033203125 0
76 : 0 727595761418342590332031250
77 : 363797880709171295166015625 0
78 : 0 -3637978807091712951660156250
79 : -1818989403545856475830078125 0
80 : 0 18189894035458564758300781250
81 : 9094947017729282379150390625 0
82 : 0 -90949470177292823791503906250
83 : -45474735088646411895751953125 0
84 : 0 454747350886464118957519531250
85 : 227373675443232059478759765625 0
86 : 0 -2273736754432320594787597656250
87 : -1136868377216160297393798828125 0
88 : 0 11368683772161602973937988281250
89 : 5684341886080801486968994140625 0
90 : 0 -56843418860808014869689941406250
91 : -28421709430404007434844970703125 0
92 : 0 284217094304040074348449707031250
93 : 142108547152020037174224853515625 0
94 : 0 -1421085471520200371742248535156250
95 : -710542735760100185871124267578125 0
96 : 0 7105427357601001858711242675781250
97 : 3552713678800500929355621337890625 0
98 : 0 -35527136788005009293556213378906250
99 : -17763568394002504646778106689453125 0
100 : 0 177635683940025046467781066894531250

Total time: 0.190 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:27:02 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl*Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
        assert (Vl eq 0 and Uh eq 0) or (Vh eq 0);
    end for;
    assert Vl*Vh eq 0;
    //assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    assert Uh*Vl eq 0;
    return Uh, Vl;
end function;

for i in [1, 100] do
    i, ":", Lucas(5, i);
end for;


Output: Magma V2.11-10    Sat Dec 10 2005 10:27:01 on modular  [Seed = 1690162413]
   -------------------------------------

1 : 1 0
100 : 0 177635683940025046467781066894531250

Total time: 0.190 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:26:01 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl*Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
        assert (Vl eq 0 and Uh eq 0) or (Vh eq 0 and Uh eq -Ql);
    end for;
    assert Vl*Vh eq 0;
    //assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    assert Uh*Vl eq 0;
    return Uh, Vl;
end function;

for i in [1, 100] do
    i, ":", Lucas(5, i);
end for;


Output: Magma V2.11-10    Sat Dec 10 2005 10:26:01 on modular  [Seed = 1874255786]
   -------------------------------------

1 : 1 0

Lucas(
    Q: 5,
    k: 100
)
>>         assert (Vl eq 0 and Uh eq 0) or (Vh eq 0 and Uh eq -Ql);
           ^
Runtime error in assert: Assertion failed

Total time: 0.190 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:24:16 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl*Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
        assert (Vl eq 0 and Uh eq 0) or (Vh eq 0 and Uh eq -Ql);
    end for;
    assert Vl*Vh eq 0;
    //assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    return Uh, Vl;
end function;

Lucas(5, 1);
Lucas(5, 2);
Lucas(5, 3);
Lucas(5, 4);
Lucas(5, 5);
Lucas(5, 6);
Lucas(5, 7);
Lucas(5, 8);


Output: Magma V2.11-10    Sat Dec 10 2005 10:24:16 on modular  [Seed = 1384899134]
   -------------------------------------

1 0
0 -10
-5 0
0 50
25 0
0 -250
-125 0
0 1250

Total time: 0.190 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:23:11 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl*Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
        assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    end for;
    assert Vl*Vh eq 0;
    //assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    return Uh, Vl;
end function;

Lucas(5, 1);
Lucas(5, 2);
Lucas(5, 3);
Lucas(5, 4);
Lucas(5, 5);
Lucas(5, 6);
Lucas(5, 7);
Lucas(5, 8);


Output: Magma V2.11-10    Sat Dec 10 2005 10:23:10 on modular  [Seed = 1535306441]
   -------------------------------------

1 0
0 -10
-5 0
0 50
25 0
0 -250

Lucas(
    Q: 5,
    k: 7
)
>>         assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq 
           ^
Runtime error in assert: Assertion failed
0 1250

Total time: 0.190 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:22:25 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl*Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
        assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    end for;
    assert Vl*Vh eq 0;
    assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    return Uh, Vl;
end function;

//Lucas(5, 1);
//Lucas(5, 2);
Lucas(5, 3);
Lucas(5, 4);
Lucas(5, 5);
Lucas(5, 6);
Lucas(5, 7);
Lucas(5, 8);


Output: Magma V2.11-10    Sat Dec 10 2005 10:22:25 on modular  [Seed = 1552280993]
   -------------------------------------

-5 0

Lucas(
    Q: 5,
    k: 4
)
>>     assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql 
       ^
Runtime error in assert: Assertion failed
25 0
0 -250

Lucas(
    Q: 5,
    k: 7
)
>>         assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq 
           ^
Runtime error in assert: Assertion failed

Lucas(
    Q: 5,
    k: 8
)
>>     assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql 
       ^
Runtime error in assert: Assertion failed

Total time: 0.200 seconds, Total memory usage: 3.34MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:21:29 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl*Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
        assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    end for;
    assert Vl*Vh eq 0;
    assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    return Uh, Vl;
end function;

Lucas(5, 1);
Lucas(5, 2);
Lucas(5, 3);
Lucas(5, 4);
Lucas(5, 5);


Output: Magma V2.11-10    Sat Dec 10 2005 10:21:29 on modular  [Seed = 3010069127]
   -------------------------------------


Lucas(
    Q: 5,
    k: 1
)
>>     assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql 
       ^
Runtime error in assert: Assertion failed

Lucas(
    Q: 5,
    k: 2
)
>>     assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql 
       ^
Runtime error in assert: Assertion failed
-5 0

Lucas(
    Q: 5,
    k: 4
)
>>     assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql 
       ^
Runtime error in assert: Assertion failed
25 0

Total time: 0.190 seconds, Total memory usage: 3.34MB


'80.184.'
************** MAGMA *****************
Host 80.184.165.238 (80.184.165.238)
Time: Sat Dec 10 10:21:23 2005

Input: gcd(105;384)

Output: Magma V2.11-10    Sat Dec 10 2005 10:21:23 on modular  [Seed = 3027043722]
   -------------------------------------


>> gcd(105;384);
          ^
User error: bad syntax

Total time: 0.180 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:14:32 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl eq 0 or Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
        assert (Vl eq 0 and Uh eq 0 and Vh eq -2*Qh) or (Vh eq 0 and Uh eq -Ql and Vl eq -2*Ql);
    end for;
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    return Uh, Vl;
end function;

Lucas(5, 3);

Output: Magma V2.11-10    Sat Dec 10 2005 10:14:31 on modular  [Seed = 2521769228]
   -------------------------------------

-5 0

Total time: 0.190 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:10:40 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        assert Vl eq 0 or Vh eq 0;
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
    end for;
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    return Uh, Vl;
end function;

Lucas(5, 3);

Output: Magma V2.11-10    Sat Dec 10 2005 10:10:40 on modular  [Seed = 2554410021]
   -------------------------------------

-5 0

Total time: 0.210 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:09:26 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

GetBit := function(k, j)
  return (k div 2^j) mod 2;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        Ql *:= Qh;
        if GetBit(k, j) eq 1 then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
    end for;
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    return Uh, Vl;
end function;

Lucas(5, 3);

Output: Magma V2.11-10    Sat Dec 10 2005 10:09:25 on modular  [Seed = 2638492021]
   -------------------------------------

-5 0

Total time: 0.200 seconds, Total memory usage: 3.24MB


'200.177'
************** MAGMA *****************
Host 200.177.7.181 (200.177.7.181)
Time: Sat Dec 10 10:07:32 2005

Input: BitLength := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; n := 0;
    while v ne 0 do
        v div:= 2; n +:= 1;
    end while;
    return n;
end function;

TrailingZeroes := function(k)
    if k lt 0 then
        return -1;
    end if;
    v := k; s := 0;
    while v ne 0 and v mod 2 eq 0 do
        v div:= 2; s +:= 1;
    end while;
    return s;
end function;

TestBit := function(k, j)
  return (2^j and k) ne 0;
end function;

Lucas := function(Q, k)
    n := BitLength(k);
    s := TrailingZeroes(k);
    Uh := 1; Vl := 2; Vh := 0; Ql := 1; Qh := 1;
    for j := n - 1 to s + 1 by -1 do
        Ql *:= Qh;
        if TestBit(k, j) then
            Qh := Ql*Q;
            Uh *:= Vh;
            Vl *:= Vh;
            Vh *:= Vh; Vh -:= 2*Qh;
        else
            Qh := Ql;
            Uh *:= Vl; Uh -:= Ql;
            Vh *:= Vl;
            Vl *:= Vl; Vl -:= 2*Ql;
        end if;
    end for;
    Ql *:= Qh; Qh := Ql*Q;
    Uh *:= Vl; Uh -:= Ql;
    Vl *:= Vh;
    Ql *:= Qh;
    for j := 1 to s do
        Uh *:= Vl;
        Vl *:= Vl; Vl -:= 2*Ql;
        Ql *:= Ql;
    end for;
    return Uh, Vl;
end function;

Lucas(5, 3);

Output: Magma V2.11-10    Sat Dec 10 2005 10:07:31 on modular  [Seed = 4045954447]
   -------------------------------------


Lucas(
    Q: 5,
    k: 3
)
TestBit(
    k: 3,
    j: 1
)
>>   return (2^j and k) ne 0;
                 ^
Runtime error: Expected a logical for the 'and' operator

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Sat Dec 10 08:40:00 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
IsSelfOrthogonal(C);
WeightDistribution(C);

Output: Magma V2.11-10    Sat Dec 10 2005 08:38:02 on modular  [Seed = 2023874932]
   -------------------------------------

false
[ <0, 1>, <16, 5082>, <20, 91168>, <24, 507045>, <28, 890560>, <32, 507045>, 
<36, 91168>, <40, 5082>, <56, 1> ]

Total time: 0.100 seconds, Total memory usage: 3.34MB


'219.108'
************** MAGMA *****************
Host 219.108.73.204 (219.108.73.204)
Time: Sat Dec 10 06:55:26 2005

Input: V:=EvenWeightCode(27);
e1:=CharacteristicVector(VectorSpace(GF(2),27),{1});
// for v1 in V do
v1:=Random(V);
  x:=v1+e1;
  v:=Vector(GF(2),56,[0: i in [1..28]] cat [1] cat Eltseq(x));

v;
Weight(v);


Output: Magma V2.11-10    Sat Dec 10 2005 06:55:10 on modular  [Seed = 1267911207]
   -------------------------------------

(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 1 0
    1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0)
16

Total time: 0.180 seconds, Total memory usage: 3.24MB


'219.108'
************** MAGMA *****************
Host 219.108.73.204 (219.108.73.204)
Time: Sat Dec 10 06:54:52 2005

Input: 
V:=EvenWeightCode(27);
e1:=CharacteristicVector(VectorSpace(GF(2),27),{1});
// for v1 in V do
v1:=Random(V);
  x:=v1+e1;
  v:=Vector(GF(2),56,[0: i in [1..28]] cat [1] cat Eltseq(x));

v;


Output: Magma V2.11-10    Sat Dec 10 2005 06:54:42 on modular  [Seed = 2959684093]
   -------------------------------------

(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 1
    1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0)

Total time: 0.200 seconds, Total memory usage: 3.24MB


'219.108'
************** MAGMA *****************
Host 219.108.73.204 (219.108.73.204)
Time: Sat Dec 10 06:54:47 2005

Input: 
V:=EvenWeightCode(27);
e1:=CharacteristicVector(VectorSpace(GF(2),27),{1});
// for v1 in V do
v1:=Random(V);
  x:=v1+e1;
  v:=Vector(GF(2),56,[0: i in [1..28]] cat [1] cat Eltseq(x));

v;


Output: Magma V2.11-10    Sat Dec 10 2005 06:54:08 on modular  [Seed = 3010081052]
   -------------------------------------

(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1
    0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0)

Total time: 0.180 seconds, Total memory usage: 3.24MB


'219.108'
************** MAGMA *****************
Host 219.108.73.204 (219.108.73.204)
Time: Sat Dec 10 06:53:02 2005

Input: V:=EvenWeightCode(27);
e1:=CharacteristicVector(VectorSpace(GF(2),27),{1});
// for v1 in V do
v1:=Randam(V);
  x:=v1+e1;
  v:=Vector(GF(2),56,[0: i in [1..28]] cat [1] cat Eltseq(x));

v;


Output: Magma V2.11-10    Sat Dec 10 2005 06:52:59 on modular  [Seed = 3143776623]
   -------------------------------------


>> v1:=Randam(V);
       ^
User error: Identifier 'Randam' has not been declared or assigned

>>   x:=v1+e1;
        ^
User error: Identifier 'v1' has not been declared or assigned

>>   v:=Vector(GF(2),56,[0: i in [1..28]] cat [1] cat Eltseq(x));
                                                             ^
User error: Identifier 'x' has not been declared or assigned

>> v;
   ^
User error: Identifier 'v' has not been declared or assigned

Total time: 0.220 seconds, Total memory usage: 3.24MB


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 10 03:43:11 2005

Input: G :=DirichletGroup(210);
G;
X :=Elements(G);
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 6, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;


Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Sat Dec 10 2005 03:42:50 on modular  [Seed = 3177475070]
   -------------------------------------

Group of Dirichlet characters of modulus 210 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2,
    $.3,
    $.1*$.3,
    $.2*$.3,
    $.1*$.2*$.3
]
1
1

Errors: /bin/sh: line 1:  2804 Alarm clock             nice -n 19 /usr/local/bin/magma


'204.210'
************** MAGMA *****************
Host 204.210.35.48 (204.210.35.48)
Time: Sat Dec 10 03:21:17 2005

Input: 
G :=DirichletGroup(610);
G;
X :=Elements(G);
X;
Y :=X[1]; Conductor(Y); Order(Y);
M := ModularSymbols(Y, 6, 1);
D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
D;


Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.11-10    Sat Dec 10 2005 03:21:10 on modular  [Seed = 3256553084]
   -------------------------------------

Group of Dirichlet characters of modulus 610 over Rational Field
[
    1,
    $.1,
    $.2,
    $.1*$.2
]
1
1

Current total memory usage: 68.2MB, failed memory request: 29.7MB
System Error: User memory limit has been reached

>> D := NewformDecomposition(NewSubspace(CuspidalSubspace(M)));
                                                          ^
Runtime error: Variable 'M' has not been initialized

>> D;
   ^
User error: Identifier 'D' has not been declared or assigned

Total time: 3.600 seconds, Total memory usage: 68.18MB


'69.175.'
************** MAGMA *****************
Host 69.175.68.230 (69.175.68.230)
Time: Fri Dec  9 12:20:25 2005

Input: x = 1 + 2

Output: Magma V2.11-10    Fri Dec  9 2005 12:20:25 on modular  [Seed = 1201518809]
   -------------------------------------


>> x = 1 + 2;
   ^
User error: Identifier 'x' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'87.69.5'
************** MAGMA *****************
Host 87.69.58.225 (87.69.58.225)
Time: Fri Dec  9 12:12:21 2005

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.11-10    Fri Dec  9 2005 12:12:20 on modular  [Seed = 2621859112]
   -------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 0.200 seconds, Total memory usage: 3.24MB


'152.6.1'
************** MAGMA *****************
Host 152.6.19.192 (152.6.19.192)
Time: Fri Dec  9 11:40:12 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
[1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
[0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);

Output: Magma V2.11-10    Fri Dec  9 2005 11:40:12 on modular  [Seed = 2170253740]
   -------------------------------------

1344
[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
{
    (3, 4)(7, 8),
    (4, 6)(5, 7),
    (4, 7)(5, 6),
    (1, 2)(5, 6),
    (2, 4, 3)(6, 8, 7)
}
true

Total time: 0.200 seconds, Total memory usage: 3.24MB


'152.6.1'
************** MAGMA *****************
Host 152.6.19.192 (152.6.19.192)
Time: Fri Dec  9 11:39:02 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
[1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
[0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);

Output: Magma V2.11-10    Fri Dec  9 2005 11:39:01 on modular  [Seed = 4196403870]
   -------------------------------------

1344
[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
{
    (3, 4)(7, 8),
    (4, 6)(5, 7),
    (4, 7)(5, 6),
    (1, 2)(5, 6),
    (2, 4, 3)(6, 8, 7)
}
true

Total time: 0.200 seconds, Total memory usage: 3.24MB


'152.6.1'
************** MAGMA *****************
Host 152.6.19.192 (152.6.19.192)
Time: Fri Dec  9 10:46:16 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);
WeightDistribution(C);

Output: Magma V2.11-10    Fri Dec  9 2005 10:46:15 on modular  [Seed = 804637353]
   -------------------------------------

7
[ <7, 1> ]
    G
    |  Cyclic(7)
    1
{
    (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14)(15, 16, 17, 18, 19, 20, 
        21)(22, 23, 24, 25, 26, 27, 28)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 
        39, 40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)
}
false
[ <0, 1>, <16, 5082>, <20, 91168>, <24, 507045>, <28, 890560>, <32, 507045>, 
<36, 91168>, <40, 5082>, <56, 1> ]

Total time: 0.310 seconds, Total memory usage: 5.51MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Fri Dec  9 09:21:10 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);
WeightDistribution(C);

Output: Magma V2.11-10    Fri Dec  9 2005 09:21:09 on modular  [Seed = 2554480911]
   -------------------------------------

7
[ <7, 1> ]
    G
    |  Cyclic(7)
    1
{
    (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14)(15, 16, 17, 18, 19, 20, 
        21)(22, 23, 24, 25, 26, 27, 28)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 
        39, 40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)
}
false
[ <0, 1>, <16, 5082>, <20, 91168>, <24, 507045>, <28, 890560>, <32, 507045>, 
<36, 91168>, <40, 5082>, <56, 1> ]

Total time: 0.300 seconds, Total memory usage: 5.51MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Fri Dec  9 09:16:23 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 56 |   [1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0],
[0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0],
[0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0],
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,1,1,0,0,1,0],
[0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0,1],
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);

Output: Magma V2.11-10    Fri Dec  9 2005 09:16:23 on modular  [Seed = 2404736378]
   -------------------------------------

7
[ <7, 1> ]
    G
    |  Cyclic(7)
    1
{
    (1, 2, 3, 4, 5, 6, 7)(8, 9, 10, 11, 12, 13, 14)(15, 16, 17, 18, 19, 20, 
        21)(22, 23, 24, 25, 26, 27, 28)(29, 30, 31, 32, 33, 34, 35)(36, 37, 38, 
        39, 40, 41, 42)(43, 44, 45, 46, 47, 48, 49)(50, 51, 52, 53, 54, 55, 56)
}
false

Total time: 0.270 seconds, Total memory usage: 5.51MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Fri Dec  9 08:49:20 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);

Output: Magma V2.11-10    Fri Dec  9 2005 08:49:19 on modular  [Seed = 3996395251]
   -------------------------------------

1344
[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
{
    (3, 4)(7, 8),
    (4, 6)(5, 7),
    (4, 7)(5, 6),
    (1, 2)(5, 6),
    (2, 4, 3)(6, 8, 7)
}
true

Total time: 0.200 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Fri Dec  9 08:48:35 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1 0 0 0 0 1 1 1] [0 1 0 0 1 0 1 1]  
>    [0 0 1 0 1 1 0 1] [0 0 0 1 1 1 1 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);

Output: Magma V2.11-10    Fri Dec  9 2005 08:48:35 on modular  [Seed = 3829279893]
   -------------------------------------


>>      [1 0 0 0 0 1 1 1] [0 1 0 0 1 0 1 1]  
           ^
User error: bad syntax

>>      [0 0 1 0 1 1 0 1] [0 0 0 1 1 1 1 0]>;
           ^
User error: bad syntax

>>   aut := AutomorphismGroup(C);
                              ^
User error: Identifier 'C' has not been declared or assigned

>> Order(aut);
         ^
User error: Identifier 'aut' has not been declared or assigned

>>   FactoredOrder(aut);
                   ^
User error: Identifier 'aut' has not been declared or assigned

>>   CompositionFactors(aut);
                        ^
User error: Identifier 'aut' has not been declared or assigned

>> Generators(aut);
              ^
User error: Identifier 'aut' has not been declared or assigned

>> IsSelfOrthogonal(C);;
                    ^
User error: Identifier 'C' has not been declared or assigned

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Fri Dec  9 08:46:50 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);

Output: Magma V2.11-10    Fri Dec  9 2005 08:46:50 on modular  [Seed = 3812174443]
   -------------------------------------

1344
[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
{
    (3, 4)(7, 8),
    (4, 6)(5, 7),
    (4, 7)(5, 6),
    (1, 2)(5, 6),
    (2, 4, 3)(6, 8, 7)
}
true

Total time: 0.190 seconds, Total memory usage: 3.24MB


'141.20.'
************** MAGMA *****************
Host 141.20.57.85 (141.20.57.85)
Time: Fri Dec  9 08:35:26 2005

Input: H := PermutationGroup< 5 | (1,2,3,5),(1,2,3,4) >;
H;
FPGroup(H);


Output: Magma V2.11-10    Fri Dec  9 2005 08:35:26 on modular  [Seed = 3474261139]
   -------------------------------------

Permutation group H acting on a set of cardinality 5
    (1, 2, 3, 5)
    (1, 2, 3, 4)
Finitely presented group on 2 generators
Relations
    $.1^4 = Id($)
    $.2^4 = Id($)
    ($.2^-1 * $.1)^3 = Id($)
    ($.1^-1, $.2^-1)^2 = Id($)
    $.2^-1 * $.1^-2 * $.2^-1 * $.1^2 * $.2^2 * $.1^-1 * $.2^-1 = Id($)

Total time: 0.190 seconds, Total memory usage: 3.34MB


'141.20.'
************** MAGMA *****************
Host 141.20.57.85 (141.20.57.85)
Time: Fri Dec  9 08:31:58 2005

Input: H := PermutationGroup< 9 | (1,2,4)(5,6,8)(3,9,7), (4,5,6)(7,9,8) >;
H;
FPGroup(H);


Output: Magma V2.11-10    Fri Dec  9 2005 08:31:57 on modular  [Seed = 3390049989]
   -------------------------------------

Permutation group H acting on a set of cardinality 9
    (1, 2, 4)(3, 9, 7)(5, 6, 8)
    (4, 5, 6)(7, 9, 8)
Finitely presented group on 2 generators
Relations
    $.1^-3 = Id($)
    $.2^-3 = Id($)
    ($.1^-1 * $.2^-1)^4 = Id($)
    $.1^-1 * $.2^-1 * $.1 * $.2^-1 * $.1^-1 * $.2^-1 * $.1 * $.2 * $.1^-1 * $.2 
    * $.1 * $.2 = Id($)

Total time: 0.190 seconds, Total memory usage: 3.34MB


'141.20.'
************** MAGMA *****************
Host 141.20.57.85 (141.20.57.85)
Time: Fri Dec  9 08:31:32 2005

Input: H := PermutationGroup< 9 | (1,2,4)(5,6,8)(3,9,7), (4,5,6)(7,9,8) >;
H;


Output: Magma V2.11-10    Fri Dec  9 2005 08:31:32 on modular  [Seed = 3323724464]
   -------------------------------------

Permutation group H acting on a set of cardinality 9
    (1, 2, 4)(3, 9, 7)(5, 6, 8)
    (4, 5, 6)(7, 9, 8)

Total time: 0.200 seconds, Total memory usage: 3.24MB


'141.20.'
************** MAGMA *****************
Host 141.20.57.85 (141.20.57.85)
Time: Fri Dec  9 08:30:49 2005

Input: H := PermutationGroup< 9 | (1,2,4)(5,6,8)(3,9,7), (4,5,6)(7,9,8) >;

Output: Magma V2.11-10    Fri Dec  9 2005 08:30:49 on modular  [Seed = 1038612854]
   -------------------------------------


Total time: 0.200 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 08:00:24 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(1-2*b)*(a+b+c-1);
print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(4*b*(b+c-1)*(a+b-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 08:00:24 on modular  [Seed = 2254223954]
   -------------------------------------

[
    <b, 1>,
    <b + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
[
    <b - 1/2, 2>,
    <a + b + c - 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:59:55 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(1-2*b)*(a+b+c-1);
print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(4*a*(a+c-1)*(a+b-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:59:54 on modular  [Seed = 1267824573]
   -------------------------------------

[
    <b, 1>,
    <b + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
[
    <a + b + c - 1, 1>,
    <a - 1/2, 2>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:57:36 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(1-2*a)*(a+b+c-1);
print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(4*a*(a+c-1)*(a+b-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:57:35 on modular  [Seed = 1622826083]
   -------------------------------------

[
    <a, 1>,
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
[
    <a + b + c - 1, 1>,
    <a - 1/2, 2>
]

Total time: 0.200 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:57:26 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(1-2*a)*(a+b+c-1);
print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(4*a*(a+c-1)*(a+b-1)*(a+b+c-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:57:26 on modular  [Seed = 1789941344]
   -------------------------------------

[
    <a, 1>,
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
[
    <a^4 + 2*a^3*b + 2*a^3*c - 3*a^3 + a^2*b^2 + 3*a^2*b*c - 4*a^2*b + a^2*c^2 -
        4*a^2*c + 3*a^2 + a*b^2*c - a*b^2 + a*b*c^2 - 4*a*b*c + 2*a*b - a*c^2 + 
        2*a*c - 3/4*a + 1/4*b + 1/4*c - 1/4, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:56:29 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(1-2*a)*(a+b+c-1);
print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(4*a*(a+c-1)*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:56:28 on modular  [Seed = 2057324474]
   -------------------------------------

[
    <a, 1>,
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
[
    <a + b + c - 1, 2>,
    <a - 1/2, 2>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:56:13 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(1-2*a)*(a+b+c-1);
print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a*(a+c-1)*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:56:13 on modular  [Seed = 64569042]
   -------------------------------------

[
    <a, 1>,
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
[
    <a + b + c - 1, 1>,
    <a^3 + a^2*b + a^2*c - 2*a^2 - 3*a*b*c - a*b - a*c + 2*a + b + c - 1, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:55:35 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(1-2*a)*(a+b+c-1);
print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a*(a+c-1)*(a*(a+b-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:55:34 on modular  [Seed = 181417968]
   -------------------------------------

[
    <a, 1>,
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]

>> print Factorization(a*(a+c-1)*(a*(a+b-1)-(4*a*b*c-a-b-c+1));;
                                                              ^
User error: bad syntax

Total time: 0.200 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:55:18 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a*(a+c-1)*(a+b+c-1)*(a+b-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:55:17 on modular  [Seed = 331951770]
   -------------------------------------

[
    <a^4 + 2*a^3*b + 2*a^3*c - 3*a^3 + a^2*b^2 + 3*a^2*b*c - 4*a^2*b + a^2*c^2 -
        4*a^2*c + 3*a^2 + a*b^2*c - a*b^2 + a*b*c^2 - 7*a*b*c + 2*a*b - a*c^2 + 
        2*a*c + b + c - 1, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:55:08 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a*(a+c-1)*(a+b-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:55:08 on modular  [Seed = 365897861]
   -------------------------------------

[
    <a^3 + a^2*b + a^2*c - 2*a^2 - 3*a*b*c - a*b - a*c + 2*a + b + c - 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:54:40 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a^2*b^2*c^3*(a+b-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:54:40 on modular  [Seed = 482746800]
   -------------------------------------

[
    <a^3*b^2*c^3 + a^2*b^3*c^3 - a^2*b^2*c^3 - 4*a*b*c + a + b + c - 1, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:54:23 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a^3*b^3*c^3*(a+b-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:54:23 on modular  [Seed = 637474918]
   -------------------------------------

[
    <a^4*b^3*c^3 + a^3*b^4*c^3 - a^3*b^3*c^3 - 4*a*b*c + a + b + c - 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:54:03 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a*b*(a+b-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:54:02 on modular  [Seed = 771166331]
   -------------------------------------

[
    <a^2*b + a*b^2 - 4*a*b*c - a*b + a + b + c - 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:52:46 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a*b*c*(a+b-1)-(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:52:45 on modular  [Seed = 1021706525]
   -------------------------------------

