'72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Wed Aug 23 14:46:53 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.056s user 0m0.007s sys 0m0.009s '69.125.' ************** PARI ***************** Host 69.125.40.37 (69.125.40.37) Time: Wed Aug 23 13:30:35 2006 Input: 9*10^9 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 9000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.009s '69.125.' ************** PARI ***************** Host 69.125.40.37 (69.125.40.37) Time: Wed Aug 23 13:30:18 2006 Input: 9*10^9 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 9000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.287s user 0m0.005s sys 0m0.012s '67.182.' ************** PARI ***************** Host 67.182.44.233 (67.182.44.233) Time: Tue Aug 22 18:02:14 2006 Input: -2.4 + 0.11 - 3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -5.2900000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '69.208.' ************** PARI ***************** Host 69.208.163.19 (69.208.163.19) Time: Tue Aug 22 17:57:06 2006 Input: 2^4*4-2/8 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 255/4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '69.208.' ************** PARI ***************** Host 69.208.163.19 (69.208.163.19) Time: Tue Aug 22 17:56:14 2006 Input: 6+4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 10 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '69.208.' ************** PARI ***************** Host 69.208.163.19 (69.208.163.19) Time: Tue Aug 22 17:55:49 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '68.225.' ************** PARI ***************** Host 68.225.63.159 (68.225.63.159) Time: Tue Aug 22 17:42:20 2006 Input: 16.5*6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 99.000000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.008s '24.252.' ************** PARI ***************** Host 24.252.118.249 (24.252.118.249) Time: Tue Aug 22 17:27:16 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '131.111' ************** PARI ***************** Host 131.111.200.200 (131.111.200.200) Time: Tue Aug 22 17:07:25 2006 Input: sqrt(2*3.99E+14*(1/6678000-1/6678001)/(1-6678000^2/6678001^2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7729.7110001915802113615387877878229188 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.011s sys 0m0.006s '131.111' ************** PARI ***************** Host 131.111.200.200 (131.111.200.200) Time: Tue Aug 22 17:07:16 2006 Input: sqrt(2*3.99E+14*(1/6678000-1/6678000)/(1-6678000^2/6678000^2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** division by zero Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '131.111' ************** PARI ***************** Host 131.111.200.200 (131.111.200.200) Time: Tue Aug 22 17:06:57 2006 Input: sqrt(2*3.99E+14*(1/6678000-1/6778000)/(1-6678000^2/6778000^2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7758.3797162510811541316832269815493887 ? Goodbye! Errors/timing (if any): Timing: real 0m0.092s user 0m0.008s sys 0m0.009s '69.238.' ************** PARI ***************** Host 69.238.128.170 (69.238.128.170) Time: Tue Aug 22 16:46:25 2006 Input: 3x-4(x+11)=-2(x+8)-43 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x-4(x+11)=-2(x+8)-43. *** unexpected character: 3x-4(x+11)=-2(x+8)-43 ^----------- Timing: real 0m0.038s user 0m0.008s sys 0m0.007s '66.27.2' ************** PARI ***************** Host 66.27.234.197 (66.27.234.197) Time: Tue Aug 22 16:24:51 2006 Input: -3*3= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: -3*3= ^- Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '72.30.9' ************** PARI ***************** Host 72.30.98.136 (72.30.98.136) Time: Tue Aug 22 05:47:23 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '71.65.2' ************** PARI ***************** Host 71.65.241.42 (71.65.241.42) Time: Mon Aug 21 20:24:17 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.048s user 0m0.006s sys 0m0.012s '72.30.1' ************** PARI ***************** Host 72.30.111.31 (72.30.111.31) Time: Mon Aug 21 19:25:39 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.182s user 0m0.006s sys 0m0.011s '69.154.' ************** PARI ***************** Host 69.154.89.104 (69.154.89.104) Time: Mon Aug 21 18:15:53 2006 Input: t-(-16)=9 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: t-(-16)=9 ^-- Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '69.154.' ************** PARI ***************** Host 69.154.89.104 (69.154.89.104) Time: Mon Aug 21 18:08:00 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '68.88.2' ************** PARI ***************** Host 68.88.200.203 (68.88.200.203) Time: Mon Aug 21 16:58:11 2006 Input: 99 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 99 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.004s sys 0m0.010s '24.110.' ************** PARI ***************** Host 24.110.168.190 (24.110.168.190) Time: Mon Aug 21 15:24:21 2006 Input: 3y/x-2cx/3y Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = y ? Goodbye! Errors/timing (if any): *** Warning: unused characters: y/x-2cx/3y. Timing: real 0m0.062s user 0m0.006s sys 0m0.011s '24.45.7' ************** PARI ***************** Host 24.45.76.206 (24.45.76.206) Time: Mon Aug 21 14:07:55 2006 Input: 5=5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 5=5 ^-- Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '24.21.1' ************** PARI ***************** Host 24.21.126.54 (24.21.126.54) Time: Mon Aug 21 13:16:03 2006 Input: 2000000000 x .01 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x.01. *** unknown member function: 2000000000x.01 ^-- Timing: real 0m0.023s user 0m0.008s sys 0m0.008s '24.21.1' ************** PARI ***************** Host 24.21.126.54 (24.21.126.54) Time: Mon Aug 21 13:15:46 2006 Input: 2000000000 x .01% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '209.99.' ************** PARI ***************** Host 209.99.19.8 (209.99.19.8) Time: Mon Aug 21 12:42:23 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.006s sys 0m0.009s '128.112' ************** PARI ***************** Host 128.112.33.159 (128.112.33.159) Time: Mon Aug 21 12:38:51 2006 Input: (1+x)^20 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^20 + 20*x^19 + 190*x^18 + 1140*x^17 + 4845*x^16 + 15504*x^15 + 38760*x^14 + 77520*x^13 + 125970*x^12 + 167960*x^11 + 184756*x^10 + 167960*x^9 + 125970*x^8 + 77520*x^7 + 38760*x^6 + 15504*x^5 + 4845*x^4 + 1140*x^3 + 190*x^2 + 20*x + 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.010s '199.172' ************** PARI ***************** Host 199.172.169.21 (199.172.169.21) Time: Mon Aug 21 10:47:03 2006 Input: a=(x^2+y^2+z^2)^15 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^30 + (15*y^2 + 15*z^2)*x^28 + (105*y^4 + 210*z^2*y^2 + 105*z^4)*x^26 + (455*y^6 + 1365*z^2*y^4 + 1365*z^4*y^2 + 455*z^6)*x^24 + (1365*y^8 + 5460*z^2*y^6 + 8190*z^4*y^4 + 5460*z^6*y^2 + 1365*z^8)*x^22 + (3003*y^10 + 15015*z^2*y^8 + 30030*z^4*y^6 + 30030*z^6*y^4 + 15015*z^8*y^2 + 3003*z^10)*x^20 + (5005*y^12 + 30030*z^2*y^10 + 75075*z^4*y^8 + 100100*z^6*y^6 + 75075*z^8*y^4 + 30030*z^10*y^2 + 5005*z^12)*x^18 + (6435*y^14 + 45045*z^2*y^12 + 135135*z^4*y^10 + 225225*z^6*y^8 + 225225*z^8*y^6 + 135135*z^10*y^4 + 45045*z^12*y^2 + 6435*z^14)*x^16 + (6435*y^16 + 51480*z^2*y^14 + 180180*z^4*y^12 + 360360*z^6*y^10 + 450450*z^8*y^8 + 360360*z^10*y^6 + 180180*z^12*y^4 + 51480*z^14*y^2 + 6435*z^16)*x^14 + (5005*y^18 + 45045*z^2*y^16 + 180180*z^4*y^14 + 420420*z^6*y^12 + 630630*z^8*y^10 + 630630*z^10*y^8 + 420420*z^12*y^6 + 180180*z^14*y^4 + 45045*z^16*y^2 + 5005*z^18)*x^12 + (3003*y^20 + 30030*z^2*y^18 + 135135*z^4*y^16 + 360360*z^6*y^14 + 630630*z^8*y^12 + 756756*z^10*y^10 + 630630*z^12*y^8 + 360360*z^14*y^6 + 135135*z^16*y^4 + 30030*z^18*y^2 + 3003*z^20)*x^10 + (1365*y^22 + 15015*z^2*y^20 + 75075*z^4*y^18 + 225225*z^6*y^16 + 450450*z^8*y^14 + 630630*z^10*y^12 + 630630*z^12*y^10 + 450450*z^14*y^8 + 225225*z^16*y^6 + 75075*z^18*y^4 + 15015*z^20*y^2 + 1365*z^22)*x^8 + (455*y^24 + 5460*z^2*y^22 + 30030*z^4*y^20 + 100100*z^6*y^18 + 225225*z^8*y^16 + 360360*z^10*y^14 + 420420*z^12*y^12 + 360360*z^14*y^10 + 225225*z^16*y^8 + 100100*z^18*y^6 + 30030*z^20*y^4 + 5460*z^22*y^2 + 455*z^24)*x^6 + (105*y^26 + 1365*z^2*y^24 + 8190*z^4*y^22 + 30030*z^6*y^20 + 75075*z^8*y^18 + 135135*z^10*y^16 + 180180*z^12*y^14 + 180180*z^14*y^12 + 135135*z^16*y^10 + 75075*z^18*y^8 + 30030*z^20*y^6 + 8190*z^22*y^4 + 1365*z^24*y^2 + 105*z^26)*x^4 + (15*y^28 + 210*z^2*y^26 + 1365*z^4*y^24 + 5460*z^6*y^22 + 15015*z^8*y^20 + 30030*z^10*y^18 + 45045*z^12*y^16 + 51480*z^14*y^14 + 45045*z^16*y^12 + 30030*z^18*y^10 + 15015*z^20*y^8 + 5460*z^22*y^6 + 1365*z^24*y^4 + 210*z^26*y^2 + 15*z^28)*x^2 + (y^30 + 15*z^2*y^28 + 105*z^4*y^26 + 455*z^6*y^24 + 1365*z^8*y^22 + 3003*z^10*y^20 + 5005*z^12*y^18 + 6435*z^14*y^16 + 6435*z^16*y^14 + 5005*z^18*y^12 + 3003*z^20*y^10 + 1365*z^22*y^8 + 455*z^24*y^6 + 105*z^26*y^4 + 15*z^28*y^2 + z^30) ? Goodbye! Errors/timing (if any): Timing: real 0m0.036s user 0m0.010s sys 0m0.006s '199.172' ************** PARI ***************** Host 199.172.169.21 (199.172.169.21) Time: Mon Aug 21 10:46:32 2006 Input: mathilbert(10)^6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [263861986074337682866598658066009962404513/18649941184431547105657600263389184000000 13916370422793057333854366486049233/1615247488573530944210078128128000 1132808775826053882967916900817043/176710836356762359708452991795200 24306250143189146865512352124950371843/4703600686726122109539747509108736000 780103421152595930763738081883394069/179184788065757032744371333680332800 63384164058838773376695119747773621031/16798573881164721819784812532531200000 134484051734565974845476800893928668937/40316577314795332367483550078074880000 16751637651306080958810077336996036063503/5597284817204085310352299535839395840000 52124191622632203761874981966328598359259/19190690801842578206922169837163642880000 3061393286661591565778580253259078356057763/1230603047668155327518884140808118599680000] [13916370422793057333854366486049233/1615247488573530944210078128128000 11840379415335103201377327521948705289858073/2256642883316217199784569631870091264000000 55035378377643639919549615899225827/14096705354823542785833409118208000 158324062652739908328394405227714059/50305889697605584059248636461056000 161971341824575226703589824385007579/61085723204235352071944772845568000 8422710658006760389428689385022798463/3665143392254121124316686370734080000 6205166512214915030771199527921026267/3054286160211767603597238642278400000 265006409219960616588529810873289648591/145384021226080137931228559372451840000 7575974009714317550266532292857727630707/4579596668621524344833699620232232960000 150674131239185450763823212432663729243433/99442670518638814344960334610757058560000] [1132808775826053882967916900817043/176710836356762359708452991795200 55035378377643639919549615899225827/14096705354823542785833409118208000 1638916057345975270846712552176757609602237/564160720829054299946142407967522816000000 93879719799953779837361780013085211/40087505852779449797213757179904000 1291337285445316726449750534452741/654489891473950200770836851916800 5995675212562349517590607409299157/3506195847181876075558054563840000 11081736910412758574165904753340618801/7330286784508242248633372741468160000 1478980742917064920881610957377939577319/1090380159195601034484214195293388800000 4832123093840029670999888975777570318207/3925368573104163724143171103056199680000 98105701915581517196594234375593138105933/87012336703808962551840292784412426240000] [24306250143189146865512352124950371843/4703600686726122109539747509108736000 158324062652739908328394405227714059/50305889697605584059248636461056000 93879719799953779837361780013085211/40087505852779449797213757179904000 179996672339190542936701642710042941995274053/95343161820110176690898066946511355904000000 3269833830457647737239392928750157/2055769530911766656267372163072000 85018584791429059906299888426749777/61673085927352999688021164892160000 4008657153739045932[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.016s sys 0m0.006s '149.169' ************** PARI ***************** Host 149.169.59.48 (149.169.59.48) Time: Mon Aug 21 10:11:37 2006 Input: log(x) + log(10^ x) - x Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** log: log is not meromorphic at 0. Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '88.70.5' ************** PARI ***************** Host 88.70.5.73 (88.70.5.73) Time: Mon Aug 21 09:58:36 2006 Input: print gap('SubgroupsSolvableGroup(SymmetricGroup(5));') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...p('SubgroupsSolvableGroup *** (SymmetricGroup(5)); ^-------------------- Timing: real 0m0.014s user 0m0.004s sys 0m0.011s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Mon Aug 21 09:53:31 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.007s '132.227' ************** PARI ***************** Host 132.227.205.230 (132.227.205.230) Time: Mon Aug 21 09:48:49 2006 Input: factor(1543542) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 1] [7 1] [11 1] [13 1] [257 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.053s user 0m0.006s sys 0m0.007s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 05:19:01 2006 Input: E = ellinit([0,0,0,5,10]); ellidentify(E) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** ellidentify: Elliptic curves files not available for conductor 400 [missing /home/was/sage/sage-0.7.5-2005-09-29/source/../local/share/pari/elldata/ell0]. Timing: real 0m0.101s user 0m0.008s sys 0m0.010s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 05:04:34 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellheight(E, [1,-4]) P = [1,4]; P2 = elladd(E,P,P) P3 = elladd(E,P2,P) P4 = elladd(E,P2,P2) P1 = [6,16]; ellbil(E,P1,P1) ellbil(E, P,P1) e1 = exp(H1) e2 = exp(H2) e2/e1 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? %4 = 0.12837506294605086906217592378339269243 ? ? %6 = [-1, -2] ? %7 = [9, -28] ? %8 = [6, 16] ? ? %10 = 2.0540010071368139049948147805342830835 ? %11 = 0.51350025178420347624870369513357077103 ? %12 = 1.1369793615653033564803326240516575848 ? %13 = 7.7990427915805383425320575762755536977 ? %14 = 6.8594409496082957922222546031236954267 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 05:03:27 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellheight(E, [1,-4]) P = [1,4]; P2 = elladd(E,P,P) P3 = elladd(E,P2,P) P4 = elladd(E,P2,P2) P1 = [6,16]; ellbil(E,P1,P1) ellbil(E, P,P1) exp(H1) exp(H2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? %4 = 0.12837506294605086906217592378339269243 ? ? %6 = [-1, -2] ? %7 = [9, -28] ? %8 = [6, 16] ? ? %10 = 2.0540010071368139049948147805342830835 ? %11 = 0.51350025178420347624870369513357077103 ? %12 = 1.1369793615653033564803326240516575848 ? %13 = 7.7990427915805383425320575762755536977 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:18:58 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellheight(E, [1,-4]) P = [1,4]; P2 = elladd(E,P,P) P3 = elladd(E,P2,P) P4 = elladd(E,P2,P2) P1 = [6,16]; ellbil(E,P1,P1) ellbil(E, P,P1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? %4 = 0.12837506294605086906217592378339269243 ? ? %6 = [-1, -2] ? %7 = [9, -28] ? %8 = [6, 16] ? ? %10 = 2.0540010071368139049948147805342830835 ? %11 = 0.51350025178420347624870369513357077103 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:14:10 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellheight(E, [1,-4]) P = [1,4]; P2 = elladd(E,P,P) P3 = elladd(E,P2,P) P4 = elladd(E,P2,P2) P1 = [6,16]; ellbil(E,P1,P1) ellbil[E, P,P1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? %4 = 0.12837506294605086906217592378339269243 ? ? %6 = [-1, -2] ? %7 = [9, -28] ? %8 = [6, 16] ? ? %10 = 2.0540010071368139049948147805342830835 ? ? Goodbye! Errors/timing (if any): *** expected character: ']' instead of: ellbil[E,P,P1) ^---- Timing: real 0m0.017s user 0m0.006s sys 0m0.011s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:13:04 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellheight(E, [1,-4]) P = [1,4]; P2 = elladd(E,P,P) P3 = elladd(E,P2,P) P4 = elladd(E,P2,P2) ellheight(E, P2) ellheight(E,P3) ellheight(E, P4) P1 = [6,16]; ellbil(E,P1,P1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? %4 = 0.12837506294605086906217592378339269243 ? ? %6 = [-1, -2] ? %7 = [9, -28] ? %8 = [6, 16] ? %9 = 0.51350025178420347624870369513357077067 ? %10 = 1.1553755665144578215595833140505342343 ? %11 = 2.0540010071368139049948147805342830833 ? ? %13 = 2.0540010071368139049948147805342830835 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:11:53 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellheight(E, [1,-4]) P = [1,4]; P2 = elladd(E,P,P) P3 = elladd(E,P2,P) P4 = elladd(E,P2,P2) ellheight(E, P2) ellheight(E,P3) ellheight(E, P4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? %4 = 0.12837506294605086906217592378339269243 ? ? %6 = [-1, -2] ? %7 = [9, -28] ? %8 = [6, 16] ? %9 = 0.51350025178420347624870369513357077067 ? %10 = 1.1553755665144578215595833140505342343 ? %11 = 2.0540010071368139049948147805342830833 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.008s sys 0m0.009s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:10:50 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellheight(E, [1,-4]) P = [1,4]; P2 = elladd(E,P,P) elladd(E,P2,P) elladd(E,P2,P2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? %4 = 0.12837506294605086906217592378339269243 ? ? %6 = [-1, -2] ? %7 = [9, -28] ? %8 = [6, 16] ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.005s sys 0m0.011s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:10:17 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellheight(E, [1,-4]) P = [1,4]; elladd(E,P,P) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? %4 = 0.12837506294605086906217592378339269243 ? ? %6 = [-1, -2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.007s sys 0m0.008s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:09:52 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellheight(E, [1,-4]) P = [1,4]; P*P Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? %4 = 0.12837506294605086906217592378339269243 ? ? ? Goodbye! Errors/timing (if any): *** forbidden multiplication t_VEC * t_VEC. Timing: real 0m0.017s user 0m0.008s sys 0m0.009s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:09:15 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellheight(E, [1,-4]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? %4 = 0.12837506294605086906217592378339269243 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.007s sys 0m0.010s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:08:49 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) ellbill(E,[1,4], [6,-16]) ellheight(E, [1,-4]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? ? %4 = 0.12837506294605086906217592378339269243 ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: ellbill(E,[1,4],[6,- ^-------------------- Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:07:20 2006 Input: E = ellinit([0,0,0,5,10]); H1 = ellheight(E,[1,4]) H2 = ellheight(E,[6,-16]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269243 ? %3 = 2.0540010071368139049948147805342830833 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.036s user 0m0.007s sys 0m0.011s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:06:49 2006 Input: E = ellinit([0,0,0,0,5]); E.a6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.011s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:06:18 2006 Input: E = ellinit([0,0,0,0,5]); E.a6; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.010s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:06:05 2006 Input: E = ellinit([0,0,0,0,5]); E.a6; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:05:18 2006 Input: 3+4; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.009s sys 0m0.007s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:04:53 2006 Input: E = ellinit([0,0,0,5,10]); E; 3+4; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.008s sys 0m0.008s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:04:24 2006 Input: E = ellinit([0,0,0,5,10]); E; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.008s sys 0m0.007s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:03:58 2006 Input: E = ellinit([0,0,0,5,10]); E; H1 = ellheight(E,[1,4]); H2 = ellheight(E,[6,-16]); H1; H2; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.006s sys 0m0.009s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:03:22 2006 Input: E = ellinit([0,0,0,5,10]); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.008s sys 0m0.008s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:02:29 2006 Input: E = ellinit([0,0,0,5,10]); ellheight(E,[1,4]); ellheight(E,[6,-16]); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.007s sys 0m0.009s '141.20.' ************** PARI ***************** Host 141.20.50.154 (141.20.50.154) Time: Mon Aug 21 04:02:07 2006 Input: E = ellinit([0,0,0,5,10]); P = [1,4]; ellheight(E,P); ellheight(E,[6,-16]); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.139s user 0m0.006s sys 0m0.014s '129.26.' ************** PARI ***************** Host 129.26.133.101 (129.26.133.101) Time: Mon Aug 21 02:34:30 2006 Input: (x+4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^3 + 12*x^2 + 48*x + 64 ? Goodbye! Errors/timing (if any): Timing: real 0m0.076s user 0m0.006s sys 0m0.009s '24.166.' ************** PARI ***************** Host 24.166.28.255 (24.166.28.255) Time: Sun Aug 20 20:24:44 2006 Input: log 15 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = log15 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 20 18:54:18 2006 Input: for(n=1,1000,if(isprime(n^2+n+1712329866165608771),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,202,213,215,217,229,230,234,235,240,245,248,253,254,263,265,267,275,280,282,283,285,292,294,297,302,305,307,311,312,315,317,321,324,325,329,333,335,338,340,341,342,345,358,362,363,365,378,381,383,393,410,412,413,421,423,428,430,434,436,437,443,450,455,457,458,459,470,473,477,478,479,483,485,490,492,494,498,500,510,518,519,522,524,528,535,543,549,553,564,567,569,572,577,578,581,582,584,590,598,609,615,616,617,621,624,628,630,636,637,638,640,643,645,647,653,657,658,660,662,665,677,679,686,694,696,700,705,707,713,714,716,721,723,726,732,733,738,741,742,750,752,755,756,761,770,776,777,783,789,794,796,797,808,813,815,819,821,828,833,840,845,849,852,854,856,864,866,869,874,882,885,886,889,892,897,899,901,902,904,907,910,914,920,924,927,928,931,933,940,942,945,957,960,963,967,970,979,984,988,993,994,998,1000, ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.023s user 0m0.016s sys 0m0.007s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 20 18:54:03 2006 Input: for(n=1,700,if(isprime(n^2+n+1712329866165608771),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,202,213,215,217,229,230,234,235,240,245,248,253,254,263,265,267,275,280,282,283,285,292,294,297,302,305,307,311,312,315,317,321,324,325,329,333,335,338,340,341,342,345,358,362,363,365,378,381,383,393,410,412,413,421,423,428,430,434,436,437,443,450,455,457,458,459,470,473,477,478,479,483,485,490,492,494,498,500,510,518,519,522,524,528,535,543,549,553,564,567,569,572,577,578,581,582,584,590,598,609,615,616,617,621,624,628,630,636,637,638,640,643,645,647,653,657,658,660,662,665,677,679,686,694,696,700, ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.016s sys 0m0.007s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 20 18:53:47 2006 Input: for(n=1,500,if(isprime(n^2+n+1712329866165608771),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,202,213,215,217,229,230,234,235,240,245,248,253,254,263,265,267,275,280,282,283,285,292,294,297,302,305,307,311,312,315,317,321,324,325,329,333,335,338,340,341,342,345,358,362,363,365,378,381,383,393,410,412,413,421,423,428,430,434,436,437,443,450,455,457,458,459,470,473,477,478,479,483,485,490,492,494,498,500, ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.008s sys 0m0.010s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 20 18:53:27 2006 Input: for(n=1,400,if(isprime(n^2+n+1712329866165608771),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,202,213,215,217,229,230,234,235,240,245,248,253,254,263,265,267,275,280,282,283,285,292,294,297,302,305,307,311,312,315,317,321,324,325,329,333,335,338,340,341,342,345,358,362,363,365,378,381,383,393, ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 20 18:51:58 2006 Input: for(n=1,300,if(isprime(n^2+n+1712329866165608771),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198,202,213,215,217,229,230,234,235,240,245,248,253,254,263,265,267,275,280,282,283,285,292,294,297, ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.010s sys 0m0.006s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 20 18:51:31 2006 Input: for(n=1,200,if(isprime(n^2+n+1712329866165608771),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96,102,103,110,115,119,120,124,130,138,140,146,148,152,155,158,159,160,161,163,167,168,175,177,178,179,187,193,195,196,197,198, ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 20 18:46:16 2006 Input: for(n=1,100,if(isprime(n^2+n+1712329866165608771),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 3,14,19,21,27,38,39,57,59,63,64,69,70,82,86,88,93,96, ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 20 18:45:30 2006 Input: for(n=1,50,if(isprime(n^2+n+1712329866165608771),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 3,14,19,21,27,38,39, ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.092s user 0m0.008s sys 0m0.007s '72.30.9' ************** PARI ***************** Host 72.30.98.145 (72.30.98.145) Time: Sun Aug 20 16:02:25 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.006s sys 0m0.008s '72.30.2' ************** PARI ***************** Host 72.30.226.160 (72.30.226.160) Time: Sun Aug 20 15:36:49 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '68.40.2' ************** PARI ***************** Host 68.40.228.245 (68.40.228.245) Time: Sun Aug 20 15:10:29 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '72.30.2' ************** PARI ***************** Host 72.30.226.223 (72.30.226.223) Time: Sun Aug 20 15:08:25 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.005s sys 0m0.011s '72.30.9' ************** PARI ***************** Host 72.30.98.35 (72.30.98.35) Time: Sun Aug 20 11:29:05 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.355s user 0m0.024s sys 0m0.011s '86.194.' ************** PARI ***************** Host 86.194.40.94 (86.194.40.94) Time: Sun Aug 20 00:09:14 2006 Input: 45! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 119622220865480194561963161495657715064383733760000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.079s user 0m0.007s sys 0m0.008s '207.111' ************** PARI ***************** Host 207.111.73.50 (207.111.73.50) Time: Sat Aug 19 23:34:00 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.073s user 0m0.011s sys 0m0.005s '69.154.' ************** PARI ***************** Host 69.154.191.237 (69.154.191.237) Time: Sat Aug 19 22:11:45 2006 Input: 15+5[5+3(8/4+2)] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ']' instead of: 15+5[5+3(8/4+2)] ^-------- Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '83.129.' ************** PARI ***************** Host 83.129.176.28 (83.129.176.28) Time: Sat Aug 19 08:02:43 2006 Input: nfroots(x*x*x+4*x*x-35,) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: nfroots(x*x*x+4*x*x-35,) ^- Timing: real 0m0.048s user 0m0.005s sys 0m0.009s '83.129.' ************** PARI ***************** Host 83.129.176.28 (83.129.176.28) Time: Sat Aug 19 08:02:24 2006 Input: nfroots(x*x*x+4*x*x-35) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: nfroots(x*x*x+4*x*x-35) ^- Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '83.129.' ************** PARI ***************** Host 83.129.176.28 (83.129.176.28) Time: Sat Aug 19 08:02:06 2006 Input: nfroots(x*x*x+4*x*x-35); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: nfroots(x*x*x+4*x*x-35); ^-- Timing: real 0m0.071s user 0m0.007s sys 0m0.008s '130.161' ************** PARI ***************** Host 130.161.135.32 (130.161.135.32) Time: Sat Aug 19 05:54:03 2006 Input: sin(3.1415) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.000092653589660671440566174108604596853276 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '130.161' ************** PARI ***************** Host 130.161.135.32 (130.161.135.32) Time: Sat Aug 19 05:53:50 2006 Input: tan(3.1415) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -0.000092653590058372507822043460533803485629 ? Goodbye! Errors/timing (if any): Timing: real 0m0.059s user 0m0.005s sys 0m0.010s '72.30.1' ************** PARI ***************** Host 72.30.107.151 (72.30.107.151) Time: Sat Aug 19 00:52:33 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.074s user 0m0.007s sys 0m0.008s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Fri Aug 18 23:36:56 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:39:59 2006 Input: [0,1,1;1,1,0;1,0,1]^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6 5 5] [5 6 5] [5 5 6] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:39:05 2006 Input: [0,1,1;1,1,0;1,0,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 3] [3 3 2] [3 2 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:38:00 2006 Input: [0,1,1;1,1,0;1,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1 1] [1 2 1] [1 1 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:37:51 2006 Input: [0,1,1;1,1,0;1,0,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 1] [1 1 0] [1 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:37:00 2006 Input: [1,0,1;1,1,0;0,1,1]^6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [22 21 21] [21 22 21] [21 21 22] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:35:42 2006 Input: [1,0,1;1,1,0;0,1,1]^5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [11 11 10] [10 11 11] [11 10 11] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:35:28 2006 Input: [1,0,1;1,1,0;0,1,1]^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5 6 5] [5 5 6] [6 5 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:35:18 2006 Input: [1,0,1;1,1,0;0,1,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 3] [3 2 3] [3 3 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:34:53 2006 Input: [1,0,1;1,1,0;0,1,1]^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5 6 5] [5 5 6] [6 5 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:34:20 2006 Input: [1,0,1;1,1,0;0,1,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 3] [3 2 3] [3 3 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:33:48 2006 Input: [1,0,1;1,1,0;0,1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 2] [2 1 1] [1 2 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:33:03 2006 Input: [1,0,1;1,1,0;0,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 1] [1 1 0] [0 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:32:46 2006 Input: [1,0,1;1,1,0;0,1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 2] [2 1 1] [1 2 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.004s sys 0m0.011s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:31:56 2006 Input: [1,0,0;0,1,0;0,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [0 1 0] [0 0 1] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:31:39 2006 Input: [1,0,0;0,1,0;0,0,1]^m Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** gpow: 0 to a forbidden power. Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:31:27 2006 Input: [1,0,0;0,1,0;0,0,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [0 1 0] [0 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.003s sys 0m0.011s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Fri Aug 18 20:31:13 2006 Input: [1,0,0;0,1,0;0,0,1]^m Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** gpow: 0 to a forbidden power. Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '72.30.9' ************** PARI ***************** Host 72.30.98.26 (72.30.98.26) Time: Fri Aug 18 19:37:26 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.131.199 (72.30.131.199) Time: Fri Aug 18 18:24:00 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '72.30.9' ************** PARI ***************** Host 72.30.99.77 (72.30.99.77) Time: Fri Aug 18 17:10:16 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.091s user 0m0.007s sys 0m0.008s '70.126.' ************** PARI ***************** Host 70.126.58.233 (70.126.58.233) Time: Fri Aug 18 16:39:16 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '70.229.' ************** PARI ***************** Host 70.229.26.148 (70.229.26.148) Time: Fri Aug 18 15:50:18 2006 Input: 1.609344 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1.6093440000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '69.213.' ************** PARI ***************** Host 69.213.205.32 (69.213.205.32) Time: Fri Aug 18 14:48:29 2006 Input: 21.60/5% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '66.91.5' ************** PARI ***************** Host 66.91.53.79 (66.91.53.79) Time: Fri Aug 18 14:24:32 2006 Input: 820.26-11.33 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 808.93000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.365s user 0m0.006s sys 0m0.011s '65.54.1' ************** PARI ***************** Host 65.54.188.53 (65.54.188.53) Time: Fri Aug 18 04:40:39 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '72.30.9' ************** PARI ***************** Host 72.30.97.221 (72.30.97.221) Time: Fri Aug 18 02:29:18 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.069s user 0m0.008s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.102.206 (72.30.102.206) Time: Thu Aug 17 23:13:49 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.064s user 0m0.009s sys 0m0.007s '66.249.' ************** PARI ***************** Host 66.249.65.113 (66.249.65.113) Time: Thu Aug 17 21:31:47 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.107s user 0m0.005s sys 0m0.011s '71.93.1' ************** PARI ***************** Host 71.93.172.203 (71.93.172.203) Time: Thu Aug 17 18:47:00 2006 Input: 6<2x<8 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x<8. *** incorrect type in comparison. Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '66.68.1' ************** PARI ***************** Host 66.68.12.46 (66.68.12.46) Time: Thu Aug 17 18:30:19 2006 Input: 3+5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 8 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '71.154.' ************** PARI ***************** Host 71.154.245.24 (71.154.245.24) Time: Thu Aug 17 17:28:25 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.005s sys 0m0.009s '24.116.' ************** PARI ***************** Host 24.116.250.166 (24.116.250.166) Time: Thu Aug 17 16:54:11 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.003s sys 0m0.011s '24.116.' ************** PARI ***************** Host 24.116.250.166 (24.116.250.166) Time: Thu Aug 17 16:54:10 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '83.92.5' ************** PARI ***************** Host 83.92.51.114 (83.92.51.114) Time: Thu Aug 17 16:22:55 2006 Input: print kash(256^512) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: printkash(256^512) ^------------------ Timing: real 0m0.033s user 0m0.009s sys 0m0.005s '70.180.' ************** PARI ***************** Host 70.180.62.77 (70.180.62.77) Time: Thu Aug 17 15:26:46 2006 Input: 2.5(x-3)+17x=10.8(x+15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 25.800000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (x-3)+17x=10.8(x+15). Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '85.182.' ************** PARI ***************** Host 85.182.66.38 (85.182.66.38) Time: Thu Aug 17 11:32:28 2006 Input: print(gap('LatticeSubgroups(SymmetricGroup(4));') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...int(gap('LatticeSubgroups *** (SymmetricGroup(4)); ^-------------------- Timing: real 0m0.015s user 0m0.007s sys 0m0.007s '85.182.' ************** PARI ***************** Host 85.182.66.38 (85.182.66.38) Time: Thu Aug 17 11:31:40 2006 Input: print(gap('SubgroupsSolvableGroup(S4)') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...p('SubgroupsSolvableGroup(S4)') ^------ Timing: real 0m0.014s user 0m0.005s sys 0m0.008s '85.182.' ************** PARI ***************** Host 85.182.66.38 (85.182.66.38) Time: Thu Aug 17 11:31:24 2006 Input: print(gap('SubgroupsSolvableGroup(SymmetricGroup(4))') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...p('SubgroupsSolvableGroup *** (SymmetricGroup(4))' ^-------------------- Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '69.236.' ************** PARI ***************** Host 69.236.179.102 (69.236.179.102) Time: Thu Aug 17 11:29:45 2006 Input: 4x^3+8x^2>0 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x^3+8x^2>0. *** incorrect type in comparison. Timing: real 0m0.299s user 0m0.005s sys 0m0.011s '72.30.2' ************** PARI ***************** Host 72.30.226.160 (72.30.226.160) Time: Thu Aug 17 06:27:31 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '75.4.16' ************** PARI ***************** Host 75.4.167.188 (75.4.167.188) Time: Thu Aug 17 02:10:42 2006 Input: 5%/1,897 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '75.4.16' ************** PARI ***************** Host 75.4.167.188 (75.4.167.188) Time: Thu Aug 17 02:10:16 2006 Input: 5% of 1,897 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '218.45.' ************** PARI ***************** Host 218.45.172.241 (218.45.172.241) Time: Thu Aug 17 01:48:07 2006 Input: (1.01)^35 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1.4166027560312678260004629407847590686 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '218.45.' ************** PARI ***************** Host 218.45.172.241 (218.45.172.241) Time: Thu Aug 17 01:47:58 2006 Input: (1.1)^35 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 28.102436848064247850612139033534048511 ? Goodbye! Errors/timing (if any): Timing: real 0m0.065s user 0m0.008s sys 0m0.007s '72.30.2' ************** PARI ***************** Host 72.30.226.223 (72.30.226.223) Time: Thu Aug 17 01:43:14 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.067s user 0m0.008s sys 0m0.006s '219.95.' ************** PARI ***************** Host 219.95.235.147 (219.95.235.147) Time: Thu Aug 17 01:24:56 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.057s user 0m0.008s sys 0m0.008s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Wed Aug 16 22:59:55 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.109s user 0m0.009s sys 0m0.005s '59.140.' ************** PARI ***************** Host 59.140.3.12 (59.140.3.12) Time: Wed Aug 16 20:51:28 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.027s user 0m0.005s sys 0m0.009s '213.114' ************** PARI ***************** Host 213.114.87.142 (213.114.87.142) Time: Wed Aug 16 15:41:29 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.545s user 0m0.007s sys 0m0.009s '65.188.' ************** PARI ***************** Host 65.188.208.165 (65.188.208.165) Time: Wed Aug 16 05:03:46 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.103.19 (72.30.103.19) Time: Wed Aug 16 01:34:00 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '71.141.' ************** PARI ***************** Host 71.141.253.153 (71.141.253.153) Time: Tue Aug 15 23:42:30 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Tue Aug 15 22:13:02 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.007s '24.64.2' ************** PARI ***************** Host 24.64.223.203 (24.64.223.203) Time: Tue Aug 15 17:22:28 2006 Input: factor(597543644043339483) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [7 1] [1019 1] [1736939 1] [16076503 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.115s user 0m0.007s sys 0m0.008s '24.64.2' ************** PARI ***************** Host 24.64.223.203 (24.64.223.203) Time: Tue Aug 15 17:18:59 2006 Input: 52 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 52 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '24.64.2' ************** PARI ***************** Host 24.64.223.203 (24.64.223.203) Time: Tue Aug 15 17:18:42 2006 Input: 57 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 57 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '72.128.' ************** PARI ***************** Host 72.128.44.217 (72.128.44.217) Time: Tue Aug 15 16:24:48 2006 Input: (1/3)(9)³= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (9)===. *** unexpected character: (1/3)(9)=== ^- Timing: real 0m0.014s user 0m0.004s sys 0m0.010s '72.128.' ************** PARI ***************** Host 72.128.44.217 (72.128.44.217) Time: Tue Aug 15 16:24:13 2006 Input: (1/3)(9)³= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (9)===. *** unexpected character: (1/3)(9)=== ^- Timing: real 0m0.028s user 0m0.007s sys 0m0.008s '70.247.' ************** PARI ***************** Host 70.247.113.187 (70.247.113.187) Time: Tue Aug 15 15:15:36 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.005s sys 0m0.010s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 11:55:56 2006 Input: Mod(7,30)^(7^7^7) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(13, 30) ? Goodbye! Errors/timing (if any): *** Warning: multiword exponent in Fl_pow. Timing: real 0m0.268s user 0m0.215s sys 0m0.013s '72.30.1' ************** PARI ***************** Host 72.30.129.138 (72.30.129.138) Time: Tue Aug 15 11:21:13 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 11:19:38 2006 Input: Mod(3,1000)^(83) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(227, 1000) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 11:12:55 2006 Input: Mod(3,400)^(2003) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(27, 400) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 10:55:13 2006 Input: Mod(3,400)^(83) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(27, 400) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.008s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 10:28:54 2006 Input: 3^83 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3990838394187339929534246675572349035227 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 10:28:33 2006 Input: 3^20 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3486784401 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 10:19:00 2006 Input: 3^83 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3990838394187339929534246675572349035227 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 10:18:46 2006 Input: 3^400 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 70550791086553325712464271575934796216507949612787315762871223209262085551582934156579298529447134158154952334825355911866929793071824566694145084454535257027960285323760313192443283334088001 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 10:13:15 2006 Input: Mod(3,1000)^(2003^2003) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(987, 1000) ? Goodbye! Errors/timing (if any): *** Warning: multiword exponent in Fl_pow. Timing: real 0m0.016s user 0m0.008s sys 0m0.009s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 09:48:20 2006 Input: Mod(3,100)^(2003^2003) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(87, 100) ? Goodbye! Errors/timing (if any): *** Warning: multiword exponent in Fl_pow. Timing: real 0m0.049s user 0m0.008s sys 0m0.009s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 09:45:41 2006 Input: 3^(2003^2003) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** length (lg) overflow Timing: real 0m0.015s user 0m0.005s sys 0m0.010s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 09:45:01 2006 Input: 3^2003 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 47192523796511593460819314717445835404284687160750089980920976318888529188136438210870134686346389999041441668795922467896826947768638733482889183456528239010568634262429383843301299968914654135021616852400619449604094035791513517490976267110993951445870348070649724838442950877697281464105603387943746139280208780890973452976589061955333899720134617153262713286486800459846999808593157946089834398450393914138264834193475885957005425265572728480321922372718342943042880916739731170887479399462363014861982530234203725804474544039577325916627591757941754987079099118539866954821154972250974284998342253129564298697533991303605099243743998763493165069920824491545486353467536460616499651953399236100304728302468297087043095519255193036095675710613231999201256180837163220902716746235182201529062324435884453986670695008281249641444785221286768136955402601273270121405513124724415388652516643729635832196015310268380966177525262817036149775193114460981880027 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.007s sys 0m0.009s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 09:44:39 2006 Input: 2003^2003 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1849019260402709591286946172272940395303112445168867902383112555669571680764331263129330914652274495344312361794223854136737235628975718111135048790603351966051089751801492286418588902467028553504583229077928836304421158684528741674751413584648058844055647193516177071717162896188397649366593550136210318645392352569990645096972351505408767255782003625775433472017371179730547137478287893507333560277638389093691937015829221890068050469248634486703551127690968842230454015685132969837483003553059495828232089447828335373623978090541832251404561839854204124893294475642540010052397603804262506936563543122526936967047474058883448638286320846501903634081589405217621172604680678266257943264554652140453584775304923366347265361889863651409967357350610120370545343116444163083489140070777265080161473074590584338930415700500346333630578065794337339456800772435468402349571596298898714975383243864935535636134581337583186012822632640943109188841366090566003571671616355255066629545340775357546670343012710596231482375467743311249226696302796942829058327257509806942696109036650762242172624273154718478553514815075003175820338775199237589617467645726633551827062674809808821496907148128685454048876323643882165409382905436659884016880864706115534311275854858879482590439605638014513404114965161328132476890310946700527095556057226375889945939398114414530519086388011842145370813116466116933677781283418754185176308541744851367722022538010448557111987710967293795913750778380493693364942128158609647913299867196028991715761098664736737689726033022049768616498578659743306410989634574595752793197774095598026370816536578149768457163093990891659686173217641139200667442352618661018059985367747557369405138674119976901185838232734027098311705631317918930369382581576149049468721347552491182500222194663605206043936720336781866516862682519809693874713689647661086241945324543523536693944148087374805375384267176609436513867966084736897671968946642626981894686304621598541991524231414384141282558288006355975293005476137974561143445115105779797830936073546368454667098115241359316617104258762436468188728754333143356008113347748174553932050079642183234048683147769732123261465567836710684328110031873160964530586628853340849483016910719803320336003623157812793587485942907628960069171712069941546144521254605696368192772610846565381585445513891947386210269254508355475189422639476055636015982352067475607003031996183489799837437930982672410956753059148884164506367316219442600996483386809306833003557091114903316063583559200044640197860848036956391379905814413562503411001844090155223225441144384859621030897061479811658231861008612105849597548707170382390239878149382462392451454760982084364281414125014558498298153586644143512342948560725715692468080071277962250555090930040064361149899149864222030853686276876495951900958363725547749789103291905846544642388789885806597704471784458460481220648107198384132908599908344227320292109752815908406413867624583806294047610747554301474744086100782707611290662006703157494157162044337566623400061356300491066346464547827504101349366387203053910739342132649163101380906928003626736950801017814100310095468922280959188145785275380839397906917702194975501151197[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.005s sys 0m0.013s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 09:44:14 2006 Input: 3^20 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3486784401 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 09:42:08 2006 Input: 3^1024 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 373391848741020043532959754184866588225409776783734007750636931722079040617265251229993688938803977220468765065431475158108727054592160858581351336982809187314191748594262580938807019951956404285571818041046681288797402925517668012340617298396574731619152386723046235125934896058590588284654793540505936202376547807442730582144527058988756251452817793413352141920744623027518729185432862375737063985485319476416926263819972887006907013899256524297198527698749274196276811060702333710356481 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 09:35:44 2006 Input: 2003^2003 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1849019260402709591286946172272940395303112445168867902383112555669571680764331263129330914652274495344312361794223854136737235628975718111135048790603351966051089751801492286418588902467028553504583229077928836304421158684528741674751413584648058844055647193516177071717162896188397649366593550136210318645392352569990645096972351505408767255782003625775433472017371179730547137478287893507333560277638389093691937015829221890068050469248634486703551127690968842230454015685132969837483003553059495828232089447828335373623978090541832251404561839854204124893294475642540010052397603804262506936563543122526936967047474058883448638286320846501903634081589405217621172604680678266257943264554652140453584775304923366347265361889863651409967357350610120370545343116444163083489140070777265080161473074590584338930415700500346333630578065794337339456800772435468402349571596298898714975383243864935535636134581337583186012822632640943109188841366090566003571671616355255066629545340775357546670343012710596231482375467743311249226696302796942829058327257509806942696109036650762242172624273154718478553514815075003175820338775199237589617467645726633551827062674809808821496907148128685454048876323643882165409382905436659884016880864706115534311275854858879482590439605638014513404114965161328132476890310946700527095556057226375889945939398114414530519086388011842145370813116466116933677781283418754185176308541744851367722022538010448557111987710967293795913750778380493693364942128158609647913299867196028991715761098664736737689726033022049768616498578659743306410989634574595752793197774095598026370816536578149768457163093990891659686173217641139200667442352618661018059985367747557369405138674119976901185838232734027098311705631317918930369382581576149049468721347552491182500222194663605206043936720336781866516862682519809693874713689647661086241945324543523536693944148087374805375384267176609436513867966084736897671968946642626981894686304621598541991524231414384141282558288006355975293005476137974561143445115105779797830936073546368454667098115241359316617104258762436468188728754333143356008113347748174553932050079642183234048683147769732123261465567836710684328110031873160964530586628853340849483016910719803320336003623157812793587485942907628960069171712069941546144521254605696368192772610846565381585445513891947386210269254508355475189422639476055636015982352067475607003031996183489799837437930982672410956753059148884164506367316219442600996483386809306833003557091114903316063583559200044640197860848036956391379905814413562503411001844090155223225441144384859621030897061479811658231861008612105849597548707170382390239878149382462392451454760982084364281414125014558498298153586644143512342948560725715692468080071277962250555090930040064361149899149864222030853686276876495951900958363725547749789103291905846544642388789885806597704471784458460481220648107198384132908599908344227320292109752815908406413867624583806294047610747554301474744086100782707611290662006703157494157162044337566623400061356300491066346464547827504101349366387203053910739342132649163101380906928003626736950801017814100310095468922280959188145785275380839397906917702194975501151197[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 