[
    <a^2*b*c + a*b^2*c - 5*a*b*c + a + b + c - 1, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:49:19 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(2*a^2*b^2*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:49:19 on modular  [Seed = 3608013221]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2*c + a^2*b^3*c - a^2*b^2*c - 2*a*b*c + 1/2*a + 1/2*b + 1/2*c - 1/2, 
    1>
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:48:58 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a^2*b^2*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:48:57 on modular  [Seed = 3724861658]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2*c + a^2*b^3*c - a^2*b^2*c - 4*a*b*c + a + b + c - 1, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:48:40 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(1/2*a*b*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:48:40 on modular  [Seed = 3778797556]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b + a*b^2 - 8*a*b*c - a*b + 2*a + 2*b + 2*c - 2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:48:33 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-1/2*a*b*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:48:33 on modular  [Seed = 3945911799]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b + a*b^2 + 8*a*b*c - a*b - 2*a - 2*b - 2*c + 2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:48:26 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-1/4*a*b*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:48:26 on modular  [Seed = 3979858890]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b + a*b^2 + 16*a*b*c - a*b - 4*a - 4*b - 4*c + 4, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:48:20 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(1/4*a*b*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:48:20 on modular  [Seed = 4146973150]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b + a*b^2 - 16*a*b*c - a*b + 4*a + 4*b + 4*c - 4, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.53MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:48:13 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(1/4*a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:48:13 on modular  [Seed = 4163028680]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c - 17*a*b*c + 4*a + 4*b + 4*c - 4, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:48:07 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-1/4*a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:48:06 on modular  [Seed = 2186853560]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c + 15*a*b*c - 4*a - 4*b - 4*c + 4, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:48:01 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-1/2*a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:48:01 on modular  [Seed = 2271066555]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c + 7*a*b*c - 2*a - 2*b - 2*c + 2, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:47:55 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(1/2*a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:47:54 on modular  [Seed = 2303964750]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c - 9*a*b*c + 2*a + 2*b + 2*c - 2, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:47:36 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(16*a^2*b^2*c^2*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:47:35 on modular  [Seed = 2471078985]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2*c^2 + a^2*b^3*c^2 - a^2*b^2*c^2 - 1/4*a*b*c + 1/16*a + 1/16*b + 
        1/16*c - 1/16, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:47:27 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(8*a^2*b^2*c^2*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:47:27 on modular  [Seed = 2505026167]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2*c^2 + a^2*b^3*c^2 - a^2*b^2*c^2 - 1/2*a*b*c + 1/8*a + 1/8*b + 1/8*c
        - 1/8, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:47:13 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(6*a^2*b^2*c^2*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:47:13 on modular  [Seed = 2672140403]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2*c^2 + a^2*b^3*c^2 - a^2*b^2*c^2 - 2/3*a*b*c + 1/6*a + 1/6*b + 1/6*c
        - 1/6, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:47:05 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(6*a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:47:05 on modular  [Seed = 2709233237]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c - 5/3*a*b*c + 1/6*a + 1/6*b + 1/6*c - 1/6, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:46:59 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(8*a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:46:58 on modular  [Seed = 2876347476]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c - 3/2*a*b*c + 1/8*a + 1/8*b + 1/8*c - 1/8, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:46:42 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-2*a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:46:41 on modular  [Seed = 2910294561]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c + a*b*c - 1/2*a - 1/2*b - 1/2*c + 1/2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:46:34 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-2*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:46:34 on modular  [Seed = 3077408800]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a*b*c - 1/6*a + 1/3*b^2*c - 1/3*b*c - 1/6*b - 1/6*c + 1/6, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:46:29 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:46:28 on modular  [Seed = 3093464865]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a*b*c - 1/5*a + 1/5*b^2*c - 1/5*b*c - 1/5*b - 1/5*c + 1/5, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.53MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:46:20 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-a*b*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:46:19 on modular  [Seed = 1117289956]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b + a*b^2 + 4*a*b*c - a*b - a - b - c + 1, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:46:12 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-a*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:46:12 on modular  [Seed = 1201502446]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*c + 5*a*b*c - a*c - a - b - c + 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:46:05 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:46:04 on modular  [Seed = 1234401016]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c + 3*a*b*c - a - b - c + 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:45:41 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-4*a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:45:41 on modular  [Seed = 1351249688]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c - 1/4*a - 1/4*b - 1/4*c + 1/4, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:45:33 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-4*a^2*b^2*c^2*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:45:32 on modular  [Seed = 1435462148]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2*c^2 + a^2*b^3*c^2 - a^2*b^2*c^2 + a*b*c - 1/4*a - 1/4*b - 1/4*c + 
        1/4, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Fri Dec  9 07:45:24 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(-2*a^2*b^2*c^2*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:45:23 on modular  [Seed = 1602576385]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2*c^2 + a^2*b^3*c^2 - a^2*b^2*c^2 + 2*a*b*c - 1/2*a - 1/2*b - 1/2*c +
        1/2, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:45:18 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(2*a^2*b^2*c^2*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:45:18 on modular  [Seed = 1639669250]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2*c^2 + a^2*b^3*c^2 - a^2*b^2*c^2 - 2*a*b*c + 1/2*a + 1/2*b + 1/2*c -
        1/2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:45:05 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(4*a^2*b^2*c^2*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:45:05 on modular  [Seed = 1806783495]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2*c^2 + a^2*b^3*c^2 - a^2*b^2*c^2 - a*b*c + 1/4*a + 1/4*b + 1/4*c - 
        1/4, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:44:58 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(4*a^2*b^2*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:44:58 on modular  [Seed = 1823888155]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2 + a^2*b^3 - a^2*b^2 - a*b*c + 1/4*a + 1/4*b + 1/4*c - 1/4, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:44:51 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(2*a^2*b^2*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:44:51 on modular  [Seed = 1991002376]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2 + a^2*b^3 - a^2*b^2 - 2*a*b*c + 1/2*a + 1/2*b + 1/2*c - 1/2, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:44:45 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a^2*b^2*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:44:44 on modular  [Seed = 2074166395]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b^2 + a^2*b^3 - a^2*b^2 - 4*a*b*c + a + b + c - 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:44:37 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a^2*b*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:44:36 on modular  [Seed = 2108113524]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3*b + a^2*b^2 - a^2*b - 4*a*b*c + a + b + c - 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:44:12 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a*b*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:44:12 on modular  [Seed = 131938342]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b + a*b^2 - 4*a*b*c - a*b + a + b + c - 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:44:06 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:44:06 on modular  [Seed = 164836898]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*c - 3*a*b*c - a*c + a + b + c - 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:43:59 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:43:59 on modular  [Seed = 315108640]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a*b*c - 1/3*a - 1/3*b^2*c + 1/3*b*c - 1/3*b - 1/3*c + 1/3, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:43:53 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(2*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:43:53 on modular  [Seed = 399321123]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a*b*c - 1/2*a - b^2*c + b*c - 1/2*b - 1/2*c + 1/2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:43:47 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(2*a*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:43:47 on modular  [Seed = 415377190]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*c - a*b*c - a*c + 1/2*a + 1/2*b + 1/2*c - 1/2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.43MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:43:41 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(2*a*b*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:43:40 on modular  [Seed = 499590620]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b + a*b^2 - 2*a*b*c - a*b + 1/2*a + 1/2*b + 1/2*c - 1/2, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:43:18 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(4*a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:43:17 on modular  [Seed = 670900223]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c - 2*a*b*c + 1/4*a + 1/4*b + 1/4*c - 1/4, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:43:11 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(2*a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:43:11 on modular  [Seed = 686952650]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c - 3*a*b*c + 1/2*a + 1/2*b + 1/2*c - 1/2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.53MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:42:47 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

//s:=(1-2*a)*(a+b+c-1);
//print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));
print Factorization(a*b*c*(a+b-1)*(a+b+c-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1));

Output: Magma V2.11-10    Fri Dec  9 2005 07:42:46 on modular  [Seed = 854067913]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^2*b*c + a*b^2*c - 5*a*b*c + a + b + c - 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:39:45 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(1-2*a)*(a+b+c-1);
print Factorization(s^2+(a+b+c-1)*(4*a*b*c-a-b-c+1));


Output: Magma V2.11-10    Fri Dec  9 2005 07:39:44 on modular  [Seed = 3239836143]
   -------------------------------------

[
    <a, 1>,
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:39:28 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(2*a-1)*(a+b+c-1);
print Factorization(s^2-(a+b+c-1)*(4*a*b*c-a-b-c+1));


Output: Magma V2.11-10    Fri Dec  9 2005 07:39:28 on modular  [Seed = 3340632057]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3 + a^2*b + a^2*c - 2*a^2 - a*b*c - a*b - a*c + 3/2*a + 1/2*b + 1/2*c - 
        1/2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:39:22 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(2*a-1)*(a+b+c-1);
print Factorization(s^2-(a+b+c-1)*(4*a*b*c-a-b-c+1));


Output: Magma V2.11-10    Fri Dec  9 2005 07:39:21 on modular  [Seed = 3440899082]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3 + a^2*b + a^2*c - 2*a^2 - a*b*c - a*b - a*c + 3/2*a + 1/2*b + 1/2*c - 
        1/2, 1>
]

Total time: 0.190 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:39:13 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=(a-b)*(a+b+c-1);
print Factorization(s^2-(a+b+c-1)*(4*a*b*c-a-b-c+1));


Output: Magma V2.11-10    Fri Dec  9 2005 07:39:13 on modular  [Seed = 3490375967]
   -------------------------------------

[
    <a + b + c - 1, 1>,
    <a^3 - a^2*b + a^2*c - a^2 - a*b^2 - 6*a*b*c + 2*a*b + a + b^3 + b^2*c - b^2
        + b + c - 1, 1>
]

Total time: 0.200 seconds, Total memory usage: 3.34MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Fri Dec  9 07:38:58 2005

Input: K<a,b,c>:=PolynomialRing(RationalField(),3);

s:=a-b;
print Factorization(s^2-(a+b+c-1)*(4*a*b*c-a-b-c+1));


Output: Magma V2.11-10    Fri Dec  9 2005 07:38:54 on modular  [Seed = 3812219395]
   -------------------------------------

[
    <a^2*b*c - 1/2*a^2 + a*b^2*c + a*b*c^2 - a*b*c - 1/2*a*c + 1/2*a - 1/2*b^2 -
        1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4, 1>
]

Total time: 0.240 seconds, Total memory usage: 3.24MB


'192.122'
************** MAGMA *****************
Host 192.122.134.249 (192.122.134.249)
Time: Fri Dec  9 00:30:06 2005

Input: F := GF(8);
a :=PrimitiveElement(F);
(1+a)^(-1);

Output: Magma V2.11-10    Fri Dec  9 2005 00:30:05 on modular  [Seed = 4213288604]
   -------------------------------------

F.1^4

Total time: 0.190 seconds, Total memory usage: 3.24MB


'192.122'
************** MAGMA *****************
Host 192.122.134.249 (192.122.134.249)
Time: Fri Dec  9 00:29:43 2005

Input: F := GF(8);
a :=PrimitiveElement(F);
a^(-1);

Output: Magma V2.11-10    Fri Dec  9 2005 00:29:43 on modular  [Seed = 2254230523]
   -------------------------------------

F.1^6

Total time: 0.190 seconds, Total memory usage: 3.24MB


'192.122'
************** MAGMA *****************
Host 192.122.134.249 (192.122.134.249)
Time: Fri Dec  9 00:29:07 2005

Input: F := GF(8);
a :=PrimitiveElement(F);
Inverse(a);

Output: Magma V2.11-10    Fri Dec  9 2005 00:29:07 on modular  [Seed = 2371344532]
   -------------------------------------


>> Inverse(a);;
          ^
Runtime error in 'Inverse': Argument 1 must be a variable reference (use ~)
Argument types given: FldFinElt

Total time: 0.190 seconds, Total memory usage: 3.24MB


'192.122'
************** MAGMA *****************
Host 192.122.134.249 (192.122.134.249)
Time: Fri Dec  9 00:28:02 2005

Input: F := GF(8);
a :=PrimitiveElement(F);
Trace(a+1);

Output: Magma V2.11-10    Fri Dec  9 2005 00:28:02 on modular  [Seed = 2337398099]
   -------------------------------------

1

Total time: 0.180 seconds, Total memory usage: 3.24MB


'192.122'
************** MAGMA *****************
Host 192.122.134.249 (192.122.134.249)
Time: Fri Dec  9 00:26:31 2005

Input: F := GF(8);
a :=PrimitiveElement(F);
Trace(a);

Output: Magma V2.11-10    Fri Dec  9 2005 00:26:31 on modular  [Seed = 2521612331]
   -------------------------------------

0

Total time: 0.190 seconds, Total memory usage: 3.24MB


'192.122'
************** MAGMA *****************
Host 192.122.134.249 (192.122.134.249)
Time: Fri Dec  9 00:25:50 2005

Input: F := GF(8);
a :=PrimitiveElement(F);
a;

Output: Magma V2.11-10    Fri Dec  9 2005 00:25:50 on modular  [Seed = 2638728185]
   -------------------------------------

F.1

Total time: 0.180 seconds, Total memory usage: 3.24MB


'192.122'
************** MAGMA *****************
Host 192.122.134.249 (192.122.134.249)
Time: Fri Dec  9 00:25:13 2005

Input: F := GF(8);
F;

Output: Magma V2.11-10    Fri Dec  9 2005 00:25:12 on modular  [Seed = 2554515098]
   -------------------------------------

Finite field of size 2^3

Total time: 0.180 seconds, Total memory usage: 3.24MB


'192.122'
************** MAGMA *****************
Host 192.122.134.249 (192.122.134.249)
Time: Fri Dec  9 00:24:46 2005

Input: F := GF(8)

Output: Magma V2.11-10    Fri Dec  9 2005 00:24:46 on modular  [Seed = 2810048899]
   -------------------------------------


Total time: 0.200 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:56:47 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfDual(C);



Output: Magma V2.11-10    Thu Dec  8 2005 23:56:47 on modular  [Seed = 131943090]
   -------------------------------------

1344
[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
{
    (3, 4)(7, 8),
    (4, 6)(5, 7),
    (4, 7)(5, 6),
    (1, 2)(5, 6),
    (2, 4, 3)(6, 8, 7)
}
true

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:56:22 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C);



Output: Magma V2.11-10    Thu Dec  8 2005 23:56:22 on modular  [Seed = 47730510]
   -------------------------------------

1344
[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
{
    (3, 4)(7, 8),
    (4, 6)(5, 7),
    (4, 7)(5, 6),
    (1, 2)(5, 6),
    (2, 4, 3)(6, 8, 7)
}
true

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:55:57 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);
IsSelfOrthogonal(C) : Code -> BoolElt



Output: Magma V2.11-10    Thu Dec  8 2005 23:55:56 on modular  [Seed = 164840559]
   -------------------------------------

1344
[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
{
    (3, 4)(7, 8),
    (4, 6)(5, 7),
    (4, 7)(5, 6),
    (1, 2)(5, 6),
    (2, 4, 3)(6, 8, 7)
}

>> IsSelfOrthogonal(C) : Code -> BoolElt
                              ^
User error: bad syntax

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:52:06 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);
Generators(aut);



Output: Magma V2.11-10    Thu Dec  8 2005 23:52:06 on modular  [Seed = 298540893]
   -------------------------------------

1344
[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1
{
    (3, 4)(7, 8),
    (4, 6)(5, 7),
    (4, 7)(5, 6),
    (1, 2)(5, 6),
    (2, 4, 3)(6, 8, 7)
}

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:50:33 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
Order(aut);
> FactoredOrder(aut);
> CompositionFactors(aut);




Output: Magma V2.11-10    Thu Dec  8 2005 23:50:33 on modular  [Seed = 482759231]
   -------------------------------------

1344
[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:49:30 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
> aut := AutomorphismGroup(C);
> FactoredOrder(aut);
> CompositionFactors(aut);




Output: Magma V2.11-10    Thu Dec  8 2005 23:49:30 on modular  [Seed = 465655035]
   -------------------------------------

[ <2, 6>, <3, 1>, <7, 1> ]
    G
    |  A(1, 7)                = L(2, 7)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    *
    |  Cyclic(2)
    1

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:43:43 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
AutomorphismGroup(C: parameters) : Code -> GrpPerm, PowMap, Map



Output: Magma V2.11-10    Thu Dec  8 2005 23:43:42 on modular  [Seed = 754345064]
   -------------------------------------


>> AutomorphismGroup(C: parameters) : Code -> GrpPerm, PowMap, Map
                                           ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:40:08 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
IsSelfOrthogonal(C) : Code -> BoolElt



Output: Magma V2.11-10    Thu Dec  8 2005 23:40:08 on modular  [Seed = 904887463]
   -------------------------------------


>> IsSelfOrthogonal(C) : Code -> BoolElt
                              ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:39:47 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;
IsSelfOrthogonal(C) : Code -> BoolElt;



Output: Magma V2.11-10    Thu Dec  8 2005 23:39:47 on modular  [Seed = 820672921]
   -------------------------------------


>> IsSelfOrthogonal(C) : Code -> BoolElt;
                              ^
User error: bad syntax

Total time: 0.180 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:39:10 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0]>;



Output: Magma V2.11-10    Thu Dec  8 2005 23:39:10 on modular  [Seed = 1072002667]
   -------------------------------------


Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:38:44 2005

Input: K := FiniteField(2);
> C := LinearCode<K, 8 |  
>    [1, 0, 0, 0, 0, 1, 1, 1], [0, 1, 0, 0, 1, 0, 1, 1],  
>    [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0];



Output: Magma V2.11-10    Thu Dec  8 2005 23:38:44 on modular  [Seed = 3474294432]
   -------------------------------------


>>      [0, 0, 1, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 1, 1, 0];
                                                          ^
User error: bad syntax

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:35:40 2005

Input: C := BCHCode(GF(2),23,2);                
C;


Output: Magma V2.11-10    Thu Dec  8 2005 23:35:40 on modular  [Seed = 3607993712]
   -------------------------------------

[23, 12, 7] "BCH code (d = 2, b = 1)" Cyclic Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:34:17 2005

Input: > C := BCHCode(GF(2),23,2);                
> C;


Output: Magma V2.11-10    Thu Dec  8 2005 23:34:17 on modular  [Seed = 3691419310]
   -------------------------------------

[23, 12, 7] "BCH code (d = 2, b = 1)" Cyclic Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1]
[0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1]

Total time: 0.190 seconds, Total memory usage: 3.24MB


'65.191.'
************** MAGMA *****************
Host 65.191.73.113 (65.191.73.113)
Time: Thu Dec  8 23:10:54 2005

Input: 2+3

Output: Magma V2.11-10    Thu Dec  8 2005 23:10:54 on modular  [Seed = 3812205334]
   -------------------------------------

5

Total time: 0.190 seconds, Total memory usage: 3.24MB


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Thu Dec  8 22:13:05 2005

Input: Factorization(1111111111111111111111111111111111112222222222222222222222222222222222222222222222222222222222222222223);

Output: Magma V2.11-10    Thu Dec  8 2005 22:13:04 on modular  [Seed = 1569122342]
   -------------------------------------

[ <3, 2>, <41, 1>, <191, 1>, <6246943, 1>, 
<252365633729939524730246496421381170326644302337345845070768633297938261556952\
8675426211359, 1> ]

Total time: 0.210 seconds, Total memory usage: 3.24MB


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Thu Dec  8 22:12:31 2005

Input: Factorization(11111111111111111111111111111111111122222222222222222222222222222222222222222222222222222222222222222233333333333333333333333333333333333333333333333333333333333333333333333333333333333333);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Thu Dec  8 2005 22:12:11 on modular  [Seed = 1518464874]
   -------------------------------------


Errors: /bin/sh: line 1: 30817 Alarm clock             nice -n 19 /usr/local/bin/magma


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Thu Dec  8 22:10:50 2005

Input: Factorization(1111111111111111111111111111111111112222222222222222222222222222222222222222222222222222222222222222223333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Thu Dec  8 2005 22:10:29 on modular  [Seed = 1740427769]
   -------------------------------------


Errors: /bin/sh: line 1: 30812 Alarm clock             nice -n 19 /usr/local/bin/magma


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Thu Dec  8 22:09:25 2005

Input: Factorization(1111111111111111111111111111111111112222222222222222222222222222222222222222222222222222222222222222223333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444455555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Thu Dec  8 2005 22:09:05 on modular  [Seed = 1823988230]
   -------------------------------------


Errors: /bin/sh: line 1: 30807 Alarm clock             nice -n 19 /usr/local/bin/magma


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Thu Dec  8 22:08:02 2005

Input: Factorization(11111111111111111111111111111111111122222222222222222222222222222222222222222222222222222222222222222233333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Thu Dec  8 2005 22:07:41 on modular  [Seed = 2024001470]
   -------------------------------------


Errors: /bin/sh: line 1: 30787 Alarm clock             nice -n 19 /usr/local/bin/magma


'60.225.'
************** MAGMA *****************
Host 60.225.131.213 (60.225.131.213)
Time: Thu Dec  8 22:06:11 2005

Input: Factorization(111111111111111111111111111111111111222222222222222222222222222222222222222222222222222222222222222222333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333344444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444445555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666677777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **


Magma V2.11-10    Thu Dec  8 2005 22:05:50 on modular  [Seed = 115192243]
   -------------------------------------


Errors: /bin/sh: line 1: 30781 Alarm clock             nice -n 19 /usr/local/bin/magma


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:52:57 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(2*a-1)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;


Output: Magma V2.11-10    Thu Dec  8 2005 18:52:57 on modular  [Seed = 432184689]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
1/a
-1
0
(-a^2 + a*c + 2*a - 1)/(a^2 + a*c - a)
0
(-2*a + 1)/(a + c - 1)
(2*a*c - c)/(a^2 + a*c - a)
0
(-a + c)/(a + c - 1)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:51:58 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;


Output: Magma V2.11-10    Thu Dec  8 2005 18:51:58 on modular  [Seed = 315201085]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(a^3 - 4*a^2*b*c + a^2*c - a^2 + 4*a*b^2*c - a*b^2 + a*b - b^2*c)/(a^4 + 2*a^3*b
    + a^3*c - 3*a^3 + a^2*b^2 + 2*a^2*b*c - 4*a^2*b - 2*a^2*c + 3*a^2 + a*b^2*c 
    - a*b^2 - 2*a*b*c + 2*a*b + a*c - a)
(-a^4 - 2*a^3*b - a^3*c + a^3 - a^2*b^2 + 6*a^2*b*c + 2*a^2*b - a*b^2*c + a*b^2 
    - 4*a*b*c - a*b + b*c)/(a^4 + 2*a^3*b + a^3*c - 3*a^3 + a^2*b^2 + 2*a^2*b*c 
    - 4*a^2*b - 2*a^2*c + 3*a^2 + a*b^2*c - a*b^2 - 2*a*b*c + 2*a*b + a*c - a)
(4*a^2*b - 4*a*b + b)/(a^3 + a^2*b + a^2*c - 2*a^2 + a*b*c - a*b - a*c + a)
(-a^4 - 2*a^3*b + a^3*c + 4*a^3 - a^2*b^2 - 6*a^2*b*c + 4*a^2*b - 4*a^2 + 
    a*b^2*c + 4*a*b*c - a*b + a - b*c)/(a^4 + 2*a^3*b + a^3*c - 3*a^3 + a^2*b^2 
    + 2*a^2*b*c - 4*a^2*b - 2*a^2*c + 3*a^2 + a*b^2*c - a*b^2 - 2*a*b*c + 2*a*b 
    + a*c - a)
(-4*a^3*c - 2*a^3 + 4*a^2*b*c - 2*a^2*b + 6*a^2*c + 3*a^2 - 2*a*b*c + a*b - 
    4*a*c - a + c)/(a^4 + 2*a^3*b + a^3*c - 3*a^3 + a^2*b^2 + 2*a^2*b*c - 
    4*a^2*b - 2*a^2*c + 3*a^2 + a*b^2*c - a*b^2 - 2*a*b*c + 2*a*b + a*c - a)
(-2*a^3 + 2*a^2*b + 5*a^2 - a*b - 4*a + 1)/(a^3 + a^2*b + a^2*c - 2*a^2 + a*b*c 
    - a*b - a*c + a)
(2*a^2*c - 2*a*b*c - a*c + b*c)/(a^3 + a^2*b + a^2*c - 2*a^2 + a*b*c - a*b - a*c
    + a)
(-4*a^2*c + 4*a*c - c)/(a^3 + a^2*b + a^2*c - 2*a^2 + a*b*c - a*b - a*c + a)
(-a^2 + a*c + 2*a - 1)/(a^2 + a*c - a)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:49:04 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator(2*(a-b)*(a+b+c-1)*(a+b-1)*(b+c-1)*(c+a-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1)));


Output: Magma V2.11-10    Thu Dec  8 2005 18:49:04 on modular  [Seed = 720482155]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
[
    <a + b + c - 1, 1>,
    <a^3*b + a^3*c - a^3 + a^2*b*c - 2*a^2*b + a^2*c^2 - 3*a^2*c + 2*a^2 - a*b^3
        - a*b^2*c + 2*a*b^2 - 2*a*b*c - a*c^2 + 2*a*c - 1/2*a - b^3*c + b^3 - 
        b^2*c^2 + 3*b^2*c - 2*b^2 + b*c^2 - 2*b*c + 3/2*b + 1/2*c - 1/2, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.72MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:48:41 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator(2*a*b*(a+b+c-1)*(a+b-1)*(b+c-1)*(c+a-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1)));


Output: Magma V2.11-10    Thu Dec  8 2005 18:48:41 on modular  [Seed = 670868047]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
[
    <a + b + c - 1, 1>,
    <a^3*b^2 + a^3*b*c - a^3*b + a^2*b^3 + 2*a^2*b^2*c - 3*a^2*b^2 + a^2*b*c^2 -
        3*a^2*b*c + 2*a^2*b + a*b^3*c - a*b^3 + a*b^2*c^2 - 3*a*b^2*c + 2*a*b^2 
        - a*b*c^2 - a*b + 1/2*a + 1/2*b + 1/2*c - 1/2, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.82MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:48:11 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator(2*a*b*c*(a+b+c-1)*(a+b-1)*(b+c-1)*(c+a-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1)));


Output: Magma V2.11-10    Thu Dec  8 2005 18:48:10 on modular  [Seed = 1055243061]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
[
    <a + b + c - 1, 1>,
    <a^3*b^2*c + a^3*b*c^2 - a^3*b*c + a^2*b^3*c + 2*a^2*b^2*c^2 - 3*a^2*b^2*c +
        a^2*b*c^3 - 3*a^2*b*c^2 + 2*a^2*b*c + a*b^3*c^2 - a*b^3*c + a*b^2*c^3 - 
        3*a*b^2*c^2 + 2*a*b^2*c - a*b*c^3 + 2*a*b*c^2 - 3*a*b*c + 1/2*a + 1/2*b 
        + 1/2*c - 1/2, 1>
]

Total time: 0.380 seconds, Total memory usage: 3.82MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:47:45 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator((a+b+c-1)*(a+b-1)*(b+c-1)*(c+a-1)-(a+b+c-1)*(4*a*b*c-a-b-c+1)));


Output: Magma V2.11-10    Thu Dec  8 2005 18:47:45 on modular  [Seed = 1004584491]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
[
    <a + b + c - 1, 1>,
    <a^2*b + a^2*c - a^2 + a*b^2 - 2*a*b*c - 3*a*b + a*c^2 - 3*a*c + 3*a + b^2*c
        - b^2 + b*c^2 - 3*b*c + 3*b - c^2 + 3*c - 2, 1>
]

Total time: 0.380 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:39:28 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;


print (2*(a+b-1)*(b+c-1)*(a+c-1)-4*a*b*c+a+b+c-1);

print Factorization(Numerator(2*a^2*b + 2*a^2*c - 2*a^2 + 2*a*b^2 - 6*a*b + 2*a*c^2 - 6*a*c + 5*a + 2*b^2*c - 
    2*b^2 + 2*b*c^2 - 6*b*c + 5*b - 2*c^2 + 5*c - 3
));


Output: Magma V2.11-10    Thu Dec  8 2005 18:39:28 on modular  [Seed = 3474213069]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
2*a^2*b + 2*a^2*c - 2*a^2 + 2*a*b^2 - 6*a*b + 2*a*c^2 - 6*a*c + 5*a + 2*b^2*c - 
    2*b^2 + 2*b*c^2 - 6*b*c + 5*b - 2*c^2 + 5*c - 3
[
    <a^2*b + a^2*c - a^2 + a*b^2 - 3*a*b + a*c^2 - 3*a*c + 5/2*a + b^2*c - b^2 +
        b*c^2 - 3*b*c + 5/2*b - c^2 + 5/2*c - 3/2, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:39:09 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;


print (2*(a+b-1)*(b+c-1)*(a+c-1)-4*a*b*c+a+b+c-1);

print Factorization(2*a^2*b + 2*a^2*c - 2*a^2 + 2*a*b^2 - 6*a*b + 2*a*c^2 - 6*a*c + 5*a + 2*b^2*c - 
    2*b^2 + 2*b*c^2 - 6*b*c + 5*b - 2*c^2 + 5*c - 3
);


Output: Magma V2.11-10    Thu Dec  8 2005 18:39:08 on modular  [Seed = 3307094763]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
2*a^2*b + 2*a^2*c - 2*a^2 + 2*a*b^2 - 6*a*b + 2*a*c^2 - 6*a*c + 5*a + 2*b^2*c - 
    2*b^2 + 2*b*c^2 - 6*b*c + 5*b - 2*c^2 + 5*c - 3

>> print Factorization(2*a^2*b + 2*a^2*c - 2*a^2 + 2*a*b^2 - 6*a*b + 2*a*c^2 -
                      ^
Runtime error in 'Factorization': Bad argument types
Argument types given: FldFunRatMElt

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:38:30 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;


print (2*(a+b-1)*(b+c-1)*(a+c-1)-4*a*b*c+a+b+c-1);



Output: Magma V2.11-10    Thu Dec  8 2005 18:38:30 on modular  [Seed = 3607910163]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
2*a^2*b + 2*a^2*c - 2*a^2 + 2*a*b^2 - 6*a*b + 2*a*c^2 - 6*a*c + 5*a + 2*b^2*c - 
    2*b^2 + 2*b*c^2 - 6*b*c + 5*b - 2*c^2 + 5*c - 3

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:37:25 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;


print ((a+b-1)*(b+c-1)*(a+c-1)-4*a*b*c+a+b+c-1);

print Factorization(Numerator(a^2*b + a^2*c - a^2 + a*b^2 - 2*a*b*c - 3*a*b + a*c^2 - 3*a*c + 3*a + b^2*c - 
    b^2 + b*c^2 - 3*b*c + 3*b - c^2 + 3*c - 2));


Output: Magma V2.11-10    Thu Dec  8 2005 18:37:25 on modular  [Seed = 3996479081]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
a^2*b + a^2*c - a^2 + a*b^2 - 2*a*b*c - 3*a*b + a*c^2 - 3*a*c + 3*a + b^2*c - 
    b^2 + b*c^2 - 3*b*c + 3*b - c^2 + 3*c - 2
[
    <a^2*b + a^2*c - a^2 + a*b^2 - 2*a*b*c - 3*a*b + a*c^2 - 3*a*c + 3*a + b^2*c
        - b^2 + b*c^2 - 3*b*c + 3*b - c^2 + 3*c - 2, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:36:58 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;


print ((a+b-1)*(b+c-1)*(a+c-1)-4*a*b*c+a+b+c-1);


Output: Magma V2.11-10    Thu Dec  8 2005 18:36:57 on modular  [Seed = 3846071630]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
a^2*b + a^2*c - a^2 + a*b^2 - 2*a*b*c - 3*a*b + a*c^2 - 3*a*c + 3*a + b^2*c - 
    b^2 + b*c^2 - 3*b*c + 3*b - c^2 + 3*c - 2

Total time: 0.360 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:34:34 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Numerator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:34:33 on modular  [Seed = 3812123608]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:34:18 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Denominator(Evaluate(q,-D/2+(1-2*a)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:34:17 on modular  [Seed = 4263870261]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <c, 2>,
    <b, 2>,
    <a, 1>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:34:01 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Denominator(Evaluate(q,-D/2+(0)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(0)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:34:01 on modular  [Seed = 4113462318]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <c, 2>,
    <b, 2>,
    <a, 2>
]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1

Total time: 0.360 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:33:47 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Denominator(Evaluate(q,-D/2+(0)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(2)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:33:46 on modular  [Seed = 4029378840]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <c, 2>,
    <b, 2>,
    <a, 2>
]
(2*a*b^2*c + a*b*c + 1/2*a*b + 1/4*a - 2*b^2*c + 1/2*b^2 - 1/2*b*c - 1/4*b + 
    1/4*c - 1/4)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 3/4*a*c - 
    3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(a^2*b*c - 1/4*a^2 - a*b^2*c - 4*a*b*c - a*b - 1/4*a*c + 1/4*a - 3/4*b^2 + 
    9/4*b*c + 3/4*b)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 3/4*a*c - 
    3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(-2*a*b + 3*b)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(-a^2*b*c - 3/4*a^2 + a*b^2*c + 4*a*b*c - a*b + 1/4*a*c + 7/4*a - 1/4*b^2 - 
    9/4*b*c + 5/4*b - 1)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 
    3/4*a*c - 3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(2*a^2*b*c + 2*a^2*c + 1/2*a^2 - 3*a*b*c + 1/2*a*b - 9/2*a*c - 5/4*a - 3/4*b + 
    9/4*c + 3/4)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 3/4*a*c - 
    3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(-2*a*b - 3*a + 3)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(2*b*c + c)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(2*a*c - 3*c)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(a*b*c - 9/4*a - 9/4*b + 3/4*c + 9/4)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:32:23 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Denominator(Evaluate(Q[3,3],-D/2+(0)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(2)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:32:23 on modular  [Seed = 2320567103]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[]
(2*a*b^2*c + a*b*c + 1/2*a*b + 1/4*a - 2*b^2*c + 1/2*b^2 - 1/2*b*c - 1/4*b + 
    1/4*c - 1/4)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 3/4*a*c - 
    3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(a^2*b*c - 1/4*a^2 - a*b^2*c - 4*a*b*c - a*b - 1/4*a*c + 1/4*a - 3/4*b^2 + 
    9/4*b*c + 3/4*b)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 3/4*a*c - 
    3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(-2*a*b + 3*b)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(-a^2*b*c - 3/4*a^2 + a*b^2*c + 4*a*b*c - a*b + 1/4*a*c + 7/4*a - 1/4*b^2 - 
    9/4*b*c + 5/4*b - 1)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 
    3/4*a*c - 3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(2*a^2*b*c + 2*a^2*c + 1/2*a^2 - 3*a*b*c + 1/2*a*b - 9/2*a*c - 5/4*a - 3/4*b + 
    9/4*c + 3/4)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 3/4*a*c - 
    3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(-2*a*b - 3*a + 3)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(2*b*c + c)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(2*a*c - 3*c)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(a*b*c - 9/4*a - 9/4*b + 3/4*c + 9/4)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:31:56 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Denominator(Evaluate(Q[3,3],-D/2+(2)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(2)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:31:55 on modular  [Seed = 2170159320]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4, 1>
]
(2*a*b^2*c + a*b*c + 1/2*a*b + 1/4*a - 2*b^2*c + 1/2*b^2 - 1/2*b*c - 1/4*b + 
    1/4*c - 1/4)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 3/4*a*c - 
    3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(a^2*b*c - 1/4*a^2 - a*b^2*c - 4*a*b*c - a*b - 1/4*a*c + 1/4*a - 3/4*b^2 + 
    9/4*b*c + 3/4*b)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 3/4*a*c - 
    3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(-2*a*b + 3*b)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(-a^2*b*c - 3/4*a^2 + a*b^2*c + 4*a*b*c - a*b + 1/4*a*c + 7/4*a - 1/4*b^2 - 
    9/4*b*c + 5/4*b - 1)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 
    3/4*a*c - 3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(2*a^2*b*c + 2*a^2*c + 1/2*a^2 - 3*a*b*c + 1/2*a*b - 9/2*a*c - 5/4*a - 3/4*b + 
    9/4*c + 3/4)/(a^2*b*c + 3/4*a^2 + a*b^2*c - a*b*c + 3/2*a*b + 3/4*a*c - 
    3/2*a + 3/4*b^2 + 3/4*b*c - 3/2*b - 3/4*c + 3/4)
(-2*a*b - 3*a + 3)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(2*b*c + c)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(2*a*c - 3*c)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)
(a*b*c - 9/4*a - 9/4*b + 3/4*c + 9/4)/(a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:31:46 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Denominator(Evaluate(Q[3,3],-D/2+(2)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(1)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:31:45 on modular  [Seed = 2571245770]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a*b*c + 3/4*a + 3/4*b + 3/4*c - 3/4, 1>
]
(2*a*b - b)/(a^2 + a*b - a)
(a^2 - a*b - 2*a + 1)/(a^2 + a*b - a)
(-a + 1)/(a*c)
(-a^2 + a*b + 2*a - 1)/(a^2 + a*b - a)
(2*a^2*b + a^2 - 2*a*b - 2*a + 1)/(a^2*b + a*b^2 - a*b)
(-a*b - a + 1)/(a*b*c)
1/a
(a - 1)/(a*b)
(a*b*c - a - b + 1)/(a*b*c)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:30:11 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Denominator(Evaluate(Q[3,3],-D/2+(1)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(1)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:30:10 on modular  [Seed = 2488210852]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <c, 1>,
    <b, 1>,
    <a, 1>
]
(2*a*b - b)/(a^2 + a*b - a)
(a^2 - a*b - 2*a + 1)/(a^2 + a*b - a)
(-a + 1)/(a*c)
(-a^2 + a*b + 2*a - 1)/(a^2 + a*b - a)
(2*a^2*b + a^2 - 2*a*b - 2*a + 1)/(a^2*b + a*b^2 - a*b)
(-a*b - a + 1)/(a*b*c)
1/a
(a - 1)/(a*b)
(a*b*c - a - b + 1)/(a*b*c)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:29:33 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Denominator(Evaluate(Q[3,3],-D/2+(1)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(2*a-1)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:29:33 on modular  [Seed = 2826119751]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <c, 1>,
    <b, 1>,
    <a, 1>
]
1/a
-1
0
(-a^2 + a*c + 2*a - 1)/(a^2 + a*c - a)
0
(-2*a + 1)/(a + c - 1)
(2*a*c - c)/(a^2 + a*c - a)
0
(-a + c)/(a + c - 1)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:28:31 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Denominator(Evaluate(Q[3,3],-D/2+(a^2+a*b-b)*(a+b+c-1)/(2*a*b*c))));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(2*a-1)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:28:31 on modular  [Seed = 2709136140]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <a^4 + 2*a^3*b + a^3*c + a^2*b^2 + a^2*b*c - 2*a^2*b + a^2*c - 2*a*b^2 - 
        2*a*b*c + a*c + b^2 + b*c + c - 1, 1>
]
1/a
-1
0
(-a^2 + a*c + 2*a - 1)/(a^2 + a*c - a)
0
(-2*a + 1)/(a + c - 1)
(2*a*c - c)/(a^2 + a*c - a)
0
(-a + c)/(a + c - 1)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:27:49 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Denominator(Evaluate(Q[3,3],-D/2+(a^2+a*b-b)*(a+b+c-1)/(2*a*b*c)));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(2*a-1)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:27:49 on modular  [Seed = 3211017720]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]

>> ^2+a*b-b)*(a+b+c-1)/(2*a*b*c)));
                                  ^
User error: bad syntax
1/a
-1
0
(-a^2 + a*c + 2*a - 1)/(a^2 + a*c - a)
0
(-2*a + 1)/(a + c - 1)
(2*a*c - c)/(a^2 + a*c - a)
0
(-a + c)/(a + c - 1)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:27:19 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);

print Factorization(Evaluate(Denominator(Q[3,3])),-D/2+(a^2+a*b-b)*(a+b+c-1)/(2*a*b*c));

for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(2*a-1)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:27:18 on modular  [Seed = 3126933726]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]

>> print Factorization(Evaluate(Denominator(Q[3,3])),-D/2+(a^2+a*b-b)*(a+b+c-1
                               ^
Runtime error in 'Evaluate': Bad argument types
Argument types given: RngUPolElt[FldFunRat]
1/a
-1
0
(-a^2 + a*c + 2*a - 1)/(a^2 + a*c - a)
0
(-2*a + 1)/(a + c - 1)
(2*a*c - c)/(a^2 + a*c - a)
0
(-a + c)/(a + c - 1)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:26:12 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(a^2+a*b-b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:26:12 on modular  [Seed = 2976527255]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^3 - 2*a^2*b*c + a^2*b + a^2*c + a^2 + 2*a*c - a + 2*b*c - b + c - 1)/(a^4 + 
    2*a^3*b + a^3*c + a^2*b^2 + a^2*b*c - 2*a^2*b + a^2*c - 2*a*b^2 - 2*a*b*c + 
    a*c + b^2 + b*c + c - 1)
(-a^4 - 2*a^3*b - a^3*c - a^3 - a^2*b^2 + a^2*b*c + a^2*b - 2*a^2*c + a^2 + 
    2*a*b^2 - 2*a*b*c + 2*a*b - a*c + a - b^2 + b*c - b)/(a^4 + 2*a^3*b + a^3*c 
    + a^2*b^2 + a^2*b*c - 2*a^2*b + a^2*c - 2*a*b^2 - 2*a*b*c + a*c + b^2 + b*c 
    + c - 1)
(2*a^3*b + 2*a^2*b^2 - 2*a^2*b - 4*a*b^2 + 2*b^2)/(a^4 + 2*a^3*b + a^3*c + 
    a^2*b^2 + a^2*b*c - 2*a^2*b + a^2*c - 2*a*b^2 - 2*a*b*c + a*c + b^2 + b*c + 
    c - 1)
(-a^4 - 2*a^3*b + a^3*c + a^3 - a^2*b^2 - a^2*b*c + 3*a^2*b + 2*a^2*c + a^2 + 
    2*a*b^2 + 2*a*b*c + a*c - a - b^2 - b*c - b)/(a^4 + 2*a^3*b + a^3*c + 
    a^2*b^2 + a^2*b*c - 2*a^2*b + a^2*c - 2*a*b^2 - 2*a*b*c + a*c + b^2 + b*c + 
    c - 1)
(-2*a^3*c - a^3 - a^2*b + a^2*c + a^2 + 2*a*b + a - b + c - 1)/(a^4 + 2*a^3*b + 
    a^3*c + a^2*b^2 + a^2*b*c - 2*a^2*b + a^2*c - 2*a*b^2 - 2*a*b*c + a*c + b^2 
    + b*c + c - 1)
(-2*a^4 - 2*a^3*b + 2*a^2*b - 2*a^2 - 2*a*b + 2*b)/(a^4 + 2*a^3*b + a^3*c + 
    a^2*b^2 + a^2*b*c - 2*a^2*b + a^2*c - 2*a*b^2 - 2*a*b*c + a*c + b^2 + b*c + 
    c - 1)
(2*a^3*c + 2*a^2*b*c + 2*a^2*c - 2*b*c)/(a^4 + 2*a^3*b + a^3*c + a^2*b^2 + 
    a^2*b*c - 2*a^2*b + a^2*c - 2*a*b^2 - 2*a*b*c + a*c + b^2 + b*c + c - 1)
(-2*a^3*c - 2*a^2*b*c + 2*a^2*c + 4*a*b*c - 2*b*c)/(a^4 + 2*a^3*b + a^3*c + 
    a^2*b^2 + a^2*b*c - 2*a^2*b + a^2*c - 2*a*b^2 - 2*a*b*c + a*c + b^2 + b*c + 
    c - 1)
(-a^4 - 2*a^3*b + a^3*c - a^2*b^2 + a^2*b*c + 2*a^2*b + a^2*c - 2*a^2 + 2*a*b^2 
    - 2*a*b*c - 2*a*b + a*c - b^2 + b*c + 2*b + c - 1)/(a^4 + 2*a^3*b + a^3*c + 
    a^2*b^2 + a^2*b*c - 2*a^2*b + a^2*c - 2*a*b^2 - 2*a*b*c + a*c + b^2 + b*c + 
    c - 1)

Total time: 0.380 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:25:18 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(a-b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:25:18 on modular  [Seed = 1285017504]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a + 2*b*c - b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b - a*c + a - b^2 + b*c - b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-2*a*b + 2*b^2)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b + a*c + a - b^2 - b*c - b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c + a - b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-2*a^2 + 2*a*b - 2*a + 2*b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c - 2*b*c)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c - 2*b*c)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b + a*c - 2*a - b^2 + b*c + 2*b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + 
    b*c + c - 1)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:25:02 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(a-b)*(a+b+c-1)/(2*a*b*c)));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:25:02 on modular  [Seed = 1267779767]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]

>>     print Evaluate(Q[i,j],-D/2+(a-b)*(a+b+c-1)/(2*a*b*c)));
                                                            ^
User error: bad syntax

>>   end for;
     ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:24:30 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(a-b)*(2*b-1)*(a+b+c-1)/((2*a*b*c)*(1-2*a)));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:24:29 on modular  [Seed = 1100661470]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(4*a*b^2*c - a*b^2 - 2*a*b*c + 1/4*a - 2*b^3*c + b^3 + b^2*c - b^2 - 1/2*b*c + 
    3/4*b + 1/4*c - 1/4)/(a^2*b^2 + 4*a^2*b*c - a^2*b - 3/4*a^2 - 2*a*b^3 - 
    3*a*b^2*c + 2*a*b^2 - a*b*c - 1/2*a*b - 3/4*a*c + a + b^4 + b^3*c - b^3 + 
    1/4*b^2 + 1/4*b*c + 1/4*c - 1/4)
(-a^2*b^2 + 4*a^2*b*c - a^2*b - 1/4*a^2 + 2*a*b^3 - 5*a*b^2*c + a*b^2 - a*b*c + 
    1/2*a*b - 1/4*a*c + 1/4*a - b^4 + b^3*c + b^2*c - 1/4*b^2 + 1/4*b*c - 
    1/4*b)/(a^2*b^2 + 4*a^2*b*c - a^2*b - 3/4*a^2 - 2*a*b^3 - 3*a*b^2*c + 
    2*a*b^2 - a*b*c - 1/2*a*b - 3/4*a*c + a + b^4 + b^3*c - b^3 + 1/4*b^2 + 
    1/4*b*c + 1/4*c - 1/4)
(4*a^2*b^2 - 2*a^2*b - 6*a*b^3 + 2*a*b^2 + 1/2*a*b + 2*b^4 - 1/2*b^2)/(a^2*b^2 +
    4*a^2*b*c - a^2*b - 3/4*a^2 - 2*a*b^3 - 3*a*b^2*c + 2*a*b^2 - a*b*c - 
    1/2*a*b - 3/4*a*c + a + b^4 + b^3*c - b^3 + 1/4*b^2 + 1/4*b*c + 1/4*c - 1/4)
(-a^2*b^2 - 4*a^2*b*c + a^2*b + 3/4*a^2 + 2*a*b^3 + 5*a*b^2*c - 3*a*b^2 + a*b*c 
    + 1/2*a*b + 1/4*a*c - 3/4*a - b^4 - b^3*c + 2*b^3 - b^2*c - 5/4*b^2 - 
    1/4*b*c + 3/4*b)/(a^2*b^2 + 4*a^2*b*c - a^2*b - 3/4*a^2 - 2*a*b^3 - 
    3*a*b^2*c + 2*a*b^2 - a*b*c - 1/2*a*b - 3/4*a*c + a + b^4 + b^3*c - b^3 + 
    1/4*b^2 + 1/4*b*c + 1/4*c - 1/4)
(4*a^2*b*c - 2*a^2*b + 2*a^2*c - a^2 - 2*a*b^2*c + 3*a*b^2 - 4*a*b*c - 3/2*a*c +
    5/4*a - b^3 + b^2*c + b*c - 1/4*b + 1/4*c - 1/4)/(a^2*b^2 + 4*a^2*b*c - 
    a^2*b - 3/4*a^2 - 2*a*b^3 - 3*a*b^2*c + 2*a*b^2 - a*b*c - 1/2*a*b - 3/4*a*c 
    + a + b^4 + b^3*c - b^3 + 1/4*b^2 + 1/4*b*c + 1/4*c - 1/4)
(2*a^2*b^2 + 2*a^2*b - 3/2*a^2 - 2*a*b^3 - 4*a*b^2 + 3/2*a*b + 1/2*a + 2*b^3 - 
    1/2*b)/(a^2*b^2 + 4*a^2*b*c - a^2*b - 3/4*a^2 - 2*a*b^3 - 3*a*b^2*c + 
    2*a*b^2 - a*b*c - 1/2*a*b - 3/4*a*c + a + b^4 + b^3*c - b^3 + 1/4*b^2 + 
    1/4*b*c + 1/4*c - 1/4)
(-2*a*b^2*c + 2*a*b*c - 1/2*a*c + 2*b^3*c - 2*b^2*c + 1/2*b*c)/(a^2*b^2 + 
    4*a^2*b*c - a^2*b - 3/4*a^2 - 2*a*b^3 - 3*a*b^2*c + 2*a*b^2 - a*b*c - 
    1/2*a*b - 3/4*a*c + a + b^4 + b^3*c - b^3 + 1/4*b^2 + 1/4*b*c + 1/4*c - 1/4)
(-4*a^2*b*c + 2*a^2*c + 6*a*b^2*c - 2*a*b*c - 1/2*a*c - 2*b^3*c + 
    1/2*b*c)/(a^2*b^2 + 4*a^2*b*c - a^2*b - 3/4*a^2 - 2*a*b^3 - 3*a*b^2*c + 
    2*a*b^2 - a*b*c - 1/2*a*b - 3/4*a*c + a + b^4 + b^3*c - b^3 + 1/4*b^2 + 
    1/4*b*c + 1/4*c - 1/4)
(-a^2*b^2 + 4*a^2*b*c + 3*a^2*b - 9/4*a^2 + 2*a*b^3 - 3*a*b^2*c - 4*a*b^2 - 
    a*b*c + 1/2*a*b - 3/4*a*c + 3/2*a - b^4 + b^3*c + b^3 + 3/4*b^2 + 1/4*b*c - 
    1/2*b + 1/4*c - 1/4)/(a^2*b^2 + 4*a^2*b*c - a^2*b - 3/4*a^2 - 2*a*b^3 - 
    3*a*b^2*c + 2*a*b^2 - a*b*c - 1/2*a*b - 3/4*a*c + a + b^4 + b^3*c - b^3 + 
    1/4*b^2 + 1/4*b*c + 1/4*c - 1/4)

Total time: 0.380 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:23:16 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(a+3*b-2)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:23:16 on modular  [Seed = 1518459148]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^3 + 2*a^2*b*c + 9*a^2*b + a^2*c - 7*a^2 + 4*a*b^2*c + 23*a*b^2 + 6*a*b*c - 
    38*a*b - 6*a*c + 15*a - 30*b^3*c + 15*b^3 + 53*b^2*c - 39*b^2 - 36*b*c + 
    33*b + 9*c - 9)/(a^4 + 8*a^3*b + a^3*c - 6*a^3 + 22*a^2*b^2 + 11*a^2*b*c - 
    34*a^2*b - 5*a^2*c + 12*a^2 + 24*a*b^3 + 19*a*b^2*c - 58*a*b^2 - 26*a*b*c + 
    44*a*b + 7*a*c - 10*a + 9*b^4 + 9*b^3*c - 30*b^3 - 21*b^2*c + 36*b^2 + 
    15*b*c - 18*b - 3*c + 3)
(-a^4 - 8*a^3*b - a^3*c + 7*a^3 - 22*a^2*b^2 - 9*a^2*b*c + 35*a^2*b + 6*a^2*c - 
    15*a^2 - 24*a*b^3 - 31*a*b^2*c + 49*a*b^2 + 32*a*b*c - 34*a*b - 9*a*c + 9*a 
    - 9*b^4 + 9*b^3*c + 21*b^3 - 6*b^2*c - 15*b^2 + b*c + 3*b)/(a^4 + 8*a^3*b + 
    a^3*c - 6*a^3 + 22*a^2*b^2 + 11*a^2*b*c - 34*a^2*b - 5*a^2*c + 12*a^2 + 
    24*a*b^3 + 19*a*b^2*c - 58*a*b^2 - 26*a*b*c + 44*a*b + 7*a*c - 10*a + 9*b^4 
    + 9*b^3*c - 30*b^3 - 21*b^2*c + 36*b^2 + 15*b*c - 18*b - 3*c + 3)
(-2*a^2*b + 2*a*b + 18*b^3 - 18*b^2 + 4*b)/(a^3 + 7*a^2*b + a^2*c - 5*a^2 + 
    15*a*b^2 + 10*a*b*c - 22*a*b - 4*a*c + 7*a + 9*b^3 + 9*b^2*c - 21*b^2 - 
    12*b*c + 15*b + 3*c - 3)
(-a^4 - 8*a^3*b + a^3*c + 7*a^3 - 22*a^2*b^2 + 9*a^2*b*c + 43*a^2*b - 6*a^2*c - 
    19*a^2 - 24*a*b^3 + 31*a*b^2*c + 81*a*b^2 - 32*a*b*c - 82*a*b + 9*a*c + 25*a
    - 9*b^4 - 9*b^3*c + 45*b^3 + 6*b^2*c - 75*b^2 - b*c + 51*b - 12)/(a^4 + 
    8*a^3*b + a^3*c - 6*a^3 + 22*a^2*b^2 + 11*a^2*b*c - 34*a^2*b - 5*a^2*c + 
    12*a^2 + 24*a*b^3 + 19*a*b^2*c - 58*a*b^2 - 26*a*b*c + 44*a*b + 7*a*c - 10*a
    + 9*b^4 + 9*b^3*c - 30*b^3 - 21*b^2*c + 36*b^2 + 15*b*c - 18*b - 3*c + 3)
(2*a^3*c + a^3 + 4*a^2*b*c + a^2*b - 3*a^2*c - 3*a^2 - 30*a*b^2*c - 9*a*b^2 + 
    22*a*b*c + 10*a*b - 4*a*c - a - 9*b^3 + 9*b^2*c + 21*b^2 - 6*b*c - 15*b + c 
    + 3)/(a^4 + 8*a^3*b + a^3*c - 6*a^3 + 22*a^2*b^2 + 11*a^2*b*c - 34*a^2*b - 
    5*a^2*c + 12*a^2 + 24*a*b^3 + 19*a*b^2*c - 58*a*b^2 - 26*a*b*c + 44*a*b + 
    7*a*c - 10*a + 9*b^4 + 9*b^3*c - 30*b^3 - 21*b^2*c + 36*b^2 + 15*b*c - 18*b 
    - 3*c + 3)
(-2*a^3 - 16*a^2*b + 8*a^2 - 30*a*b^2 + 38*a*b - 10*a + 18*b^2 - 18*b + 4)/(a^3 
    + 7*a^2*b + a^2*c - 5*a^2 + 15*a*b^2 + 10*a*b*c - 22*a*b - 4*a*c + 7*a + 
    9*b^3 + 9*b^2*c - 21*b^2 - 12*b*c + 15*b + 3*c - 3)
(2*a^2*c + 16*a*b*c - 10*a*c + 30*b^2*c - 38*b*c + 12*c)/(a^3 + 7*a^2*b + a^2*c 
    - 5*a^2 + 15*a*b^2 + 10*a*b*c - 22*a*b - 4*a*c + 7*a + 9*b^3 + 9*b^2*c - 
    21*b^2 - 12*b*c + 15*b + 3*c - 3)
(2*a^2*c - 2*a*c - 18*b^2*c + 18*b*c - 4*c)/(a^3 + 7*a^2*b + a^2*c - 5*a^2 + 
    15*a*b^2 + 10*a*b*c - 22*a*b - 4*a*c + 7*a + 9*b^3 + 9*b^2*c - 21*b^2 - 
    12*b*c + 15*b + 3*c - 3)
(-a^2 - 6*a*b + a*c + 2*a - 9*b^2 + 9*b*c + 6*b - 3*c - 1)/(a^2 + 6*a*b + a*c - 
    4*a + 9*b^2 + 9*b*c - 12*b - 3*c + 3)