09:35:30 2006 Input: 3^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 27 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '84.107.' ************** PARI ***************** Host 84.107.150.174 (84.107.150.174) Time: Tue Aug 15 09:29:37 2006 Input: 2003^2003 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1849019260402709591286946172272940395303112445168867902383112555669571680764331263129330914652274495344312361794223854136737235628975718111135048790603351966051089751801492286418588902467028553504583229077928836304421158684528741674751413584648058844055647193516177071717162896188397649366593550136210318645392352569990645096972351505408767255782003625775433472017371179730547137478287893507333560277638389093691937015829221890068050469248634486703551127690968842230454015685132969837483003553059495828232089447828335373623978090541832251404561839854204124893294475642540010052397603804262506936563543122526936967047474058883448638286320846501903634081589405217621172604680678266257943264554652140453584775304923366347265361889863651409967357350610120370545343116444163083489140070777265080161473074590584338930415700500346333630578065794337339456800772435468402349571596298898714975383243864935535636134581337583186012822632640943109188841366090566003571671616355255066629545340775357546670343012710596231482375467743311249226696302796942829058327257509806942696109036650762242172624273154718478553514815075003175820338775199237589617467645726633551827062674809808821496907148128685454048876323643882165409382905436659884016880864706115534311275854858879482590439605638014513404114965161328132476890310946700527095556057226375889945939398114414530519086388011842145370813116466116933677781283418754185176308541744851367722022538010448557111987710967293795913750778380493693364942128158609647913299867196028991715761098664736737689726033022049768616498578659743306410989634574595752793197774095598026370816536578149768457163093990891659686173217641139200667442352618661018059985367747557369405138674119976901185838232734027098311705631317918930369382581576149049468721347552491182500222194663605206043936720336781866516862682519809693874713689647661086241945324543523536693944148087374805375384267176609436513867966084736897671968946642626981894686304621598541991524231414384141282558288006355975293005476137974561143445115105779797830936073546368454667098115241359316617104258762436468188728754333143356008113347748174553932050079642183234048683147769732123261465567836710684328110031873160964530586628853340849483016910719803320336003623157812793587485942907628960069171712069941546144521254605696368192772610846565381585445513891947386210269254508355475189422639476055636015982352067475607003031996183489799837437930982672410956753059148884164506367316219442600996483386809306833003557091114903316063583559200044640197860848036956391379905814413562503411001844090155223225441144384859621030897061479811658231861008612105849597548707170382390239878149382462392451454760982084364281414125014558498298153586644143512342948560725715692468080071277962250555090930040064361149899149864222030853686276876495951900958363725547749789103291905846544642388789885806597704471784458460481220648107198384132908599908344227320292109752815908406413867624583806294047610747554301474744086100782707611290662006703157494157162044337566623400061356300491066346464547827504101349366387203053910739342132649163101380906928003626736950801017814100310095468922280959188145785275380839397906917702194975501151197[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.084s user 0m0.010s sys 0m0.010s '72.30.1' ************** PARI ***************** Host 72.30.110.15 (72.30.110.15) Time: Tue Aug 15 08:13:30 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.255s user 0m0.009s sys 0m0.008s '72.30.2' ************** PARI ***************** Host 72.30.226.160 (72.30.226.160) Time: Tue Aug 15 03:09:45 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '72.30.2' ************** PARI ***************** Host 72.30.226.223 (72.30.226.223) Time: Tue Aug 15 02:42:02 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.006s sys 0m0.010s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 23:56:53 2006 Input: [1,0,1,0;0,1,0,1;1,1,0,0;0,0,1,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 2 2 1] [1 2 2 3] [2 2 2 2] [2 2 2 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 23:56:45 2006 Input: [1,0,1,0;0,1,0,1;1,1,0,0;0,0,1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1 1 0] [0 1 1 2] [1 1 1 1] [1 1 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 23:56:30 2006 Input: [1,0,1,0;0,1,0,1;1,1,0,0;0,0,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 1 0] [0 1 0 1] [1 1 0 0] [0 0 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 23:55:38 2006 Input: [1,1,1,0;0,1,1,1;1,1,0,1;1,0,1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 2 2] [2 2 2 3] [2 2 3 2] [3 2 2 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 23:55:18 2006 Input: [1,1,1,0;0,1,1,1;1,1,0,1;1,0,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 1 0] [0 1 1 1] [1 1 0 1] [1 0 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '203.5.3' ************** PARI ***************** Host 203.5.3.200 (203.5.3.200) Time: Mon Aug 14 23:04:49 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:47:40 2006 Input: [0,1,0;1,0,0;0,0,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 0] [1 0 0] [0 0 1] ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:46:31 2006 Input: [0,1,0;1,0,0;0,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [0 1 0] [0 0 1] ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:46:18 2006 Input: [0,1,0;1,0,0;0,0,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 0] [1 0 0] [0 0 1] ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:46:02 2006 Input: [0,1,0;1,0,0;0,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [0 1 0] [0 0 1] ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:42:57 2006 Input: [0,1,0;1,0,0;0,0,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 0] [1 0 0] [0 0 1] ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:42:46 2006 Input: [0,1,0;1,0,0;0,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [0 1 0] [0 0 1] ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.004s sys 0m0.011s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:42:37 2006 Input: [0,1,0;1,0,0;0,0,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 0] [1 0 0] [0 0 1] ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:41:36 2006 Input: [1,1,0;1,0,1;0,1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1 1] [1 2 1] [1 1 2] ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:41:00 2006 Input: [1,1,0;1,0,1;0,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 0] [1 0 1] [0 1 1] ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:33:08 2006 Input: [0,1,1;1,0,1;1,1,0]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1 1] [1 2 1] [1 1 2] ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:32:53 2006 Input: [0,1,1;1,0,1;1,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 1] [1 0 1] [1 1 0] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:32:38 2006 Input: [0,1,;1,0,1;1,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: [0,1,;1,0,1;1,1,0] ^------------- Timing: real 0m0.014s user 0m0.009s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:30:21 2006 Input: [1,1,0;0,1,1;1,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 2 1] [1 1 2] [2 1 1] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Mon Aug 14 22:30:09 2006 Input: [1,1,0;0,1,1;1,0,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 0] [0 1 1] [1 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '72.30.1' ************** PARI ***************** Host 72.30.111.28 (72.30.111.28) Time: Mon Aug 14 22:18:27 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Mon Aug 14 20:42:02 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '203.57.' ************** PARI ***************** Host 203.57.240.95 (203.57.240.95) Time: Mon Aug 14 20:11:05 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Mon Aug 14 19:27:20 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.078s user 0m0.027s sys 0m0.006s '69.230.' ************** PARI ***************** Host 69.230.18.219 (69.230.18.219) Time: Mon Aug 14 19:02:14 2006 Input: (4-3)(x+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x + 1 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (x+1). Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '69.208.' ************** PARI ***************** Host 69.208.186.15 (69.208.186.15) Time: Mon Aug 14 18:56:45 2006 Input: 9.72+14.88+10.88+10.88+14.88+10.88 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 72.119999999999999999999999999999999999 ? Goodbye! Errors/timing (if any): Timing: real 0m0.056s user 0m0.005s sys 0m0.009s '208.19.' ************** PARI ***************** Host 208.19.62.11 (208.19.62.11) Time: Mon Aug 14 16:27:35 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '80.55.1' ************** PARI ***************** Host 80.55.14.2 (80.55.14.2) Time: Mon Aug 14 15:30:17 2006 Input: a(n)=2*n-n^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '80.55.1' ************** PARI ***************** Host 80.55.14.2 (80.55.14.2) Time: Mon Aug 14 15:30:02 2006 Input: a(n)=2*n-n%2 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '80.55.1' ************** PARI ***************** Host 80.55.14.2 (80.55.14.2) Time: Mon Aug 14 15:17:49 2006 Input: print kash('NumberField(X^3 + 15*X^2 - 15*X + 15)') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printkash('NumberField *** (X^3+15*X^2-15*X+15) ^-------------------- Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '80.55.1' ************** PARI ***************** Host 80.55.14.2 (80.55.14.2) Time: Mon Aug 14 15:09:10 2006 Input: f=x^5-x^4-x^3-x^2-x-1; Galois(f); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: Galois(f); ^- Timing: real 0m0.068s user 0m0.010s sys 0m0.005s '80.55.1' ************** PARI ***************** Host 80.55.14.2 (80.55.14.2) Time: Mon Aug 14 15:07:33 2006 Input: Zx:=PolynomialRing(Integers()); f:=x^5-x^4-x^3-x^2-x-1; G:=GaloisGroup(f); a,b:=TransitiveGroupIdentification(G); "Number of group is", a; TransitiveGroupDescription(a,b); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: Zx:=PolynomialRing(Int ^-------------------- *** Warning: unused characters: :=x^5-x^4-x^3-x^2-x-1;. *** unexpected character: f:=x^5-x^4-x^3-x^2-x- ^-------------------- *** Warning: unused characters: :=GaloisGroup(f);. *** unexpected character: G:=GaloisGroup(f); ^----------------- *** Warning: unused characters: ,b:=TransitiveGroupIdentification(G);. *** Warning: unused characters: ,a;. *** expected character: '=' instead of: ...tiveGroupDescription(a,b); ^- Timing: real 0m0.284s user 0m0.006s sys 0m0.010s '72.30.1' ************** PARI ***************** Host 72.30.132.102 (72.30.132.102) Time: Mon Aug 14 02:33:30 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '71.105.' ************** PARI ***************** Host 71.105.149.13 (71.105.149.13) Time: Sun Aug 13 22:07:23 2006 Input: x+7=15 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: x+7=15 ^--- Timing: real 0m0.015s user 0m0.007s sys 0m0.009s '72.30.1' ************** PARI ***************** Host 72.30.129.123 (72.30.129.123) Time: Sun Aug 13 20:32:01 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.072s user 0m0.007s sys 0m0.008s '68.47.1' ************** PARI ***************** Host 68.47.182.155 (68.47.182.155) Time: Sun Aug 13 14:59:35 2006 Input: print kash('NumberField(X^3 + 15*X^2 - 15*X + 15)') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printkash('NumberField *** (X^3+15*X^2-15*X+15) ^-------------------- Timing: real 0m0.021s user 0m0.007s sys 0m0.009s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:08:46 2006 Input: [0,1,1,1;1,0,1,1;1,1,0,1;1,1,1,0]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 2 2 2] [2 3 2 2] [2 2 3 2] [2 2 2 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:08:36 2006 Input: [0,1,1,1;1,0,1,1;1,1,0,1;1,1,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 1 1] [1 0 1 1] [1 1 0 1] [1 1 1 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:07:58 2006 Input: [1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1]^12 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2048 2048 0 0] [2048 2048 0 0] [0 0 2048 2048] [0 0 2048 2048] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:07:04 2006 Input: [1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1]^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [8 8 0 0] [8 8 0 0] [0 0 8 8] [0 0 8 8] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:06:59 2006 Input: [1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [4 4 0 0] [4 4 0 0] [0 0 4 4] [0 0 4 4] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:06:52 2006 Input: [1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 2 0 0] [2 2 0 0] [0 0 2 2] [0 0 2 2] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:06:43 2006 Input: [1,1,0,0;1,1,0,0;0,0,1,1;0,0,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 0 0] [1 1 0 0] [0 0 1 1] [0 0 1 1] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:06:02 2006 Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 3 1 1] [1 3 1 3] [3 1 3 1] [1 1 3 3] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:05:49 2006 Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 3 1 1] [1 3 1 3] [3 1 3 1] [1 1 3 3] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:05:42 2006 Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 4 4 6] [4 2 6 4] [4 6 2 4] [6 4 4 2] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:05:35 2006 Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 3 1 1] [1 3 1 3] [3 1 3 1] [1 1 3 3] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:05:24 2006 Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 2 1] [2 1 1 0] [0 1 1 2] [1 2 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:05:11 2006 Input: [0,1,0,1;0,0,1,1;1,1,0,0;1,0,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 0 1] [0 0 1 1] [1 1 0 0] [1 0 1 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:04:27 2006 Input: [1,0,0,1;1,1,0,0;0,1,1,0;0,0,1,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 3 3] [3 1 1 3] [3 3 1 1] [1 3 3 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:04:22 2006 Input: [1,0,0,1;1,1,0,0;0,1,1,0;0,0,1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 1 2] [2 1 0 1] [1 2 1 0] [0 1 2 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 14:04:11 2006 Input: [1,0,0,1;1,1,0,0;0,1,1,0;0,0,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0 1] [1 1 0 0] [0 1 1 0] [0 0 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 13:58:40 2006 Input: [0,1,1,1;1,0,1,1;1,1,1,0;1,1,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 2 2 2] [2 3 2 2] [2 2 3 2] [2 2 2 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 13:58:40 2006 Input: [0,1,1,1;1,0,1,1;1,1,1,0;1,1,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 2 2 2] [2 3 2 2] [2 2 3 2] [2 2 2 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 13:53:53 2006 Input: [0,1,1,0;1,1,0,0;1,0,0,1;0,0,1,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 3 3 1] [3 3 1 1] [3 1 1 3] [1 1 3 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '169.231' ************** PARI ***************** Host 169.231.33.177 (169.231.33.177) Time: Sun Aug 13 13:53:14 2006 Input: [0,1,1,0;1,1,0,0;1,0,0,1;0,0,1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1 0 1] [1 2 1 0] [0 1 2 1] [1 0 1 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '67.10.1' ************** PARI ***************** Host 67.10.132.208 (67.10.132.208) Time: Sun Aug 13 13:52:08 2006 Input: 2^85 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 38685626227668133590597632 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '68.199.' ************** PARI ***************** Host 68.199.60.254 (68.199.60.254) Time: Sun Aug 13 13:36:13 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '194.165' ************** PARI ***************** Host 194.165.182.38 (194.165.182.38) Time: Sun Aug 13 13:17:25 2006 Input: 47/3000.001 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.015666661444446185184604938465020511660 ? Goodbye! Errors/timing (if any): Timing: real 0m0.052s user 0m0.005s sys 0m0.009s '72.30.1' ************** PARI ***************** Host 72.30.111.93 (72.30.111.93) Time: Sun Aug 13 12:26:48 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.080s user 0m0.008s sys 0m0.008s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sun Aug 13 10:46:05 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.266s user 0m0.007s sys 0m0.010s '193.171' ************** PARI ***************** Host 193.171.131.247 (193.171.131.247) Time: Sat Aug 12 04:07:02 2006 Input: 1/2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1/2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sat Aug 12 00:17:00 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '72.30.2' ************** PARI ***************** Host 72.30.226.223 (72.30.226.223) Time: Fri Aug 11 17:41:28 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.115s user 0m0.006s sys 0m0.009s '220.239' ************** PARI ***************** Host 220.239.147.13 (220.239.147.13) Time: Fri Aug 11 03:04:58 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.006s '220.239' ************** PARI ***************** Host 220.239.147.13 (220.239.147.13) Time: Fri Aug 11 03:02:22 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.089s user 0m0.005s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Fri Aug 11 01:28:29 2006 Input: [1,1,0;0,1,1;1,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 2 1] [1 1 2] [2 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.069s user 0m0.006s sys 0m0.009s '66.249.' ************** PARI ***************** Host 66.249.66.144 (66.249.66.144) Time: Thu Aug 10 21:18:19 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.101s user 0m0.007s sys 0m0.008s '66.249.' ************** PARI ***************** Host 66.249.66.144 (66.249.66.144) Time: Thu Aug 10 19:43:53 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '66.249.' ************** PARI ***************** Host 66.249.66.144 (66.249.66.144) Time: Thu Aug 10 19:43:51 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.005s sys 0m0.011s '68.13.2' ************** PARI ***************** Host 68.13.201.86 (68.13.201.86) Time: Thu Aug 10 19:29:54 2006 Input: 3.35 x 10 - 3 + 4.5 x 10 - 4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x10 - 4 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x10-3+4.5x10-4. Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '68.13.2' ************** PARI ***************** Host 68.13.201.86 (68.13.201.86) Time: Thu Aug 10 19:29:30 2006 Input: 3.35x10-3 + 4.5x10-4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x10 - 4 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x10-3+4.5x10-4. Timing: real 0m0.216s user 0m0.004s sys 0m0.010s '66.249.' ************** PARI ***************** Host 66.249.72.66 (66.249.72.66) Time: Thu Aug 10 17:59:00 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '68.207.' ************** PARI ***************** Host 68.207.106.75 (68.207.106.75) Time: Thu Aug 10 16:06:26 2006 Input: 3x5-2x3+5x2-2x+7, if x=-2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x + 7 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x5-2x3+5x2-2x+7,ifx=-2. Timing: real 0m0.014s user 0m0.005s sys 0m0.007s '68.207.' ************** PARI ***************** Host 68.207.106.75 (68.207.106.75) Time: Thu Aug 10 16:06:09 2006 Input: 3x5-2x3+5x2-2x+7, if x=-2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x + 7 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x5-2x3+5x2-2x+7,ifx=-2. Timing: real 0m0.068s user 0m0.007s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Thu Aug 10 13:08:03 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.072s user 0m0.008s sys 0m0.007s '60.49.1' ************** PARI ***************** Host 60.49.128.6 (60.49.128.6) Time: Thu Aug 10 13:07:03 2006 Input: 328310094-10% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '199.9.6' ************** PARI ***************** Host 199.9.64.2 (199.9.64.2) Time: Thu Aug 10 09:24:43 2006 Input: (-1/2)(-6/7) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -6/7 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (-6/7). Timing: real 0m0.283s user 0m0.005s sys 0m0.008s '72.30.2' ************** PARI ***************** Host 72.30.252.149 (72.30.252.149) Time: Thu Aug 10 05:41:19 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '193.171' ************** PARI ***************** Host 193.171.131.248 (193.171.131.248) Time: Thu Aug 10 05:03:02 2006 Input: matrix(3,4,X,Y,-X+Y^20) a = exp(x) a Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1048575 3486784400 1099511627775] [-1 1048574 3486784399 1099511627774] [-2 1048573 3486784398 1099511627773] ? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? %3 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '193.171' ************** PARI ***************** Host 193.171.131.248 (193.171.131.248) Time: Thu Aug 10 04:58:32 2006 Input: matrix(3,4,X,Y,X-Y^20) a = exp(x) a Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 -1048575 -3486784400 -1099511627775] [1 -1048574 -3486784399 -1099511627774] [2 -1048573 -3486784398 -1099511627773] ? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? %3 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '193.171' ************** PARI ***************** Host 193.171.131.248 (193.171.131.248) Time: Thu Aug 10 04:58:15 2006 Input: matrix(3,4,X,Y,X-Y^3) a = exp(x) a Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 -7 -26 -63] [1 -6 -25 -62] [2 -5 -24 -61] ? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? %3 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '193.171' ************** PARI ***************** Host 193.171.131.248 (193.171.131.248) Time: Thu Aug 10 04:57:04 2006 Input: matrix(3,4,X,Y,X+Y) a = exp(x) a Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 4 5] [3 4 5 6] [4 5 6 7] ? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? %3 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '193.171' ************** PARI ***************** Host 193.171.131.248 (193.171.131.248) Time: Thu Aug 10 04:56:55 2006 Input: matrix(3,4,X,Y,X+Y) a = exp(x) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 4 5] [3 4 5 6] [4 5 6 7] ? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '193.171' ************** PARI ***************** Host 193.171.131.248 (193.171.131.248) Time: Thu Aug 10 04:55:56 2006 Input: matrix(3,4,X,Y,X+Y) exp(x) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 4 5] [3 4 5 6] [4 5 6 7] ? %2 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? Goodbye! Errors/timing (if any): Timing: real 0m0.082s user 0m0.007s sys 0m0.007s '193.171' ************** PARI ***************** Host 193.171.131.248 (193.171.131.248) Time: Thu Aug 10 04:54:53 2006 Input: matrix(3,4,X,Y,X+Y) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 4 5] [3 4 5 6] [4 5 6 7] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.008s '193.171' ************** PARI ***************** Host 193.171.131.248 (193.171.131.248) Time: Thu Aug 10 04:40:54 2006 Input: matrix(3,4,X,Y,X+Y) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 4 5] [3 4 5 6] [4 5 6 7] ? Goodbye! Errors/timing (if any): Timing: real 0m0.056s user 0m0.005s sys 0m0.009s '193.171' ************** PARI ***************** Host 193.171.131.248 (193.171.131.248) Time: Thu Aug 10 04:39:08 2006 Input: gp('ellinit([1,2,3,4,5])').j Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: gp('ellinit([1,2,3,4,5])').j ^----------------- Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '193.171' ************** PARI ***************** Host 193.171.131.248 (193.171.131.248) Time: Thu Aug 10 04:38:59 2006 Input: print gp('ellinit([1,2,3,4,5])').j Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printgp('ellinit([1,2,3,4,5])').j ^----------------- Timing: real 0m0.019s user 0m0.008s sys 0m0.006s '24.196.' ************** PARI ***************** Host 24.196.114.198 (24.196.114.198) Time: Wed Aug 9 16:19:36 2006 Input: (x-9) + (x2 - x + 17) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x2 + 8 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '69.130.' ************** PARI ***************** Host 69.130.157.157 (69.130.157.157) Time: Wed Aug 9 15:02:28 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.009s '192.25.' ************** PARI ***************** Host 192.25.240.225 (192.25.240.225) Time: Wed Aug 9 14:24:32 2006 Input: 10 log 20 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = log20 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: log20. Timing: real 0m0.013s user 0m0.006s sys 0m0.009s '192.25.' ************** PARI ***************** Host 192.25.240.225 (192.25.240.225) Time: Wed Aug 9 14:24:19 2006 Input: 10 log 1 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = log1 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: log1. Timing: real 0m0.014s user 0m0.006s sys 0m0.009s '75.2.16' ************** PARI ***************** Host 75.2.165.226 (75.2.165.226) Time: Wed Aug 9 14:02:59 2006 Input: (4.09*10^6)(5.87*10^-7) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.00000058700000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (5.87*10^-7). Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '75.2.16' ************** PARI ***************** Host 75.2.165.226 (75.2.165.226) Time: Wed Aug 9 14:02:21 2006 Input: (4.09*10^6)(5.87*10^-7) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.00000058700000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (5.87*10^-7). Timing: real 0m0.145s user 0m0.008s sys 0m0.007s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Wed Aug 9 08:25:11 2006 Input: ? free group Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? freegroup: unknown identifier ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.008s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Wed Aug 9 07:58:33 2006 Input: ? free group Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? freegroup: unknown identifier ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.004s sys 0m0.009s '134.219' ************** PARI ***************** Host 134.219.148.42 (134.219.148.42) Time: Wed Aug 9 07:58:16 2006 Input: free group Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = freegroup ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Wed Aug 9 06:45:40 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.283s user 0m0.008s sys 0m0.011s '82.182.' ************** PARI ***************** Host 82.182.86.196 (82.182.86.196) Time: Wed Aug 9 04:01:21 2006 Input: factor((10^67-1)/9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 1207 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.004s user 0m20.965s sys 0m0.037s '82.182.' ************** PARI ***************** Host 82.182.86.196 (82.182.86.196) Time: Wed Aug 9 03:59:40 2006 Input: factor((10^43-1)/9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [173 1] [1527791 1] [1963506722254397 1] [2140992015395526641 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.219s user 0m0.070s sys 0m0.023s '66.169.' ************** PARI ***************** Host 66.169.108.181 (66.169.108.181) Time: Tue Aug 8 19:03:52 2006 Input: 3x+2y=3 -y+4x=1 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? %2 = 1 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x+2y=3. *** Warning: unused characters: x=1. Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '82.45.2' ************** PARI ***************** Host 82.45.250.169 (82.45.250.169) Time: Tue Aug 8 17:37:55 2006 Input: 19-5+4+3*2+6-5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 25 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '82.45.2' ************** PARI ***************** Host 82.45.250.169 (82.45.250.169) Time: Tue Aug 8 17:36:28 2006 Input: Nineteen,Minus,Five 4+3*2 6-5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Nineteen ? %2 = 10 ? %3 = 1 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: ,Minus,Five. Timing: real 0m0.075s user 0m0.006s sys 0m0.008s '82.45.2' ************** PARI ***************** Host 82.45.250.169 (82.45.250.169) Time: Tue Aug 8 17:35:01 2006 Input: Add the numbers Nineteen Minus Five= 4+3*2= 6-5= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Addthenumbers ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: NineteenMinusFive=4+3*2=6-5= ^----- Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '72.229.' ************** PARI ***************** Host 72.229.120.226 (72.229.120.226) Time: Tue Aug 8 16:52:18 2006 Input: 5% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '200.185' ************** PARI ***************** Host 200.185.104.245 (200.185.104.245) Time: Tue Aug 8 13:36:23 2006 Input: factor(19631212) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 2] [251 1] [19553 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.185s user 0m0.006s sys 0m0.006s '63.193.' ************** PARI ***************** Host 63.193.144.46 (63.193.144.46) Time: Tue Aug 8 10:31:42 2006 Input: 4/5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4/5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.054s user 0m0.006s sys 0m0.008s '63.193.' ************** PARI ***************** Host 63.193.144.46 (63.193.144.46) Time: Tue Aug 8 10:20:12 2006 Input: 1250x4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x4 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x4. Timing: real 0m0.299s user 0m0.007s sys 0m0.012s '24.59.1' ************** PARI ***************** Host 24.59.161.234 (24.59.161.234) Time: Mon Aug 7 22:58:47 2006 Input: 761855+19875 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 781730 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '146.151' ************** PARI ***************** Host 146.151.49.239 (146.151.49.239) Time: Mon Aug 7 18:40:40 2006 Input: 42+45 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 87 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '68.121.' ************** PARI ***************** Host 68.121.22.156 (68.121.22.156) Time: Mon Aug 7 16:45:11 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.107.151 (72.30.107.151) Time: Mon Aug 7 15:50:17 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.076s user 0m0.003s sys 0m0.011s '72.40.2' ************** PARI ***************** Host 72.40.25.145 (72.40.25.145) Time: Mon Aug 7 14:15:45 2006 Input: 187416 x 187416 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x187416 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x187416. Timing: real 0m0.030s user 0m0.009s sys 0m0.004s '72.75.2' ************** PARI ***************** Host 72.75.2.9 (72.75.2.9) Time: Mon Aug 7 14:02:37 2006 Input: ? Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Help topics: for a list of relevant subtopics, type ?n for n in 0: user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.007s '72.75.2' ************** PARI ***************** Host 72.75.2.9 (72.75.2.9) Time: Mon Aug 7 14:01:49 2006 Input: ?5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.002s sys 0m0.011s '72.75.2' ************** PARI ***************** Host 72.75.2.9 (72.75.2.9) Time: Mon Aug 7 14:01:38 2006 Input: ? Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Help topics: for a list of relevant subtopics, type ?n for n in 0: user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Goodbye! Errors/timing (if any): Timing: real 0m0.308s user 0m0.005s sys 0m0.010s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Mon Aug 7 06:12:35 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '216.184' ************** PARI ***************** Host 216.184.80.146 (216.184.80.146) Time: Mon Aug 7 05:27:30 2006 Input: for(n=1,1000,if(isprime(2^(2^n-1)-1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 2,3,5,7, Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 22874 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.093s user 0m20.844s sys 0m0.174s '216.184' ************** PARI ***************** Host 216.184.80.146 (216.184.80.146) Time: Mon Aug 7 05:26:49 2006 Input: for(n=1,1000,if(isprime(2*(2^n-1)-1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 2,3,4,5,8,9,11,13,19,21,23,28,93,115,121,149,173,212,220,232,265,335,451,544,688,693,849, ? Goodbye! Errors/timing (if any): Timing: real 0m15.616s user 0m15.592s sys 0m0.014s '216.184' ************** PARI ***************** Host 216.184.80.146 (216.184.80.146) Time: Mon Aug 7 05:26:18 2006 Input: for(n=1,1000,if(isprime(2*(2^n-1)),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1, ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.010s sys 0m0.006s '216.184' ************** PARI ***************** Host 216.184.80.146 (216.184.80.146) Time: Mon Aug 7 05:25:28 2006 Input: for(n=1,1000,if(isprime((2^n-1)-(n^2+1)),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 5,215,253,323, ? Goodbye! Errors/timing (if any): Timing: real 0m0.446s user 0m0.438s sys 0m0.008s '216.184' ************** PARI ***************** Host 216.184.80.146 (216.184.80.146) Time: Mon Aug 7 05:24:35 2006 Input: for(n=1,1000,if(isprime((2^n-1)-(n^2-1)),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 5,7,9,17,19,51,53,81,83,119,189,219,227,301,455,461,623, ? Goodbye! Errors/timing (if any): Timing: real 0m4.340s user 0m4.317s sys 0m0.020s '216.184' ************** PARI ***************** Host 216.184.80.146 (216.184.80.146) Time: Mon Aug 7 05:24:10 2006 Input: for(n=1,1000,if(isprime((2^n-1)-(n^2)),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 8,14,26,70,112,122,178,352, ? Goodbye! Errors/timing (if any): Timing: real 0m0.801s user 0m0.551s sys 0m0.009s '216.184' ************** PARI ***************** Host 216.184.80.146 (216.184.80.146) Time: Mon Aug 7 05:23:03 2006 Input: for(n=1,500,if(isprime(613*10^n+1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,6,9,10,18,75,122,165,402, ? Goodbye! Errors/timing (if any): Timing: real 0m1.002s user 0m0.988s sys 0m0.010s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Mon Aug 7 04:32:16 2006 Input: for(n=1,1000,if(isprime((2^n-1)+2),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,2,4,8,16, ? Goodbye! Errors/timing (if any): Timing: real 0m0.073s user 0m0.068s sys 0m0.006s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Mon Aug 7 04:31:51 2006 Input: for(n=1,500,if(isprime((2^n-1)+2),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,2,4,8,16, ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.015s sys 0m0.005s '85.89.1' ************** PARI ***************** Host 85.89.168.182 (85.89.168.182) Time: Mon Aug 7 04:20:51 2006 Input: factor(2^31-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2147483647 1] ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '85.89.1' ************** PARI ***************** Host 85.89.168.182 (85.89.168.182) Time: Mon Aug 7 04:20:10 2006 Input: factor(123) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [41 1] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '85.89.1' ************** PARI ***************** Host 85.89.168.182 (85.89.168.182) Time: Mon Aug 7 04:13:02 2006 Input: factor(2^31-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2147483647 1] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '85.89.1' ************** PARI ***************** Host 85.89.168.182 (85.89.168.182) Time: Mon Aug 7 04:12:15 2006 Input: factor(2^31-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2147483647 1] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '85.89.1' ************** PARI ***************** Host 85.89.168.182 (85.89.168.182) Time: Mon Aug 7 04:10:50 2006 Input: 2^31-1 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2147483647 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.002s sys 0m0.010s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sun Aug 6 21:39:30 2006 Input: contfrac(sqrt(61)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [7, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sun Aug 6 21:38:06 2006 Input: contfrac(sqrt(41)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.085s user 0m0.010s sys 0m0.003s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 20:57:18 2006 Input: for(n=1,1000,if(isprime(n!+1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,2,3,11,27,37,41,73,77,116,154,320, Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 18102 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m24.558s user 0m20.962s sys 0m0.039s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 20:56:34 2006 Input: for(n=1,100,if(isprime(n!+1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,2,3,11,27,37,41,73,77, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.198s user 0m0.090s sys 0m0.009s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 20:56:14 2006 Input: for(n=1,100,if(isprime(n),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 19:54:18 2006 Input: for(n=1,42,if(isprime(n^2+n+41),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,42, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 19:54:02 2006 Input: for(n=1,48,if(isprime(n^2+n+41),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,42,43,45,46,47,48, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 19:53:31 2006 Input: for(n=1,41,if(isprime(n^2+n+41),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 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, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 19:53:14 2006 Input: for(n=1,40,if(isprime(n^2+n+41),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 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, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 19:52:49 2006 Input: for(n=1,42,if(isprime(n^2+n+41),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,42, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 19:51:45 2006 Input: for(n=1,6521,if(isprime(n),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.026s user 0m0.020s sys 0m0.007s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 19:49:35 2006 Input: for(n=1,1000,if(isprime(n),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.010s sys 0m0.005s '69.121.' ************** PARI ***************** Host 69.121.152.231 (69.121.152.231) Time: Sun Aug 6 17:16:38 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.039s user 0m0.006s sys 0m0.010s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sun Aug 6 17:11:05 2006 Input: for(n=0,1000,if(isprime(n^2-n+27941),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 0,1,2,3,4,5,7,8,10,11,13,14,15,16,19,22,23,24,25,26,27,28,29,31,32,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,58,60,61,62,63,64,67,68,69,70,71,72,74,76,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,103,104,105,111,113,114,115,116,117,119,120,121,122,125,126,127,129,130,131,132,133,134,136,137,139,141,142,143,144,145,148,149,150,151,152,153,154,156,157,158,160,163,164,165,166,167,168,169,170,173,174,175,176,177,178,180,181,184,185,186,187,188,189,191,192,193,196,197,198,199,200,201,202,203,205,207,208,209,211,212,214,215,216,219,221,222,223,224,225,226,228,229,230,231,232,234,236,237,238,241,242,245,246,250,252,254,261,262,263,264,267,268,271,272,273,275,276,277,278,279,281,282,283,285,286,287,288,290,291,292,293,294,295,297,298,299,302,303,305,306,307,308,309,310,311,313,314,315,316,317,318,320,322,323,325,328,330,333,335,341,342,344,346,349,350,351,353,355,356,358,360,361,363,364,366,367,368,369,370,371,374,377,378,379,381,382,384,385,386,387,389,390,392,393,395,397,398,399,403,404,405,407,409,412,413,415,417,420,422,423,424,425,426,430,432,434,435,440,442,443,444,447,448,449,451,455,457,459,460,463,464,465,467,468,469,470,471,472,473,474,476,477,478,479,480,482,483,484,485,486,490,491,492,494,497,498,499,502,505,507,508,509,511,512,513,516,521,522,524,526,527,529,530,531,532,534,538,539,540,541,542,543,544,550,553,555,556,557,558,559,561,563,564,565,566,569,570,571,572,573,577,578,580,581,585,590,591,593,595,597,599,600,601,602,604,605,606,608,609,611,613,614,620,622,623,624,625,626,628,631,633,636,637,638,639,642,644,648,652,654,656,658,660,661,662,664,665,666,667,668,671,672,677,678,679,683,684,685,686,690,692,693,695,697,699,700,702,703,704,705,706,710,711,712,714,716,718,719,720,721,722,725,727,728,733,737,738,740,744,745,752,754,756,757,758,760,761,762,765,768,771,775,776,777,778,779,783,784,786,787,788,790,791,792,794,795,797,800,801,802,803,804,805,806,807,809,810,812,813,814,820,822,823,828,832,833,834,835,837,841,842,843,844,845,847,848,851,852,854,855,856,857,861,862,866,867,875,877,878,880,882,885,886,892,893,894,895,897,902,903,904,905,906,910,914,915,916,917,918,920,921,924,926,929,932,933,938,939,941,942,945,946,948,952,953,955,956,959,960,961,962,964,966,967,972,974,975,976,977,978,979,980,981,983,987,988,989,992,993,995,999,1000, ? Goodbye! Errors/timing (if any): Timing: real 0m0.092s user 0m0.010s sys 0m0.008s '69.230.' ************** PARI ***************** Host 69.230.18.219 (69.230.18.219) Time: Sun Aug 6 16:12:30 2006 Input: 1700 = 8000c - 77800/6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 1700=8000c-77800/6 ^-------------- Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '72.30.2' ************** PARI ***************** Host 72.30.226.160 (72.30.226.160) Time: Sun Aug 6 15:18:08 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.253s user 0m0.007s sys 0m0.012s '24.255.' ************** PARI ***************** Host 24.255.160.206 (24.255.160.206) Time: Sun Aug 6 09:36:37 2006 Input: v-4(4-v)=-2(2v-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (4-v)=-2(2v-1). *** unexpected character: v-4(4-v)=-2(2v-1) ^--------- Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '129.67.' ************** PARI ***************** Host 129.67.126.38 (129.67.126.38) Time: Sun Aug 6 07:28:52 2006 Input: polrootspadic(162*x^2 + 7164*x + 19177,7,12) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 + 2*7 + 5*7^2 + 5*7^3 + 4*7^4 + 3*7^5 + 4*7^6 + 3*7^7 + 3*7^8 + 2*7^9 + 2*7^11 + O(7^12), 2 + 2*7 + 2*7^2 + 6*7^4 + 4*7^5 + 7^6 + 5*7^8 + 3*7^9 + 3*7^10 + 6*7^11 + O(7^12), 2 + 2*7 + 5*7^2 + 5*7^3 + 4*7^4 + 3*7^5 + 4*7^6 + 3*7^7 + 3*7^8 + 2*7^9 + 2*7^11 + O(7^12), 2 + 2*7 + 2*7^2 + 6*7^4 + 4*7^5 + 7^6 + 5*7^8 + 3*7^9 + 3*7^10 + 6*7^11 + O(7^12), 4 + 5*7 + 3*7^3 + 5*7^4 + 3*7^6 + 5*7^7 + 3*7^9 + 5*7^10 + O(7^12)]~ ? Goodbye! Errors/timing (if any): Timing: real 0m0.095s user 0m0.011s sys 0m0.006s '61.5.4.' ************** PARI ***************** Host 61.5.4.144 (61.5.4.144) Time: Sun Aug 6 05:17:30 2006 Input: 2^32 mod 47 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = mod47 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: mod47. Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '69.92.1' ************** PARI ***************** Host 69.92.12.82 (69.92.12.82) Time: Sun Aug 6 02:46:58 2006 Input: for(n=1,500,if(isprime(613*10^n+1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,6,9,10,18,75,122,165,402, ? Goodbye! Errors/timing (if any): Timing: real 0m2.253s user 0m0.986s sys 0m0.013s '164.107' ************** PARI ***************** Host 164.107.186.40 (164.107.186.40) Time: Sat Aug 5 23:44:43 2006 Input: primepi(500000) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41538 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '164.107' ************** PARI ***************** Host 164.107.186.40 (164.107.186.40) Time: Sat Aug 5 23:44:25 2006 Input: primepi(1000) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 168 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 20:56:11 2006 Input: Do[ If[ PrimeQ[ FromDigits[ RealDigits[ N[ P, n+10], 10, n] [ [1] ] ] ], Print[n] ], {n, 1, 9016} ] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ']' instead of: ...s[RealDigits[N[P,n+10],10 *** ,n][[1]]]],Print[n]] ^-------------------- Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '208.191' ************** PARI ***************** Host 208.191.162.223 (208.191.162.223) Time: Sat Aug 5 20:42:27 2006 Input: what is 20% of 1250.00 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '24.247.' ************** PARI ***************** Host 24.247.238.196 (24.247.238.196) Time: Sat Aug 5 19:32:03 2006 Input: 9.95+9.95+7.95+7.95 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 35.800000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.008s sys 0m0.005s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 15:46:01 2006 Input: for(n=0,2000,if(isprime(2^n-1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 2,3,5,7,13,17,19,31,61,89,107,127,521,607, Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 12443 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.011s user 0m20.987s sys 0m0.013s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 15:45:06 2006 Input: for(n=0,1000,if(isprime(2^n-1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 2,3,5,7,13,17,19,31,61,89,107,127,521,607, ? Goodbye! Errors/timing (if any): Timing: real 0m3.059s user 0m3.047s sys 0m0.011s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 15:44:34 2006 Input: for(n=0,1000,if(isprime(n^2-n+27941),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 0,1,2,3,4,5,7,8,10,11,13,14,15,16,19,22,23,24,25,26,27,28,29,31,32,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,58,60,61,62,63,64,67,68,69,70,71,72,74,76,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,103,104,105,111,113,114,115,116,117,119,120,121,122,125,126,127,129,130,131,132,133,134,136,137,139,141,142,143,144,145,148,149,150,151,152,153,154,156,157,158,160,163,164,165,166,167,168,169,170,173,174,175,176,177,178,180,181,184,185,186,187,188,189,191,192,193,196,197,198,199,200,201,202,203,205,207,208,209,211,212,214,215,216,219,221,222,223,224,225,226,228,229,230,231,232,234,236,237,238,241,242,245,246,250,252,254,261,262,263,264,267,268,271,272,273,275,276,277,278,279,281,282,283,285,286,287,288,290,291,292,293,294,295,297,298,299,302,303,305,306,307,308,309,310,311,313,314,315,316,317,318,320,322,323,325,328,330,333,335,341,342,344,346,349,350,351,353,355,356,358,360,361,363,364,366,367,368,369,370,371,374,377,378,379,381,382,384,385,386,387,389,390,392,393,395,397,398,399,403,404,405,407,409,412,413,415,417,420,422,423,424,425,426,430,432,434,435,440,442,443,444,447,448,449,451,455,457,459,460,463,464,465,467,468,469,470,471,472,473,474,476,477,478,479,480,482,483,484,485,486,490,491,492,494,497,498,499,502,505,507,508,509,511,512,513,516,521,522,524,526,527,529,530,531,532,534,538,539,540,541,542,543,544,550,553,555,556,557,558,559,561,563,564,565,566,569,570,571,572,573,577,578,580,581,585,590,591,593,595,597,599,600,601,602,604,605,606,608,609,611,613,614,620,622,623,624,625,626,628,631,633,636,637,638,639,642,644,648,652,654,656,658,660,661,662,664,665,666,667,668,671,672,677,678,679,683,684,685,686,690,692,693,695,697,699,700,702,703,704,705,706,710,711,712,714,716,718,719,720,721,722,725,727,728,733,737,738,740,744,745,752,754,756,757,758,760,761,762,765,768,771,775,776,777,778,779,783,784,786,787,788,790,791,792,794,795,797,800,801,802,803,804,805,806,807,809,810,812,813,814,820,822,823,828,832,833,834,835,837,841,842,843,844,845,847,848,851,852,854,855,856,857,861,862,866,867,875,877,878,880,882,885,886,892,893,894,895,897,902,903,904,905,906,910,914,915,916,917,918,920,921,924,926,929,932,933,938,939,941,942,945,946,948,952,953,955,956,959,960,961,962,964,966,967,972,974,975,976,977,978,979,980,981,983,987,988,989,992,993,995,999,1000, ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.007s sys 0m0.013s '68.93.1' ************** PARI ***************** Host 68.93.143.153 (68.93.143.153) Time: Sat Aug 5 15:38:03 2006 Input: what is grams Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = whatisgrams ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 14:25:54 2006 Input: for(n=0,1000,if(isprime(n^2-n+27941),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 0,1,2,3,4,5,7,8,10,11,13,14,15,16,19,22,23,24,25,26,27,28,29,31,32,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,58,60,61,62,63,64,67,68,69,70,71,72,74,76,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,103,104,105,111,113,114,115,116,117,119,120,121,122,125,126,127,129,130,131,132,133,134,136,137,139,141,142,143,144,145,148,149,150,151,152,153,154,156,157,158,160,163,164,165,166,167,168,169,170,173,174,175,176,177,178,180,181,184,185,186,187,188,189,191,192,193,196,197,198,199,200,201,202,203,205,207,208,209,211,212,214,215,216,219,221,222,223,224,225,226,228,229,230,231,232,234,236,237,238,241,242,245,246,250,252,254,261,262,263,264,267,268,271,272,273,275,276,277,278,279,281,282,283,285,286,287,288,290,291,292,293,294,295,297,298,299,302,303,305,306,307,308,309,310,311,313,314,315,316,317,318,320,322,323,325,328,330,333,335,341,342,344,346,349,350,351,353,355,356,358,360,361,363,364,366,367,368,369,370,371,374,377,378,379,381,382,384,385,386,387,389,390,392,393,395,397,398,399,403,404,405,407,409,412,413,415,417,420,422,423,424,425,426,430,432,434,435,440,442,443,444,447,448,449,451,455,457,459,460,463,464,465,467,468,469,470,471,472,473,474,476,477,478,479,480,482,483,484,485,486,490,491,492,494,497,498,499,502,505,507,508,509,511,512,513,516,521,522,524,526,527,529,530,531,532,534,538,539,540,541,542,543,544,550,553,555,556,557,558,559,561,563,564,565,566,569,570,571,572,573,577,578,580,581,585,590,591,593,595,597,599,600,601,602,604,605,606,608,609,611,613,614,620,622,623,624,625,626,628,631,633,636,637,638,639,642,644,648,652,654,656,658,660,661,662,664,665,666,667,668,671,672,677,678,679,683,684,685,686,690,692,693,695,697,699,700,702,703,704,705,706,710,711,712,714,716,718,719,720,721,722,725,727,728,733,737,738,740,744,745,752,754,756,757,758,760,761,762,765,768,771,775,776,777,778,779,783,784,786,787,788,790,791,792,794,795,797,800,801,802,803,804,805,806,807,809,810,812,813,814,820,822,823,828,832,833,834,835,837,841,842,843,844,845,847,848,851,852,854,855,856,857,861,862,866,867,875,877,878,880,882,885,886,892,893,894,895,897,902,903,904,905,906,910,914,915,916,917,918,920,921,924,926,929,932,933,938,939,941,942,945,946,948,952,953,955,956,959,960,961,962,964,966,967,972,974,975,976,977,978,979,980,981,983,987,988,989,992,993,995,999,1000, ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.013s sys 0m0.007s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 14:09:49 2006 Input: for(n=0,1000,if(isprime(n^2-n+27941),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 0,1,2,3,4,5,7,8,10,11,13,14,15,16,19,22,23,24,25,26,27,28,29,31,32,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,58,60,61,62,63,64,67,68,69,70,71,72,74,76,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,103,104,105,111,113,114,115,116,117,119,120,121,122,125,126,127,129,130,131,132,133,134,136,137,139,141,142,143,144,145,148,149,150,151,152,153,154,156,157,158,160,163,164,165,166,167,168,169,170,173,174,175,176,177,178,180,181,184,185,186,187,188,189,191,192,193,196,197,198,199,200,201,202,203,205,207,208,209,211,212,214,215,216,219,221,222,223,224,225,226,228,229,230,231,232,234,236,237,238,241,242,245,246,250,252,254,261,262,263,264,267,268,271,272,273,275,276,277,278,279,281,282,283,285,286,287,288,290,291,292,293,294,295,297,298,299,302,303,305,306,307,308,309,310,311,313,314,315,316,317,318,320,322,323,325,328,330,333,335,341,342,344,346,349,350,351,353,355,356,358,360,361,363,364,366,367,368,369,370,371,374,377,378,379,381,382,384,385,386,387,389,390,392,393,395,397,398,399,403,404,405,407,409,412,413,415,417,420,422,423,424,425,426,430,432,434,435,440,442,443,444,447,448,449,451,455,457,459,460,463,464,465,467,468,469,470,471,472,473,474,476,477,478,479,480,482,483,484,485,486,490,491,492,494,497,498,499,502,505,507,508,509,511,512,513,516,521,522,524,526,527,529,530,531,532,534,538,539,540,541,542,543,544,550,553,555,556,557,558,559,561,563,564,565,566,569,570,571,572,573,577,578,580,581,585,590,591,593,595,597,599,600,601,602,604,605,606,608,609,611,613,614,620,622,623,624,625,626,628,631,633,636,637,638,639,642,644,648,652,654,656,658,660,661,662,664,665,666,667,668,671,672,677,678,679,683,684,685,686,690,692,693,695,697,699,700,702,703,704,705,706,710,711,712,714,716,718,719,720,721,722,725,727,728,733,737,738,740,744,745,752,754,756,757,758,760,761,762,765,768,771,775,776,777,778,779,783,784,786,787,788,790,791,792,794,795,797,800,801,802,803,804,805,806,807,809,810,812,813,814,820,822,823,828,832,833,834,835,837,841,842,843,844,845,847,848,851,852,854,855,856,857,861,862,866,867,875,877,878,880,882,885,886,892,893,894,895,897,902,903,904,905,906,910,914,915,916,917,918,920,921,924,926,929,932,933,938,939,941,942,945,946,948,952,953,955,956,959,960,961,962,964,966,967,972,974,975,976,977,978,979,980,981,983,987,988,989,992,993,995,999,1000, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.012s sys 0m0.006s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 14:09:01 2006 Input: for(n=1,1000,if(isprime(n^2-n+27941),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,2,3,4,5,7,8,10,11,13,14,15,16,19,22,23,24,25,26,27,28,29,31,32,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,58,60,61,62,63,64,67,68,69,70,71,72,74,76,80,81,82,83,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,103,104,105,111,113,114,115,116,117,119,120,121,122,125,126,127,129,130,131,132,133,134,136,137,139,141,142,143,144,145,148,149,150,151,152,153,154,156,157,158,160,163,164,165,166,167,168,169,170,173,174,175,176,177,178,180,181,184,185,186,187,188,189,191,192,193,196,197,198,199,200,201,202,203,205,207,208,209,211,212,214,215,216,219,221,222,223,224,225,226,228,229,230,231,232,234,236,237,238,241,242,245,246,250,252,254,261,262,263,264,267,268,271,272,273,275,276,277,278,279,281,282,283,285,286,287,288,290,291,292,293,294,295,297,298,299,302,303,305,306,307,308,309,310,311,313,314,315,316,317,318,320,322,323,325,328,330,333,335,341,342,344,346,349,350,351,353,355,356,358,360,361,363,364,366,367,368,369,370,371,374,377,378,379,381,382,384,385,386,387,389,390,392,393,395,397,398,399,403,404,405,407,409,412,413,415,417,420,422,423,424,425,426,430,432,434,435,440,442,443,444,447,448,449,451,455,457,459,460,463,464,465,467,468,469,470,471,472,473,474,476,477,478,479,480,482,483,484,485,486,490,491,492,494,497,498,499,502,505,507,508,509,511,512,513,516,521,522,524,526,527,529,530,531,532,534,538,539,540,541,542,543,544,550,553,555,556,557,558,559,561,563,564,565,566,569,570,571,572,573,577,578,580,581,585,590,591,593,595,597,599,600,601,602,604,605,606,608,609,611,613,614,620,622,623,624,625,626,628,631,633,636,637,638,639,642,644,648,652,654,656,658,660,661,662,664,665,666,667,668,671,672,677,678,679,683,684,685,686,690,692,693,695,697,699,700,702,703,704,705,706,710,711,712,714,716,718,719,720,721,722,725,727,728,733,737,738,740,744,745,752,754,756,757,758,760,761,762,765,768,771,775,776,777,778,779,783,784,786,787,788,790,791,792,794,795,797,800,801,802,803,804,805,806,807,809,810,812,813,814,820,822,823,828,832,833,834,835,837,841,842,843,844,845,847,848,851,852,854,855,856,857,861,862,866,867,875,877,878,880,882,885,886,892,893,894,895,897,902,903,904,905,906,910,914,915,916,917,918,920,921,924,926,929,932,933,938,939,941,942,945,946,948,952,953,955,956,959,960,961,962,964,966,967,972,974,975,976,977,978,979,980,981,983,987,988,989,992,993,995,999,1000, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.017s sys 0m0.004s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 14:07:05 2006 Input: for(n=1,1000,if(isprime(2^n-1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 2,3,5,7,13,17,19,31,61,89,107,127,521,607, ? ? Goodbye! Errors/timing (if any): Timing: real 0m3.071s user 0m3.045s sys 0m0.008s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 14:06:51 2006 Input: for(n=1,500,if(isprime(2^n-1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 2,3,5,7,13,17,19,31,61,89,107,127, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.060s user 0m0.052s sys 0m0.008s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 14:06:09 2006 Input: for(n=1,500,if(isprime(2^n-1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 2,3,5,7,13,17,19,31,61,89,107,127, ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.177s user 0m0.055s sys 0m0.003s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 14:04:51 2006 Input: for(n=1,42,if(isprime(n^2+x+41),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** isprime: not an integer argument in an arithmetic function Timing: real 0m0.035s user 0m0.006s sys 0m0.010s '69.27.6' ************** PARI ***************** Host 69.27.68.214 (69.27.68.214) Time: Sat Aug 5 14:02:21 2006 Input: for(n=1,500,if(isprime(613*10^n+1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,6,9,10,18,75,122,165,402, ? Goodbye! Errors/timing (if any): Timing: real 0m1.127s user 0m0.980s sys 0m0.011s '69.92.1' ************** PARI ***************** Host 69.92.12.82 (69.92.12.82) Time: Sat Aug 5 12:43:48 2006 Input: for(n=1,500,if(isprime(613*10^n+1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,6,9,10,18,75,122,165,402, ? Goodbye! Errors/timing (if any): Timing: real 0m0.999s user 0m0.992s sys 0m0.007s '69.92.1' ************** PARI ***************** Host 69.92.12.82 (69.92.12.82) Time: Sat Aug 5 12:32:50 2006 Input: for(n=1,500,if(isprime(613*10^n+1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,6,9,10,18,75,122,165,402, ? Goodbye! Errors/timing (if any): Timing: real 0m1.093s user 0m0.982s sys 0m0.009s '69.92.1' ************** PARI ***************** Host 69.92.12.82 (69.92.12.82) Time: Sat Aug 5 12:32:28 2006 Input: ? for(n=1,500,if(isprime(613*10^n+1),print1(n","))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? for(X=a,b,seq): the sequence is evaluated, X going from a up to b. ? Goodbye! Errors/timing (if any): Timing: real 0m0.048s user 0m0.007s sys 0m0.007s '24.131.' ************** PARI ***************** Host 24.131.127.122 (24.131.127.122) Time: Sat Aug 5 10:35:47 2006 Input: print kash('NumberField(X^3 + 15*X^2 - 15*X + 15)') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printkash('NumberField *** (X^3+15*X^2-15*X+15) ^-------------------- Timing: real 0m0.273s user 0m0.003s sys 0m0.015s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sat Aug 5 05:52:11 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.101s user 0m0.004s sys 0m0.014s '75.6.14' ************** PARI ***************** Host 75.6.149.232 (75.6.149.232) Time: Fri Aug 4 20:54:39 2006 Input: 56124+546523567 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 546579691 ? Goodbye! Errors/timing (if any): Timing: real 0m0.059s user 0m0.004s sys 0m0.008s '75.6.14' ************** PARI ***************** Host 75.6.149.232 (75.6.149.232) Time: Fri Aug 4 20:54:28 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.003s sys 0m0.010s '24.161.' ************** PARI ***************** Host 24.161.97.99 (24.161.97.99) Time: Fri Aug 4 18:35:34 2006 Input: 2700 divided by 27 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = dividedby27 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: dividedby27. Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '128.208' ************** PARI ***************** Host 128.208.47.43 (128.208.47.43) Time: Fri Aug 4 10:40:26 2006 Input: 2^15 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 32768 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '212.158' ************** PARI ***************** Host 212.158.224.83 (212.158.224.83) Time: Fri Aug 4 06:58:58 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.285s user 0m0.006s sys 0m0.009s '81.190.' ************** PARI ***************** Host 81.190.2.171 (81.190.2.171) Time: Thu Aug 3 17:15:35 2006 Input: E = EllipticCurve([10,20,30,49,50]); E E.anlist(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = E ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: E=EllipticCurve([10,20 ^-------------------- *** Warning: unused characters: (10). *** unknown member function: E.anlist(10) ^---------- Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '81.190.' ************** PARI ***************** Host 81.190.2.171 (81.190.2.171) Time: Thu Aug 3 16:54:22 2006 Input: def h1(x): return sqrt(x) def h2(x): return -sqrt(x) plot([h1, h2], 0,4).show(dpi=70) Output: WARNING: PARI command contains unsafe command 'plot', so it will not be executed. '159.242' ************** PARI ***************** Host 159.242.10.178 (159.242.10.178) Time: Thu Aug 3 16:20:19 2006 Input: 2660999956459044462496559697895207916164979^2484967380701451508112337181106320041688653 3391644668254683815130414077708852650402483 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 3391644668254683815130414077708852650402483 ? Goodbye! Errors/timing (if any): *** length (lg) overflow Timing: real 0m0.049s user 0m0.004s sys 0m0.010s '65.31.3' ************** PARI ***************** Host 65.31.34.63 (65.31.34.63) Time: Thu Aug 3 13:03:52 2006 Input: 19.99+7.99= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 19.99+7.99= ^- Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.244' ************** PARI ***************** Host 128.244.70.112 (128.244.70.112) Time: Thu Aug 3 08:55:23 2006 Input: 2^312413 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4830981466364580262319339049818562968558761028106272923126514918538223897345359936316446318720231182550935815005772315073996555250585693298540893393869965893092771427023973324398278248218175680359827444393509313174684525735678463663338125756964551115437342798314289976505148315466828279216135786601845924061519374988636778812138166301482869293619842397899083644391558537625975319346404544929515996170044151227529786416523393368140240692057558960136886977969459360853671139303206053306955723152430599303215851072815557007673966645878385823632646218356155873846606739507321092585440396351621511927850798205826923798017416153927206387891124567627792684687510179774180313271224111160927439702146890826412635562210651443065158752867553952036555744295988140356916766792733492711250785640478897306333920929841764065832622350747877946551823482187314115902814391938118045061893243257030360736440272387702746257151958562194110609391650030004236271161198917478149407972601791080340416289522217831842149279835538796034145741705373260384364903648065949011881512804322037289046950099011614522708194273468684859406801874157091529832148222328299288313083228093653170268904942449665323783818837931336547816485989215516595643436703960125472804421950729227643775424995665390226098088488420100130103202545344023974701370579360668132145456011523239722123972684999166344157597865557207037334973510208063181572044506866127826166579937040799836980091022005227178463709705067496410505882900234294540070905246120172453872075795510741926131987494670876917571998688053327730386004753469605546394017699620434253124319245235951810127531919801525874034179211514938805278780987944202820044826836109855430759065424813753651861469841704258187919970528928014675879351276720340559579087972476623295822223256347083299401660105337688691448979289075269637164710330897111913041037586535860271603582020639730941234472075388266368302732481390873310271931083219652448099445946604508098857863980957866978377596203570650593766139429847724575195075838452342188246180245513226058215761886236117380443043123188663192557854403152613949044031622909678213681857845610600954804960235913101079902222795134480736652982982306766632503957094862757822086275527390021267896804427483984420687621291870473384994140112770042378319084403156285698992746136555119097875362718125399775260346689252902321886998054019345588595360882048534031439836686597038653268510372778634363156608776954240697148964494042709310374969327886434368252414271912929608815903278270130329523383727733574741070197722548872017944205273685505986533424364627848013888396034174195379168695180492227053312063678932172222808341805857627358459578999746596179020196440429462841970944863716607653637977238621947036196999534721518103803089055338642715622544832669893314068824953086229567991687773603189917159336397138091179415373638117214282655295695467216071610962126082335992862627083119989314386660945600212361119249805546888549357680640983743435475894367263052538391431935336285944258022846877654513700214633120016244441249251826123582445040257840215040969299396786619548604192248415312061624538590283139363792089759812403413123484683794638570913639713120216938900897808778338252786564[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.542s user 0m0.416s sys 0m0.117s '128.244' ************** PARI ***************** Host 128.244.70.112 (128.244.70.112) Time: Thu Aug 3 08:55:08 2006 Input: 2^312413 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4830981466364580262319339049818562968558761028106272923126514918538223897345359936316446318720231182550935815005772315073996555250585693298540893393869965893092771427023973324398278248218175680359827444393509313174684525735678463663338125756964551115437342798314289976505148315466828279216135786601845924061519374988636778812138166301482869293619842397899083644391558537625975319346404544929515996170044151227529786416523393368140240692057558960136886977969459360853671139303206053306955723152430599303215851072815557007673966645878385823632646218356155873846606739507321092585440396351621511927850798205826923798017416153927206387891124567627792684687510179774180313271224111160927439702146890826412635562210651443065158752867553952036555744295988140356916766792733492711250785640478897306333920929841764065832622350747877946551823482187314115902814391938118045061893243257030360736440272387702746257151958562194110609391650030004236271161198917478149407972601791080340416289522217831842149279835538796034145741705373260384364903648065949011881512804322037289046950099011614522708194273468684859406801874157091529832148222328299288313083228093653170268904942449665323783818837931336547816485989215516595643436703960125472804421950729227643775424995665390226098088488420100130103202545344023974701370579360668132145456011523239722123972684999166344157597865557207037334973510208063181572044506866127826166579937040799836980091022005227178463709705067496410505882900234294540070905246120172453872075795510741926131987494670876917571998688053327730386004753469605546394017699620434253124319245235951810127531919801525874034179211514938805278780987944202820044826836109855430759065424813753651861469841704258187919970528928014675879351276720340559579087972476623295822223256347083299401660105337688691448979289075269637164710330897111913041037586535860271603582020639730941234472075388266368302732481390873310271931083219652448099445946604508098857863980957866978377596203570650593766139429847724575195075838452342188246180245513226058215761886236117380443043123188663192557854403152613949044031622909678213681857845610600954804960235913101079902222795134480736652982982306766632503957094862757822086275527390021267896804427483984420687621291870473384994140112770042378319084403156285698992746136555119097875362718125399775260346689252902321886998054019345588595360882048534031439836686597038653268510372778634363156608776954240697148964494042709310374969327886434368252414271912929608815903278270130329523383727733574741070197722548872017944205273685505986533424364627848013888396034174195379168695180492227053312063678932172222808341805857627358459578999746596179020196440429462841970944863716607653637977238621947036196999534721518103803089055338642715622544832669893314068824953086229567991687773603189917159336397138091179415373638117214282655295695467216071610962126082335992862627083119989314386660945600212361119249805546888549357680640983743435475894367263052538391431935336285944258022846877654513700214633120016244441249251826123582445040257840215040969299396786619548604192248415312061624538590283139363792089759812403413123484683794638570913639713120216938900897808778338252786564[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.731s user 0m0.414s sys 0m0.195s '84.163.' ************** PARI ***************** Host 84.163.68.223 (84.163.68.223) Time: Thu Aug 3 08:29:46 2006 Input: integrate(3^x,x); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: integrate(3^x,x); ^----------------- Timing: real 0m0.100s user 0m0.010s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Thu Aug 3 05:23:34 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.107s user 0m0.009s sys 0m0.006s '62.104.' ************** PARI ***************** Host 62.104.129.89 (62.104.129.89) Time: Wed Aug 2 22:03:34 2006 Input: 2+2; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '66.69.2' ************** PARI ***************** Host 66.69.229.35 (66.69.229.35) Time: Wed Aug 2 20:12:55 2006 Input: 35.10 X 7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = X7 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: X7. Timing: real 0m0.067s user 0m0.004s sys 0m0.008s '146.186' ************** PARI ***************** Host 146.186.134.174 (146.186.134.174) Time: Wed Aug 2 10:49:31 2006 Input: sum(n=1,20,1/(1-q^n)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.091s user 0m0.007s sys 0m0.009s '146.186' ************** PARI ***************** Host 146.186.134.174 (146.186.134.174) Time: Wed Aug 2 10:43:15 2006 Input: sum(n*q^n/(1-q^n), n=1..20); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: sum(n*q^n/(1-q^n),n=1..20 ^-------------------- Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '71.111.' ************** PARI ***************** Host 71.111.254.139 (71.111.254.139) Time: Wed Aug 2 07:37:05 2006 Input: 1057.33-3448.41 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -2391.0800000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.119s user 0m0.009s sys 0m0.003s '140.105' ************** PARI ***************** Host 140.105.63.31 (140.105.63.31) Time: Wed Aug 2 04:25:35 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '72.30.9' ************** PARI ***************** Host 72.30.97.221 (72.30.97.221) Time: Tue Aug 1 22:06:17 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '68.126.' ************** PARI ***************** Host 68.126.176.117 (68.126.176.117) Time: Tue Aug 1 21:30:17 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '72.30.9' ************** PARI ***************** Host 72.30.98.145 (72.30.98.145) Time: Tue Aug 1 18:17:45 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.456s user 0m0.005s sys 0m0.014s '12.34.2' ************** PARI ***************** Host 12.34.246.7 (12.34.246.7) Time: Tue Aug 1 13:25:12 2006 Input: 200.00 x 8.25% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '71.121.' ************** PARI ***************** Host 71.121.101.100 (71.121.101.100) Time: Tue Aug 1 09:38:42 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.004s sys 0m0.008s '134.76.' ************** PARI ***************** Host 134.76.82.189 (134.76.82.189) Time: Tue Aug 1 09:19:15 2006 Input: solve(x*x+x=2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: solve(x*x+x=2) ^------- Timing: real 0m0.109s user 0m0.008s sys 0m0.006s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:22:39 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.4142135,40) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^2 - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:22:31 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.414213,40) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = 0.5854497518247262726 ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.013s sys 0m0.008s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:22:25 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.414213,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = 11995.101306366822445 ? Goodbye! Errors/timing (if any): Timing: real 0m0.071s user 0m0.009s sys 0m0.007s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:22:14 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.414213562,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^4 - 4*x^2 + 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.027s user 0m0.005s sys 0m0.009s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:22:05 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.414213562373,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^4 - 4*x^2 + 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.044s user 0m0.008s sys 0m0.007s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:21:53 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.414213562373095,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^3 - x^2 - 2*x + 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:21:36 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.41421356237309503,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^2 - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.031s user 0m0.010s sys 0m0.004s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:21:30 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.4142135623730950,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^3 - x^2 - 2*x + 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.032s user 0m0.008s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:21:23 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.41421356237309504,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^2 - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:21:13 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.41421356237309504,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^2 - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.063s user 0m0.005s sys 0m0.008s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:21:06 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.4142135623730950,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^3 - x^2 - 2*x + 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.096s user 0m0.007s sys 0m0.006s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:20:55 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.414213562373095,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^3 - x^2 - 2*x + 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:20:46 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.4142135623730950488,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^2 - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:20:38 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.41421356237309504880168,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^2 - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.066s user 0m0.007s sys 0m0.006s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:20:29 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.414213562373095048801688724,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^2 - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.099s user 0m0.006s sys 0m0.007s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:20:21 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.4142135623730950488016887242096,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^2 - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:20:11 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.4142135623730950488016887242096980,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^2 - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.046s user 0m0.009s sys 0m0.004s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:20:01 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(1.4142135623730950488016887242096980786,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = x^2 - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.135s user 0m0.007s sys 0m0.007s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:19:34 2006 Input: algdep(sqrt(2)+sqrt(3),6) x=sqrt(2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = 1.4142135623730950488016887242096980786 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.111s user 0m0.006s sys 0m0.009s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:19:17 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(3.1622776,4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = 8553.919552935008545 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.010s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:18:52 2006 Input: algdep(sqrt(2)+sqrt(3),6) algdep(67.68755647,10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? %2 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:18:32 2006 Input: algdep(sqrt(2)+sqrt(3),6) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 10*x^2 + 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.124s user 0m0.006s sys 0m0.008s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:17:45 2006 Input: ?algdep ? Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? algdep(x,n,{flag=0}): algebraic relations up to degree n of x, using lindep([1,x,...,x^(n-1)], flag). ? Help topics: for a list of relevant subtopics, type ?n for n in 0: user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:17:27 2006 Input: ?algdep Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? algdep(x,n,{flag=0}): algebraic relations up to degree n of x, using lindep([1,x,...,x^(n-1)], flag). ? Goodbye! Errors/timing (if any): Timing: real 0m0.033s user 0m0.007s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:17:15 2006 Input: ?8 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? algdep charpoly concat lindep listcreate listinsert listkill listput listsort matadjoint matcompanion matdet matdetint matdiagonal mateigen matfrobenius mathess mathilbert mathnf mathnfmod mathnfmodid matid matimage matimagecompl matindexrank matintersect matinverseimage matisdiagonal matker matkerint matmuldiagonal matmultodiagonal matpascal matrank matrix matrixqz matsize matsnf matsolve matsolvemod matsupplement mattranspose qfgaussred qfjacobi qflll qflllgram qfminim qfperfection qfrep qfsign setintersect setisset setminus setsearch setunion trace vecextract vecsort vector vectorsmall vectorv ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:17:06 2006 Input: ?7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? O deriv eval factorpadic intformal padicappr polcoeff polcyclo poldegree poldisc poldiscreduced polhensellift polinterpolate polisirreducible pollead pollegendre polrecip polresultant polroots polrootsmod polrootspadic polsturm polsubcyclo polsylvestermatrix polsym poltchebi polzagier serconvol serlaplace serreverse subst substpol taylor thue thueinit ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:17:00 2006 Input: ?6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark dirzetak factornf galoisexport galoisfixedfield galoisidentify galoisinit galoisisabelian galoispermtopol galoissubcyclo galoissubfields galoissubgroups idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal matalgtobasis matbasistoalg modreverse newtonpoly nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields polcompositum polgalois polred polredabs polredord poltschirnhaus rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfisnorminit rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz subgrouplist zetak zetakinit ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:16:45 2006 Input: ? Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Help topics: for a list of relevant subtopics, type ?n for n in 0: user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.190 (134.76.82.190) Time: Tue Aug 1 02:16:34 2006 Input: ?algred Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? algred: unknown identifier ? Goodbye! Errors/timing (if any): Timing: real 0m0.105s user 0m0.005s sys 0m0.009s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Tue Aug 1 01:34:39 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '67.42.1' ************** PARI ***************** Host 67.42.147.15 (67.42.147.15) Time: Mon Jul 31 22:58:30 2006 Input: 4(-2)² + 8(-2) + 3(-2) + 6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (-2)+8(-2)+3(-2)+6. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '67.42.1' ************** PARI ***************** Host 67.42.147.15 (67.42.147.15) Time: Mon Jul 31 22:58:04 2006 Input: 4(-2)² + 8(-2) + 3(-2) + 6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (-2)+8(-2)+3(-2)+6. Timing: real 0m0.032s user 0m0.006s sys 0m0.006s '68.39.8' ************** PARI ***************** Host 68.39.84.231 (68.39.84.231) Time: Mon Jul 31 18:59:13 2006 Input: (x/2)=(3x/4)+5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: (x/2)=(3x/4)+5 ^--------- Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.39.8' ************** PARI ***************** Host 68.39.84.231 (68.39.84.231) Time: Mon Jul 31 18:58:22 2006 Input: x/2=3x/4+5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: x/2=3x/4+5 ^------- Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '131.172' ************** PARI ***************** Host 131.172.42.15 (131.172.42.15) Time: Mon Jul 31 18:09:53 2006 Input: default(realprecision,100) Pi Output: WARNING: PARI command contains unsafe command 'default', so it will not be executed. '131.172' ************** PARI ***************** Host 131.172.42.15 (131.172.42.15) Time: Mon Jul 31 18:08:46 2006 Input: Pi Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3.1415926535897932384626433832795028842 ? Goodbye! Errors/timing (if any): Timing: real 0m0.086s user 0m0.006s sys 0m0.006s '65.64.1' ************** PARI ***************** Host 65.64.101.176 (65.64.101.176) Time: Mon Jul 31 18:04:55 2006 Input: 163 divided by 7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = dividedby7 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: dividedby7. Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Mon Jul 31 18:04:27 2006 Input: znorder(Mod(17, 7)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6 ? Goodbye! Errors/timing (if any): Timing: real 0m0.047s user 0m0.006s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Mon Jul 31 18:00:27 2006 Input: Mod(17, 7) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(3, 7) ? Goodbye! Errors/timing (if any): Timing: real 0m0.064s user 0m0.009s sys 0m0.006s '83.130.' ************** PARI ***************** Host 83.130.58.173 (83.130.58.173) Time: Mon Jul 31 13:55:31 2006 Input: c100 = 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139; factor(c100); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 5488 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.011s user 0m20.991s sys 0m0.008s '83.130.' ************** PARI ***************** Host 83.130.58.173 (83.130.58.173) Time: Mon Jul 31 13:53:05 2006 Input: print("***",factor(129)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ***[3, 1; 43, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '83.130.' ************** PARI ***************** Host 83.130.58.173 (83.130.58.173) Time: Mon Jul 31 13:51:51 2006 Input: factor(129^20+1) /ra ?0 r=123456; print(factor(r)); print("Hullo"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [41 1] [281 1] [5486561 1] [138461441 1] [93034702779013170299681 1] ? ? x ? ? [2, 6; 3, 1; 643, 1] ? Hullo ? Goodbye! Errors/timing (if any): *** unexpected character: /ra ^--- Timing: real 0m0.049s user 0m0.036s sys 0m0.014s '83.130.' ************** PARI ***************** Host 83.130.58.173 (83.130.58.173) Time: Mon Jul 31 13:51:19 2006 Input: factor(129^20+1) /ra ?0 r=123456; print(factor(r)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [41 1] [281 1] [5486561 1] [138461441 1] [93034702779013170299681 1] ? ? x ? ? [2, 6; 3, 1; 643, 1] ? Goodbye! Errors/timing (if any): *** unexpected character: /ra ^--- Timing: real 0m0.051s user 0m0.039s sys 0m0.012s '83.130.' ************** PARI ***************** Host 83.130.58.173 (83.130.58.173) Time: Mon Jul 31 13:50:49 2006 Input: factor(129^20+1) /ra ?0 r=123456; print(factor(r)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [41 1] [281 1] [5486561 1] [138461441 1] [93034702779013170299681 1] ? ? x ? ? [2, 6; 3, 1; 643, 1] ? Goodbye! Errors/timing (if any): *** unexpected character: /ra ^--- Timing: real 0m0.049s user 0m0.038s sys 0m0.011s '83.130.' ************** PARI ***************** Host 83.130.58.173 (83.130.58.173) Time: Mon Jul 31 13:49:48 2006 Input: factor(129^20+1) /ra ?0 r=123456; factor(r); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [41 1] [281 1] [5486561 1] [138461441 1] [93034702779013170299681 1] ? ? x ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: /ra ^--- Timing: real 0m0.094s user 0m0.042s sys 0m0.009s '83.130.' ************** PARI ***************** Host 83.130.58.173 (83.130.58.173) Time: Mon Jul 31 11:52:18 2006 Input: factor(129) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [43 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '128.111' ************** PARI ***************** Host 128.111.88.139 (128.111.88.139) Time: Mon Jul 31 09:35:01 2006 Input: qfbclassno(-1234567) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 496 ? Goodbye! Errors/timing (if any): Timing: real 0m0.178s user 0m0.007s sys 0m0.008s '72.30.1' ************** PARI ***************** Host 72.30.103.96 (72.30.103.96) Time: Mon Jul 31 09:25:47 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.080s user 0m0.006s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Mon Jul 31 02:39:35 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 2000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 1002---0000 1004---0000 1006---0000 1008---0000 1010---0000 1012---0000 1014---0000 1016---0000 1018---0000 1020---0000 1022---0000 1024---0000 1026---0000 1028---0000 1030---0000 1032---0000 1034---0000 1036---0000 1038---0000 1040---0000 1042---0000 1044---0000 1046---0000 1048---0000 1050---0000 1052---0000 1054---0000 1056---0000 1058---0000 1060---0000 1062---0000 1064---0000 1066---0000 1068---0000 1070---0000 1072---0000 1074---0000 1076---0000 1078---0000 1080---0000 1082---0000 1084---0000 1086---0000 1088---0000 1090---0000 1092---0000 1094---0000 1096---0000 1098---0000 1100---0000 1102---0000 1104---0000 1106---0000 1108---0000 1110---0000 1112---0000 1114---0000 1116---0000 1118---0000 1120---0000 1122---0000 1124---0000 1126---0000 1128---0000 1130---0000 1132---0000 1134---0000 1136---0000 1138---0000 1140---0000 1142---0000 1144---0000 1146---0000 1148---0000 1150---0000 1152---0000 1154---0000 1156---0000 1158---0000 1160---0000 1162---0000 1164---0000 1166---0000 1168---0000 1170---0000 1172---0000 1174---0000 1176---0000 1178---0000 1180---0000 1182---0000 1184---0000 1186---0000 1188---0000 1190---0000 1192---0000 1194---0000 1196---0000 1198---0000 1200---0000 1202---0000 1204---0000 1206---0000 1208---0000 1210---0000 1212---0000 1214---0000 1216---0000 1218---0000 1220---0000 1222---0000 1224---0000 1226---0000 1228---0000 1230---0000 1232---0000 1234---0000 1236---0000 1238---0000 1240---0000 1242---0000 1244---0000 1246---0000 1248---0000 1250---0000 1252---0000 1254---0000 1256---0000 1258---0000 1260---0000 1262---0000 1264---0000 1266---0000 1268---0000 1270---0000 1272---0000 1274---0000 1276---0000 1278---0000 1280---0000 1282---0000 1284---0000 1286---0000 1288---0000 1290---0000 1292---0000 1294---0000 1296---0000 1298---0000 1300---0000 1302---0000 1304---0000 1306---0000 1308---0000 1310---0000 1312---0000 1314---0000 1316---0000 1318---0000 1320---0000 1322---0000 1324---0000 1326---0000 1328---0000 1330---0000 1332---0000 1334---0000 1336---0000 1338---0000 1340---0000 1342---0000 1344---0000 1346---0000 1348---0000 1350---0000 1352---0000 1354---0000 1356---0000 1358---0000 1360---0000 1362---0000 1364---0000 1366---0000 1368---0000 1370---0000 1372---0000 1374---0000 1376---0000 1378---0000 1380---0000 1382---0000 1384---0000 1386---0000 1388---0000 1390---0000 1392---0000 1394---0000 1396---0000 1398---0000 1400---0000 1402---0000 1404---0000 1406---0000 1408---0000 1410---0000 1412---0000 1414---0000 1416---0000 1418---0000 1420---0000 1422---0000 1424---0000 1426---0000 1428---0000 1430---0000 1432---0000 1434---0000 1436---0000 1438---0000 1440---0000 1442---0000 1444---0000 1446---0000 1448---0000 1450---0000 1452---0000 1454---0000 1456---0000 1458---0000 1460---0000 1462---0000 1464---0000 1466---0000 1468---0000 1470---0000 1472---0000 1474---0000 1476---0000 1478---0000 1480---0000 1482---0000 1484---0000 1486---0000 1488---0000 1490---0000 1492---0000 1494---0000 1496---0000 1498---0000 1500---0000 1502---0000 1504---0000 1506---0000 1508---0000 1510---0000 1512---0000 1514---0000 1516---0000 1518---0000 1520---0000 1522---0000 1524---0000 1526---0000 1528---0000 1530---0000 1532---0000 1534---0000 1536---0000 1538---0000 1540---0000 1542---0000 1544---0000 1546---0000 1548---0000 1550---0000 1552---0000 1554---0000 1556---0000 1558---0000 1560---0000 1562---0000 1564---0000 1566---0000 1568---0000 1570---0000 1572---0000 1574---0000 1576---0000 1578---0000 1580---0000 1582---0000 1584---0000 1586---0000 1588---0000 1590---0000 1592---0000 1594---0000 1596---0000 1598---0000 1600---0000 1602---0000 1604---0000 1606---0000 1608---0000 1610---0000 1612---0000 1614---0000 1616---0000 1618---0000 1620---0000 1622---0000 1624---0000 1626---0000 1628---0000 1630---0000 1632---0000 1634---0000 1636---0000 1638---0000 1640---0000 1642---0000 1644---0000 1646---0000 1648---0000 1650---0000 1652---0000 1654---0000 1656---0000 1658---0000 1660---0000 1662---0000 1664---0000 1666---0000 1668---0000 1670---0000 1672---0000 1674---0000 1676---0000 1678---0000 1680---0000 1682---0000 1684---0000 1686---0000 1688---0000 1690---0000 1692---0000 1694---0000 1696---0000 1698---0000 1700---0000 1702---0000 1704---0000 1706---0000 1708---0000 1710---0000 1712---0000 1714---0000 1716---0000 1718---0000 1720---0000 1722---0000 1724---0000 1726 ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m7.495s user 0m3.858s sys 0m0.015s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Mon Jul 31 01:56:58 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m3.692s user 0m1.864s sys 0m0.012s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Mon Jul 31 01:56:47 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=0, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? ? ? Goodbye! Errors/timing (if any): *** nfinit: reducible polynomial in nfinit. Timing: real 0m0.015s user 0m0.009s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Mon Jul 31 01:56:37 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=1, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? ? ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. Timing: real 0m0.109s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Mon Jul 31 01:56:10 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=1300, 3300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 1300---0000 1302---0000 1304---0000 1306---0000 1308---0000 1310---0000 1312---0000 1314---0000 1316---0000 1318---0000 1320---0000 1322---0000 1324---0000 1326---0000 1328---0000 1330---0000 1332---0000 1334---0000 1336---0000 1338---0000 1340---0000 1342---0000 1344---0000 1346---0000 1348---0000 1350---0000 1352---0000 1354---0000 1356---0000 1358---0000 1360---0000 1362---0000 1364---0000 1366---0000 1368---0000 1370---0000 1372---0000 1374---0000 1376---0000 1378---0000 1380---0000 1382---0000 1384---0000 1386---0000 1388---0000 1390---0000 1392---0000 1394---0000 1396---0000 1398---0000 1400---0000 1402---0000 1404---0000 1406---0000 1408---0000 1410---0000 1412---0000 1414---0000 1416---0000 1418---0000 1420---0000 1422---0000 1424---0000 1426---0000 1428---0000 1430---0000 1432---0000 1434---0000 1436---0000 1438---0000 1440---0000 1442---0000 1444---0000 1446---0000 1448---0000 1450---0000 1452---0000 1454---0000 1456---0000 1458---0000 1460---0000 1462---0000 1464---0000 1466---0000 1468---0000 1470---0000 1472---0000 1474---0000 1476---0000 1478---0000 1480---0000 1482---0000 1484---0000 1486---0000 1488---0000 1490---0000 1492---0000 1494---0000 1496---0000 1498---0000 1500---0000 1502---0000 1504---0000 1506---0000 1508---0000 1510---0000 1512---0000 1514---0000 1516---0000 1518---0000 1520---0000 1522---0000 1524---0000 1526---0000 1528---0000 1530---0000 1532---0000 1534---0000 1536---0000 1538---0000 1540---0000 1542---0000 1544---0000 1546---0000 1548---0000 1550---0000 1552---0000 1554---0000 1556---0000 1558---0000 1560---0000 1562---0000 1564---0000 1566---0000 1568---0000 1570---0000 1572---0000 1574---0000 1576---0000 1578---0000 1580---0000 1582---0000 1584---0000 1586---0000 1588---0000 1590---0000 1592---0000 1594---0000 1596---0000 1598---0000 1600---0000 1602---0000 1604---0000 1606---0000 1608---0000 1610---0000 1612---0000 1614---0000 1616---0000 1618---0000 1620---0000 1622---0000 1624---0000 1626---0000 1628---0000 1630---0000 1632---0000 1634---0000 1636---0000 1638---0000 1640---0000 1642---0000 1644---0000 1646---0000 1648---0000 1650---0000 1652---0000 1654---0000 1656---0000 1658---0000 1660---0000 1662---0000 1664---0000 1666---0000 1668---0000 1670---0000 1672---0000 1674---0000 1676---0000 1678---0000 1680---0000 1682---0000 1684---0000 1686---0000 1688---0000 1690---0000 1692---0000 1694---0000 1696---0000 1698---0000 1700---0000 1702---0000 1704---0000 1706---0000 1708---0000 1710---0000 1712---0000 1714---0000 1716---0000 1718---0000 1720---0000 1722---0000 1724---0000 1726---0000 1728---0000 1730---0000 1732---0000 1734---0000 1736---0000 1738---0000 1740---0000 1742---0000 1744---0000 1746---0000 1748---0000 1750---0000 1752---0000 1754---0000 1756---0000 1758---0000 1760---0000 1762---0000 1764---0000 1766---0000 1768---0000 1770---0000 1772---0000 1774---0000 1776---0000 1778---0000 1780---0000 1782---0000 1784---0000 1786---0000 1788---0000 1790---0000 1792---0000 1794---0000 1796---0000 1798---0000 1800---0000 1802---0000 1804---0000 1806---0000 1808---0000 1810---0000 1812---0000 1814---0000 1816---0000 1818---0000 1820---0000 1822---0000 1824---0000 1826---0000 1828---0000 1830---0000 1832---0000 1834---0000 1836---0000 1838---0000 1840---0000 1842---0000 1844---0000 1846---0000 1848---0000 1850---0000 1852---0000 1854---0000 1856---0000 1858---0000 1860---0000 1862---0000 1864---0000 1866---0000 1868---0000 1870---0000 1872---0000 1874---0000 1876---0000 1878---0000 1880---0000 1882---0000 1884---0000 1886---0000 1888---0000 1890---0000 1892---0000 1894---0000 1896---0000 1898---0000 1900---0000 1902---0000 1904---0000 1906---0000 1908---0000 1910---0000 1912---0000 1914---0000 1916---0000 1918---0000 1920---0000 1922---0000 1924---0000 1926---0000 1928---0000 1930---0000 1932---0000 1934---0000 1936---0000 1938---0000 1940---0000 1942---0000 1944---0000 1946---0000 1948---0000 1950---0000 1952---0000 1954---0000 1956---0000 1958---0000 1960---0000 1962---0000 1964---0000 1966---0000 1968---0000 1970---0000 1972---0000 1974---0000 1976---0000 1978---0000 1980---0000 1982---0000 1984---0000 1986---0000 1988---0000 1990---0000 1992---0000 1994---0000 1996---0000 1998---0000 2000---0000 2002---0000 2004---0000 2006---0000 2008---0000 2010---0000 2012---0000 2014---0000 2016---0000 2018---0000 2020---0000 2022---0000 2024---0000 2026---0000 2028---0000 2030---0000 2032---0000 2034---0000 2036---0000 2038---0000 2040---0000 2042---0000 2044---0000 2046---0000 2048---0000 2050---0000 2052---0000 2054---0000 2056---0000 2058---0000 2060---0000 2062---0000 2064---0000 2066---0000 2068---0000 2070---0000 2072---0000 2074---0000 2076---0000 2078---0000 2080---0000 2082---0000 2084---0000 2086---0000 2088---0000 2090---0000 2092---0000 2094---0000 2096---0000 2098---0000 2100---0000 2102---0000 2104---0000 2106---0000 2108---0000 2110---0000 2112---0000 2114---0000 2116---0000 2118---0000 2120---0000 2122---0000 2124---0000 2126---0000 2128---0000 2130---0000 2132---0000 2134---0000 2136---0000 2138---0000 2140---0000 2142---0000 2144---0000 2146---0000 2148---0000 2150---0000 2152---0000 2154---0000 2156---0000 2158---0000 2160---0000 2162---0000 2164---0000 2166---0000 2168---0000 2170---0000 2172---0000 2174---0000 2176---0000 2178---0000 2180---0000 2182---0000 2184---0000 2186---0000 2188---0000 2190---0000 2192---0000 2194---0000 2196---0000 2198---0000 2200---0000 2202---0000 2204---0000 2206---0000 2208---0000 2210---0000 2212---0000 2214---0000 2216---0000 2218---0000 2220---0000 2222---0000 2224---0000 2226---0000 2228---0000 2230---0000 2232---0000 2234---0000 2236---0000 2238---0000 2240---0000 2242---0000 2244---0000 2246---0000 2248---0000 2250---0000 2252---0000 2254---0000 2256---0000 2258---0000 2260---0000 2262---0000 2264---0000 2266---0000 2268---0000 2270---0000 2272---0000 2274---0000 2276---0000 2278---0000 2280---0000 2282---0000 2284---0000 2286---0000 2288---0000 2290---0000 2292---0000 2294---0000 2296---0000 2298---0000 2300---0000 2302---0000 2304---0000 2306---0000 2308---0000 2310---0000 2312---0000 2314---0000 2316---0000 2318---0000 2320---0000 2322---0000 2324---0000 2326---0000 2328---0000 2330---0000 2332---0000 2334---0000 2336---0000 2338---0000 2340---0000 2342---0000 2344---0000 2346---0000 2348---0000 2350---0000 2352---0000 2354---0000 2356---0000 2358---0000 2360---0000 2362---0000 2364---0000 2366---0000 2368---0000 2370---0000 2372---0000 2374---0000 2376---0000 2378---0000 2380---0000 2382---0000 2384---0000 2386---0000 2388---0000 2390---0000 2392---0000 2394---0000 2396---0000 2398---0000 2400---0000 2402---0000 2404---0000 2406---0000 2408---0000 2410---0000 2412---0000 2414---0000 2416---0000 2418---0000 2420---0000 2422---0000 2424---0000 2426---0000 2428---0000 2430---0000 2432---0000 2434---0000 2436---0000 2438---0000 2440---0000 2442---0000 2444---0000 2446---0000 2448---0000 2450---0000 2452---0000 2454---0000 2456---0000 2458---0000 2460---0000 2462---0000 2464---0000 2466---0000 2468---0000 2470---0000 2472---0000 2474---0000 2476---0000 2478---0000 2480---0000 2482---0000 2484---0000 2486---0000 2488---0000 2490---0000 2492---0000 2494---0000 2496---0000 2498---0000 2500---0000 2502---0000 2504---0000 2506---0000 2508---0000 2510---0000 2512---0000 2514---0000 2516---0000 2518---0000 2520---0000 2522---0000 2524---0000 2526---0000 2528---0000 2530---0000 2532---0000 2534---0000 2536---0000 2538---0000 2540---0000 2542---0000 2544---0000 2546---0000 2548---0000 2550---0000 2552---0000 2554---0000 2556---0000 2558---0000 2560---0000 2562---0000 2564---0000 2566---0000 2568---0000 2570---0000 2572---0000 2574---0000 2576---0000 2578---0000 2580---0000 2582---0000 2584---0000 2586---0000 2588---0000 2590---0000 2592---0000 2594---0000 2596---0000 2598---0000 2600---0000 2602---0000 2604---0000 2606---0000 2608---0000 2610---0000 2612---0000 2614---0000 2616---0000 2618---0000 2620---0000 2622---0000 2624---0000 2626---0000 2628---0000 2630---0000 2632---0000 2634---0000 2636---0000 2638---0000 2640---0000 2642---0000 2644---0000 2646---0000 2648---0000 2650---0000 2652---0000 2654---0000 2656---0000 2658---0000 2660---0000 2662---0000 2664---0000 2666---0000 2668---0000 2670---0000 2672---0000 2674---0000 2676---0000 2678---0000 2680---0000 2682---0000 2684---0000 2686---0000 2688---0000 2690---0000 2692---0000 2694---0000 2696---0000 2698---0000 2700---0000 2702---0000 2704---0000 2706---0000 2708---0000 2710---0000 2712---0000 2714---0000 2716---0000 2718---0000 2720---0000 2722---0000 2724---0000 2726---0000 2728---0000 2730---0000 2732---0000 2734---0000 2736---0000 2738---0000 2740---0000 2742---0000 2744---0000 2746---0000 2748---0000 2750---0000 2752---0000 2754---0000 2756---0000 2758---0000 2760---0000 2762---0000 2764---0000 2766---0000 2768---0000 2770---0000 2772---0000 2774---0000 2776---0000 2778---0000 2780---0000 2782---0000 2784---0000 2786---0000 2788---0000 2790---0000 2792---0000 2794---0000 2796---0000 2798---0000 2800---0000 2802---0000 2804---0000 2806---0000 2808---0000 2810---0000 2812---0000 2814---0000 2816---0000 2818---0000 2820---0000 2822---0000 2824---0000 2826---0000 2828---0000 2830---0000 2832---0000 2834---0000 2836---0000 2838---0000 2840---0000 2842---0000 2844---0000 2846---0000 2848---0000 2850---0000 2852---0000 2854---0000 2856---0000 2858---0000 2860---0000 2862---0000 2864---0000 2866---0000 2868---0000 2870---0000 2872---0000 2874---0000 2876---0000 2878---0000 2880---0000 2882---0000 2884---0000 2886---0000 2888---0000 2890---0000 2892---0000 2894---0000 2896---0000 2898---0000 2900---0000 2902---0000 2904---0000 2906---0000 2908---0000 2910---0000 2912---0000 2914---0000 2916---0000 2918---0000 2920---0000 2922---0000 2924---0000 2926---0000 2928---0000 2930---0000 2932 ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m8.388s user 0m4.103s sys 0m0.022s '24.155.' ************** PARI ***************** Host 24.155.217.187 (24.155.217.187) Time: Sun Jul 30 15:21:46 2006 Input: what is 39.59 + 16.75% of tax Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '72.30.1' ************** PARI ***************** Host 72.30.102.206 (72.30.102.206) Time: Sun Jul 30 04:46:27 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.066s user 0m0.006s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sun Jul 30 00:49:59 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.023s user 0m0.007s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:45:58 2006 Input: [1+0+1+1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.003s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:16:46 2006 Input: [1,1,0,1;1,0,1,1;0,1,1,1;1,1,1,0]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 2 2 2] [2 3 2 2] [2 