Total time: 0.380 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:17:06 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(-1+2*a)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:17:06 on modular  [Seed = 2057406394]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
1/a
-1
0
(-a^2 + a*c + 2*a - 1)/(a^2 + a*c - a)
0
(-2*a + 1)/(a + c - 1)
(2*a*c - c)/(a^2 + a*c - a)
0
(-a + c)/(a + c - 1)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:16:00 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(1-2*b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:15:59 on modular  [Seed = 115211163]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
0
(-b + c)/(b + c - 1)
(2*b - 1)/(b + c - 1)
-1
(-b + c)/(b^2 + b*c - b)
(2*b - 1)/(b^2 + b*c - b)
0
(-2*b*c + c)/(b^2 + b*c - b)
(-b^2 + b*c + 2*b - 1)/(b^2 + b*c - b)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:15:21 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Denominator(Q[i,j]),-D/2+(1-2*b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1));


Output: Magma V2.11-10    Thu Dec  8 2005 18:15:21 on modular  [Seed = 349170095]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
[
    <b + c - 1, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:14:46 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Denominator(Q[i,j]),-D/2+(1-2*b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4));


Output: Magma V2.11-10    Thu Dec  8 2005 18:14:45 on modular  [Seed = 331935300]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
(a^2*b + a^2*c - a^2 + 2*a*b^2 + 3*a*b*c - 4*a*b + a*c^2 - 3*a*c + 2*a + b^3 + 
    2*b^2*c - 3*b^2 + b*c^2 - 4*b*c + 3*b - c^2 + 2*c - 1)/(a^2*b*c^2)
[
    <a + b - 1, 1>,
    <a + b + c - 1, 1>,
    <a^2 - 2*a*b + a*c + b^2 + b*c + c - 1, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:12:48 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Denominator(Q[i,j]),-D/2+(a-b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4));


Output: Magma V2.11-10    Thu Dec  8 2005 18:12:48 on modular  [Seed = 703780843]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
[
    <a + b - 1, 1>,
    <a + b + c - 1, 1>,
    <a^2 - 2*a*b + a*c + b^2 + b*c + c - 1, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:12:25 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Denominator(Q[i,j]),-D/2+(a-b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1));


Output: Magma V2.11-10    Thu Dec  8 2005 18:12:24 on modular  [Seed = 620747470]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
(1/4*a^4 + 1/2*a^3*c - 1/2*a^3 - 1/2*a^2*b^2 + 1/2*a^2*b*c + 1/2*a^2*b + 
    1/4*a^2*c^2 - 1/2*a^2*c + 1/2*a*b^2*c + 1/2*a*b^2 + 1/2*a*b*c^2 - a*b - 
    1/2*a*c + 1/2*a + 1/4*b^4 + 1/2*b^3*c - 1/2*b^3 + 1/4*b^2*c^2 - 1/2*b^2*c - 
    1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c - 1/4)/(a^2*b^2*c^2)
[
    <a^2 - 2*a*b + a*c + b^2 + b*c + c - 1, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:11:51 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(a-b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1));


Output: Magma V2.11-10    Thu Dec  8 2005 18:11:51 on modular  [Seed = 603512230]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a + 2*b*c - b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b - a*c + a - b^2 + b*c - b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-2*a*b + 2*b^2)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b + a*c + a - b^2 - b*c - b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c + a - b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-2*a^2 + 2*a*b - 2*a + 2*b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c - 2*b*c)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c - 2*b*c)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b + a*c - 2*a - b^2 + b*c + 2*b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + 
    b*c + c - 1)
[
    <a^2 - 2*a*b + a*c + b^2 + b*c + c - 1, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:11:06 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2-(a-b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1));


Output: Magma V2.11-10    Thu Dec  8 2005 18:11:06 on modular  [Seed = 1055244422]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^3 - 6*a^2*b*c - 3*a^2*b + a^2*c + a^2 + 20*a*b^2*c - a*b^2 - 10*a*b*c + 2*a*b
    + 2*a*c - a - 6*b^3*c + 3*b^3 + 5*b^2*c - 7*b^2 - 4*b*c + 5*b + c - 1)/(a^4 
    + a^3*c - 2*a^3 - 2*a^2*b^2 + 3*a^2*b*c + 2*a^2*b - a^2*c + 3*a*b^2*c + 
    2*a*b^2 - 2*a*b*c - 4*a*b - a*c + 2*a + b^4 + b^3*c - 2*b^3 - b^2*c - b*c + 
    2*b + c - 1)
(-a^4 - a^3*c - a^3 + 2*a^2*b^2 + 15*a^2*b*c - a^2*b - 2*a^2*c + a^2 - 
    15*a*b^2*c + a*b^2 - 2*a*b - a*c + a - b^4 + b^3*c + b^3 + 2*b^2*c + b^2 + 
    b*c - b)/(a^4 + a^3*c - 2*a^3 - 2*a^2*b^2 + 3*a^2*b*c + 2*a^2*b - a^2*c + 
    3*a*b^2*c + 2*a*b^2 - 2*a*b*c - 4*a*b - a*c + 2*a + b^4 + b^3*c - 2*b^3 - 
    b^2*c - b*c + 2*b + c - 1)
(6*a^2*b - 8*a*b^2 - 2*a*b + 2*b^3 + 2*b^2)/(a^3 - a^2*b + a^2*c - a^2 - a*b^2 +
    2*a*b*c + 2*a*b - a + b^3 + b^2*c - b^2 - b - c + 1)
(-a^4 + a^3*c + 3*a^3 + 2*a^2*b^2 - 15*a^2*b*c - 5*a^2*b + 2*a^2*c + a^2 + 
    15*a*b^2*c - 3*a*b^2 + 6*a*b + a*c - 3*a - b^4 - b^3*c + 5*b^3 - 2*b^2*c - 
    7*b^2 - b*c + 3*b)/(a^4 + a^3*c - 2*a^3 - 2*a^2*b^2 + 3*a^2*b*c + 2*a^2*b - 
    a^2*c + 3*a*b^2*c + 2*a*b^2 - 2*a*b*c - 4*a*b - a*c + 2*a + b^4 + b^3*c - 
    2*b^3 - b^2*c - b*c + 2*b + c - 1)
(-6*a^3*c - 3*a^3 + 20*a^2*b*c + a^2*b + 5*a^2*c + a^2 - 6*a*b^2*c + 3*a*b^2 - 
    10*a*b*c - 6*a*b - 4*a*c + 3*a - b^3 + b^2*c + b^2 + 2*b*c + b + c - 1)/(a^4
    + a^3*c - 2*a^3 - 2*a^2*b^2 + 3*a^2*b*c + 2*a^2*b - a^2*c + 3*a*b^2*c + 
    2*a*b^2 - 2*a*b*c - 4*a*b - a*c + 2*a + b^4 + b^3*c - 2*b^3 - b^2*c - b*c + 
    2*b + c - 1)
(-2*a^3 + 8*a^2*b + 4*a^2 - 6*a*b^2 - 6*a*b - 2*a + 2*b^2 + 2*b)/(a^3 - a^2*b + 
    a^2*c - a^2 - a*b^2 + 2*a*b*c + 2*a*b - a + b^3 + b^2*c - b^2 - b - c + 1)
(2*a^2*c - 8*a*b*c + 2*a*c + 6*b^2*c - 2*b*c)/(a^3 - a^2*b + a^2*c - a^2 - a*b^2
    + 2*a*b*c + 2*a*b - a + b^3 + b^2*c - b^2 - b - c + 1)
(-6*a^2*c + 8*a*b*c + 2*a*c - 2*b^2*c - 2*b*c)/(a^3 - a^2*b + a^2*c - a^2 - 
    a*b^2 + 2*a*b*c + 2*a*b - a + b^3 + b^2*c - b^2 - b - c + 1)
(-a^2 + 2*a*b + a*c + 2*a - b^2 + b*c - 2*b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + 
    b*c + c - 1)
[
    <a^2 - 2*a*b + a*c + b^2 + b*c + c - 1, 1>
]

Total time: 0.380 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:10:33 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(a-b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;

print Factorization(Numerator(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1));


Output: Magma V2.11-10    Thu Dec  8 2005 18:10:32 on modular  [Seed = 904842095]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a + 2*b*c - b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b - a*c + a - b^2 + b*c - b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-2*a*b + 2*b^2)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b + a*c + a - b^2 - b*c - b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c + a - b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-2*a^2 + 2*a*b - 2*a + 2*b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c - 2*b*c)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c - 2*b*c)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b + a*c - 2*a - b^2 + b*c + 2*b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + 
    b*c + c - 1)
[
    <a^2 - 2*a*b + a*c + b^2 + b*c + c - 1, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:09:23 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(a-b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;


Output: Magma V2.11-10    Thu Dec  8 2005 18:09:22 on modular  [Seed = 820760096]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a + 2*b*c - b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b - a*c + a - b^2 + b*c - b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-2*a*b + 2*b^2)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b + a*c + a - b^2 - b*c - b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c + a - b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-2*a^2 + 2*a*b - 2*a + 2*b)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c - 2*b*c)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(2*a*c - 2*b*c)/(a^2 - 2*a*b + a*c + b^2 + b*c + c - 1)
(-a^2 + 2*a*b + a*c - 2*a - b^2 + b*c + 2*b + c - 1)/(a^2 - 2*a*b + a*c + b^2 + 
    b*c + c - 1)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:09:07 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j]),-D/2+(a-b)*(a+b+c-1)/(2*a*b*c));
  end for;
end for;


Output: Magma V2.11-10    Thu Dec  8 2005 18:09:07 on modular  [Seed = 3457495278]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]

>>     print Evaluate(Q[i,j]),-D/2+(a-b)*(a+b+c-1)/(2*a*b*c));
                                                            ^
User error: bad syntax

>>   end for;
     ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

Total time: 0.360 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:05:30 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Denominator(Q[i,j]),-D/2+(a-b)/(2*a*b));
  end for;
end for;

print Factorization(Numerator(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4));


Output: Magma V2.11-10    Thu Dec  8 2005 18:05:29 on modular  [Seed = 3657508304]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
[
    <a + b - 1, 1>,
    <a*b*c + 1/4*a*c^2 - 1/4*a + 1/4*b*c^2 - 1/4*b + 1/4*c^2 - 1/2*c + 1/4, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:04:49 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Denominator(Q[i,j]),-D/2+(a-b)/(2*a*b));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:04:49 on modular  [Seed = 3607898357]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)

Total time: 0.360 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:04:16 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Factorization(Evaluate(Denominator(Q[i,j]),-D/2+(a-b)/(2*a*b)));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:04:15 on modular  [Seed = 3963032624]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]

>>     print Factorization(Evaluate(Denominator(Q[i,j]),-D/2+(a-b)/(2*a*b)));
                          ^
Runtime error in 'Factorization': Bad argument types
Argument types given: FldFunRatMElt

Total time: 0.360 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 18:03:59 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Denominator(Q[i,j]),-D/2+(a-b)/(2*a*b));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:03:58 on modular  [Seed = 3912372484]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)
(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 - a*b*c - 1/2*a*b - 
    1/2*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 - 1/2*b*c + 1/2*b - 1/4*c^2 + 1/2*c 
    - 1/4)/(a^2*b^2*c^2)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:03:31 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2-(a-b)/(2*a*b));
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 18:03:30 on modular  [Seed = 3862765079]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*a^3*b^2*c - a^3*b*c^2 - 3/2*a^3*b*c - 1/2*a^3*b + 1/4*a^3*c^2 + 1/2*a^3*c + 
    1/4*a^3 + 4*a^2*b^3*c + 5*a^2*b^2*c^2 - 13/2*a^2*b^2*c - 3/2*a^2*b^2 - 
    3/2*a^2*b*c^3 - 11/4*a^2*b*c^2 + 2*a^2*b*c + 9/4*a^2*b + 1/4*a^2*c^3 + 
    3/4*a^2*c^2 - 1/4*a^2*c - 3/4*a^2 + 2*a*b^4*c + 5*a*b^3*c^2 - 9/2*a*b^3*c - 
    3/2*a*b^3 + 5*a*b^2*c^3 - 33/4*a*b^2*c^2 + 1/2*a*b^2*c + 15/4*a*b^2 - 
    5/2*a*b*c^3 + 5/2*a*b*c^2 + 3*a*b*c - 3*a*b + 1/2*a*c^3 - 1/4*a*c^2 - a*c + 
    3/4*a - b^4*c^2 + 1/2*b^4*c - 1/2*b^4 - 3/2*b^3*c^3 + 11/4*b^3*c^2 - 3*b^3*c
    + 7/4*b^3 + 5/4*b^2*c^3 - 17/4*b^2*c^2 + 21/4*b^2*c - 9/4*b^2 - b*c^3 + 
    13/4*b*c^2 - 7/2*b*c + 5/4*b + 1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)/(a^4*b*c + 
    1/4*a^4*c^2 - 1/4*a^4 + 3*a^3*b^2*c + 2*a^3*b*c^2 - 3*a^3*b*c - a^3*b + 
    1/4*a^3*c^3 - 1/2*a^3*c^2 - 3/4*a^3*c + a^3 + 3*a^2*b^3*c + 7/2*a^2*b^2*c^2 
    - 6*a^2*b^2*c - 3/2*a^2*b^2 + 3/4*a^2*b*c^3 - 7/2*a^2*b*c^2 + 3/4*a^2*b*c + 
    3*a^2*b - 1/4*a^2*c^3 - 1/2*a^2*c^2 + 9/4*a^2*c - 3/2*a^2 + a*b^4*c + 
    2*a*b^3*c^2 - 3*a*b^3*c - a*b^3 + 3/4*a*b^2*c^3 - 7/2*a*b^2*c^2 + 
    3/4*a*b^2*c + 3*a*b^2 - 1/2*a*b*c^3 + 7/2*a*b*c - 3*a*b - 1/4*a*c^3 + 
    3/2*a*c^2 - 9/4*a*c + a + 1/4*b^4*c^2 - 1/4*b^4 + 1/4*b^3*c^3 - 1/2*b^3*c^2 
    - 3/4*b^3*c + b^3 - 1/4*b^2*c^3 - 1/2*b^2*c^2 + 9/4*b^2*c - 3/2*b^2 - 
    1/4*b*c^3 + 3/2*b*c^2 - 9/4*b*c + b + 1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)
(a^4*b*c - 1/4*a^4*c^2 - 1/2*a^4*c - 1/4*a^4 + a^3*b^2*c + 4*a^3*b*c^2 - 
    5/2*a^3*b*c - 1/2*a^3*b - 1/4*a^3*c^3 - 3/4*a^3*c^2 + 1/4*a^3*c + 3/4*a^3 - 
    a^2*b^3*c + 1/2*a^2*b^2*c^2 + 1/2*a^2*b^2*c + 15/4*a^2*b*c^3 - 
    19/4*a^2*b*c^2 + 1/4*a^2*b*c + 3/4*a^2*b - 1/2*a^2*c^3 + 1/4*a^2*c^2 + a^2*c
    - 3/4*a^2 - a*b^4*c - 4*a*b^3*c^2 + 5/2*a*b^3*c + 1/2*a*b^3 - 15/4*a*b^2*c^3
    + 19/4*a*b^2*c^2 - 5/4*a*b^2*c - 3/4*a*b^2 - 1/2*a*b*c^2 + 1/2*a*b*c - 
    1/4*a*c^3 + 3/4*a*c^2 - 3/4*a*c + 1/4*a - 1/4*b^4*c^2 + 1/4*b^4 + 
    1/4*b^3*c^3 + 3/4*b^3*c^2 + 3/4*b^3*c - 3/4*b^3 + 1/2*b^2*c^3 + 1/4*b^2*c^2 
    - 3/2*b^2*c + 3/4*b^2 + 1/4*b*c^3 - 3/4*b*c^2 + 3/4*b*c - 1/4*b)/(a^4*b*c + 
    1/4*a^4*c^2 - 1/4*a^4 + 3*a^3*b^2*c + 2*a^3*b*c^2 - 3*a^3*b*c - a^3*b + 
    1/4*a^3*c^3 - 1/2*a^3*c^2 - 3/4*a^3*c + a^3 + 3*a^2*b^3*c + 7/2*a^2*b^2*c^2 
    - 6*a^2*b^2*c - 3/2*a^2*b^2 + 3/4*a^2*b*c^3 - 7/2*a^2*b*c^2 + 3/4*a^2*b*c + 
    3*a^2*b - 1/4*a^2*c^3 - 1/2*a^2*c^2 + 9/4*a^2*c - 3/2*a^2 + a*b^4*c + 
    2*a*b^3*c^2 - 3*a*b^3*c - a*b^3 + 3/4*a*b^2*c^3 - 7/2*a*b^2*c^2 + 
    3/4*a*b^2*c + 3*a*b^2 - 1/2*a*b*c^3 + 7/2*a*b*c - 3*a*b - 1/4*a*c^3 + 
    3/2*a*c^2 - 9/4*a*c + a + 1/4*b^4*c^2 - 1/4*b^4 + 1/4*b^3*c^3 - 1/2*b^3*c^2 
    - 3/4*b^3*c + b^3 - 1/4*b^2*c^3 - 1/2*b^2*c^2 + 9/4*b^2*c - 3/2*b^2 - 
    1/4*b*c^3 + 3/2*b*c^2 - 9/4*b*c + b + 1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)
(a^3*b*c + 3/2*a^2*b*c^2 - 3/2*a^2*b*c - a*b^3*c - 2*a*b^2*c^2 + a*b^2*c - 
    1/2*a*b*c^2 + 1/2*a*b*c + 1/2*b^3*c^2 + 1/2*b^3*c + 1/2*b^2*c^2 - 
    1/2*b^2*c)/(a^3*b*c + 1/4*a^3*c^2 - 1/4*a^3 + 2*a^2*b^2*c + 7/4*a^2*b*c^2 - 
    2*a^2*b*c - 3/4*a^2*b + 1/4*a^2*c^3 - 1/4*a^2*c^2 - 3/4*a^2*c + 3/4*a^2 + 
    a*b^3*c + 7/4*a*b^2*c^2 - 2*a*b^2*c - 3/4*a*b^2 + 1/2*a*b*c^3 - 3/2*a*b*c^2 
    - 1/2*a*b*c + 3/2*a*b - 3/4*a*c^2 + 3/2*a*c - 3/4*a + 1/4*b^3*c^2 - 1/4*b^3 
    + 1/4*b^2*c^3 - 1/4*b^2*c^2 - 3/4*b^2*c + 3/4*b^2 - 3/4*b*c^2 + 3/2*b*c - 
    3/4*b - 1/4*c^3 + 3/4*c^2 - 3/4*c + 1/4)
(-a^4*b*c - 1/4*a^4*c^2 + 1/4*a^4 - a^3*b^2*c - 4*a^3*b*c^2 + 3/2*a^3*b*c + 
    1/2*a^3*b + 1/4*a^3*c^3 + 5/4*a^3*c^2 + 5/4*a^3*c - 3/4*a^3 + a^2*b^3*c + 
    1/2*a^2*b^2*c^2 - 1/2*a^2*b^2*c - 15/4*a^2*b*c^3 + 13/4*a^2*b*c^2 + 
    5/4*a^2*b*c - 3/4*a^2*b + 1/2*a^2*c^3 + 1/4*a^2*c^2 - 5/2*a^2*c + 3/4*a^2 + 
    a*b^4*c + 4*a*b^3*c^2 - 3/2*a*b^3*c - 1/2*a*b^3 + 15/4*a*b^2*c^3 - 
    21/4*a*b^2*c^2 - 1/4*a*b^2*c + 3/4*a*b^2 + 3/2*a*b*c^2 - 1/2*a*b*c + 
    1/4*a*c^3 - 5/4*a*c^2 + 5/4*a*c - 1/4*a - 1/4*b^4*c^2 + 1/2*b^4*c - 1/4*b^4 
    - 1/4*b^3*c^3 + 3/4*b^3*c^2 - 9/4*b^3*c + 3/4*b^3 - 1/2*b^2*c^3 - 
    7/4*b^2*c^2 + 3*b^2*c - 3/4*b^2 - 1/4*b*c^3 + 5/4*b*c^2 - 5/4*b*c + 
    1/4*b)/(a^4*b*c + 1/4*a^4*c^2 - 1/4*a^4 + 3*a^3*b^2*c + 2*a^3*b*c^2 - 
    3*a^3*b*c - a^3*b + 1/4*a^3*c^3 - 1/2*a^3*c^2 - 3/4*a^3*c + a^3 + 
    3*a^2*b^3*c + 7/2*a^2*b^2*c^2 - 6*a^2*b^2*c - 3/2*a^2*b^2 + 3/4*a^2*b*c^3 - 
    7/2*a^2*b*c^2 + 3/4*a^2*b*c + 3*a^2*b - 1/4*a^2*c^3 - 1/2*a^2*c^2 + 
    9/4*a^2*c - 3/2*a^2 + a*b^4*c + 2*a*b^3*c^2 - 3*a*b^3*c - a*b^3 + 
    3/4*a*b^2*c^3 - 7/2*a*b^2*c^2 + 3/4*a*b^2*c + 3*a*b^2 - 1/2*a*b*c^3 + 
    7/2*a*b*c - 3*a*b - 1/4*a*c^3 + 3/2*a*c^2 - 9/4*a*c + a + 1/4*b^4*c^2 - 
    1/4*b^4 + 1/4*b^3*c^3 - 1/2*b^3*c^2 - 3/4*b^3*c + b^3 - 1/4*b^2*c^3 - 
    1/2*b^2*c^2 + 9/4*b^2*c - 3/2*b^2 - 1/4*b*c^3 + 3/2*b*c^2 - 9/4*b*c + b + 
    1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)
(2*a^4*b*c - a^4*c^2 - 1/2*a^4*c - 1/2*a^4 + 4*a^3*b^2*c + 5*a^3*b*c^2 - 
    11/2*a^3*b*c - 3/2*a^3*b - 3/2*a^3*c^3 + 5/4*a^3*c^2 - 1/2*a^3*c + 7/4*a^3 +
    2*a^2*b^3*c + 5*a^2*b^2*c^2 - 11/2*a^2*b^2*c - 3/2*a^2*b^2 + 5*a^2*b*c^3 - 
    31/4*a^2*b*c^2 + a^2*b*c + 15/4*a^2*b + 5/4*a^2*c^3 - 9/4*a^2*c^2 + 
    13/4*a^2*c - 9/4*a^2 - a*b^3*c^2 - 1/2*a*b^3*c - 1/2*a*b^3 - 3/2*a*b^2*c^3 -
    5/4*a*b^2*c^2 - 1/2*a*b^2*c + 9/4*a*b^2 - 5/2*a*b*c^3 + 1/2*a*b*c^2 + 
    4*a*b*c - 3*a*b - a*c^3 + 11/4*a*c^2 - 3*a*c + 5/4*a - 1/4*b^3*c^2 + 1/4*b^3
    + 1/4*b^2*c^3 + 3/4*b^2*c^2 + 3/4*b^2*c - 3/4*b^2 + 1/2*b*c^3 + 1/4*b*c^2 - 
    3/2*b*c + 3/4*b + 1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)/(a^4*b*c + 1/4*a^4*c^2 - 
    1/4*a^4 + 3*a^3*b^2*c + 2*a^3*b*c^2 - 3*a^3*b*c - a^3*b + 1/4*a^3*c^3 - 
    1/2*a^3*c^2 - 3/4*a^3*c + a^3 + 3*a^2*b^3*c + 7/2*a^2*b^2*c^2 - 6*a^2*b^2*c 
    - 3/2*a^2*b^2 + 3/4*a^2*b*c^3 - 7/2*a^2*b*c^2 + 3/4*a^2*b*c + 3*a^2*b - 
    1/4*a^2*c^3 - 1/2*a^2*c^2 + 9/4*a^2*c - 3/2*a^2 + a*b^4*c + 2*a*b^3*c^2 - 
    3*a*b^3*c - a*b^3 + 3/4*a*b^2*c^3 - 7/2*a*b^2*c^2 + 3/4*a*b^2*c + 3*a*b^2 - 
    1/2*a*b*c^3 + 7/2*a*b*c - 3*a*b - 1/4*a*c^3 + 3/2*a*c^2 - 9/4*a*c + a + 
    1/4*b^4*c^2 - 1/4*b^4 + 1/4*b^3*c^3 - 1/2*b^3*c^2 - 3/4*b^3*c + b^3 - 
    1/4*b^2*c^3 - 1/2*b^2*c^2 + 9/4*b^2*c - 3/2*b^2 - 1/4*b*c^3 + 3/2*b*c^2 - 
    9/4*b*c + b + 1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)
(a^3*b*c - 1/2*a^3*c^2 + 1/2*a^3*c + 2*a^2*b*c^2 - a^2*b*c + a^2*c^2 - a^2*c - 
    a*b^3*c - 3/2*a*b^2*c^2 + 1/2*a*b^2*c - 3/2*a*b*c^2 + 1/2*a*b*c - 1/2*a*c^2 
    + 1/2*a*c + 1/2*b^2*c^2 + 1/2*b^2*c + 1/2*b*c^2 - 1/2*b*c)/(a^3*b*c + 
    1/4*a^3*c^2 - 1/4*a^3 + 2*a^2*b^2*c + 7/4*a^2*b*c^2 - 2*a^2*b*c - 3/4*a^2*b 
    + 1/4*a^2*c^3 - 1/4*a^2*c^2 - 3/4*a^2*c + 3/4*a^2 + a*b^3*c + 7/4*a*b^2*c^2 
    - 2*a*b^2*c - 3/4*a*b^2 + 1/2*a*b*c^3 - 3/2*a*b*c^2 - 1/2*a*b*c + 3/2*a*b - 
    3/4*a*c^2 + 3/2*a*c - 3/4*a + 1/4*b^3*c^2 - 1/4*b^3 + 1/4*b^2*c^3 - 
    1/4*b^2*c^2 - 3/4*b^2*c + 3/4*b^2 - 3/4*b*c^2 + 3/2*b*c - 3/4*b - 1/4*c^3 + 
    3/4*c^2 - 3/4*c + 1/4)
(-a^2*b*c^2 + 1/2*a^2*c^3 + 1/2*a^2*c^2 - 2*a*b*c^3 + a*b*c^2 + 1/2*a*c^3 - 
    1/2*a*c^2 + b^3*c^2 + 3/2*b^2*c^3 - 3/2*b^2*c^2 - 1/2*b*c^3 + 
    1/2*b*c^2)/(a^3*b*c + 1/4*a^3*c^2 - 1/4*a^3 + 2*a^2*b^2*c + 7/4*a^2*b*c^2 - 
    2*a^2*b*c - 3/4*a^2*b + 1/4*a^2*c^3 - 1/4*a^2*c^2 - 3/4*a^2*c + 3/4*a^2 + 
    a*b^3*c + 7/4*a*b^2*c^2 - 2*a*b^2*c - 3/4*a*b^2 + 1/2*a*b*c^3 - 3/2*a*b*c^2 
    - 1/2*a*b*c + 3/2*a*b - 3/4*a*c^2 + 3/2*a*c - 3/4*a + 1/4*b^3*c^2 - 1/4*b^3 
    + 1/4*b^2*c^3 - 1/4*b^2*c^2 - 3/4*b^2*c + 3/4*b^2 - 3/4*b*c^2 + 3/2*b*c - 
    3/4*b - 1/4*c^3 + 3/4*c^2 - 3/4*c + 1/4)
(-a^3*c^2 - 3/2*a^2*c^3 + 3/2*a^2*c^2 + a*b^2*c^2 + 2*a*b*c^3 - a*b*c^2 + 
    1/2*a*c^3 - 1/2*a*c^2 - 1/2*b^2*c^3 - 1/2*b^2*c^2 - 1/2*b*c^3 + 
    1/2*b*c^2)/(a^3*b*c + 1/4*a^3*c^2 - 1/4*a^3 + 2*a^2*b^2*c + 7/4*a^2*b*c^2 - 
    2*a^2*b*c - 3/4*a^2*b + 1/4*a^2*c^3 - 1/4*a^2*c^2 - 3/4*a^2*c + 3/4*a^2 + 
    a*b^3*c + 7/4*a*b^2*c^2 - 2*a*b^2*c - 3/4*a*b^2 + 1/2*a*b*c^3 - 3/2*a*b*c^2 
    - 1/2*a*b*c + 3/2*a*b - 3/4*a*c^2 + 3/2*a*c - 3/4*a + 1/4*b^3*c^2 - 1/4*b^3 
    + 1/4*b^2*c^3 - 1/4*b^2*c^2 - 3/4*b^2*c + 3/4*b^2 - 3/4*b*c^2 + 3/2*b*c - 
    3/4*b - 1/4*c^3 + 3/4*c^2 - 3/4*c + 1/4)
(a^2*b*c - 1/4*a^2*c^2 + 1/2*a^2*c - 1/4*a^2 + a*b^2*c + 5/2*a*b*c^2 - a*b*c - 
    1/2*a*b + 1/4*a*c^3 + 1/2*a*c^2 - 5/4*a*c + 1/2*a - 1/4*b^2*c^2 - 1/2*b^2*c 
    - 1/4*b^2 + 1/4*b*c^3 - 1/2*b*c^2 - 1/4*b*c + 1/2*b + 1/4*c^3 - 3/4*c^2 + 
    3/4*c - 1/4)/(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 3/2*a*b*c^2 - 
    a*b*c - 1/2*a*b + 1/4*a*c^3 - 3/4*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 + 
    1/4*b*c^3 - 3/4*b*c + 1/2*b + 1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)

Total time: 0.380 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 18:01:41 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2+(a-b)/(2*a*b));
  end for;
end for;
print (1-D/2), (1+D/2);


Output: Magma V2.11-10    Thu Dec  8 2005 18:01:41 on modular  [Seed = 4230415514]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*a*b^2*c + a*b*c^2 - 1/2*a*b*c - 1/2*a*b + 1/4*a*c^2 - 1/2*a*c + 1/4*a + 
    b^2*c^2 - 1/2*b^2*c - 1/2*b^2 + 1/2*b*c^3 - 1/4*b*c^2 - b*c + 3/4*b + 
    1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)/(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c 
    + 3/2*a*b*c^2 - a*b*c - 1/2*a*b + 1/4*a*c^3 - 3/4*a*c + 1/2*a + 1/4*b^2*c^2 
    - 1/4*b^2 + 1/4*b*c^3 - 3/4*b*c + 1/2*b + 1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)
(a^2*b*c - 1/4*a^2*c^2 + 1/2*a^2*c - 1/4*a^2 - a*b^2*c + 1/2*a*b*c^2 - 1/2*a*b*c
    - 1/4*a*c^3 + 3/4*a*c^2 - 3/4*a*c + 1/4*a - 1/4*b^2*c^2 + 1/4*b^2 + 
    1/4*b*c^3 - 3/4*b*c^2 + 3/4*b*c - 1/4*b)/(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + 
    a*b^2*c + 3/2*a*b*c^2 - a*b*c - 1/2*a*b + 1/4*a*c^3 - 3/4*a*c + 1/2*a + 
    1/4*b^2*c^2 - 1/4*b^2 + 1/4*b*c^3 - 3/4*b*c + 1/2*b + 1/4*c^3 - 3/4*c^2 + 
    3/4*c - 1/4)
(-a^2*b*c + a*b^2*c - 1/2*a*b*c^2 + 1/2*a*b*c + 1/2*b^2*c^2 - 
    1/2*b^2*c)/(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 3/2*a*b*c^2 - a*b*c 
    - 1/2*a*b + 1/4*a*c^3 - 3/4*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 + 1/4*b*c^3 
    - 3/4*b*c + 1/2*b + 1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)
(-a^2*b*c - 1/4*a^2*c^2 + 1/4*a^2 + a*b^2*c + 1/2*a*b*c^2 + 1/2*a*b*c + 
    1/4*a*c^3 - 1/4*a*c^2 + 1/4*a*c - 1/4*a - 1/4*b^2*c^2 - 1/2*b^2*c - 1/4*b^2 
    - 1/4*b*c^3 + 1/4*b*c^2 - 1/4*b*c + 1/4*b)/(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 
    + a*b^2*c + 3/2*a*b*c^2 - a*b*c - 1/2*a*b + 1/4*a*c^3 - 3/4*a*c + 1/2*a + 
    1/4*b^2*c^2 - 1/4*b^2 + 1/4*b*c^3 - 3/4*b*c + 1/2*b + 1/4*c^3 - 3/4*c^2 + 
    3/4*c - 1/4)
(2*a^2*b*c + a^2*c^2 + 1/2*a^2*c - 1/2*a^2 + a*b*c^2 - 3/2*a*b*c - 1/2*a*b + 
    1/2*a*c^3 + 1/4*a*c^2 - 3/2*a*c + 3/4*a - 1/4*b*c^2 + 1/4*b + 1/4*c^3 - 
    3/4*c^2 + 3/4*c - 1/4)/(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 
    3/2*a*b*c^2 - a*b*c - 1/2*a*b + 1/4*a*c^3 - 3/4*a*c + 1/2*a + 1/4*b^2*c^2 - 
    1/4*b^2 + 1/4*b*c^3 - 3/4*b*c + 1/2*b + 1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)
(-a^2*b*c - 1/2*a^2*c^2 - 1/2*a^2*c + a*b^2*c + 1/2*a*b*c^2 + 1/2*a*b*c - 
    1/2*a*c^2 + 1/2*a*c + 1/2*b*c^2 - 1/2*b*c)/(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 
    + a*b^2*c + 3/2*a*b*c^2 - a*b*c - 1/2*a*b + 1/4*a*c^3 - 3/4*a*c + 1/2*a + 
    1/4*b^2*c^2 - 1/4*b^2 + 1/4*b*c^3 - 3/4*b*c + 1/2*b + 1/4*c^3 - 3/4*c^2 + 
    3/4*c - 1/4)
(a*b*c^2 + 1/2*a*c^3 - 1/2*a*c^2 - b^2*c^2 - 1/2*b*c^3 + 1/2*b*c^2)/(a^2*b*c + 
    1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 3/2*a*b*c^2 - a*b*c - 1/2*a*b + 1/4*a*c^3 
    - 3/4*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 + 1/4*b*c^3 - 3/4*b*c + 1/2*b + 
    1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)
(a^2*c^2 - a*b*c^2 + 1/2*a*c^3 - 1/2*a*c^2 - 1/2*b*c^3 + 1/2*b*c^2)/(a^2*b*c + 
    1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 3/2*a*b*c^2 - a*b*c - 1/2*a*b + 1/4*a*c^3 
    - 3/4*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 + 1/4*b*c^3 - 3/4*b*c + 1/2*b + 
    1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)
(a^2*b*c - 1/4*a^2*c^2 - 1/2*a^2*c - 1/4*a^2 + a*b^2*c + 5/2*a*b*c^2 - a*b*c - 
    1/2*a*b + 1/4*a*c^3 - 1/2*a*c^2 - 1/4*a*c + 1/2*a - 1/4*b^2*c^2 + 1/2*b^2*c 
    - 1/4*b^2 + 1/4*b*c^3 + 1/2*b*c^2 - 5/4*b*c + 1/2*b + 1/4*c^3 - 3/4*c^2 + 
    3/4*c - 1/4)/(a^2*b*c + 1/4*a^2*c^2 - 1/4*a^2 + a*b^2*c + 3/2*a*b*c^2 - 
    a*b*c - 1/2*a*b + 1/4*a*c^3 - 3/4*a*c + 1/2*a + 1/4*b^2*c^2 - 1/4*b^2 + 
    1/4*b*c^3 - 3/4*b*c + 1/2*b + 1/4*c^3 - 3/4*c^2 + 3/4*c - 1/4)
(1/2*a + 1/2*b + 1/2*c - 1/2)/(a*b*c)
(2*a*b*c - 1/2*a - 1/2*b - 1/2*c + 1/2)/(a*b*c)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 17:50:10 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2);
  end for;
end for;
print (1-D/2), (1+D/2);


Output: Magma V2.11-10    Thu Dec  8 2005 17:50:10 on modular  [Seed = 1117370835]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
(1/2*a + 1/2*b + 1/2*c - 1/2)/(a*b*c)
(2*a*b*c - 1/2*a - 1/2*b - 1/2*c + 1/2)/(a*b*c)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 17:46:34 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D);
  end for;
end for;



Output: Magma V2.11-10    Thu Dec  8 2005 17:46:33 on modular  [Seed = 1501736355]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(-a^3*c + a^3 - 2*a^2*b*c^2 + a^2*b*c + 2*a^2*b - a^2*c^2 + 4*a^2*c - 3*a^2 + 
    2*a*b^2*c + a*b^2 + 2*a*b*c^2 + a*b*c - 4*a*b + 2*a*c^2 - 5*a*c + 3*a - b^2 
    - 2*b*c + 2*b - c^2 + 2*c - 1)/(a^4*c + 2*a^3*b*c + a^3*c^2 - 2*a^3*c + 
    a^2*b^2*c + a^2*b*c^2 - 2*a^2*b*c - a^2*c^2 + a^2*c)
(-a^4*b*c + a^4 - 2*a^3*b^2*c - a^3*b*c^2 + 5*a^3*b*c + 2*a^3*b + 2*a^3*c - 
    4*a^3 - a^2*b^3*c + a^2*b^2*c^2 + 5*a^2*b^2*c + a^2*b^2 + 4*a^2*b*c^2 - 
    5*a^2*b*c - 6*a^2*b + a^2*c^2 - 6*a^2*c + 6*a^2 - 3*a*b^2*c - 2*a*b^2 - 
    3*a*b*c^2 - a*b*c + 6*a*b - 2*a*c^2 + 6*a*c - 4*a + b^2 + 2*b*c - 2*b + c^2 
    - 2*c + 1)/(a^4*b*c + 2*a^3*b^2*c + a^3*b*c^2 - 2*a^3*b*c + a^2*b^3*c + 
    a^2*b^2*c^2 - 2*a^2*b^2*c - a^2*b*c^2 + a^2*b*c)
(2*a^3*b*c - a^3 + 2*a^2*b^2*c^2 + 2*a^2*b^2*c + 2*a^2*b*c^2 - 5*a^2*b*c - 
    2*a^2*b - 2*a^2*c + 3*a^2 - 3*a*b^2*c - a*b^2 - 3*a*b*c^2 + a*b*c + 4*a*b - 
    a*c^2 + 4*a*c - 3*a + b^2 + 2*b*c - 2*b + c^2 - 2*c + 1)/(a^3*b*c^2 + 
    a^2*b^2*c^2 + a^2*b*c^3 - a^2*b*c^2)
(-a^4*b*c - 2*a^3*b^2*c + a^3*b*c^2 - a^3*b*c + a^3*b - a^3*c + a^3 - a^2*b^3*c 
    - a^2*b^2*c^2 - a^2*b^2*c + 2*a^2*b^2 - 4*a^2*b*c^2 + 5*a^2*b*c - a^2*c^2 + 
    4*a^2*c - 3*a^2 + a*b^3 + 4*a*b^2*c - a*b^2 + 3*a*b*c^2 - a*b*c - 3*a*b + 
    2*a*c^2 - 5*a*c + 3*a - b^2 - 2*b*c + 2*b - c^2 + 2*c - 1)/(a^4*b*c + 
    2*a^3*b^2*c + a^3*b*c^2 - 2*a^3*b*c + a^2*b^3*c + a^2*b^2*c^2 - 2*a^2*b^2*c 
    - a^2*b*c^2 + a^2*b*c)
(-2*a^4*b*c + a^4*b + a^4 - 2*a^3*b^2*c^2 - a^3*b^2*c + 2*a^3*b^2 - 2*a^3*b*c^2 
    + 9*a^3*b*c - a^3*b + 2*a^3*c - 4*a^3 + a^2*b^3*c + a^2*b^3 + 3*a^2*b^2*c^2 
    + 6*a^2*b^2*c - 3*a^2*b^2 + 6*a^2*b*c^2 - 10*a^2*b*c - 3*a^2*b + a^2*c^2 - 
    6*a^2*c + 6*a^2 - a*b^3 - 5*a*b^2*c - 4*a*b*c^2 + a*b*c + 5*a*b - 2*a*c^2 + 
    6*a*c - 4*a + b^2 + 2*b*c - 2*b + c^2 - 2*c + 1)/(a^4*b^2*c + 2*a^3*b^3*c + 
    a^3*b^2*c^2 - 2*a^3*b^2*c + a^2*b^4*c + a^2*b^3*c^2 - 2*a^2*b^3*c - 
    a^2*b^2*c^2 + a^2*b^2*c)
(-2*a^3*b^2*c^2 + 2*a^3*b^2*c + 3*a^3*b*c - a^3*b - a^3 + 2*a^2*b^3*c + 
    4*a^2*b^2*c^2 + a^2*b^2*c - 2*a^2*b^2 + 3*a^2*b*c^2 - 8*a^2*b*c - 2*a^2*c + 
    3*a^2 - a*b^3 - 5*a*b^2*c + a*b^2 - 4*a*b*c^2 + 3*a*b*c + 3*a*b - a*c^2 + 
    4*a*c - 3*a + b^2 + 2*b*c - 2*b + c^2 - 2*c + 1)/(a^3*b^2*c^2 + a^2*b^3*c^2 
    + a^2*b^2*c^3 - a^2*b^2*c^2)
(2*a^2*b*c^2 - 2*a^2*b*c - a^2*c + a^2 - 2*a*b^2*c - 2*a*b*c^2 + a*b*c + 2*a*b -
    a*c^2 + 3*a*c - 2*a + b^2 + 2*b*c - 2*b + c^2 - 2*c + 1)/(a^3*b*c + 
    a^2*b^2*c + a^2*b*c^2 - a^2*b*c)
(-2*a^3*b*c + a^3 - 2*a^2*b^2*c^2 - 2*a^2*b^2*c - 2*a^2*b*c^2 + 5*a^2*b*c + 
    2*a^2*b + 2*a^2*c - 3*a^2 + 3*a*b^2*c + a*b^2 + 3*a*b*c^2 - a*b*c - 4*a*b + 
    a*c^2 - 4*a*c + 3*a - b^2 - 2*b*c + 2*b - c^2 + 2*c - 1)/(a^3*b^2*c + 
    a^2*b^3*c + a^2*b^2*c^2 - a^2*b^2*c)
(-a^3*b^2*c^2 + 3*a^3*b*c - a^3 - a^2*b^3*c^2 + a^2*b^2*c^3 + a^2*b^2*c^2 + 
    6*a^2*b^2*c + 3*a^2*b*c^2 - 6*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 + 
    3*a*b^3*c + 3*a*b^2*c^2 - 6*a*b^2*c - 3*a*b^2 - 3*a*b*c^2 - a*b*c + 6*a*b - 
    a*c^2 + 4*a*c - 3*a - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 
    2*c + 1)/(a^3*b^2*c^2 + a^2*b^3*c^2 + a^2*b^2*c^3 - a^2*b^2*c^2)

Total time: 0.360 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 17:19:27 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2);
  end for;
end for;
print Factorization(Numerator((1-(D/2))^2-(a+b+c-1)/(a*b*c)));


Output: Magma V2.11-10    Thu Dec  8 2005 17:19:26 on modular  [Seed = 2124778531]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
[
    <a + b + c - 1, 1>,
    <a*b*c - 1/4*a - 1/4*b - 1/4*c + 1/4, 1>
]

Total time: 0.360 seconds, Total memory usage: 3.72MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 17:19:02 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2);
  end for;
end for;
print (1-(D/2))^2-(a+b+c-1)/(a*b*c);


Output: Magma V2.11-10    Thu Dec  8 2005 17:19:02 on modular  [Seed = 2074118430]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
(-a^2*b*c + 1/4*a^2 - a*b^2*c - a*b*c^2 + a*b*c + 1/2*a*b + 1/2*a*c - 1/2*a + 
    1/4*b^2 + 1/2*b*c - 1/2*b + 1/4*c^2 - 1/2*c + 1/4)/(a^2*b^2*c^2)

Total time: 0.360 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 17:18:17 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2);
  end for;
end for;
print (1-(D/2))^2;


Output: Magma V2.11-10    Thu Dec  8 2005 17:18:16 on modular  [Seed = 1907000170]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
(1/4*a^2 + 1/2*a*b + 1/2*a*c - 1/2*a + 1/4*b^2 + 1/2*b*c - 1/2*b + 1/4*c^2 - 
    1/2*c + 1/4)/(a^2*b^2*c^2)

Total time: 0.360 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 17:10:34 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-(2*a*b*c-a-b+1)/(2*a*b*c));
  end for;
end for;


Output: Magma V2.11-10    Thu Dec  8 2005 17:10:33 on modular  [Seed = 131918701]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*a^3*b^2*c - a^3*b*c - 1/2*a^3*b + 1/4*a^3 + 4*a^2*b^3*c + 4*a^2*b^2*c^2 - 
    6*a^2*b^2*c - 3/2*a^2*b^2 - 3*a^2*b*c^2 + 9/4*a^2*b + 5/4*a^2*c - 3/4*a^2 + 
    2*a*b^4*c + 4*a*b^3*c^2 - 5*a*b^3*c - 3/2*a*b^3 + 2*a*b^2*c^3 - 6*a*b^2*c^2 
    + 15/4*a*b^2 - 2*a*b*c^3 + 11/2*a*b*c - 3*a*b + 2*a*c^2 - 5/2*a*c + 3/4*a - 
    1/2*b^4 + b^3*c^2 - 2*b^3*c + 7/4*b^3 + b^2*c^3 - 4*b^2*c^2 + 21/4*b^2*c - 
    9/4*b^2 - 2*b*c^3 + 5*b*c^2 - 9/2*b*c + 5/4*b + c^3 - 2*c^2 + 5/4*c - 
    1/4)/(a^4*b*c - 1/4*a^4 + 3*a^3*b^2*c + 2*a^3*b*c^2 - 3*a^3*b*c - a^3*b - 
    3/4*a^3*c + a^3 + 3*a^2*b^3*c + 4*a^2*b^2*c^2 - 6*a^2*b^2*c - 3/2*a^2*b^2 + 
    a^2*b*c^3 - 4*a^2*b*c^2 + 3/4*a^2*b*c + 3*a^2*b - 1/2*a^2*c^2 + 9/4*a^2*c - 
    3/2*a^2 + a*b^4*c + 2*a*b^3*c^2 - 3*a*b^3*c - a*b^3 + a*b^2*c^3 - 
    4*a*b^2*c^2 + 3/4*a*b^2*c + 3*a*b^2 - a*b*c^3 + a*b*c^2 + 7/2*a*b*c - 3*a*b 
    + a*c^2 - 9/4*a*c + a - 1/4*b^4 - 3/4*b^3*c + b^3 - 1/2*b^2*c^2 + 9/4*b^2*c 
    - 3/2*b^2 + b*c^2 - 9/4*b*c + b - 1/2*c^2 + 3/4*c - 1/4)
(a^4*b*c - 1/4*a^4 + a^3*b^2*c + 2*a^3*b*c^2 - 2*a^3*b*c - 1/2*a^3*b - 5/4*a^3*c
    + 3/4*a^3 - a^2*b^3*c + a^2*b*c^3 - 3/4*a^2*b*c + 3/4*a^2*b - 2*a^2*c^2 + 
    5/2*a^2*c - 3/4*a^2 - a*b^4*c - 2*a*b^3*c^2 + 2*a*b^3*c + 1/2*a*b^3 - 
    a*b^2*c^3 + 4*a*b^2*c^2 - 3/4*a*b^2*c - 3/4*a*b^2 + 2*a*b*c^3 - 4*a*b*c^2 + 
    a*b*c - a*c^3 + 2*a*c^2 - 5/4*a*c + 1/4*a + 1/4*b^4 + 3/4*b^3*c - 3/4*b^3 - 
    3/2*b^2*c + 3/4*b^2 + 3/4*b*c - 1/4*b)/(a^4*b*c - 1/4*a^4 + 3*a^3*b^2*c + 
    2*a^3*b*c^2 - 3*a^3*b*c - a^3*b - 3/4*a^3*c + a^3 + 3*a^2*b^3*c + 
    4*a^2*b^2*c^2 - 6*a^2*b^2*c - 3/2*a^2*b^2 + a^2*b*c^3 - 4*a^2*b*c^2 + 
    3/4*a^2*b*c + 3*a^2*b - 1/2*a^2*c^2 + 9/4*a^2*c - 3/2*a^2 + a*b^4*c + 
    2*a*b^3*c^2 - 3*a*b^3*c - a*b^3 + a*b^2*c^3 - 4*a*b^2*c^2 + 3/4*a*b^2*c + 
    3*a*b^2 - a*b*c^3 + a*b*c^2 + 7/2*a*b*c - 3*a*b + a*c^2 - 9/4*a*c + a - 
    1/4*b^4 - 3/4*b^3*c + b^3 - 1/2*b^2*c^2 + 9/4*b^2*c - 3/2*b^2 + b*c^2 - 
    9/4*b*c + b - 1/2*c^2 + 3/4*c - 1/4)
(a^2*b*c + a*b^2*c + a*b*c^2 - 3/2*a*b*c - 1/2*b^2*c + 1/2*b*c)/(a^3*b*c - 
    1/4*a^3 + 2*a^2*b^2*c + 2*a^2*b*c^2 - 2*a^2*b*c - 3/4*a^2*b - 3/4*a^2*c + 
    3/4*a^2 + a*b^3*c + 2*a*b^2*c^2 - 2*a*b^2*c - 3/4*a*b^2 + a*b*c^3 - 
    2*a*b*c^2 - 1/2*a*b*c + 3/2*a*b - 1/2*a*c^2 + 3/2*a*c - 3/4*a - 1/4*b^3 - 
    3/4*b^2*c + 3/4*b^2 - 1/2*b*c^2 + 3/2*b*c - 3/4*b + 1/2*c^2 - 3/4*c + 1/4)
(-a^4*b*c + 1/4*a^4 - a^3*b^2*c - 2*a^3*b*c^2 + 2*a^3*b*c + 1/2*a^3*b + 
    3/4*a^3*c - 3/4*a^3 + a^2*b^3*c - a^2*b*c^3 - 3/4*a^2*b*c - 3/4*a^2*b + 
    a^2*c^2 - a^2*c + 3/4*a^2 + a*b^4*c + 2*a*b^3*c^2 - 2*a*b^3*c - 1/2*a*b^3 + 
    a*b^2*c^3 - 4*a*b^2*c^2 - 3/4*a*b^2*c + 3/4*a*b^2 - 2*a*b*c^3 + 2*a*b*c^2 + 
    2*a*b*c + a*c^3 - 1/4*a*c - 1/4*a - 1/4*b^4 - 5/4*b^3*c + 3/4*b^3 - b^2*c^2 
    + 3*b^2*c - 3/4*b^2 + 2*b*c^2 - 9/4*b*c + 1/4*b - c^2 + 1/2*c)/(a^4*b*c - 
    1/4*a^4 + 3*a^3*b^2*c + 2*a^3*b*c^2 - 3*a^3*b*c - a^3*b - 3/4*a^3*c + a^3 + 
    3*a^2*b^3*c + 4*a^2*b^2*c^2 - 6*a^2*b^2*c - 3/2*a^2*b^2 + a^2*b*c^3 - 
    4*a^2*b*c^2 + 3/4*a^2*b*c + 3*a^2*b - 1/2*a^2*c^2 + 9/4*a^2*c - 3/2*a^2 + 
    a*b^4*c + 2*a*b^3*c^2 - 3*a*b^3*c - a*b^3 + a*b^2*c^3 - 4*a*b^2*c^2 + 
    3/4*a*b^2*c + 3*a*b^2 - a*b*c^3 + a*b*c^2 + 7/2*a*b*c - 3*a*b + a*c^2 - 
    9/4*a*c + a - 1/4*b^4 - 3/4*b^3*c + b^3 - 1/2*b^2*c^2 + 9/4*b^2*c - 3/2*b^2 
    + b*c^2 - 9/4*b*c + b - 1/2*c^2 + 3/4*c - 1/4)
(2*a^4*b*c - 1/2*a^4 + 4*a^3*b^2*c + 4*a^3*b*c^2 - 5*a^3*b*c - 3/2*a^3*b - 
    a^3*c^2 - 2*a^3*c + 7/4*a^3 + 2*a^2*b^3*c + 4*a^2*b^2*c^2 - 6*a^2*b^2*c - 
    3/2*a^2*b^2 + 2*a^2*b*c^3 - 6*a^2*b*c^2 + 15/4*a^2*b - a^2*c^3 + 19/4*a^2*c 
    - 9/4*a^2 - a*b^3*c - 1/2*a*b^3 - a*b^2*c^2 + 9/4*a*b^2 + 9/2*a*b*c - 3*a*b 
    + a*c^2 - 7/2*a*c + 5/4*a + 1/4*b^3 + 3/4*b^2*c - 3/4*b^2 - 3/2*b*c + 3/4*b 
    + 3/4*c - 1/4)/(a^4*b*c - 1/4*a^4 + 3*a^3*b^2*c + 2*a^3*b*c^2 - 3*a^3*b*c - 
    a^3*b - 3/4*a^3*c + a^3 + 3*a^2*b^3*c + 4*a^2*b^2*c^2 - 6*a^2*b^2*c - 
    3/2*a^2*b^2 + a^2*b*c^3 - 4*a^2*b*c^2 + 3/4*a^2*b*c + 3*a^2*b - 1/2*a^2*c^2 
    + 9/4*a^2*c - 3/2*a^2 + a*b^4*c + 2*a*b^3*c^2 - 3*a*b^3*c - a*b^3 + 
    a*b^2*c^3 - 4*a*b^2*c^2 + 3/4*a*b^2*c + 3*a*b^2 - a*b*c^3 + a*b*c^2 + 
    7/2*a*b*c - 3*a*b + a*c^2 - 9/4*a*c + a - 1/4*b^4 - 3/4*b^3*c + b^3 - 
    1/2*b^2*c^2 + 9/4*b^2*c - 3/2*b^2 + b*c^2 - 9/4*b*c + b - 1/2*c^2 + 3/4*c - 
    1/4)
(a^2*b*c + 1/2*a^2*c + a*b^2*c + a*b*c^2 - 1/2*a*b*c - a*c - 1/2*b*c + 
    1/2*c)/(a^3*b*c - 1/4*a^3 + 2*a^2*b^2*c + 2*a^2*b*c^2 - 2*a^2*b*c - 
    3/4*a^2*b - 3/4*a^2*c + 3/4*a^2 + a*b^3*c + 2*a*b^2*c^2 - 2*a*b^2*c - 
    3/4*a*b^2 + a*b*c^3 - 2*a*b*c^2 - 1/2*a*b*c + 3/2*a*b - 1/2*a*c^2 + 3/2*a*c 
    - 3/4*a - 1/4*b^3 - 3/4*b^2*c + 3/4*b^2 - 1/2*b*c^2 + 3/2*b*c - 3/4*b + 
    1/2*c^2 - 3/4*c + 1/4)
(-a*b*c^2 + 1/2*a*c^2 - b^2*c^2 - b*c^3 + 3/2*b*c^2 + c^3 - 1/2*c^2)/(a^3*b*c - 
    1/4*a^3 + 2*a^2*b^2*c + 2*a^2*b*c^2 - 2*a^2*b*c - 3/4*a^2*b - 3/4*a^2*c + 
    3/4*a^2 + a*b^3*c + 2*a*b^2*c^2 - 2*a*b^2*c - 3/4*a*b^2 + a*b*c^3 - 
    2*a*b*c^2 - 1/2*a*b*c + 3/2*a*b - 1/2*a*c^2 + 3/2*a*c - 3/4*a - 1/4*b^3 - 
    3/4*b^2*c + 3/4*b^2 - 1/2*b*c^2 + 3/2*b*c - 3/4*b + 1/2*c^2 - 3/4*c + 1/4)
(-a^2*c^2 - a*b*c^2 - a*c^3 + 3/2*a*c^2 + 1/2*b*c^2 - 1/2*c^2)/(a^3*b*c - 
    1/4*a^3 + 2*a^2*b^2*c + 2*a^2*b*c^2 - 2*a^2*b*c - 3/4*a^2*b - 3/4*a^2*c + 
    3/4*a^2 + a*b^3*c + 2*a*b^2*c^2 - 2*a*b^2*c - 3/4*a*b^2 + a*b*c^3 - 
    2*a*b*c^2 - 1/2*a*b*c + 3/2*a*b - 1/2*a*c^2 + 3/2*a*c - 3/4*a - 1/4*b^3 - 
    3/4*b^2*c + 3/4*b^2 - 1/2*b*c^2 + 3/2*b*c - 3/4*b + 1/2*c^2 - 3/4*c + 1/4)
(a^3*b*c - 1/4*a^3 + 2*a^2*b^2*c + 2*a^2*b*c^2 - 2*a^2*b*c - 3/4*a^2*b - 
    1/4*a^2*c + 3/4*a^2 + a*b^3*c + 2*a*b^2*c^2 - 2*a*b^2*c - 3/4*a*b^2 + 
    a*b*c^3 - 2*a*b*c^2 + 1/2*a*b*c + 3/2*a*b - 1/2*a*c^2 + 1/2*a*c - 3/4*a - 
    1/4*b^3 - 1/4*b^2*c + 3/4*b^2 - 1/2*b*c^2 + 1/2*b*c - 3/4*b + 1/2*c^2 - 
    1/4*c + 1/4)/(a^3*b*c - 1/4*a^3 + 2*a^2*b^2*c + 2*a^2*b*c^2 - 2*a^2*b*c - 
    3/4*a^2*b - 3/4*a^2*c + 3/4*a^2 + a*b^3*c + 2*a*b^2*c^2 - 2*a*b^2*c - 
    3/4*a*b^2 + a*b*c^3 - 2*a*b*c^2 - 1/2*a*b*c + 3/2*a*b - 1/2*a*c^2 + 3/2*a*c 
    - 3/4*a - 1/4*b^3 - 3/4*b^2*c + 3/4*b^2 - 1/2*b*c^2 + 3/2*b*c - 3/4*b + 
    1/2*c^2 - 3/4*c + 1/4)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 17:09:51 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],c);
  end for;
end for;