2 3 2] [2 2 2 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:16:31 2006 Input: [1,1,0,1;1,0,1,1;0,1,1,1;1,1,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 0 1] [1 0 1 1] [0 1 1 1] [1 1 1 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:11:46 2006 Input: [1,0,0,0;1,1,0,0;0,1,1,0;0,0,1,1]^6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0 0] [6 1 0 0] [15 6 1 0] [20 15 6 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:11:35 2006 Input: [1,0,0,0;1,1,0,0;0,1,1,0;0,0,1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0 0] [2 1 0 0] [1 2 1 0] [0 1 2 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:11:21 2006 Input: [1,0,0,0;1,1,0,0;0,1,1,0;0,0,1,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0 0] [3 1 0 0] [3 3 1 0] [1 3 3 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:08:08 2006 Input: [1,1,0,0;0,1,1,0;0,0,1,1;1,0,0,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 3 3 1] [1 1 3 3] [3 1 1 3] [3 3 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:07:51 2006 Input: [1,1,0,0;0,1,1,0;0,0,1,1;1,0,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 2 1 0] [0 1 2 1] [1 0 1 2] [2 1 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.102s user 0m0.003s sys 0m0.010s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:07:41 2006 Input: [1,1,0,0;0,1,1,0;0,0,1,1;1,0,0,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 0 0] [0 1 1 0] [0 0 1 1] [1 0 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:03:07 2006 Input: [0,1,1,1;1,1,0,1;1,0,1,1;1,1,1,0]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 2 2 2] [2 3 2 2] [2 2 3 2] [2 2 2 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 23:02:53 2006 Input: [0,1,1,1;1,1,0,1;1,0,1,1;1,1,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 1 1] [1 1 0 1] [1 0 1 1] [1 1 1 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:58:38 2006 Input: [0,1,1,0;0,1,1,0;1,0,0,1;1,0,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 1 1] [1 1 1 1] [1 1 1 1] [1 1 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:58:23 2006 Input: [0,1,1,0;0,1,1,0;1,0,0,1;1,0,0,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 1 0] [0 1 1 0] [1 0 0 1] [1 0 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:55:54 2006 Input: [1,0,0,1;1,0,1,0;0,1,1,0;0,1,0,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 2 1 3] [2 2 2 2] [2 2 3 1] [2 2 2 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:55:23 2006 Input: [1,0,0,1;1,0,1,0;0,1,1,0;0,1,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 0 2] [1 1 1 1] [1 1 2 0] [1 1 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.007s sys 0m0.004s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:55:08 2006 Input: [1,0,0,1;1,0,1,0;0,1,1,0;0,1,0,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0 1] [1 0 1 0] [0 1 1 0] [0 1 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:47:23 2006 Input: [1,1,1,0;1,1,0,1;0,1,1,1;1,0,1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 2 2] [3 2 2 2] [2 2 2 3] [2 2 3 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:47:04 2006 Input: [1,1,1,0;1,1,0,1;0,1,1,1;1,0,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 1 0] [1 1 0 1] [0 1 1 1] [1 0 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:45:02 2006 Input: [1,0,1,0;1,0,1,0;0,1,0,1;0,1,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 1 1] [1 1 1 1] [1 1 1 1] [1 1 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:43:38 2006 Input: [1,0,1,0;1,0,1,0;0,1,0,1;0,1,0,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 1 0] [1 0 1 0] [0 1 0 1] [0 1 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.004s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:40:20 2006 Input: [0,1,1,1;1,0,1,1;1,1,0,1;1,1,1,0]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 2 2 2] [2 3 2 2] [2 2 3 2] [2 2 2 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:40:06 2006 Input: [0,1,1,1;1,0,1,1;1,1,0,1;1,1,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 1 1 1] [1 0 1 1] [1 1 0 1] [1 1 1 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:35:46 2006 Input: [1,0,0,1;1,0,0,1;0,1,1,0;0,1,1,0]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 1 1] [1 1 1 1] [1 1 1 1] [1 1 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.032s user 0m0.007s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 29 22:35:24 2006 Input: [1,0,0,1;1,0,0,1;0,1,1,0;0,1,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0 1] [1 0 0 1] [0 1 1 0] [0 1 1 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.190s user 0m0.007s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Sat Jul 29 20:23:17 2006 Input: contfrac(4*sqrt(11)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7, 1, 1, 1, 7, 2, 7] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Sat Jul 29 20:23:00 2006 Input: contfrac(3*sqrt(11)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 2, 1, 1, 32, 1, 1, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Sat Jul 29 20:22:53 2006 Input: contfrac(2*sqrt(11)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 2, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.056s user 0m0.007s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Sat Jul 29 20:22:28 2006 Input: contfrac(sqrt(11)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 4, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 8, 1, 1, 10, 1, 1, 9] ? Goodbye! Errors/timing (if any): Timing: real 0m0.071s user 0m0.007s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Sat Jul 29 20:22:07 2006 Input: contfrac(2*sqrt(11)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 2, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3, 1, 4, 1, 3, 4, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.072s user 0m0.007s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Sat Jul 29 20:19:14 2006 Input: contfrac(3/5+2*sqrt(11)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 23, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Sat Jul 29 20:18:14 2006 Input: contfrac(3/5+2*sqrt(5)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 8, 1, 4, 2, 14, 2, 4, 1, 7, 1, 1, 3, 5, 12, 134, 12, 5, 3, 1, 1, 7, 1, 4, 2, 14, 2, 4, 1, 7, 1, 1, 3, 4] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Sat Jul 29 20:17:27 2006 Input: contfrac(3/5+2*sqrt(7)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 20, 5, 1, 4, 1, 5, 19, 1, 2, 22, 2, 1, 19, 5, 1, 4, 1, 5, 19, 1, 2, 22, 2, 1, 19, 5, 1, 4, 1, 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Sat Jul 29 20:17:14 2006 Input: contfrac(3/5+2*sqrt(39)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:45:45 2006 Input: contfrac(3/5+2*sqrt(13)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 12, 2, 1, 1, 2, 7, 13, 2, 1, 1, 2, 7, 13, 2, 1, 1, 2, 7, 13, 2, 1, 1, 2, 7, 13, 2, 1, 1, 2, 7, 13, 2, 1, 1, 2, 7] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:45:28 2006 Input: contfrac(3/5+2*sqrt(11)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 23, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5, 24, 1, 2, 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:45:16 2006 Input: contfrac(3/5+2*sqrt(10)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 46, 4, 1, 1, 1, 1, 5, 1, 1, 20, 1, 1, 5, 1, 1, 1, 1, 4, 47, 4, 1, 1, 1, 1, 5, 1, 1, 20, 1, 1, 5, 1, 1, 1, 1, 4, 47, 4, 1, 1, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:44:48 2006 Input: contfrac(3/5+2*sqrt(7)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 20, 5, 1, 4, 1, 5, 19, 1, 2, 22, 2, 1, 19, 5, 1, 4, 1, 5, 19, 1, 2, 22, 2, 1, 19, 5, 1, 4, 1, 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.007s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:44:09 2006 Input: contfrac(3/5+2*sqrt(5)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 8, 1, 4, 2, 14, 2, 4, 1, 7, 1, 1, 3, 5, 12, 134, 12, 5, 3, 1, 1, 7, 1, 4, 2, 14, 2, 4, 1, 7, 1, 1, 3, 4] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:43:58 2006 Input: contfrac(3/5+2*sqrt(3)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 4, 1, 10, 1, 3, 2, 2, 2, 3, 1, 10, 1, 3, 2, 2, 2, 3, 1, 10, 1, 3, 2, 2, 2, 3, 1, 10, 1, 3, 2, 2, 2, 3, 1, 10, 1, 3, 2, 2, 2, 3, 1, 10, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.054s user 0m0.008s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:43:30 2006 Input: contfrac(3/5+2*sqrt(2)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 3, 1, 2, 1, 2, 3, 3, 10, 3, 3, 2, 1, 2, 1, 2, 3, 3, 10, 3, 3, 2, 1, 2, 1, 2, 3, 3, 10, 3, 3, 2, 1, 2, 1, 2, 3, 3, 10, 3, 3, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:42:19 2006 Input: contfrac(3/5+2*sqrt(39)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.031s user 0m0.007s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:42:01 2006 Input: contfrac(2*sqrt(39)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 4, 1, 40, 1, 4, 2, 4, 1, 40, 1, 4, 2, 4, 1, 40, 1, 4, 2, 4, 1, 40, 1, 4, 2, 4, 1, 40, 1, 4, 2, 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.047s user 0m0.005s sys 0m0.009s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:41:45 2006 Input: contfrac(sqrt(39)/15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 2, 2, 2, 20, 2, 2, 4, 2, 2, 20, 2, 2, 4, 2, 2, 20, 2, 2, 4, 2, 2, 20, 2, 2, 4, 2, 2, 20, 2, 2, 4, 2, 2, 20] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:41:31 2006 Input: contfrac(sqrt(39)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.047s user 0m0.005s sys 0m0.008s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:30:24 2006 Input: contfrac(sqrt(7)/17) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 6, 2, 2, 1, 5, 1, 2, 2, 12, 2, 2, 1, 5, 1, 2, 2, 12, 2, 2, 1, 5, 1, 2, 2, 12, 2, 2, 1, 5, 1, 2, 2, 12, 2, 2, 1, 5, 1, 2, 2, 12, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:30:15 2006 Input: contfrac(sqrt(7)/16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 6, 21, 12, 21, 12, 21, 12, 21, 12, 21, 12, 21, 12, 21, 12, 21] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:30:08 2006 Input: contfrac(sqrt(7)/7) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:29:54 2006 Input: contfrac(sqrt(7)/5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 7] ? Goodbye! Errors/timing (if any): Timing: real 0m0.041s user 0m0.009s sys 0m0.003s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:29:19 2006 Input: contfrac((2+sqrt(7))/5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 13, 8, 1, 2, 1, 8, 12] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.204.151 (164.107.204.151) Time: Sat Jul 29 18:29:11 2006 Input: contfrac((2+sqrt(7))/3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.127s user 0m0.007s sys 0m0.006s '24.118.' ************** PARI ***************** Host 24.118.196.126 (24.118.196.126) Time: Sat Jul 29 16:11:30 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.004s '72.30.9' ************** PARI ***************** Host 72.30.98.136 (72.30.98.136) Time: Sat Jul 29 14:56:22 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.086s user 0m0.007s sys 0m0.009s '67.182.' ************** PARI ***************** Host 67.182.66.86 (67.182.66.86) Time: Sat Jul 29 10:35:47 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.250s user 0m0.006s sys 0m0.008s '65.54.1' ************** PARI ***************** Host 65.54.188.53 (65.54.188.53) Time: Fri Jul 28 22:13:16 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '66.142.' ************** PARI ***************** Host 66.142.153.233 (66.142.153.233) Time: Fri Jul 28 21:37:08 2006 Input: 500000000*0.016 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7999999.9999999999999999999999999999999 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:52:06 2006 Input: contfrac(43^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:51:59 2006 Input: contfrac(42^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:51:56 2006 Input: contfrac(42^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:51:47 2006 Input: contfrac(41^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2, 2, 12, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:51:39 2006 Input: contfrac(40^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:51:28 2006 Input: contfrac(38^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 11] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:51:21 2006 Input: contfrac(37^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:51:14 2006 Input: contfrac(35^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:51:07 2006 Input: contfrac(34^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 10, 1, 4, 1, 11] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:50:59 2006 Input: contfrac(33^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 11] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:50:19 2006 Input: contfrac(31^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:50:08 2006 Input: contfrac(30^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 9] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:49:56 2006 Input: contfrac(29^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2, 10, 2, 1, 1, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:49:45 2006 Input: contfrac(26^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:48:32 2006 Input: contfrac(23^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [4, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 8, 1, 3, 1, 9] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:48:13 2006 Input: contfrac(22^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [4, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2, 4, 2, 1, 8, 1, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:47:56 2006 Input: contfrac(21^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [4, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 1, 1, 2, 1, 1, 8, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:47:37 2006 Input: contfrac(15^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 7] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:47:27 2006 Input: contfrac(14^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:47:10 2006 Input: contfrac(13^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 1, 1, 7] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:46:53 2006 Input: contfrac(11^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:45:25 2006 Input: contfrac(259^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [16, 10, 1, 2, 3, 4, 3, 2, 1, 10, 32, 10, 1, 2, 3, 4, 3, 2, 1, 10, 32, 10, 1, 2, 3, 4, 3, 2, 1, 10] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:42:43 2006 Input: contfrac(199^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [14, 9, 2, 1, 2, 2, 5, 4, 1, 1, 13, 1, 1, 4, 5, 2, 2, 1, 2, 9, 28, 9, 2, 1, 2, 2, 5, 4, 1, 1, 13, 1, 1, 4, 5, 2, 2, 1, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:41:51 2006 Input: contfrac(172^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [13, 8, 1, 2, 2, 1, 1, 3, 6, 3, 1, 1, 2, 2, 1, 8, 26, 8, 1, 2, 2, 1, 1, 3, 6, 3, 1, 1, 2, 2, 1, 8, 26, 8, 1, 2, 2, 1, 1, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:41:24 2006 Input: contfrac(147^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [12, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 23] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:38:28 2006 Input: contfrac(84^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [9, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 17] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:37:46 2006 Input: contfrac(124^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [11, 7, 2, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 2, 7, 22, 7, 2, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 2, 7, 22, 7, 2, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:37:32 2006 Input: contfrac(28^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:37:11 2006 Input: contfrac(28^(1/2)) contfracpnqn(%) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:35:14 2006 Input: contfrac(28^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:29:49 2006 Input: contfrac(103^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [10, 6, 1, 2, 1, 1, 9, 1, 1, 2, 1, 6, 20, 6, 1, 2, 1, 1, 9, 1, 1, 2, 1, 6, 20, 6, 1, 2, 1, 1, 9, 1, 1, 2, 1, 6, 20, 6, 1, 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:28:54 2006 Input: contfrac(2^(1/2), 10, 90) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:28:39 2006 Input: contfrac(2^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:27:49 2006 Input: contfrac(sqrt(67)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [8, 5, 2, 1, 1, 7, 1, 1, 2, 5, 16, 5, 2, 1, 1, 7, 1, 1, 2, 5, 16, 5, 2, 1, 1, 7, 1, 1, 2, 5, 16, 5, 2, 1, 1, 7, 1, 1, 2, 4] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:27:20 2006 Input: contfrac(39^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 11] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:27:05 2006 Input: contfrac(19^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [4, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 3, 1, 2, 8, 2, 1, 4] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:26:58 2006 Input: contfrac(7^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 4, 1, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:26:12 2006 Input: contfrac(2^(1/3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 3, 1, 5, 1, 1, 4, 1, 1, 8, 1, 14, 1, 10, 2, 1, 4, 12, 2, 3, 2, 1, 3, 4, 1, 1, 2, 14, 3, 12, 1, 15, 3, 1, 4] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:26:00 2006 Input: contfrac(2^(1/2)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:24:54 2006 Input: contfrac(2^{1/2},5,5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:24:22 2006 Input: contfrac(2^{1/2}) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:23:54 2006 Input: contfrac(7/5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '164.107' ************** PARI ***************** Host 164.107.205.56 (164.107.205.56) Time: Fri Jul 28 20:22:53 2006 Input: contfrac(2^{1/3}) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1, 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '207.38.' ************** PARI ***************** Host 207.38.199.36 (207.38.199.36) Time: Fri Jul 28 18:27:56 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '69.118.' ************** PARI ***************** Host 69.118.114.229 (69.118.114.229) Time: Fri Jul 28 15:34:34 2006 Input: 25x20 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x20 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x20. Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '69.152.' ************** PARI ***************** Host 69.152.202.120 (69.152.202.120) Time: Fri Jul 28 15:10:08 2006 Input: 1.8643 x 12 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x12 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x12. Timing: real 0m0.077s user 0m0.007s sys 0m0.005s '70.20.1' ************** PARI ***************** Host 70.20.177.202 (70.20.177.202) Time: Fri Jul 28 14:34:26 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '70.20.1' ************** PARI ***************** Host 70.20.177.202 (70.20.177.202) Time: Fri Jul 28 14:34:21 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.038s user 0m0.004s sys 0m0.008s '70.20.1' ************** PARI ***************** Host 70.20.177.202 (70.20.177.202) Time: Fri Jul 28 14:33:21 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.096s user 0m0.007s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.132.102 (72.30.132.102) Time: Fri Jul 28 10:07:05 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.088s user 0m0.008s sys 0m0.005s '72.30.2' ************** PARI ***************** Host 72.30.226.223 (72.30.226.223) Time: Fri Jul 28 07:02:39 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m1.161s user 0m0.003s sys 0m0.012s '81.69.2' ************** PARI ***************** Host 81.69.212.71 (81.69.212.71) Time: Fri Jul 28 02:43:42 2006 Input: print gap('SymmetricGroup(7)') print kash('NumberField(X^3 + 15*X^2 - 15*X + 15)') print maxima('tan(x)').integrate('x') print singular.ring(0, '(x,y,z)', 'dp') print gp('ellinit([1,2,3,4,5])').j Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printgap('SymmetricGroup(7)') ^----- *** expected character: ',' instead of: printkash('NumberField *** (X^3+15*X^2-15*X+15) ^-------------------- *** expected character: ',' instead of: printmaxima('tan *** (x)').integrate('x') ^-------------------- *** Warning: unused characters: (0,'(x,y,z)','dp'). *** unknown member function: printsingular.ring(0,'(x,y,z)','dp ^-------------------- *** expected character: ',' instead of: printgp('ellinit([1,2,3,4,5])').j ^----------------- Timing: real 0m0.168s user 0m0.008s sys 0m0.005s '72.30.9' ************** PARI ***************** Host 72.30.98.35 (72.30.98.35) Time: Thu Jul 27 23:35:33 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.313s user 0m0.024s sys 0m0.010s '160.39.' ************** PARI ***************** Host 160.39.34.2 (160.39.34.2) Time: Thu Jul 27 19:45:36 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Thu Jul 27 19:35:17 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.144s user 0m0.024s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.111.31 (72.30.111.31) Time: Thu Jul 27 17:01:35 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.288s user 0m0.009s sys 0m0.009s '141.209' ************** PARI ***************** Host 141.209.171.175 (141.209.171.175) Time: Thu Jul 27 12:28:42 2006 Input: factor(2^256+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1238926361552897 1] [93461639715357977769163558199606896584051237541638188580280321 1] ? Goodbye! Errors/timing (if any): Timing: real 0m17.638s user 0m3.120s sys 0m0.012s '141.209' ************** PARI ***************** Host 141.209.171.175 (141.209.171.175) Time: Thu Jul 27 12:28:04 2006 Input: factor(2^256-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [5 1] [17 1] [257 1] [641 1] [65537 1] [274177 1] [6700417 1] [67280421310721 1] [59649589127497217 1] [5704689200685129054721 1] ? Goodbye! Errors/timing (if any): Timing: real 0m26.683s user 0m4.662s sys 0m0.076s '141.209' ************** PARI ***************** Host 141.209.171.175 (141.209.171.175) Time: Thu Jul 27 12:27:09 2006 Input: 200! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 788657867364790503552363213932185062295135977687173263294742533244359449963403342920304284011984623904177212138919638830257642790242637105061926624952829931113462857270763317237396988943922445621451664240254033291864131227428294853277524242407573903240321257405579568660226031904170324062351700858796178922222789623703897374720000000000000000000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.066s user 0m0.005s sys 0m0.007s '141.158' ************** PARI ***************** Host 141.158.63.163 (141.158.63.163) Time: Thu Jul 27 09:02:26 2006 Input: 66% of 480$ Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '72.30.9' ************** PARI ***************** Host 72.30.98.26 (72.30.98.26) Time: Thu Jul 27 08:25:08 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.261s user 0m0.003s sys 0m0.011s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:48:39 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=11504, 13000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? 