Output: Magma V2.11-10    Thu Dec  8 2005 17:09:51 on modular  [Seed = 499577089]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^3*b^2*c^4 + 4*a^3*b^2*c^3 + 4*a^3*b^2*c^2 + 3*a^3*b^2*c - 2*a^3*b*c^2 - 
    4*a^3*b*c - a^3*b + a^3 - 2*a^2*b^3*c^5 - 3*a^2*b^3*c^4 + 3*a^2*b^3*c^2 + 
    6*a^2*b^3*c + a^2*b^2*c^5 + 3*a^2*b^2*c^4 + 4*a^2*b^2*c^3 - 13*a^2*b^2*c - 
    3*a^2*b^2 - 4*a^2*b*c^3 - 4*a^2*b*c^2 + 4*a^2*b*c + 6*a^2*b + 3*a^2*c - 
    3*a^2 - 2*a*b^4*c^3 - a*b^4*c^2 + 3*a*b^4*c - 2*a*b^3*c^4 + 5*a*b^3*c^3 + 
    7*a*b^3*c^2 - 8*a*b^3*c - 3*a*b^3 + 4*a*b^2*c^4 - 3*a*b^2*c^3 - 10*a*b^2*c^2
    + a*b^2*c + 9*a*b^2 - 2*a*b*c^4 + a*b*c^2 + 10*a*b*c - 9*a*b + 3*a*c^2 - 
    6*a*c + 3*a + b^4*c - b^4 + 2*b^3*c^2 - 6*b^3*c + 4*b^3 + b^2*c^3 - 
    7*b^2*c^2 + 12*b^2*c - 6*b^2 - 2*b*c^3 + 8*b*c^2 - 10*b*c + 4*b + c^3 - 
    3*c^2 + 3*c - 1)/(a^4*b^2*c^4 + 2*a^4*b^2*c^3 + a^4*b^2*c^2 - a^4*b*c^2 + 
    2*a^3*b^3*c^4 + 4*a^3*b^3*c^3 + 2*a^3*b^3*c^2 + a^3*b^2*c^5 - 3*a^3*b^2*c^3 
    - 5*a^3*b^2*c^2 - 2*a^3*b*c^3 + 3*a^3*b*c^2 + a^2*b^4*c^4 + 2*a^2*b^4*c^3 + 
    a^2*b^4*c^2 + a^2*b^3*c^5 - 3*a^2*b^3*c^3 - 5*a^2*b^3*c^2 - a^2*b^2*c^5 - 
    a^2*b^2*c^4 - 3*a^2*b^2*c^3 + 7*a^2*b^2*c^2 - a^2*b*c^4 + 4*a^2*b*c^3 - 
    3*a^2*b*c^2 - a*b^4*c^2 - 2*a*b^3*c^3 + 3*a*b^3*c^2 - a*b^2*c^4 + 
    4*a*b^2*c^3 - 3*a*b^2*c^2 + a*b*c^4 - 2*a*b*c^3 + a*b*c^2)
(-a^3*b^2*c^4 - 2*a^3*b^2*c^3 - a^3*b^2*c^2 + 2*a^3*b*c^2 + 3*a^3*b*c - a^3 - 
    2*a^2*b^3*c^4 - 4*a^2*b^3*c^3 - 2*a^2*b^3*c^2 - a^2*b^2*c^5 - a^2*b^2*c^4 - 
    3*a^2*b^2*c^3 + 2*a^2*b^2*c^2 + 6*a^2*b^2*c + 4*a^2*b*c^3 + 2*a^2*b*c^2 - 
    4*a^2*b*c - 3*a^2*b - 3*a^2*c + 3*a^2 - a*b^4*c^4 - 2*a*b^4*c^3 - a*b^4*c^2 
    + a*b^3*c^5 + 3*a*b^3*c^4 - a*b^3*c^3 + a*b^3*c^2 + 3*a*b^3*c - 4*a*b^2*c^4 
    + 5*a*b^2*c^3 + 3*a*b^2*c^2 - 2*a*b^2*c - 3*a*b^2 + 2*a*b*c^4 - a*b*c^3 - 
    7*a*b*c + 6*a*b - 3*a*c^2 + 6*a*c - 3*a + b^4*c^2 + b^3*c^3 - 3*b^3*c^2 + 
    2*b^3*c - b^3 - 2*b^2*c^3 + 6*b^2*c^2 - 7*b^2*c + 3*b^2 + 2*b*c^3 - 7*b*c^2 
    + 8*b*c - 3*b - c^3 + 3*c^2 - 3*c + 1)/(a^3*b^2*c^4 + 2*a^3*b^2*c^3 + 
    a^3*b^2*c^2 - a^3*b*c^2 + 2*a^2*b^3*c^4 + 4*a^2*b^3*c^3 + 2*a^2*b^3*c^2 + 
    a^2*b^2*c^5 - 3*a^2*b^2*c^3 - 5*a^2*b^2*c^2 - 2*a^2*b*c^3 + 3*a^2*b*c^2 + 
    a*b^4*c^4 + 2*a*b^4*c^3 + a*b^4*c^2 + a*b^3*c^5 - 3*a*b^3*c^3 - 5*a*b^3*c^2 
    - a*b^2*c^5 - a*b^2*c^4 - 3*a*b^2*c^3 + 7*a*b^2*c^2 - a*b*c^4 + 4*a*b*c^3 - 
    3*a*b*c^2 - b^4*c^2 - 2*b^3*c^3 + 3*b^3*c^2 - b^2*c^4 + 4*b^2*c^3 - 
    3*b^2*c^2 + b*c^4 - 2*b*c^3 + b*c^2)
(-2*a^2*b*c^2 - 2*a^2*b*c + a^2 + 2*a*b^2*c^4 + 4*a*b^2*c^3 - 2*a*b^2*c - 
    2*a*b*c^3 - a*b*c^2 + a*b*c + 2*a*b + 2*a*c - 2*a - b^2*c^2 - b^2*c + b^2 - 
    b*c^3 + 3*b*c - 2*b + c^2 - 2*c + 1)/(a^2*b*c^4 + 2*a^2*b*c^3 + a^2*b*c^2 - 
    a^2*c^2 + a*b^2*c^4 + 2*a*b^2*c^3 + a*b^2*c^2 + a*b*c^5 + a*b*c^4 - a*b*c^3 
    - 3*a*b*c^2 - 2*a*c^3 + 2*a*c^2 - b^2*c^2 - 2*b*c^3 + 2*b*c^2 - c^4 + 2*c^3 
    - c^2)
(-a^4*b^2*c^4 - 2*a^4*b^2*c^3 - a^4*b^2*c^2 + a^4*b*c^2 - 2*a^3*b^3*c^4 - 
    4*a^3*b^3*c^3 - 2*a^3*b^3*c^2 + a^3*b^2*c^5 + 5*a^3*b^2*c^4 + 11*a^3*b^2*c^3
    + 11*a^3*b^2*c^2 + 3*a^3*b^2*c - a^3*b*c^3 - 8*a^3*b*c^2 - 5*a^3*b*c - a^3*b
    + a^3*c + a^3 - a^2*b^4*c^4 - 2*a^2*b^4*c^3 - a^2*b^4*c^2 - a^2*b^3*c^5 + 
    a^2*b^3*c^4 + 9*a^2*b^3*c^3 + 12*a^2*b^3*c^2 + 6*a^2*b^3*c + 2*a^2*b^2*c^4 -
    3*a^2*b^2*c^3 - 17*a^2*b^2*c^2 - 16*a^2*b^2*c - 3*a^2*b^2 - 2*a^2*b*c^4 - 
    5*a^2*b*c^3 + 3*a^2*b*c^2 + 10*a^2*b*c + 6*a^2*b + 2*a^2*c^2 - 3*a^2 + 
    2*a*b^4*c^2 + 3*a*b^4*c + 2*a*b^3*c^3 - 3*a*b^3*c^2 - 11*a*b^3*c - 3*a*b^3 -
    4*a*b^2*c^3 - 3*a*b^2*c^2 + 10*a*b^2*c + 9*a*b^2 + a*b*c^3 + 5*a*b*c^2 + 
    a*b*c - 9*a*b + a*c^3 - a*c^2 - 3*a*c + 3*a - b^4 - 2*b^3*c + 4*b^3 - 
    b^2*c^2 + 6*b^2*c - 6*b^2 + 2*b*c^2 - 6*b*c + 4*b - c^2 + 2*c - 
    1)/(a^4*b^2*c^4 + 2*a^4*b^2*c^3 + a^4*b^2*c^2 - a^4*b*c^2 + 2*a^3*b^3*c^4 + 
    4*a^3*b^3*c^3 + 2*a^3*b^3*c^2 + a^3*b^2*c^5 - 3*a^3*b^2*c^3 - 5*a^3*b^2*c^2 
    - 2*a^3*b*c^3 + 3*a^3*b*c^2 + a^2*b^4*c^4 + 2*a^2*b^4*c^3 + a^2*b^4*c^2 + 
    a^2*b^3*c^5 - 3*a^2*b^3*c^3 - 5*a^2*b^3*c^2 - a^2*b^2*c^5 - a^2*b^2*c^4 - 
    3*a^2*b^2*c^3 + 7*a^2*b^2*c^2 - a^2*b*c^4 + 4*a^2*b*c^3 - 3*a^2*b*c^2 - 
    a*b^4*c^2 - 2*a*b^3*c^3 + 3*a*b^3*c^2 - a*b^2*c^4 + 4*a*b^2*c^3 - 
    3*a*b^2*c^2 + a*b*c^4 - 2*a*b*c^3 + a*b*c^2)
(2*a^3*b*c^3 + 3*a^3*b*c^2 + 3*a^3*b*c - a^3*c - a^3 - 2*a^2*b^2*c^5 - 
    5*a^2*b^2*c^4 - 4*a^2*b^2*c^3 + a^2*b^2*c^2 + 6*a^2*b^2*c + 2*a^2*b*c^4 + 
    a^2*b*c^3 + 2*a^2*b*c^2 - 7*a^2*b*c - 3*a^2*b - 2*a^2*c^2 + 3*a^2 - 
    a*b^3*c^4 - 4*a*b^3*c^3 - 2*a*b^3*c^2 + 3*a*b^3*c + a*b^2*c^5 + a*b^2*c^4 + 
    4*a*b^2*c^3 + 8*a*b^2*c^2 - 5*a*b^2*c - 3*a*b^2 + 2*a*b*c^3 - 7*a*b*c^2 - 
    a*b*c + 6*a*b - a*c^3 + a*c^2 + 3*a*c - 3*a + b^3*c^2 + b^3*c - b^3 + 
    b^2*c^3 - b^2*c^2 - 4*b^2*c + 3*b^2 - b*c^3 - b*c^2 + 5*b*c - 3*b + c^2 - 
    2*c + 1)/(a^3*b^2*c^4 + 2*a^3*b^2*c^3 + a^3*b^2*c^2 - a^3*b*c^2 + 
    2*a^2*b^3*c^4 + 4*a^2*b^3*c^3 + 2*a^2*b^3*c^2 + a^2*b^2*c^5 - 3*a^2*b^2*c^3 
    - 5*a^2*b^2*c^2 - 2*a^2*b*c^3 + 3*a^2*b*c^2 + a*b^4*c^4 + 2*a*b^4*c^3 + 
    a*b^4*c^2 + a*b^3*c^5 - 3*a*b^3*c^3 - 5*a*b^3*c^2 - a*b^2*c^5 - a*b^2*c^4 - 
    3*a*b^2*c^3 + 7*a*b^2*c^2 - a*b*c^4 + 4*a*b*c^3 - 3*a*b*c^2 - b^4*c^2 - 
    2*b^3*c^3 + 3*b^3*c^2 - b^2*c^4 + 4*b^2*c^3 - 3*b^2*c^2 + b*c^4 - 2*b*c^3 + 
    b*c^2)
(-2*a^2*b*c^4 - 4*a^2*b*c^3 - 4*a^2*b*c^2 - 2*a^2*b*c + a^2*c^2 + a^2*c + a^2 - 
    2*a*b^2*c^2 - 2*a*b^2*c + 2*a*b*c^4 + 2*a*b*c^3 + 3*a*b*c^2 + 3*a*b*c + 
    2*a*b + a*c^3 - a*c^2 - 2*a + b^2 - b*c^2 + b*c - 2*b - c^3 + c^2 - c + 
    1)/(a^2*b*c^4 + 2*a^2*b*c^3 + a^2*b*c^2 - a^2*c^2 + a*b^2*c^4 + 2*a*b^2*c^3 
    + a*b^2*c^2 + a*b*c^5 + a*b*c^4 - a*b*c^3 - 3*a*b*c^2 - 2*a*c^3 + 2*a*c^2 - 
    b^2*c^2 - 2*b*c^3 + 2*b*c^2 - c^4 + 2*c^3 - c^2)
(2*a^2*b^2*c^4 + 4*a^2*b^2*c^3 + 4*a^2*b^2*c^2 + 2*a^2*b^2*c - 3*a^2*b*c^2 - 
    3*a^2*b*c - a^2*b + a^2 + 2*a*b^3*c^2 + 2*a*b^3*c + 2*a*b^2*c^3 - 
    3*a*b^2*c^2 - 5*a*b^2*c - 2*a*b^2 - 3*a*b*c^3 + a*b*c + 4*a*b + 2*a*c - 2*a 
    - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 2*c + 1)/(a^3*b^2*c^3 
    + 2*a^3*b^2*c^2 + a^3*b^2*c - a^3*b*c + a^2*b^3*c^3 + 2*a^2*b^3*c^2 + 
    a^2*b^3*c + a^2*b^2*c^4 + a^2*b^2*c^3 - a^2*b^2*c^2 - 3*a^2*b^2*c - 
    2*a^2*b*c^2 + 2*a^2*b*c - a*b^3*c - 2*a*b^2*c^2 + 2*a*b^2*c - a*b*c^3 + 
    2*a*b*c^2 - a*b*c)
(2*a^2*b*c^2 + 2*a^2*b*c - a^2 - 2*a*b^2*c^4 - 4*a*b^2*c^3 + 2*a*b^2*c + 
    2*a*b*c^3 + a*b*c^2 - a*b*c - 2*a*b - 2*a*c + 2*a + b^2*c^2 + b^2*c - b^2 + 
    b*c^3 - 3*b*c + 2*b - c^2 + 2*c - 1)/(a^2*b^2*c^3 + 2*a^2*b^2*c^2 + 
    a^2*b^2*c - a^2*b*c + a*b^3*c^3 + 2*a*b^3*c^2 + a*b^3*c + a*b^2*c^4 + 
    a*b^2*c^3 - a*b^2*c^2 - 3*a*b^2*c - 2*a*b*c^2 + 2*a*b*c - b^3*c - 2*b^2*c^2 
    + 2*b^2*c - b*c^3 + 2*b*c^2 - b*c)
(-a^2*b*c^3 - 2*a^2*b*c^2 - a^2*b*c + a^2 - a*b^2*c^3 - 2*a*b^2*c^2 - a*b^2*c + 
    a*b*c^4 + 3*a*b*c^3 + 3*a*b*c^2 + a*b*c + 2*a*b - a*c^2 + a*c - 2*a + b^2 - 
    b*c^2 + b*c - 2*b - c^3 + c^2 - c + 1)/(a^2*b*c^3 + 2*a^2*b*c^2 + a^2*b*c - 
    a^2*c + a*b^2*c^3 + 2*a*b^2*c^2 + a*b^2*c + a*b*c^4 + a*b*c^3 - a*b*c^2 - 
    3*a*b*c - 2*a*c^2 + 2*a*c - b^2*c - 2*b*c^2 + 2*b*c - c^3 + 2*c^2 - c)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 17:03:08 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2);
  end for;
end for;

print Factorization(Numerator(1-D^2/4));


Output: Magma V2.11-10    Thu Dec  8 2005 17:03:07 on modular  [Seed = 1038537621]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1
[
    <a + b + c - 1, 1>,
    <a*b*c - 1/4*a - 1/4*b - 1/4*c + 1/4, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 17:02:01 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2);
  end for;
end for;





Output: Magma V2.11-10    Thu Dec  8 2005 17:02:01 on modular  [Seed = 987878480]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 17:01:41 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],+D/2);
  end for;
end for;





Output: Magma V2.11-10    Thu Dec  8 2005 17:01:40 on modular  [Seed = 938268992]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*a^3*b^2*c^2 + a^3*b^2*c - 9/4*a^3*b*c - 3/8*a^3*b + 9/16*a^3 - 2*a^2*b^3*c^3 
    + a^2*b^3*c^2 + 2*a^2*b^3*c + 2*a^2*b^2*c^3 + 5/2*a^2*b^2*c^2 - 6*a^2*b^2*c 
    - 9/8*a^2*b^2 - 9/2*a^2*b*c^2 + 21/8*a^2*b*c + 45/16*a^2*b + 27/16*a^2*c - 
    27/16*a^2 - a*b^4*c^2 + a*b^4*c - a*b^3*c^3 + 11/2*a*b^3*c^2 - 13/4*a*b^3*c 
    - 9/8*a*b^3 + 7/2*a*b^2*c^3 - 8*a*b^2*c^2 + 3/4*a*b^2*c + 63/16*a*b^2 - 
    9/4*a*b*c^3 + 15/8*a*b*c^2 + 39/8*a*b*c - 9/2*a*b + 27/16*a*c^2 - 27/8*a*c +
    27/16*a + 1/2*b^4*c - 3/8*b^4 + b^3*c^2 - 23/8*b^3*c + 27/16*b^3 + 
    1/2*b^2*c^3 - 29/8*b^2*c^2 + 95/16*b^2*c - 45/16*b^2 - 9/8*b*c^3 + 
    69/16*b*c^2 - 21/4*b*c + 33/16*b + 9/16*c^3 - 27/16*c^2 + 27/16*c - 
    9/16)/(a^4*b^2*c^2 - 3/4*a^4*b*c + 3/16*a^4 + 2*a^3*b^3*c^2 + a^3*b^2*c^3 - 
    2*a^3*b^2*c^2 - 9/4*a^3*b^2*c - 3/2*a^3*b*c^2 + 9/4*a^3*b*c + 3/4*a^3*b + 
    9/16*a^3*c - 3/4*a^3 + a^2*b^4*c^2 + a^2*b^3*c^3 - 2*a^2*b^3*c^2 - 
    9/4*a^2*b^3*c - a^2*b^2*c^3 - 2*a^2*b^2*c^2 + 9/2*a^2*b^2*c + 9/8*a^2*b^2 - 
    3/4*a^2*b*c^3 + 3*a^2*b*c^2 - 9/16*a^2*b*c - 9/4*a^2*b + 9/16*a^2*c^2 - 
    27/16*a^2*c + 9/8*a^2 - 3/4*a*b^4*c - 3/2*a*b^3*c^2 + 9/4*a*b^3*c + 
    3/4*a*b^3 - 3/4*a*b^2*c^3 + 3*a*b^2*c^2 - 9/16*a*b^2*c - 9/4*a*b^2 + 
    3/4*a*b*c^3 - 3/8*a*b*c^2 - 21/8*a*b*c + 9/4*a*b + 3/16*a*c^3 - 9/8*a*c^2 + 
    27/16*a*c - 3/4*a + 3/16*b^4 + 9/16*b^3*c - 3/4*b^3 + 9/16*b^2*c^2 - 
    27/16*b^2*c + 9/8*b^2 + 3/16*b*c^3 - 9/8*b*c^2 + 27/16*b*c - 3/4*b - 
    3/16*c^3 + 9/16*c^2 - 9/16*c + 3/16)
(-a^4*b^2*c^2 + 7/4*a^4*b*c - 9/16*a^4 - 2*a^3*b^3*c^2 - a^3*b^2*c^3 - 
    a^3*b^2*c^2 + 17/4*a^3*b^2*c + 7/2*a^3*b*c^2 - 5/2*a^3*b*c - 15/8*a^3*b - 
    27/16*a^3*c + 27/16*a^3 - a^2*b^4*c^2 + a^2*b^3*c^3 - a^2*b^3*c^2 + 
    13/4*a^2*b^3*c - 2*a^2*b^2*c^3 + 11/2*a^2*b^2*c^2 - 3*a^2*b^2*c - 
    9/4*a^2*b^2 + 7/4*a^2*b*c^3 - 3/2*a^2*b*c^2 - 63/16*a^2*b*c + 63/16*a^2*b - 
    27/16*a^2*c^2 + 27/8*a^2*c - 27/16*a^2 + 3/4*a*b^4*c - 1/2*a*b^3*c - 
    9/8*a*b^3 - 3/4*a*b^2*c^3 + 2*a*b^2*c^2 - 57/16*a*b^2*c + 45/16*a*b^2 + 
    a*b*c^3 - 15/4*a*b*c^2 + 5*a*b*c - 9/4*a*b - 9/16*a*c^3 + 27/16*a*c^2 - 
    27/16*a*c + 9/16*a - 3/16*b^4 - 5/16*b^3*c + 9/16*b^3 - 1/16*b^2*c^2 + 
    5/8*b^2*c - 9/16*b^2 + 1/16*b*c^3 + 1/16*b*c^2 - 5/16*b*c + 
    3/16*b)/(a^4*b^2*c^2 - 3/4*a^4*b*c + 3/16*a^4 + 2*a^3*b^3*c^2 + a^3*b^2*c^3 
    - 2*a^3*b^2*c^2 - 9/4*a^3*b^2*c - 3/2*a^3*b*c^2 + 9/4*a^3*b*c + 3/4*a^3*b + 
    9/16*a^3*c - 3/4*a^3 + a^2*b^4*c^2 + a^2*b^3*c^3 - 2*a^2*b^3*c^2 - 
    9/4*a^2*b^3*c - a^2*b^2*c^3 - 2*a^2*b^2*c^2 + 9/2*a^2*b^2*c + 9/8*a^2*b^2 - 
    3/4*a^2*b*c^3 + 3*a^2*b*c^2 - 9/16*a^2*b*c - 9/4*a^2*b + 9/16*a^2*c^2 - 
    27/16*a^2*c + 9/8*a^2 - 3/4*a*b^4*c - 3/2*a*b^3*c^2 + 9/4*a*b^3*c + 
    3/4*a*b^3 - 3/4*a*b^2*c^3 + 3*a*b^2*c^2 - 9/16*a*b^2*c - 9/4*a*b^2 + 
    3/4*a*b*c^3 - 3/8*a*b*c^2 - 21/8*a*b*c + 9/4*a*b + 3/16*a*c^3 - 9/8*a*c^2 + 
    27/16*a*c - 3/4*a + 3/16*b^4 + 9/16*b^3*c - 3/4*b^3 + 9/16*b^2*c^2 - 
    27/16*b^2*c + 9/8*b^2 + 3/16*b*c^3 - 9/8*b*c^2 + 27/16*b*c - 3/4*b - 
    3/16*c^3 + 9/16*c^2 - 9/16*c + 3/16)
(-a^3*b^2*c + 1/2*a^3*b + 2*a^2*b^3*c^2 - a^2*b^3*c - a^2*b^2*c^2 - 
    1/2*a^2*b^2*c + a^2*b^2 + a^2*b*c - 3/4*a^2*b - 3/2*a*b^3*c + 1/2*a*b^3 - 
    3/2*a*b^2*c^2 + 5/2*a*b^2*c - 1/2*a*b^2 + 1/2*a*b*c^2 - 1/2*a*b*c + 1/4*b^3 
    + 1/2*b^2*c - 1/2*b^2 + 1/4*b*c^2 - 1/2*b*c + 1/4*b)/(a^3*b^2*c^2 - 
    3/4*a^3*b*c + 3/16*a^3 + a^2*b^3*c^2 + a^2*b^2*c^3 - a^2*b^2*c^2 - 
    3/2*a^2*b^2*c - 3/2*a^2*b*c^2 + 3/2*a^2*b*c + 9/16*a^2*b + 9/16*a^2*c - 
    9/16*a^2 - 3/4*a*b^3*c - 3/2*a*b^2*c^2 + 3/2*a*b^2*c + 9/16*a*b^2 - 
    3/4*a*b*c^3 + 3/2*a*b*c^2 + 3/8*a*b*c - 9/8*a*b + 9/16*a*c^2 - 9/8*a*c + 
    9/16*a + 3/16*b^3 + 9/16*b^2*c - 9/16*b^2 + 9/16*b*c^2 - 9/8*b*c + 9/16*b + 
    3/16*c^3 - 9/16*c^2 + 9/16*c - 3/16)
(-a^4*b^2*c^2 + 3/4*a^4*b*c - 3/16*a^4 - 2*a^3*b^3*c^2 + a^3*b^2*c^3 + 
    5*a^3*b^2*c^2 + 13/4*a^3*b^2*c - a^3*b*c^2 - 5*a^3*b*c - 9/8*a^3*b + 
    3/16*a^3*c + 21/16*a^3 - a^2*b^4*c^2 - a^2*b^3*c^3 + 5*a^2*b^3*c^2 + 
    17/4*a^2*b^3*c + 2*a^2*b^2*c^3 - 5/2*a^2*b^2*c^2 - 12*a^2*b^2*c - 
    9/4*a^2*b^2 - 7/4*a^2*b*c^3 - 7/2*a^2*b*c^2 + 111/16*a^2*b*c + 81/16*a^2*b +
    15/16*a^2*c^2 + 9/8*a^2*c - 45/16*a^2 + 7/4*a*b^4*c + 5/2*a*b^3*c^2 - 
    7*a*b^3*c - 15/8*a*b^3 + 3/4*a*b^2*c^3 - 7*a*b^2*c^2 + 105/16*a*b^2*c + 
    99/16*a*b^2 - a*b*c^3 + 19/4*a*b*c^2 + 3/2*a*b*c - 27/4*a*b + 9/16*a*c^3 - 
    3/16*a*c^2 - 45/16*a*c + 39/16*a - 9/16*b^4 - 19/16*b^3*c + 39/16*b^3 - 
    11/16*b^2*c^2 + 31/8*b^2*c - 63/16*b^2 - 1/16*b*c^3 + 23/16*b*c^2 - 
    67/16*b*c + 45/16*b - 3/4*c^2 + 3/2*c - 3/4)/(a^4*b^2*c^2 - 3/4*a^4*b*c + 
    3/16*a^4 + 2*a^3*b^3*c^2 + a^3*b^2*c^3 - 2*a^3*b^2*c^2 - 9/4*a^3*b^2*c - 
    3/2*a^3*b*c^2 + 9/4*a^3*b*c + 3/4*a^3*b + 9/16*a^3*c - 3/4*a^3 + a^2*b^4*c^2
    + a^2*b^3*c^3 - 2*a^2*b^3*c^2 - 9/4*a^2*b^3*c - a^2*b^2*c^3 - 2*a^2*b^2*c^2 
    + 9/2*a^2*b^2*c + 9/8*a^2*b^2 - 3/4*a^2*b*c^3 + 3*a^2*b*c^2 - 9/16*a^2*b*c -
    9/4*a^2*b + 9/16*a^2*c^2 - 27/16*a^2*c + 9/8*a^2 - 3/4*a*b^4*c - 
    3/2*a*b^3*c^2 + 9/4*a*b^3*c + 3/4*a*b^3 - 3/4*a*b^2*c^3 + 3*a*b^2*c^2 - 
    9/16*a*b^2*c - 9/4*a*b^2 + 3/4*a*b*c^3 - 3/8*a*b*c^2 - 21/8*a*b*c + 9/4*a*b 
    + 3/16*a*c^3 - 9/8*a*c^2 + 27/16*a*c - 3/4*a + 3/16*b^4 + 9/16*b^3*c - 
    3/4*b^3 + 9/16*b^2*c^2 - 27/16*b^2*c + 9/8*b^2 + 3/16*b*c^3 - 9/8*b*c^2 + 
    27/16*b*c - 3/4*b - 3/16*c^3 + 9/16*c^2 - 9/16*c + 3/16)
(a^4*b*c^2 + a^4*b*c - 1/2*a^4*c - 3/8*a^4 - 2*a^3*b^2*c^3 - a^3*b^2*c^2 + 
    2*a^3*b^2*c + a^3*b*c^3 + 3/2*a^3*b*c^2 - 7/4*a^3*b*c - 9/8*a^3*b - a^3*c^2 
    + 1/8*a^3*c + 15/16*a^3 - 2*a^2*b^3*c^2 + a^2*b^3*c + 9/2*a^2*b^2*c^2 - 
    9/8*a^2*b^2 + 3/2*a^2*b*c^3 - 5/2*a^2*b*c^2 - 9/4*a^2*b*c + 27/16*a^2*b - 
    1/2*a^2*c^3 + 3/8*a^2*c^2 + 15/16*a^2*c - 9/16*a^2 + 5/4*a*b^3*c - 3/8*a*b^3
    + a*b^2*c^2 - 27/8*a*b^2*c + 9/16*a*b^2 - 1/4*a*b*c^3 - 13/8*a*b*c^2 + 
    19/8*a*b*c - 1/8*a*c^3 + 9/16*a*c^2 - 1/4*a*c - 3/16*a - 3/16*b^3 - 
    5/16*b^2*c + 9/16*b^2 - 1/16*b*c^2 + 5/8*b*c - 9/16*b + 1/16*c^3 + 1/16*c^2 
    - 5/16*c + 3/16)/(a^4*b^2*c^2 - 3/4*a^4*b*c + 3/16*a^4 + 2*a^3*b^3*c^2 + 
    a^3*b^2*c^3 - 2*a^3*b^2*c^2 - 9/4*a^3*b^2*c - 3/2*a^3*b*c^2 + 9/4*a^3*b*c + 
    3/4*a^3*b + 9/16*a^3*c - 3/4*a^3 + a^2*b^4*c^2 + a^2*b^3*c^3 - 2*a^2*b^3*c^2
    - 9/4*a^2*b^3*c - a^2*b^2*c^3 - 2*a^2*b^2*c^2 + 9/2*a^2*b^2*c + 9/8*a^2*b^2 
    - 3/4*a^2*b*c^3 + 3*a^2*b*c^2 - 9/16*a^2*b*c - 9/4*a^2*b + 9/16*a^2*c^2 - 
    27/16*a^2*c + 9/8*a^2 - 3/4*a*b^4*c - 3/2*a*b^3*c^2 + 9/4*a*b^3*c + 
    3/4*a*b^3 - 3/4*a*b^2*c^3 + 3*a*b^2*c^2 - 9/16*a*b^2*c - 9/4*a*b^2 + 
    3/4*a*b*c^3 - 3/8*a*b*c^2 - 21/8*a*b*c + 9/4*a*b + 3/16*a*c^3 - 9/8*a*c^2 + 
    27/16*a*c - 3/4*a + 3/16*b^4 + 9/16*b^3*c - 3/4*b^3 + 9/16*b^2*c^2 - 
    27/16*b^2*c + 9/8*b^2 + 3/16*b*c^3 - 9/8*b*c^2 + 27/16*b*c - 3/4*b - 
    3/16*c^3 + 9/16*c^2 - 9/16*c + 3/16)
(-2*a^3*b^2*c^2 - a^3*b^2*c + 3/2*a^3*b*c + 1/2*a^3*b - 1/4*a^3 - a^2*b^3*c + 
    a^2*b^2*c^2 + 5/2*a^2*b^2*c + a^2*b^2 + 3/2*a^2*b*c^2 - 2*a^2*b*c - 
    3/2*a^2*b - 1/2*a^2*c + 3/4*a^2 + 1/2*a*b^3 - 1/2*a*b^2*c - 5/4*a*b^2 - 
    a*b*c^2 + 3/2*a*b - 1/4*a*c^2 + a*c - 3/4*a + 1/4*b^2 + 1/2*b*c - 1/2*b + 
    1/4*c^2 - 1/2*c + 1/4)/(a^3*b^2*c^2 - 3/4*a^3*b*c + 3/16*a^3 + a^2*b^3*c^2 +
    a^2*b^2*c^3 - a^2*b^2*c^2 - 3/2*a^2*b^2*c - 3/2*a^2*b*c^2 + 3/2*a^2*b*c + 
    9/16*a^2*b + 9/16*a^2*c - 9/16*a^2 - 3/4*a*b^3*c - 3/2*a*b^2*c^2 + 
    3/2*a*b^2*c + 9/16*a*b^2 - 3/4*a*b*c^3 + 3/2*a*b*c^2 + 3/8*a*b*c - 9/8*a*b +
    9/16*a*c^2 - 9/8*a*c + 9/16*a + 3/16*b^3 + 9/16*b^2*c - 9/16*b^2 + 
    9/16*b*c^2 - 9/8*b*c + 9/16*b + 3/16*c^3 - 9/16*c^2 + 9/16*c - 3/16)
(2*a^2*b^2*c^3 + a^2*b^2*c^2 - 5/2*a^2*b*c^2 - 1/2*a^2*b*c + 3/4*a^2*c + 
    a*b^3*c^2 + a*b^2*c^3 - 7/2*a*b^2*c^2 - a*b^2*c - 5/2*a*b*c^3 + 3/2*a*b*c^2 
    + 5/2*a*b*c + 3/2*a*c^2 - 3/2*a*c - 1/2*b^3*c - b^2*c^2 + 7/4*b^2*c - 
    1/2*b*c^3 + 5/2*b*c^2 - 2*b*c + 3/4*c^3 - 3/2*c^2 + 3/4*c)/(a^3*b^2*c^2 - 
    3/4*a^3*b*c + 3/16*a^3 + a^2*b^3*c^2 + a^2*b^2*c^3 - a^2*b^2*c^2 - 
    3/2*a^2*b^2*c - 3/2*a^2*b*c^2 + 3/2*a^2*b*c + 9/16*a^2*b + 9/16*a^2*c - 
    9/16*a^2 - 3/4*a*b^3*c - 3/2*a*b^2*c^2 + 3/2*a*b^2*c + 9/16*a*b^2 - 
    3/4*a*b*c^3 + 3/2*a*b*c^2 + 3/8*a*b*c - 9/8*a*b + 9/16*a*c^2 - 9/8*a*c + 
    9/16*a + 3/16*b^3 + 9/16*b^2*c - 9/16*b^2 + 9/16*b*c^2 - 9/8*b*c + 9/16*b + 
    3/16*c^3 - 9/16*c^2 + 9/16*c - 3/16)
(a^3*b*c^2 - 1/2*a^3*c - 2*a^2*b^2*c^3 + a^2*b^2*c^2 + a^2*b*c^3 + 1/2*a^2*b*c^2
    - a^2*b*c - a^2*c^2 + 3/4*a^2*c + 3/2*a*b^2*c^2 - 1/2*a*b^2*c + 3/2*a*b*c^3 
    - 5/2*a*b*c^2 + 1/2*a*b*c - 1/2*a*c^3 + 1/2*a*c^2 - 1/4*b^2*c - 1/2*b*c^2 + 
    1/2*b*c - 1/4*c^3 + 1/2*c^2 - 1/4*c)/(a^3*b^2*c^2 - 3/4*a^3*b*c + 3/16*a^3 +
    a^2*b^3*c^2 + a^2*b^2*c^3 - a^2*b^2*c^2 - 3/2*a^2*b^2*c - 3/2*a^2*b*c^2 + 
    3/2*a^2*b*c + 9/16*a^2*b + 9/16*a^2*c - 9/16*a^2 - 3/4*a*b^3*c - 
    3/2*a*b^2*c^2 + 3/2*a*b^2*c + 9/16*a*b^2 - 3/4*a*b*c^3 + 3/2*a*b*c^2 + 
    3/8*a*b*c - 9/8*a*b + 9/16*a*c^2 - 9/8*a*c + 9/16*a + 3/16*b^3 + 9/16*b^2*c 
    - 9/16*b^2 + 9/16*b*c^2 - 9/8*b*c + 9/16*b + 3/16*c^3 - 9/16*c^2 + 9/16*c - 
    3/16)
(-a^3*b^2*c^2 + 3/4*a^3*b*c - 1/16*a^3 - a^2*b^3*c^2 + a^2*b^2*c^3 + a^2*b^2*c^2
    + 3/2*a^2*b^2*c - 3/2*a^2*b*c - 3/16*a^2*b + 1/16*a^2*c + 3/16*a^2 + 
    3/4*a*b^3*c - 3/2*a*b^2*c - 3/16*a*b^2 - 3/4*a*b*c^3 + 7/8*a*b*c + 3/8*a*b +
    5/16*a*c^2 - 1/8*a*c - 3/16*a - 1/16*b^3 + 1/16*b^2*c + 3/16*b^2 + 
    5/16*b*c^2 - 1/8*b*c - 3/16*b + 3/16*c^3 - 5/16*c^2 + 1/16*c + 
    1/16)/(a^3*b^2*c^2 - 3/4*a^3*b*c + 3/16*a^3 + a^2*b^3*c^2 + a^2*b^2*c^3 - 
    a^2*b^2*c^2 - 3/2*a^2*b^2*c - 3/2*a^2*b*c^2 + 3/2*a^2*b*c + 9/16*a^2*b + 
    9/16*a^2*c - 9/16*a^2 - 3/4*a*b^3*c - 3/2*a*b^2*c^2 + 3/2*a*b^2*c + 
    9/16*a*b^2 - 3/4*a*b*c^3 + 3/2*a*b*c^2 + 3/8*a*b*c - 9/8*a*b + 9/16*a*c^2 - 
    9/8*a*c + 9/16*a + 3/16*b^3 + 9/16*b^2*c - 9/16*b^2 + 9/16*b*c^2 - 9/8*b*c +
    9/16*b + 3/16*c^3 - 9/16*c^2 + 9/16*c - 3/16)

T
 ** WARNING: Output too long, hence truncated.

'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 17:01:30 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j],-D/2);
  end for;
end for;





Output: Magma V2.11-10    Thu Dec  8 2005 17:01:30 on modular  [Seed = 3540532677]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(2*b - 1)/(a + b - 1)
(a - b)/(a + b - 1)
0
(-a + b)/(a + b - 1)
(2*a - 1)/(a + b - 1)
0
0
0
1

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 17:01:20 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Q[i,j]),-D/2);
  end for;
end for;





Output: Magma V2.11-10    Thu Dec  8 2005 17:01:19 on modular  [Seed = 3591190741]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]

>>     print Evaluate(Q[i,j]),-D/2);
                                  ^
User error: bad syntax

>>   end for;
     ^
User error: bad syntax

>> end for;
   ^
User error: bad syntax

Total time: 0.360 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 16:58:15 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Factorization(Denominator(Evaluate(Numerator(Q[i,j]),0)));
  end for;
end for;





Output: Magma V2.11-10    Thu Dec  8 2005 16:58:14 on modular  [Seed = 3624089474]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
[
    <c, 2>,
    <b, 2>,
    <a, 2>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
[
    <c, 2>,
    <b, 2>,
    <a, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
[
    <c, 2>,
    <b, 1>,
    <a, 1>,
    <a + b + c - 1, 1>
]
[
    <c, 2>,
    <b, 2>,
    <a, 2>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
[
    <c, 2>,
    <b, 2>,
    <a, 1>,
    <a + b - 1, 1>,
    <a + b + c - 1, 1>
]
[
    <c, 2>,
    <b, 1>,
    <a, 1>,
    <a + b + c - 1, 1>
]
[
    <c, 1>,
    <b, 2>,
    <a, 2>,
    <a + b + c - 1, 1>
]
[
    <c, 1>,
    <b, 2>,
    <a, 1>,
    <a + b + c - 1, 1>
]
[
    <c, 1>,
    <b, 1>,
    <a, 1>,
    <a + b + c - 1, 1>
]

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 16:57:34 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Evaluate(Numerator(Q[i,j]),0);
  end for;
end for;





Output: Magma V2.11-10    Thu Dec  8 2005 16:57:34 on modular  [Seed = 3256429984]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(3*a^3*b^2*c^2 + 3*a^3*b^2*c - 4*a^3*b*c - a^3*b + a^3 - 2*a^2*b^3*c^3 + 
    a^2*b^3*c^2 + 6*a^2*b^3*c + 3*a^2*b^2*c^3 + 6*a^2*b^2*c^2 - 13*a^2*b^2*c - 
    3*a^2*b^2 - 8*a^2*b*c^2 + 4*a^2*b*c + 6*a^2*b + 3*a^2*c - 3*a^2 - 
    2*a*b^4*c^2 + 3*a*b^4*c - 2*a*b^3*c^3 + 11*a*b^3*c^2 - 8*a*b^3*c - 3*a*b^3 +
    6*a*b^2*c^3 - 15*a*b^2*c^2 + a*b^2*c + 9*a*b^2 - 4*a*b*c^3 + 3*a*b*c^2 + 
    10*a*b*c - 9*a*b + 3*a*c^2 - 6*a*c + 3*a + b^4*c - b^4 + 2*b^3*c^2 - 6*b^3*c
    + 4*b^3 + b^2*c^3 - 7*b^2*c^2 + 12*b^2*c - 6*b^2 - 2*b*c^3 + 8*b*c^2 - 
    10*b*c + 4*b + c^3 - 3*c^2 + 3*c - 1)/(a^4*b^2*c^2 + 2*a^3*b^3*c^2 + 
    a^3*b^2*c^3 - 2*a^3*b^2*c^2 + a^2*b^4*c^2 + a^2*b^3*c^3 - 2*a^2*b^3*c^2 - 
    a^2*b^2*c^3 + a^2*b^2*c^2)
(-a^3*b^2*c^2 + 3*a^3*b*c - a^3 - 2*a^2*b^3*c^2 - a^2*b^2*c^3 - 3*a^2*b^2*c^2 + 
    6*a^2*b^2*c + 6*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 3*a^2*c + 3*a^2 - 
    a*b^4*c^2 + a*b^3*c^3 - 3*a*b^3*c^2 + 3*a*b^3*c - 4*a*b^2*c^3 + 9*a*b^2*c^2 
    - 2*a*b^2*c - 3*a*b^2 + 3*a*b*c^3 - 2*a*b*c^2 - 7*a*b*c + 6*a*b - 3*a*c^2 + 
    6*a*c - 3*a - b^3*c^2 + 2*b^3*c - b^3 - b^2*c^3 + 5*b^2*c^2 - 7*b^2*c + 
    3*b^2 + 2*b*c^3 - 7*b*c^2 + 8*b*c - 3*b - c^3 + 3*c^2 - 3*c + 
    1)/(a^3*b^2*c^2 + 2*a^2*b^3*c^2 + a^2*b^2*c^3 - 2*a^2*b^2*c^2 + a*b^4*c^2 + 
    a*b^3*c^3 - 2*a*b^3*c^2 - a*b^2*c^3 + a*b^2*c^2)
(-2*a^2*b*c + a^2 + 2*a*b^2*c^2 - 2*a*b^2*c - 2*a*b*c^2 + a*b*c + 2*a*b + 2*a*c 
    - 2*a - b^2*c + b^2 - b*c^2 + 3*b*c - 2*b + c^2 - 2*c + 1)/(a^2*b*c^2 + 
    a*b^2*c^2 + a*b*c^3 - a*b*c^2)
(-a^4*b^2*c^2 - 2*a^3*b^3*c^2 + a^3*b^2*c^3 + 7*a^3*b^2*c^2 + 3*a^3*b^2*c - 
    3*a^3*b*c^2 - 5*a^3*b*c - a^3*b + a^3*c + a^3 - a^2*b^4*c^2 - a^2*b^3*c^3 + 
    7*a^2*b^3*c^2 + 6*a^2*b^3*c + 4*a^2*b^2*c^3 - 5*a^2*b^2*c^2 - 16*a^2*b^2*c -
    3*a^2*b^2 - 3*a^2*b*c^3 - 4*a^2*b*c^2 + 10*a^2*b*c + 6*a^2*b + 2*a^2*c^2 - 
    3*a^2 + 3*a*b^4*c + 4*a*b^3*c^2 - 11*a*b^3*c - 3*a*b^3 + a*b^2*c^3 - 
    11*a*b^2*c^2 + 10*a*b^2*c + 9*a*b^2 - 2*a*b*c^3 + 8*a*b*c^2 + a*b*c - 9*a*b 
    + a*c^3 - a*c^2 - 3*a*c + 3*a - b^4 - 2*b^3*c + 4*b^3 - b^2*c^2 + 6*b^2*c - 
    6*b^2 + 2*b*c^2 - 6*b*c + 4*b - c^2 + 2*c - 1)/(a^4*b^2*c^2 + 2*a^3*b^3*c^2 
    + a^3*b^2*c^3 - 2*a^3*b^2*c^2 + a^2*b^4*c^2 + a^2*b^3*c^3 - 2*a^2*b^3*c^2 - 
    a^2*b^2*c^3 + a^2*b^2*c^2)
(2*a^3*b*c^2 + 3*a^3*b*c - a^3*c - a^3 - 2*a^2*b^2*c^3 - a^2*b^2*c^2 + 
    6*a^2*b^2*c + 2*a^2*b*c^3 + 3*a^2*b*c^2 - 7*a^2*b*c - 3*a^2*b - 2*a^2*c^2 + 
    3*a^2 - 3*a*b^3*c^2 + 3*a*b^3*c - a*b^2*c^3 + 8*a*b^2*c^2 - 5*a*b^2*c - 
    3*a*b^2 + 2*a*b*c^3 - 6*a*b*c^2 - a*b*c + 6*a*b - a*c^3 + a*c^2 + 3*a*c - 
    3*a + b^3*c - b^3 + b^2*c^2 - 4*b^2*c + 3*b^2 - 2*b*c^2 + 5*b*c - 3*b + c^2 
    - 2*c + 1)/(a^3*b^2*c^2 + 2*a^2*b^3*c^2 + a^2*b^2*c^3 - 2*a^2*b^2*c^2 + 
    a*b^4*c^2 + a*b^3*c^3 - 2*a*b^3*c^2 - a*b^2*c^3 + a*b^2*c^2)
(-2*a^2*b*c^2 - 2*a^2*b*c + a^2*c + a^2 - 2*a*b^2*c + 3*a*b*c + 2*a*b + a*c^2 - 
    2*a + b^2 + b*c - 2*b - c + 1)/(a^2*b*c^2 + a*b^2*c^2 + a*b*c^3 - a*b*c^2)
(2*a^2*b^2*c^2 + 2*a^2*b^2*c - 3*a^2*b*c - a^2*b + a^2 + 2*a*b^3*c + 2*a*b^2*c^2
    - 5*a*b^2*c - 2*a*b^2 - 3*a*b*c^2 + a*b*c + 4*a*b + 2*a*c - 2*a - b^3 - 
    2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 2*c + 1)/(a^3*b^2*c + 
    a^2*b^3*c + a^2*b^2*c^2 - a^2*b^2*c)
(2*a^2*b*c - a^2 - 2*a*b^2*c^2 + 2*a*b^2*c + 2*a*b*c^2 - a*b*c - 2*a*b - 2*a*c +
    2*a + b^2*c - b^2 + b*c^2 - 3*b*c + 2*b - c^2 + 2*c - 1)/(a^2*b^2*c + 
    a*b^3*c + a*b^2*c^2 - a*b^2*c)
(-a^2*b*c + a^2 - a*b^2*c + a*b*c^2 + a*b*c + 2*a*b + a*c - 2*a + b^2 + b*c - 
    2*b - c + 1)/(a^2*b*c + a*b^2*c + a*b*c^2 - a*b*c)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 16:55:47 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Denominator(Q[i,j])*(a+b+c-1)*(a+b-1);
  end for;
end for;





Output: Magma V2.11-10    Thu Dec  8 2005 16:55:47 on modular  [Seed = 3307089162]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1)*$.1^2 + (2*a^3*b*c - a^3 + 
    4*a^2*b^2*c + 2*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 + 
    2*a*b^3*c + 2*a*b^2*c^2 - 4*a*b^2*c - 3*a*b^2 - 2*a*b*c^2 - 2*a*b*c + 6*a*b 
    - a*c^2 + 4*a*c - 3*a - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 
    2*c + 1)/(a*b*c)*$.1 + a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1
(a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1)*$.1^2 + (2*a^3*b*c - a^3 + 
    4*a^2*b^2*c + 2*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 + 
    2*a*b^3*c + 2*a*b^2*c^2 - 4*a*b^2*c - 3*a*b^2 - 2*a*b*c^2 - 2*a*b*c + 6*a*b 
    - a*c^2 + 4*a*c - 3*a - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 
    2*c + 1)/(a*b*c)*$.1 + a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1
(a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1)*$.1^2 + (2*a^3*b*c - a^3 + 
    4*a^2*b^2*c + 2*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 + 
    2*a*b^3*c + 2*a*b^2*c^2 - 4*a*b^2*c - 3*a*b^2 - 2*a*b*c^2 - 2*a*b*c + 6*a*b 
    - a*c^2 + 4*a*c - 3*a - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 
    2*c + 1)/(a*b*c)*$.1 + a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1
(a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1)*$.1^2 + (2*a^3*b*c - a^3 + 
    4*a^2*b^2*c + 2*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 + 
    2*a*b^3*c + 2*a*b^2*c^2 - 4*a*b^2*c - 3*a*b^2 - 2*a*b*c^2 - 2*a*b*c + 6*a*b 
    - a*c^2 + 4*a*c - 3*a - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 
    2*c + 1)/(a*b*c)*$.1 + a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1
(a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1)*$.1^2 + (2*a^3*b*c - a^3 + 
    4*a^2*b^2*c + 2*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 + 
    2*a*b^3*c + 2*a*b^2*c^2 - 4*a*b^2*c - 3*a*b^2 - 2*a*b*c^2 - 2*a*b*c + 6*a*b 
    - a*c^2 + 4*a*c - 3*a - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 
    2*c + 1)/(a*b*c)*$.1 + a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1
(a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1)*$.1^2 + (2*a^3*b*c - a^3 + 
    4*a^2*b^2*c + 2*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 + 
    2*a*b^3*c + 2*a*b^2*c^2 - 4*a*b^2*c - 3*a*b^2 - 2*a*b*c^2 - 2*a*b*c + 6*a*b 
    - a*c^2 + 4*a*c - 3*a - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 
    2*c + 1)/(a*b*c)*$.1 + a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1
(a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1)*$.1^2 + (2*a^3*b*c - a^3 + 
    4*a^2*b^2*c + 2*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 + 
    2*a*b^3*c + 2*a*b^2*c^2 - 4*a*b^2*c - 3*a*b^2 - 2*a*b*c^2 - 2*a*b*c + 6*a*b 
    - a*c^2 + 4*a*c - 3*a - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 
    2*c + 1)/(a*b*c)*$.1 + a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1
(a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1)*$.1^2 + (2*a^3*b*c - a^3 + 
    4*a^2*b^2*c + 2*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 + 
    2*a*b^3*c + 2*a*b^2*c^2 - 4*a*b^2*c - 3*a*b^2 - 2*a*b*c^2 - 2*a*b*c + 6*a*b 
    - a*c^2 + 4*a*c - 3*a - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 
    2*c + 1)/(a*b*c)*$.1 + a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1
(a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1)*$.1^2 + (2*a^3*b*c - a^3 + 
    4*a^2*b^2*c + 2*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 + 
    2*a*b^3*c + 2*a*b^2*c^2 - 4*a*b^2*c - 3*a*b^2 - 2*a*b*c^2 - 2*a*b*c + 6*a*b 
    - a*c^2 + 4*a*c - 3*a - b^3 - 2*b^2*c + 3*b^2 - b*c^2 + 4*b*c - 3*b + c^2 - 
    2*c + 1)/(a*b*c)*$.1 + a^2 + 2*a*b + a*c - 2*a + b^2 + b*c - 2*b - c + 1

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 16:52:11 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..1] do
  for j in [1..3] do
    print Numerator(Q[i,j])*(a+b+c-1)*(a+b-1);
  end for;
end for;





Output: Magma V2.11-10    Thu Dec  8 2005 16:52:11 on modular  [Seed = 3424068843]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a - 2*b*c + b + c - 1)*$.1^2 + (4*a^2*b*c + a^2*b - 2*a^2 - 4*a*b^2*c^2 + 
    2*a*b^2*c + 2*a*b^2 + 4*a*b*c^2 + a*b*c - 6*a*b - 4*a*c + 4*a - 2*b^3*c + 
    b^3 - 2*b^2*c^2 + 7*b^2*c - 4*b^2 + 4*b*c^2 - 9*b*c + 5*b - 2*c^2 + 4*c - 
    2)/(a*b*c)*$.1 + (3*a^3*b^2*c^2 + 3*a^3*b^2*c - 4*a^3*b*c - a^3*b + a^3 - 
    2*a^2*b^3*c^3 + a^2*b^3*c^2 + 6*a^2*b^3*c + 3*a^2*b^2*c^3 + 6*a^2*b^2*c^2 - 
    13*a^2*b^2*c - 3*a^2*b^2 - 8*a^2*b*c^2 + 4*a^2*b*c + 6*a^2*b + 3*a^2*c - 
    3*a^2 - 2*a*b^4*c^2 + 3*a*b^4*c - 2*a*b^3*c^3 + 11*a*b^3*c^2 - 8*a*b^3*c - 
    3*a*b^3 + 6*a*b^2*c^3 - 15*a*b^2*c^2 + a*b^2*c + 9*a*b^2 - 4*a*b*c^3 + 
    3*a*b*c^2 + 10*a*b*c - 9*a*b + 3*a*c^2 - 6*a*c + 3*a + b^4*c - b^4 + 
    2*b^3*c^2 - 6*b^3*c + 4*b^3 + b^2*c^3 - 7*b^2*c^2 + 12*b^2*c - 6*b^2 - 
    2*b*c^3 + 8*b*c^2 - 10*b*c + 4*b + c^3 - 3*c^2 + 3*c - 1)/(a^2*b^2*c^2)
(-a^2 - 2*a*b - a*c + a - b^2 + b*c + b)*$.1^2 + (-2*a^3*b*c + 2*a^3 - 
    4*a^2*b^2*c - 2*a^2*b*c^2 - 2*a^2*b*c + 5*a^2*b + 4*a^2*c - 4*a^2 - 
    2*a*b^3*c + 2*a*b^2*c^2 - 2*a*b^2*c + 4*a*b^2 - 4*a*b*c^2 + 9*a*b*c - 6*a*b 
    + 2*a*c^2 - 4*a*c + 2*a + b^3 + b^2*c - 2*b^2 - b*c + b)/(a*b*c)*$.1 + 
    (-a^3*b^2*c^2 + 3*a^3*b*c - a^3 - 2*a^2*b^3*c^2 - a^2*b^2*c^3 - 
    3*a^2*b^2*c^2 + 6*a^2*b^2*c + 6*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 3*a^2*c + 
    3*a^2 - a*b^4*c^2 + a*b^3*c^3 - 3*a*b^3*c^2 + 3*a*b^3*c - 4*a*b^2*c^3 + 
    9*a*b^2*c^2 - 2*a*b^2*c - 3*a*b^2 + 3*a*b*c^3 - 2*a*b*c^2 - 7*a*b*c + 6*a*b 
    - 3*a*c^2 + 6*a*c - 3*a - b^3*c^2 + 2*b^3*c - b^3 - b^2*c^3 + 5*b^2*c^2 - 
    7*b^2*c + 3*b^2 + 2*b*c^3 - 7*b*c^2 + 8*b*c - 3*b - c^3 + 3*c^2 - 3*c + 
    1)/(a*b^2*c^2)
(2*a*b + 2*b^2 - 2*b)*$.1^2 + (-2*a^3 + 4*a^2*b*c - 4*a^2*b - 2*a^2*c + 3*a^2 + 
    4*a*b^2*c - 2*a*b^2 - 6*a*b*c + 2*a*b + a*c - b^2 - b*c + 2*b + c - 
    1)/(a*c)*$.1 + (-2*a^3*b*c + a^3 + 2*a^2*b^2*c^2 - 4*a^2*b^2*c - 2*a^2*b*c^2
    + 3*a^2*b*c + 3*a^2*b + 2*a^2*c - 3*a^2 + 2*a*b^3*c^2 - 2*a*b^3*c - 
    4*a*b^2*c^2 + 2*a*b^2*c + 3*a*b^2 + a*b*c^2 + 4*a*b*c - 6*a*b + a*c^2 - 
    4*a*c + 3*a - b^3*c + b^3 - b^2*c^2 + 4*b^2*c - 3*b^2 + 2*b*c^2 - 5*b*c + 
    3*b - c^2 + 2*c - 1)/(a*b*c^2)

Total time: 0.360 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.36 (128.139.226.36)
Time: Thu Dec  8 16:51:18 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..1] do
  for j in [1..3] do
    print Evaluate(Numerator(Q[i,j]),(a+b+c-1)*(a+b-1));
  end for;
end for;





Output: Magma V2.11-10    Thu Dec  8 2005 16:51:17 on modular  [Seed = 4146863630]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a^7*b^2*c^2 - 2*a^6*b^3*c^3 + 5*a^6*b^3*c^2 + 3*a^6*b^2*c^3 - 5*a^6*b^2*c^2 - 
    8*a^5*b^4*c^3 + 10*a^5*b^4*c^2 - 4*a^5*b^3*c^4 + 20*a^5*b^3*c^3 - 
    20*a^5*b^3*c^2 + 3*a^5*b^2*c^4 - 12*a^5*b^2*c^3 + 14*a^5*b^2*c^2 + a^5*b^2*c
    - 2*a^5*b*c - 12*a^4*b^5*c^3 + 10*a^4*b^5*c^2 - 12*a^4*b^4*c^4 + 
    42*a^4*b^4*c^3 - 30*a^4*b^4*c^2 - 2*a^4*b^3*c^5 + 21*a^4*b^3*c^4 - 
    52*a^4*b^3*c^3 + 40*a^4*b^3*c^2 + 4*a^4*b^3*c + a^4*b^2*c^5 - 9*a^4*b^2*c^4 
    + 26*a^4*b^2*c^3 - 16*a^4*b^2*c^2 - 12*a^4*b^2*c - 6*a^4*b*c^2 + 8*a^4*b*c -
    8*a^3*b^6*c^3 + 5*a^3*b^6*c^2 - 12*a^3*b^5*c^4 + 36*a^3*b^5*c^3 - 
    20*a^3*b^5*c^2 - 4*a^3*b^4*c^5 + 33*a^3*b^4*c^4 - 68*a^3*b^4*c^3 + 
    36*a^3*b^4*c^2 + 6*a^3*b^4*c + 6*a^3*b^3*c^5 - 34*a^3*b^3*c^4 + 
    64*a^3*b^3*c^3 - 20*a^3*b^3*c^2 - 24*a^3*b^3*c - 2*a^3*b^2*c^5 + 
    13*a^3*b^2*c^4 - 19*a^3*b^2*c^3 - 16*a^3*b^2*c^2 + 33*a^3*b^2*c - 
    6*a^3*b*c^3 + 18*a^3*b*c^2 - 16*a^3*b*c - a^3*b + a^3 - 2*a^2*b^7*c^3 + 
    a^2*b^7*c^2 - 4*a^2*b^6*c^4 + 11*a^2*b^6*c^3 - 5*a^2*b^6*c^2 - 2*a^2*b^5*c^5
    + 15*a^2*b^5*c^4 - 28*a^2*b^5*c^3 + 8*a^2*b^5*c^2 + 4*a^2*b^5*c + 
    5*a^2*b^4*c^5 - 25*a^2*b^4*c^4 + 34*a^2*b^4*c^3 + 8*a^2*b^4*c^2 - 
    20*a^2*b^4*c - 4*a^2*b^3*c^5 + 19*a^2*b^3*c^4 - 10*a^2*b^3*c^3 - 
    42*a^2*b^3*c^2 + 42*a^2*b^3*c + a^2*b^2*c^5 - 3*a^2*b^2*c^4 - 16*a^2*b^2*c^3
    + 55*a^2*b^2*c^2 - 41*a^2*b^2*c - 3*a^2*b^2 - 2*a^2*b*c^4 + 12*a^2*b*c^3 - 
    26*a^2*b*c^2 + 12*a^2*b*c + 6*a^2*b + 3*a^2*c - 3*a^2 - 2*a*b^6*c^2 + 
    a*b^6*c - 4*a*b^5*c^3 + 12*a*b^5*c^2 - 6*a*b^5*c - 2*a*b^4*c^4 + 
    17*a*b^4*c^3 - 32*a*b^4*c^2 + 17*a*b^4*c + 6*a*b^3*c^4 - 30*a*b^3*c^3 + 
    49*a*b^3*c^2 - 24*a*b^3*c - 3*a*b^3 - 6*a*b^2*c^4 + 27*a*b^2*c^3 - 
    39*a*b^2*c^2 + 10*a*b^2*c + 9*a*b^2 + 2*a*b*c^4 - 10*a*b*c^3 + 9*a*b*c^2 + 
    8*a*b*c - 9*a*b + 3*a*c^2 - 6*a*c + 3*a + b^4*c - b^4 + 2*b^3*c^2 - 6*b^3*c 
    + 4*b^3 + b^2*c^3 - 7*b^2*c^2 + 12*b^2*c - 6*b^2 - 2*b*c^3 + 8*b*c^2 - 
    10*b*c + 4*b + c^3 - 3*c^2 + 3*c - 1)/(a^4*b^2*c^2 + 2*a^3*b^3*c^2 + 
    a^3*b^2*c^3 - 2*a^3*b^2*c^2 + a^2*b^4*c^2 + a^2*b^3*c^3 - 2*a^2*b^3*c^2 - 
    a^2*b^2*c^3 + a^2*b^2*c^2)
(-a^7*b^2*c^2 - 6*a^6*b^3*c^2 - 3*a^6*b^2*c^3 + 5*a^6*b^2*c^2 - 15*a^5*b^4*c^2 -
    13*a^5*b^3*c^3 + 25*a^5*b^3*c^2 - 3*a^5*b^2*c^4 + 12*a^5*b^2*c^3 - 
    12*a^5*b^2*c^2 + 2*a^5*b*c - 20*a^4*b^5*c^2 - 22*a^4*b^4*c^3 + 
    50*a^4*b^4*c^2 - 8*a^4*b^3*c^4 + 40*a^4*b^3*c^3 - 48*a^4*b^3*c^2 - 
    a^4*b^2*c^5 + 9*a^4*b^2*c^4 - 22*a^4*b^2*c^3 + 12*a^4*b^2*c^2 + 9*a^4*b^2*c 
    + 6*a^4*b*c^2 - 8*a^4*b*c - 15*a^3*b^6*c^2 - 18*a^3*b^5*c^3 + 50*a^3*b^5*c^2
    - 6*a^3*b^4*c^4 + 48*a^3*b^4*c^3 - 72*a^3*b^4*c^2 - a^3*b^3*c^5 + 
    15*a^3*b^3*c^4 - 50*a^3*b^3*c^3 + 36*a^3*b^3*c^2 + 16*a^3*b^3*c + 
    2*a^3*b^2*c^5 - 11*a^3*b^2*c^4 + 12*a^3*b^2*c^3 + 20*a^3*b^2*c^2 - 
    28*a^3*b^2*c + 6*a^3*b*c^3 - 18*a^3*b*c^2 + 15*a^3*b*c - a^3 - 6*a^2*b^7*c^2
    - 7*a^2*b^6*c^3 + 25*a^2*b^6*c^2 + 24*a^2*b^5*c^3 - 48*a^2*b^5*c^2 + 
    a^2*b^4*c^5 + 3*a^2*b^4*c^4 - 34*a^2*b^4*c^3 + 36*a^2*b^4*c^2 + 14*a^2*b^4*c
    - 6*a^2*b^3*c^4 + 8*a^2*b^3*c^3 + 24*a^2*b^3*c^2 - 36*a^2*b^3*c - 
    a^2*b^2*c^5 + a^2*b^2*c^4 + 21*a^2*b^2*c^3 - 54*a^2*b^2*c^2 + 36*a^2*b^2*c +
    2*a^2*b*c^4 - 12*a^2*b*c^3 + 24*a^2*b*c^2 - 12*a^2*b*c - 3*a^2*b - 3*a^2*c +
    3*a^2 - a*b^8*c^2 - a*b^7*c^3 + 5*a*b^7*c^2 + a*b^6*c^4 + 4*a*b^6*c^3 - 
    12*a*b^6*c^2 + a*b^5*c^5 - 3*a*b^5*c^4 - 6*a*b^5*c^3 + 12*a*b^5*c^2 + 
    6*a*b^5*c - 2*a*b^4*c^5 + 5*a*b^4*c^4 - 4*a*b^4*c^3 + 12*a*b^4*c^2 - 
    20*a*b^4*c + a*b^3*c^5 - 7*a*b^3*c^4 + 24*a*b^3*c^3 - 42*a*b^3*c^2 + 
    27*a*b^3*c + 6*a*b^2*c^4 - 26*a*b^2*c^3 + 37*a*b^2*c^2 - 14*a*b^2*c - 
    3*a*b^2 - 2*a*b*c^4 + 9*a*b*c^3 - 8*a*b*c^2 - 5*a*b*c + 6*a*b - 3*a*c^2 + 
    6*a*c - 3*a + b^6*c + 2*b^5*c^2 - 4*b^5*c + b^4*c^3 - 6*b^4*c^2 + 6*b^4*c - 
    2*b^3*c^3 + 5*b^3*c^2 - 2*b^3*c - b^3 + 3*b^2*c^2 - 6*b^2*c + 3*b^2 + 
    2*b*c^3 - 7*b*c^2 + 8*b*c - 3*b - c^3 + 3*c^2 - 3*c + 1)/(a^3*b^2*c^2 + 
    2*a^2*b^3*c^2 + a^2*b^2*c^3 - 2*a^2*b^2*c^2 + a*b^4*c^2 + a*b^3*c^3 - 
    2*a*b^3*c^2 - a*b^2*c^3 + a*b^2*c^2)
(2*a^5*b^2*c^2 + 8*a^4*b^3*c^2 + 4*a^4*b^2*c^3 - 8*a^4*b^2*c^2 - 2*a^4*b*c + 
    12*a^3*b^4*c^2 + 12*a^3*b^3*c^3 - 24*a^3*b^3*c^2 + 2*a^3*b^2*c^4 - 
    12*a^3*b^2*c^3 + 16*a^3*b^2*c^2 - 6*a^3*b^2*c - 4*a^3*b*c^2 + 5*a^3*b*c + 
    8*a^2*b^5*c^2 + 12*a^2*b^4*c^3 - 24*a^2*b^4*c^2 + 4*a^2*b^3*c^4 - 
    24*a^2*b^3*c^3 + 32*a^2*b^3*c^2 - 6*a^2*b^3*c - 4*a^2*b^2*c^4 + 
    16*a^2*b^2*c^3 - 24*a^2*b^2*c^2 + 9*a^2*b^2*c - 2*a^2*b*c^3 + 6*a^2*b*c^2 - 
    5*a^2*b*c + a^2 + 2*a*b^6*c^2 + 4*a*b^5*c^3 - 8*a*b^5*c^2 + 2*a*b^4*c^4 - 
    12*a*b^4*c^3 + 16*a*b^4*c^2 - 2*a*b^4*c - 4*a*b^3*c^4 + 16*a*b^3*c^3 - 
    20*a*b^3*c^2 + 3*a*b^3*c + 2*a*b^2*c^4 - 10*a*b^2*c^3 + 12*a*b^2*c^2 - 
    2*a*b^2*c + a*b*c^3 - 2*a*b*c^2 + 2*a*b + 2*a*c - 2*a - b^4*c - 2*b^3*c^2 + 
    3*b^3*c - b^2*c^3 + 4*b^2*c^2 - 4*b^2*c + b^2 + b*c^3 - 3*b*c^2 + 4*b*c - 
    2*b + c^2 - 2*c + 1)/(a^2*b*c^2 + a*b^2*c^2 + a*b*c^3 - a*b*c^2)

Total time: 0.370 seconds, Total memory usage: 3.63MB


'128.139'
************** MAGMA *****************
Host 128.139.226.37 (128.139.226.37)
Time: Thu Dec  8 16:47:53 2005

Input: K<a,b,c>:=FunctionField(RationalField(),3);
A:=Matrix(K,3,3,[[a,1,1],[0,b,1],[0,0,c]]);
A1:=Matrix(K,3,3,[[b,1,1],[0,a,1],[0,0,c]]);
S:=Transpose(A)*A^(-1);
F,T:=PrimaryRationalForm(S);
B:=T*A*Transpose(T);

R:=PolynomialRing(K,9);
P:=Matrix(R,3,3,[R.1,R.2,R.3,R.4,R.5,R.6,R.7,R.8,R.9]);
I:=Ideal(Eltseq(P*B*Transpose(P)-B));
G:=GroebnerBasis(I);

Q1:=Matrix(K,3,3,[(2*b-1)/(a+b-1),(a-b)/(a+b-1),0,(b-a)/(a+b-1),(2*a-1)/(a+b-1),0,
0,0,1]);

Kt<t>:=FunctionField(K);
D:=(2*a*b*c-a-b-c+1)/(a*b*c);
s:=t;
px:=-(2*s+D);
py:=1-s^2;
q:=s^2+s*D+1;
Q:=Matrix(Kt,3,3,[1,0,0,0,D*px/q+py/q,-px/q,0,px/q,py/q]);
Q:=Q1*T^(-1)*Q*T;
print (Q*A*Transpose(Q)-A1);
for i in [1..3] do
  for j in [1..3] do
    print Numerator(Q[i,j])*(a+b+c-1)*(a+b-1);
  end for;
end for;





Output: Magma V2.11-10    Thu Dec  8 2005 16:47:52 on modular  [Seed = 2538372787]
   -------------------------------------

[0 0 0]
[0 0 0]
[0 0 0]
(a - 2*b*c + b + c - 1)*$.1^2 + (4*a^2*b*c + a^2*b - 2*a^2 - 4*a*b^2*c^2 + 
    2*a*b^2*c + 2*a*b^2 + 4*a*b*c^2 + a*b*c - 6*a*b - 4*a*c + 4*a - 2*b^3*c + 
    b^3 - 2*b^2*c^2 + 7*b^2*c - 4*b^2 + 4*b*c^2 - 9*b*c + 5*b - 2*c^2 + 4*c - 
    2)/(a*b*c)*$.1 + (3*a^3*b^2*c^2 + 3*a^3*b^2*c - 4*a^3*b*c - a^3*b + a^3 - 
    2*a^2*b^3*c^3 + a^2*b^3*c^2 + 6*a^2*b^3*c + 3*a^2*b^2*c^3 + 6*a^2*b^2*c^2 - 
    13*a^2*b^2*c - 3*a^2*b^2 - 8*a^2*b*c^2 + 4*a^2*b*c + 6*a^2*b + 3*a^2*c - 
    3*a^2 - 2*a*b^4*c^2 + 3*a*b^4*c - 2*a*b^3*c^3 + 11*a*b^3*c^2 - 8*a*b^3*c - 
    3*a*b^3 + 6*a*b^2*c^3 - 15*a*b^2*c^2 + a*b^2*c + 9*a*b^2 - 4*a*b*c^3 + 
    3*a*b*c^2 + 10*a*b*c - 9*a*b + 3*a*c^2 - 6*a*c + 3*a + b^4*c - b^4 + 
    2*b^3*c^2 - 6*b^3*c + 4*b^3 + b^2*c^3 - 7*b^2*c^2 + 12*b^2*c - 6*b^2 - 
    2*b*c^3 + 8*b*c^2 - 10*b*c + 4*b + c^3 - 3*c^2 + 3*c - 1)/(a^2*b^2*c^2)
(-a^2 - 2*a*b - a*c + a - b^2 + b*c + b)*$.1^2 + (-2*a^3*b*c + 2*a^3 - 
    4*a^2*b^2*c - 2*a^2*b*c^2 - 2*a^2*b*c + 5*a^2*b + 4*a^2*c - 4*a^2 - 
    2*a*b^3*c + 2*a*b^2*c^2 - 2*a*b^2*c + 4*a*b^2 - 4*a*b*c^2 + 9*a*b*c - 6*a*b 
    + 2*a*c^2 - 4*a*c + 2*a + b^3 + b^2*c - 2*b^2 - b*c + b)/(a*b*c)*$.1 + 
    (-a^3*b^2*c^2 + 3*a^3*b*c - a^3 - 2*a^2*b^3*c^2 - a^2*b^2*c^3 - 
    3*a^2*b^2*c^2 + 6*a^2*b^2*c + 6*a^2*b*c^2 - 4*a^2*b*c - 3*a^2*b - 3*a^2*c + 
    3*a^2 - a*b^4*c^2 + a*b^3*c^3 - 3*a*b^3*c^2 + 3*a*b^3*c - 4*a*b^2*c^3 + 
    9*a*b^2*c^2 - 2*a*b^2*c - 3*a*b^2 + 3*a*b*c^3 - 2*a*b*c^2 - 7*a*b*c + 6*a*b 
    - 3*a*c^2 + 6*a*c - 3*a - b^3*c^2 + 2*b^3*c - b^3 - b^2*c^3 + 5*b^2*c^2 - 
    7*b^2*c + 3*b^2 + 2*b*c^3 - 7*b*c^2 + 8*b*c - 3*b - c^3 + 3*c^2 - 3*c + 
    1)/(a*b^2*c^2)
(2*a*b + 2*b^2 - 2*b)*$.1^2 + (-2*a^3 + 4*a^2*b*c - 4*a^2*b - 2*a^2*c + 3*a^2 + 
    4*a*b^2*c - 2*a*b^2 - 6*a*b*c + 2*a*b + a*c - b^2 - b*c + 2*b + c - 
    1)/(a*c)*$.1 + (-2*a^3*b*c + a^3 + 2*a^2*b^2*c^2 - 4*a^2*b^2*c - 2*a^2*b*c^2
    + 3*a^2*b*c + 3*a^2*b + 2*a^2*c - 3*a^2 + 2*a*b^3*c^2 - 2*a*b^3*c - 
    4*a*b^2*c^2 + 2*a*b^2*c + 3*a*b^2 + a*b*c^2 + 4*a*b*c - 6*a*b + a*c^2 - 
    4*a*c + 3*a - b^3*c + b^3 - b^2*c^2 + 4*b^2*c - 3*b^2 + 2*b*c^2 - 5*b*c + 
    3*b - c^2 + 2*c - 1)/(a*b*c^2)
(-a^2 - 2*a*b + a*c + 3*a - b^2 - b*c + 3*b - 2)*$.1^2 + (-2*a^3*b*c + a^3 - 
    4*a^2*b^2*c + 2*a^2*b*c^2 + 10*a^2*b*c + 4*a^2*b - a^2*c - 5*a^2 - 2*a*b^3*c
    - 2*a*b^2*c^2 + 10*a*b^2*c + 5*a*b^2 + 4*a*b*c^2 - 7*a*b*c - 12*a*b - 
    2*a*c^2 - 2*a*c + 7*a + 2*b^3 + 2*b^2*c - 7*b^2 - 5*b*c + 8*b + 3*c - 
    3)/(a*b*c)*$.1 + (-a^4*b^2*c^2 - 2*a^3*b^3*c^2 + a^3*b^2*c^3 + 7*a^3*b^2*c^2
    + 3*a^3*b^2*c - 3*a^3*b*c^2 - 5*a^3*b*c - a^3*b + a^3*c + a^3 - a^2*b^4*c^2 
    - a^2*b^3*c^3 + 7*a^2*b^3*c^2 + 6*a^2*b^3*c + 4*a^2*b^2*c^3 - 5*a^2*b^2*c^2 
    - 16*a^2*b^2*c - 3*a^2*b^2 - 3*a^2*b*c^3 - 4*a^2*b*c^2 + 10*a^2*b*c + 
    6*a^2*b + 2*a^2*c^2 - 3*a^2 + 3*a*b^4*c + 4*a*b^3*c^2 - 11*a*b^3*c - 3*a*b^3
    + a*b^2*c^3 - 11*a*b^2*c^2 + 10*a*b^2*c + 9*a*b^2 - 2*a*b*c^3 + 8*a*b*c^2 + 
    a*b*c - 9*a*b + a*c^3 - a*c^2 - 3*a*c + 3*a - b^4 - 2*b^3*c + 4*b^3 - 
    b^2*c^2 + 6*b^2*c - 6*b^2 + 2*b*c^2 - 6*b*c + 4*b - c^2 + 2*c - 
    1)/(a^2*b^2*c^2)
(-2*a*c - a - b + c + 1)*$.1^2 + (2*a^3*c + a^3 - 4*a^2*b*c^2 - 2*a^2*b*c + 
    2*a^2*b + 2*a^2*c^2 - a^2*c - a^2 - 4*a*b^2*c + a*b^2 + 5*a*b*c - a + b^2 + 
    b*c - 2*b - c + 1)/(a*b*c)*$.1 + (2*a^3*b*c^2 + 3*a^3*b*c - a^3*c - a^3 - 
    2*a^2*b^2*c^3 - a^2*b^2*c^2 + 6*a^2*b^2*c + 2*a^2*b*c^3 + 3*a^2*b*c^2 - 
    7*a^2*b*c - 3*a^2*b - 2*a^2*c^2 + 3*a^2 - 3*a*b^3*c^2 + 3*a*b^3*c - 
    a*b^2*c^3 + 8*a*b^2*c^2 - 5*a*b^2*c - 3*a*b^2 + 2*a*b*c^3 - 6*a*b*c^2 - 
    a*b*c + 6*a*b - a*c^3 + a*c^2 + 3*a*c - 3*a + b^3*c - b^3 + b^2*c^2 - 
    4*b^2*c + 3*b^2 - 2*b*c^2 + 5*b*c - 3*b + c^2 - 2*c + 1)/(a*b^2*c^2)
(-2*a^2 - 2*a*b + 4*a + 2*b - 2)*$.1^2 + (-4*a^3*b*c - 2*a^3*b + a^3 - 
    4*a^2*b^2*c - 4*a^2*b^2 + 6*a^2*b*c + 6*a^2*b + a^2*c - 3*a^2 - 2*a*b^3 + 
    2*a*b^2*c + 5*a*b^2 - a*b*c - 6*a*b - 2*a*c + 3*a - b^2 - b*c + 2*b + c - 
    1)/(a*b*c)*$.1 + (-2*a^3*b*c^2 - 2*a^3*b*c + a^3*c + a^3 - 2*a^2*b^2*c^2 - 
    4*a^2*b^2*c + 2*a^2*b*c^2 + 6*a^2*b*c + 3*a^2*b + a^2*c^2 - a^2*c - 3*a^2 - 
    2*a*b^3*c + 5*a*b^2*c + 3*a*b^2 + a*b*c^2 - 2*a*b*c - 6*a*b - a*c^2 - a*c + 
    3*a + b^3 + b^2*c - 3*b^2 - 2*b*c + 3*b + c - 1)/(a*b*c^2)
(2*a*c + 2*b*c - 2*c)*$.1^2 + (4*a^2*b*c + 2*a^2*b - 3*a^2 + 4*a*b^2*c + 4*a*b^2
    - 2*a*b*c - 10*a*b - 3*a*c + 6*a + 2*b^3 + 2*b^2*c - 7*b^2 - 5*b*c + 8*b + 
    3*c - 3)/(a*b)*$.1 + (2*a^3*b^2*c^2 + 2*a^3*b^2*c - 3*a^3*b*c - a^3*b + a^3 
    + 2*a^2*b^3*c^2 + 4*a^2*b^3*c - 10*a^2*b^2*c - 3*a^2*b^2 - 3*a^2*b*c^2 + 
    4*a^2*b*c + 6*a^2*b + 2*a^2*c - 3*a^2 + 2*a*b^4*c + 2*a*b^3*c^2 - 7*a*b^3*c 
    - 3*a*b^3 - 5*a*b^2*c^2 + 4*a*b^2*c + 9*a*b^2 + 2*a*b*c^2 + 5*a*b*c - 9*a*b 
    + a*c^2 - 4*a*c + 3*a - b^4 - 2*b^3*c + 4*b^3 - b^2*c^2 + 6*b^2*c - 6*b^2 + 
    2*b*c^2 - 6*b*c + 4*b - c^2 + 2*c - 1)/(a^2*b^2*c)
(-2*a*c - 2*b*c + 2*c)*$.1^2 + (2*a^3 - 4*a^2*b*c + 4*a^2*b + 2*a^2*c - 3*a^2 - 
    4*a*b^2*c + 2*a*b^2 + 6*a*b*c - 2*a*b - a*c + b^2 + b*c - 2*b - c + 
    1)/(a*b)*$.1 + (2*a^3*b*c - a^3 - 2*a^2*b^2*c^2 + 4*a^2*b^2*c + 2*a^2*b*c^2 
    - 3*a^2*b*c - 3*a^2*b - 2*a^2*c + 3*a^2 - 2*a*b^3*c^2 + 2*a*b^3*c + 
    4*a*b^2*c^2 - 2*a*b^2*c - 3*a*b^2 - a*b*c^2 - 4*a*b*c + 6*a*b - a*c^2 + 
    4*a*c - 3*a + b^3*c - b^3 + b^2*c^2 - 4*b^2*c + 3*b^2 - 2*b*c^2 + 5*b*c - 
    3*b + c^2 - 2*c + 1)/(a*b^2*c)
(-a^2 - 2*a*b + a*c + 2*a - b^2 + b*c + 2*b - c - 1)*$.1^2 + (-2*a^3