11504---0000 11506---0000 11508---0000 11510---0000 11512---0000 11514---0000 11516---0000 11518---0000 11520---0000 11522---0000 11524---0000 11526---0000 11528---0000 11530---0000 11532---0000 11534---0000 11536---0000 11538---0000 11540---0000 11542---0000 11544---0000 11546---0000 11548---0000 11550---0000 11552---0000 11554---0000 11556---0000 11558---0000 11560---0000 11562---0000 11564---0000 11566---0000 11568---0000 11570---0000 11572---0000 11574---0000 11576---0000 11578---0000 11580---0000 11582---0000 11584---0000 11586---0000 11588---0000 11590---0000 11592---0000 11594---0000 11596---0000 11598---0000 11600---0000 11602---0000 11604---0000 11606---0000 11608---0000 11610---0000 11612---0000 11614---0000 11616---0000 11618---0000 11620---0000 11622---0000 11624---0000 11626---0000 11628---0000 11630---0000 11632---0000 11634---0000 11636---0000 11638---0000 11640---0000 11642---0000 11644---0000 11646---0000 11648---0000 11650---0000 11652---0000 11654---0000 11656---0000 11658---0000 11660---0000 11662---0000 11664---0000 11666---0000 11668---0000 11670---0000 11672---0000 11674---0000 11676---0000 11678---0000 11680---0000 11682---0000 11684---0000 11686---0000 11688---0000 11690---0000 11692---0000 11694---0000 11696---0000 11698---0000 11700---0000 11702---0000 11704---0000 11706---0000 11708---0000 11710---0000 11712---0000 11714---0000 11716---0000 11718---0000 11720---0000 11722---0000 11724---0000 11726---0000 11728---0000 11730---0000 11732---0000 11734---0000 11736---0000 11738---0000 11740---0000 11742---0000 11744---0000 11746---0000 11748---0000 11750---0000 11752---0000 11754---0000 11756---0000 11758---0000 11760---0000 11762---0000 11764---0000 11766---0000 11768---0000 11770---0000 11772---0000 11774---0000 11776---0000 11778---0000 11780---0000 11782---0000 11784---0000 11786---0000 11788---0000 11790---0000 11792---0000 11794---0000 11796---0000 11798---0000 11800---0000 11802---0000 11804---0000 11806---0000 11808---0000 11810---0000 11812---0000 11814---0000 11816---0000 11818---0000 11820---0000 11822---0000 11824---0000 11826---0000 11828---0000 11830---0000 11832---0000 11834---0000 11836---0000 11838---0000 11840---0000 11842---0000 11844---0000 11846---0000 11848---0000 11850---0000 11852---0000 11854---0000 11856---0000 11858---0000 11860---0000 11862---0000 11864---0000 11866---0000 11868---0000 11870---0000 11872---0000 11874---0000 11876---0000 11878---0000 11880---0000 11882---0000 11884---0000 11886---0000 11888---0000 11890---0000 11892---0000 11894---0000 11896---0000 11898---0000 11900---0000 11902---0000 11904---0000 11906---0000 11908---0000 11910---0000 11912---0000 11914---0000 11916---0000 11918---0000 11920---0000 11922---0000 11924---0000 11926---0000 11928---0000 11930---0000 11932---0000 11934---0000 11936---0000 11938---0000 11940---0000 11942---0000 11944---0000 11946---0000 11948---0000 11950---0000 11952---0000 11954---0000 11956---0000 11958---0000 11960---0000 11962---0000 11964---0000 11966---0000 11968---0000 11970---0000 11972---0000 11974---0000 11976---0000 11978---0000 11980---0000 11982---0000 11984---0000 11986---0000 11988---0000 11990---0000 11992---0000 11994---0000 11996---0000 11998---0000 12000---0000 12002---0000 12004---0000 12006---0000 12008---0000 12010---0000 12012---0000 12014---0000 12016---0000 12018---0000 12020---0000 12022---0000 12024---0000 12026---0000 12028---0000 12030---0000 12032---0000 12034---0000 12036---0000 12038---0000 12040---0000 12042---0000 12044---0000 12046---0000 12048---0000 12050---0000 12052---0000 12054---0000 12056---0000 12058---0000 12060---0000 12062---0000 12064---0000 12066---0000 12068---0000 12070---0000 12072---0000 12074---0000 12076---0000 12078---0000 12080---0000 12082---0000 12084---0000 12086---0000 12088---0000 12090---0000 12092---0000 12094---0000 12096---0000 12098---0000 12100---0000 12102---0000 12104---0000 12106---0000 12108---0000 12110---0000 12112---0000 12114---0000 12116---0000 12118---0000 12120---0000 12122---0000 12124---0000 12126---0000 12128---0000 12130---0000 12132---0000 12134---0000 12136---0000 12138---0000 12140---0000 12142---0000 12144---0000 12146---0000 12148---0000 12150---0000 12152---0000 12154---0000 12156---0000 12158---0000 12160---0000 12162---0000 12164---0000 12166---0000 12168---0000 12170---0000 12172---0000 12174---0000 12176---0000 12178---0000 12180---0000 12182---0000 12184---0000 12186---0000 12188---0000 12190---0000 12192---0000 12194---0000 12196---0000 12198---0000 12200---0000 12202---0000 12204---0000 12206---0000 12208---0000 12210---0000 12212---0000 12214---0000 12216---0000 12218---0000 12220---0000 12222---0000 12224---0000 12226---0000 12228---0000 12230---0000 12232---0000 12234---0000 12236---0000 12238---0000 12240---0000 12242---0000 12244---0000 12246---0000 12248---0000 12250---0000 12252---0000 12254---0000 12256---0000 12258---0000 12260---0000 12262---0000 12264---0000 12266---0000 12268---0000 12270---0000 12272---0000 12274---0000 12276---0000 12278---0000 12280---0000 12282---0000 12284---0000 12286---0000 12288---0000 12290---0000 12292---0000 12294---0000 12296---0000 12298---0000 12300---0000 12302---0000 12304---0000 12306---0000 12308---0000 12310---0000 12312---0000 12314---0000 12316---0000 12318---0000 12320---0000 12322---0000 12324---0000 12326---0000 12328---0000 12330---0000 12332---0000 12334---0000 12336---0000 12338---0000 12340---0000 12342---0000 12344---0000 12346---0000 12348---0000 12350---0000 12352---0000 12354---0000 12356---0000 12358---0000 12360---0000 12362---0000 12364---0000 12366---0000 12368---0000 12370---0000 12372---0000 12374---0000 12376---0000 12378---0000 12380---0000 12382---0000 12384---0000 12386---0000 12388---0000 12390---0000 12392---0000 12394---0000 12396---0000 12398---0000 12400---0000 12402---0000 12404---0000 12406---0000 12408---0000 12410---0000 12412---0000 12414---0000 12416---0000 12418---0000 12420---0000 12422---0000 12424---0000 12426---0000 12428---0000 12430---0000 12432---0000 12434---0000 12436---0000 12438---0000 12440---0000 12442---0000 12444---0000 12446---0000 12448---0000 12450---0000 12452---0000 12454---0000 12456---0000 12458---0000 12460---0000 12462---0000 12464---0000 12466---0000 12468---0000 12470---0000 12472---0000 12474---0000 12476---0000 12478---0000 12480---0000 12482---0000 12484---0000 12486---0000 12488---0000 12490---0000 12492---0000 12494---0000 12496---0000 12498---0000 12500---0000 12502---0000 12504---0000 12506---0000 12508---0000 12510---0000 12512---0000 12514---0000 12516---0000 12518---0000 12520---0000 12522---0000 12524---0000 12526---0000 12528---0000 12530---0000 12532---0000 12534---0000 12536---0000 12538---0000 12540---0000 12542---0000 12544---0000 12546---0000 12548---0000 12550---0000 12552---0000 12554---0000 12556---0000 12558---0000 12560---0000 12562---0000 12564---0000 12566---0000 12568---0000 12570---0000 12572---0000 12574---0000 12576---0000 12578---0000 12580---0000 12582---0000 12584---0000 12586---0000 12588---0000 12590---0000 12592---0000 12594---0000 12596---0000 12598---0000 12600---0000 12602---0000 12604---0000 12606---0000 12608---0000 12610---0000 12612---0000 12614---0000 12616---0000 12618---0000 12620---0000 12622---0000 12624---0000 12626---0000 12628---0000 12630---0000 12632---0000 12634---0000 12636---0000 12638---0000 12640---0000 12642---0000 12644---0000 12646---0000 12648---0000 12650---0000 12652---0000 12654---0000 12656---0000 12658---0000 12660---0000 12662---0000 12664---0000 12666---0000 12668---0000 12670---0000 12672---0000 12674---0000 12676---0000 12678---0000 12680---0000 12682---0000 12684---0000 12686---0000 12688---0000 12690---0000 12692---0000 12694---0000 12696---0000 12698---0000 12700---0000 12702---0000 12704---0000 12706---0000 12708---0000 12710---0000 12712---0000 12714---0000 12716---0000 12718---0000 12720---0000 12722---0000 12724---0000 12726---0000 12728---0000 12730---0000 12732---0000 12734---0000 12736---0000 12738---0000 12740---0000 12742---0000 12744---0000 12746---0000 12748---0000 12750---0000 12752---0000 12754---0000 12756---0000 12758---0000 12760---0000 12762---0000 12764---0000 12766---0000 12768---0000 12770---0000 12772---0000 12774---0000 12776---0000 12778---0000 12780---0000 12782---0000 12784---0000 12786---0000 12788---0000 12790---0000 12792---0000 12794---0000 12796---0000 12798---0000 12800---0000 12802---0000 12804---0000 12806---0000 12808---0000 12810---0000 12812---0000 12814---0000 12816---0000 12818---0000 12820---0000 12822---0000 12824---0000 12826---0000 12828---0000 12830---0000 12832---0000 12834---0000 12836---0000 12838---0000 12840---0000 12842---0000 12844---0000 12846---0000 12848---0000 12850---0000 12852---0000 12854---0000 12856---0000 12858---0000 12860---0000 12862---0000 12864---0000 12866---0000 12868---0000 12870---0000 12872---0000 12874---0000 12876---0000 12878---0000 12880---0000 12882---0000 12884---0000 12886---0000 12888---0000 12890---0000 12892---0000 12894---0000 12896---0000 12898---0000 12900---0000 12902---0000 12904---0000 12906---0000 12908---0000 12910---0000 12912---0000 12914---0000 12916---0000 12918---0000 12920---0000 12922---0000 12924---0000 12926---0000 12928---0000 12930---0000 12932---0000 12934---0000 12936---0000 12938---0000 12940---0000 12942---0000 12944---0000 12946---0000 12948---0000 12950---0000 12952---0000 12954---0000 12956---0000 12958---0000 12960---0000 12962---0000 12964---0000 12966---0000 12968---0000 12970---0000 12972---0000 12974---0000 12976---0000 12978---0000 12980---0000 12982---0000 12984---0000 12986---0000 12988---0000 12990---0000 12992---0000 12994---0000 12996---0000 12998---0000 13000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m19.086s user 0m3.372s sys 0m0.013s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:47:41 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=10000, 12000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? 10000---0000 10002---0000 10004---0000 10006---0000 10008---0000 10010---0000 10012---0000 10014---0000 10016---0000 10018---0000 10020---0000 10022---0000 10024---0000 10026---0000 10028---0000 10030---0000 10032---0000 10034---0000 10036---0000 10038---0000 10040---0000 10042---0000 10044---0000 10046---0000 10048---0000 10050---0000 10052---0000 10054---0000 10056---0000 10058---0000 10060---0000 10062---0000 10064---0000 10066---0000 10068---0000 10070---0000 10072---0000 10074---0000 10076---0000 10078---0000 10080---0000 10082---0000 10084---0000 10086---0000 10088---0000 10090---0000 10092---0000 10094---0000 10096---0000 10098---0000 10100---0000 10102---0000 10104---0000 10106---0000 10108---0000 10110---0000 10112---0000 10114---0000 10116---0000 10118---0000 10120---0000 10122---0000 10124---0000 10126---0000 10128---0000 10130---0000 10132---0000 10134---0000 10136---0000 10138---0000 10140---0000 10142---0000 10144---0000 10146---0000 10148---0000 10150---0000 10152---0000 10154---0000 10156---0000 10158---0000 10160---0000 10162---0000 10164---0000 10166---0000 10168---0000 10170---0000 10172---0000 10174---0000 10176---0000 10178---0000 10180---0000 10182---0000 10184---0000 10186---0000 10188---0000 10190---0000 10192---0000 10194---0000 10196---0000 10198---0000 10200---0000 10202---0000 10204---0000 10206---0000 10208---0000 10210---0000 10212---0000 10214---0000 10216---0000 10218---0000 10220---0000 10222---0000 10224---0000 10226---0000 10228---0000 10230---0000 10232---0000 10234---0000 10236---0000 10238---0000 10240---0000 10242---0000 10244---0000 10246---0000 10248---0000 10250---0000 10252---0000 10254---0000 10256---0000 10258---0000 10260---0000 10262---0000 10264---0000 10266---0000 10268---0000 10270---0000 10272---0000 10274---0000 10276---0000 10278---0000 10280---0000 10282---0000 10284---0000 10286---0000 10288---0000 10290---0000 10292---0000 10294---0000 10296---0000 10298---0000 10300---0000 10302---0000 10304---0000 10306---0000 10308---0000 10310---0000 10312---0000 10314---0000 10316---0000 10318---0000 10320---0000 10322---0000 10324---0000 10326---0000 10328---0000 10330---0000 10332---0000 10334---0000 10336---0000 10338---0000 10340---0000 10342---0000 10344---0000 10346---0000 10348---0000 10350---0000 10352---0000 10354---0000 10356---0000 10358---0000 10360---0000 10362---0000 10364---0000 10366---0000 10368---0000 10370---0000 10372---0000 10374---0000 10376---0000 10378---0000 10380---0000 10382---0000 10384---0000 10386---0000 10388---0000 10390---0000 10392---0000 10394---0000 10396---0000 10398---0000 10400---0000 10402---0000 10404---0000 10406---0000 10408---0000 10410---0000 10412---0000 10414---0000 10416---0000 10418---0000 10420---0000 10422---0000 10424---0000 10426---0000 10428---0000 10430---0000 10432---0000 10434---0000 10436---0000 10438---0000 10440---0000 10442---0000 10444---0000 10446---0000 10448---0000 10450---0000 10452---0000 10454---0000 10456---0000 10458---0000 10460---0000 10462---0000 10464---0000 10466---0000 10468---0000 10470---0000 10472---0000 10474---0000 10476---0000 10478---0000 10480---0000 10482---0000 10484---0000 10486---0000 10488---0000 10490---0000 10492---0000 10494---0000 10496---0000 10498---0000 10500---0000 10502---0000 10504---0000 10506---0000 10508---0000 10510---0000 10512---0000 10514---0000 10516---0000 10518---0000 10520---0000 10522---0000 10524---0000 10526---0000 10528---0000 10530---0000 10532---0000 10534---0000 10536---0000 10538---0000 10540---0000 10542---0000 10544---0000 10546---0000 10548---0000 10550---0000 10552---0000 10554---0000 10556---0000 10558---0000 10560---0000 10562---0000 10564---0000 10566---0000 10568---0000 10570---0000 10572---0000 10574---0000 10576---0000 10578---0000 10580---0000 10582---0000 10584---0000 10586---0000 10588---0000 10590---0000 10592---0000 10594---0000 10596---0000 10598---0000 10600---0000 10602---0000 10604---0000 10606---0000 10608---0000 10610---0000 10612---0000 10614---0000 10616---0000 10618---0000 10620---0000 10622---0000 10624---0000 10626---0000 10628---0000 10630---0000 10632---0000 10634---0000 10636---0000 10638---0000 10640---0000 10642---0000 10644---0000 10646---0000 10648---0000 10650---0000 10652---0000 10654---0000 10656---0000 10658---0000 10660---0000 10662---0000 10664---0000 10666---0000 10668---0000 10670---0000 10672---0000 10674---0000 10676---0000 10678---0000 10680---0000 10682---0000 10684---0000 10686---0000 10688---0000 10690---0000 10692---0000 10694---0000 10696---0000 10698---0000 10700---0000 10702---0000 10704---0000 10706---0000 10708---0000 10710---0000 10712---0000 10714---0000 10716---0000 10718---0000 10720---0000 10722---0000 10724---0000 10726---0000 10728---0000 10730---0000 10732---0000 10734---0000 10736---0000 10738---0000 10740---0000 10742---0000 10744---0000 10746---0000 10748---0000 10750---0000 10752---0000 10754---0000 10756---0000 10758---0000 10760---0000 10762---0000 10764---0000 10766---0000 10768---0000 10770---0000 10772---0000 10774---0000 10776---0000 10778---0000 10780---0000 10782---0000 10784---0000 10786---0000 10788---0000 10790---0000 10792---0000 10794---0000 10796---0000 10798---0000 10800---0000 10802---0000 10804---0000 10806---0000 10808---0000 10810---0000 10812---0000 10814---0000 10816---0000 10818---0000 10820---0000 10822---0000 10824---0000 10826---0000 10828---0000 10830---0000 10832---0000 10834---0000 10836---0000 10838---0000 10840---0000 10842---0000 10844---0000 10846---0000 10848---0000 10850---0000 10852---0000 10854---0000 10856---0000 10858---0000 10860---0000 10862---0000 10864---0000 10866---0000 10868---0000 10870---0000 10872---0000 10874---0000 10876---0000 10878---0000 10880---0000 10882---0000 10884---0000 10886---0000 10888---0000 10890---0000 10892---0000 10894---0000 10896---0000 10898---0000 10900---0000 10902---0000 10904---0000 10906---0000 10908---0000 10910---0000 10912---0000 10914---0000 10916---0000 10918---0000 10920---0000 10922---0000 10924---0000 10926---0000 10928---0000 10930---0000 10932---0000 10934---0000 10936---0000 10938---0000 10940---0000 10942---0000 10944---0000 10946---0000 10948---0000 10950---0000 10952---0000 10954---0000 10956---0000 10958---0000 10960---0000 10962---0000 10964---0000 10966---0000 10968---0000 10970---0000 10972---0000 10974---0000 10976---0000 10978---0000 10980---0000 10982---0000 10984---0000 10986---0000 10988---0000 10990---0000 10992---0000 10994---0000 10996---0000 10998---0000 11000---0000 11002---0000 11004---0000 11006---0000 11008---0000 11010---0000 11012---0000 11014---0000 11016---0000 11018---0000 11020---0000 11022---0000 11024---0000 11026---0000 11028---0000 11030---0000 11032---0000 11034---0000 11036---0000 11038---0000 11040---0000 11042---0000 11044---0000 11046---0000 11048---0000 11050---0000 11052---0000 11054---0000 11056---0000 11058---0000 11060---0000 11062---0000 11064---0000 11066---0000 11068---0000 11070---0000 11072---0000 11074---0000 11076---0000 11078---0000 11080---0000 11082---0000 11084---0000 11086---0000 11088---0000 11090---0000 11092---0000 11094---0000 11096---0000 11098---0000 11100---0000 11102---0000 11104---0000 11106---0000 11108---0000 11110---0000 11112---0000 11114---0000 11116---0000 11118---0000 11120---0000 11122---0000 11124---0000 11126---0000 11128---0000 11130---0000 11132---0000 11134---0000 11136---0000 11138---0000 11140---0000 11142---0000 11144---0000 11146---0000 11148---0000 11150---0000 11152---0000 11154---0000 11156---0000 11158---0000 11160---0000 11162---0000 11164---0000 11166---0000 11168---0000 11170---0000 11172---0000 11174---0000 11176---0000 11178---0000 11180---0000 11182---0000 11184---0000 11186---0000 11188---0000 11190---0000 11192---0000 11194---0000 11196---0000 11198---0000 11200---0000 11202---0000 11204---0000 11206---0000 11208---0000 11210---0000 11212---0000 11214---0000 11216---0000 11218---0000 11220---0000 11222---0000 11224---0000 11226---0000 11228---0000 11230---0000 11232---0000 11234---0000 11236---0000 11238---0000 11240---0000 11242---0000 11244---0000 11246---0000 11248---0000 11250---0000 11252---0000 11254---0000 11256---0000 11258---0000 11260---0000 11262---0000 11264---0000 11266---0000 11268---0000 11270---0000 11272---0000 11274---0000 11276---0000 11278---0000 11280---0000 11282---0000 11284---0000 11286---0000 11288---0000 11290---0000 11292---0000 11294---0000 11296---0000 11298---0000 11300---0000 11302---0000 11304---0000 11306---0000 11308---0000 11310---0000 11312---0000 11314---0000 11316---0000 11318---0000 11320---0000 11322---0000 11324---0000 11326---0000 11328---0000 11330---0000 11332---0000 11334---0000 11336---0000 11338---0000 11340---0000 11342---0000 11344---0000 11346---0000 11348---0000 11350---0000 11352---0000 11354---0000 11356---0000 11358---0000 11360---0000 11362---0000 11364---0000 11366---0000 11368---0000 11370---0000 11372---0000 11374---0000 11376---0000 11378---0000 11380---0000 11382---0000 11384---0000 11386---0000 11388---0000 11390---0000 11392---0000 11394---0000 11396---0000 11398---0000 11400---0000 11402---0000 11404---0000 11406---0000 11408---0000 11410---0000 11412---0000 11414---0000 11416---0000 11418---0000 11420---0000 11422---0000 11424---0000 11426---0000 11428---0000 11430---0000 11432---0000 11434---0000 11436---0000 11438---0000 11440---0000 11442---0000 11444---0000 11446---0000 11448---0000 11450---0000 11452---0000 11454---0000 11456---0000 11458---0000 11460---0000 11462---0000 11464---0000 11466---0000 11468---0000 11470---0000 11472---0000 11474---0000 11476---0000 11478---0000 11480---0000 11482---0000 11484---0000 11486---0000 11488---0000 11490---0000 11492---0000 11494---0000 11496---0000 11498---0000 11500---0000 11502---0000 11504---0000 115 ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m25.679s user 0m4.522s sys 0m0.013s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:46:54 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=8630, 10000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? 8630---0000 8632---0000 8634---0000 8636---0000 8638---0000 8640---0000 8642---0000 8644---0000 8646---0000 8648---0000 8650---0000 8652---0000 8654---0000 8656---0000 8658---0000 8660---0000 8662---0000 8664---0000 8666---0000 8668---0000 8670---0000 8672---0000 8674---0000 8676---0000 8678---0000 8680---0000 8682---0000 8684---0000 8686---0000 8688---0000 8690---0000 8692---0000 8694---0000 8696---0000 8698---0000 8700---0000 8702---0000 8704---0000 8706---0000 8708---0000 8710---0000 8712---0000 8714---0000 8716---0000 8718---0000 8720---0000 8722---0000 8724---0000 8726---0000 8728---0000 8730---0000 8732---0000 8734---0000 8736---0000 8738---0000 8740---0000 8742---0000 8744---0000 8746---0000 8748---0000 8750---0000 8752---0000 8754---0000 8756---0000 8758---0000 8760---0000 8762---0000 8764---0000 8766---0000 8768---0000 8770---0000 8772---0000 8774---0000 8776---0000 8778---0000 8780---0000 8782---0000 8784---0000 8786---0000 8788---0000 8790---0000 8792---0000 8794---0000 8796---0000 8798---0000 8800---0000 8802---0000 8804---0000 8806---0000 8808---0000 8810---0000 8812---0000 8814---0000 8816---0000 8818---0000 8820---0000 8822---0000 8824---0000 8826---0000 8828---0000 8830---0000 8832---0000 8834---0000 8836---0000 8838---0000 8840---0000 8842---0000 8844---0000 8846---0000 8848---0000 8850---0000 8852---0000 8854---0000 8856---0000 8858---0000 8860---0000 8862---0000 8864---0000 8866---0000 8868---0000 8870---0000 8872---0000 8874---0000 8876---0000 8878---0000 8880---0000 8882---0000 8884---0000 8886---0000 8888---0000 8890---0000 8892---0000 8894---0000 8896---0000 8898---0000 8900---0000 8902---0000 8904---0000 8906---0000 8908---0000 8910---0000 8912---0000 8914---0000 8916---0000 8918---0000 8920---0000 8922---0000 8924---0000 8926---0000 8928---0000 8930---0000 8932---0000 8934---0000 8936---0000 8938---0000 8940---0000 8942---0000 8944---0000 8946---0000 8948---0000 8950---0000 8952---0000 8954---0000 8956---0000 8958---0000 8960---0000 8962---0000 8964---0000 8966---0000 8968---0000 8970---0000 8972---0000 8974---0000 8976---0000 8978---0000 8980---0000 8982---0000 8984---0000 8986---0000 8988---0000 8990---0000 8992---0000 8994---0000 8996---0000 8998---0000 9000---0000 9002---0000 9004---0000 9006---0000 9008---0000 9010---0000 9012---0000 9014---0000 9016---0000 9018---0000 9020---0000 9022---0000 9024---0000 9026---0000 9028---0000 9030---0000 9032---0000 9034---0000 9036---0000 9038---0000 9040---0000 9042---0000 9044---0000 9046---0000 9048---0000 9050---0000 9052---0000 9054---0000 9056---0000 9058---0000 9060---0000 9062---0000 9064---0000 9066---0000 9068---0000 9070---0000 9072---0000 9074---0000 9076---0000 9078---0000 9080---0000 9082---0000 9084---0000 9086---0000 9088---0000 9090---0000 9092---0000 9094---0000 9096---0000 9098---0000 9100---0000 9102---0000 9104---0000 9106---0000 9108---0000 9110---0000 9112---0000 9114---0000 9116---0000 9118---0000 9120---0000 9122---0000 9124---0000 9126---0000 9128---0000 9130---0000 9132---0000 9134---0000 9136---0000 9138---0000 9140---0000 9142---0000 9144---0000 9146---0000 9148---0000 9150---0000 9152---0000 9154---0000 9156---0000 9158---0000 9160---0000 9162---0000 9164---0000 9166---0000 9168---0000 9170---0000 9172---0000 9174---0000 9176---0000 9178---0000 9180---0000 9182---0000 9184---0000 9186---0000 9188---0000 9190---0000 9192---0000 9194---0000 9196---0000 9198---0000 9200---0000 9202---0000 9204---0000 9206---0000 9208---0000 9210---0000 9212---0000 9214---0000 9216---0000 9218---0000 9220---0000 9222---0000 9224---0000 9226---0000 9228---0000 9230---0000 9232---0000 9234---0000 9236---0000 9238---0000 9240---0000 9242---0000 9244---0000 9246---0000 9248---0000 9250---0000 9252---0000 9254---0000 9256---0000 9258---0000 9260---0000 9262---0000 9264---0000 9266---0000 9268---0000 9270---0000 9272---0000 9274---0000 9276---0000 9278---0000 9280---0000 9282---0000 9284---0000 9286---0000 9288---0000 9290---0000 9292---0000 9294---0000 9296---0000 9298---0000 9300---0000 9302---0000 9304---0000 9306---0000 9308---0000 9310---0000 9312---0000 9314---0000 9316---0000 9318---0000 9320---0000 9322---0000 9324---0000 9326---0000 9328---0000 9330---0000 9332---0000 9334---0000 9336---0000 9338---0000 9340---0000 9342---0000 9344---0000 9346---0000 9348---0000 9350---0000 9352---0000 9354---0000 9356---0000 9358---0000 9360---0000 9362---0000 9364---0000 9366---0000 9368---0000 9370---0000 9372---0000 9374---0000 9376---0000 9378---0000 9380---0000 9382---0000 9384---0000 9386---0000 9388---0000 9390---0000 9392---0000 9394---0000 9396---0000 9398---0000 9400---0000 9402---0000 9404---0000 9406---0000 9408---0000 9410---0000 9412---0000 9414---0000 9416---0000 9418---0000 9420---0000 9422---0000 9424---0000 9426---0000 9428---0000 9430---0000 9432---0000 9434---0000 9436---0000 9438---0000 9440---0000 9442---0000 9444---0000 9446---0000 9448---0000 9450---0000 9452---0000 9454---0000 9456---0000 9458---0000 9460---0000 9462---0000 9464---0000 9466---0000 9468---0000 9470---0000 9472---0000 9474---0000 9476---0000 9478---0000 9480---0000 9482---0000 9484---0000 9486---0000 9488---0000 9490---0000 9492---0000 9494---0000 9496---0000 9498---0000 9500---0000 9502---0000 9504---0000 9506---0000 9508---0000 9510---0000 9512---0000 9514---0000 9516---0000 9518---0000 9520---0000 9522---0000 9524---0000 9526---0000 9528---0000 9530---0000 9532---0000 9534---0000 9536---0000 9538---0000 9540---0000 9542---0000 9544---0000 9546---0000 9548---0000 9550---0000 9552---0000 9554---0000 9556---0000 9558---0000 9560---0000 9562---0000 9564---0000 9566---0000 9568---0000 9570---0000 9572---0000 9574---0000 9576---0000 9578---0000 9580---0000 9582---0000 9584---0000 9586---0000 9588---0000 9590---0000 9592---0000 9594---0000 9596---0000 9598---0000 9600---0000 9602---0000 9604---0000 9606---0000 9608---0000 9610---0000 9612---0000 9614---0000 9616---0000 9618---0000 9620---0000 9622---0000 9624---0000 9626---0000 9628---0000 9630---0000 9632---0000 9634---0000 9636---0000 9638---0000 9640---0000 9642---0000 9644---0000 9646---0000 9648---0000 9650---0000 9652---0000 9654---0000 9656---0000 9658---0000 9660---0000 9662---0000 9664---0000 9666---0000 9668---0000 9670---0000 9672---0000 9674---0000 9676---0000 9678---0000 9680---0000 9682---0000 9684---0000 9686---0000 9688---0000 9690---0000 9692---0000 9694---0000 9696---0000 9698---0000 9700---0000 9702---0000 9704---0000 9706---0000 9708---0000 9710---0000 9712---0000 9714---0000 9716---0000 9718---0000 9720---0000 9722---0000 9724---0000 9726---0000 9728---0000 9730---0000 9732---0000 9734---0000 9736---0000 9738---0000 9740---0000 9742---0000 9744---0000 9746---0000 9748---0000 9750---0000 9752---0000 9754---0000 9756---0000 9758---0000 9760---0000 9762---0000 9764---0000 9766---0000 9768---0000 9770---0000 9772---0000 9774---0000 9776---0000 9778---0000 9780---0000 9782---0000 9784---0000 9786---0000 9788---0000 9790---0000 9792---0000 9794---0000 9796---0000 9798---0000 9800---0000 9802---0000 9804---0000 9806---0000 9808---0000 9810---0000 9812---0000 9814---0000 9816---0000 9818---0000 9820---0000 9822---0000 9824---0000 9826---0000 9828---0000 9830---0000 9832---0000 9834---0000 9836---0000 9838---0000 9840---0000 9842---0000 9844---0000 9846---0000 9848---0000 9850---0000 9852---0000 9854---0000 9856---0000 9858---0000 9860---0000 9862---0000 9864---0000 9866---0000 9868---0000 9870---0000 9872---0000 9874---0000 9876---0000 9878---0000 9880---0000 9882---0000 9884---0000 9886---0000 9888---0000 9890---0000 9892---0000 9894---0000 9896---0000 9898---0000 9900---0000 9902---0000 9904---0000 9906---0000 9908---0000 9910---0000 9912---0000 9914---0000 9916---0000 9918---0000 9920---0000 9922---0000 9924---0000 9926---0000 9928---0000 9930---0000 9932---0000 9934---0000 9936---0000 9938---0000 9940---0000 9942---0000 9944---0000 9946---0000 9948---0000 9950---0000 9952---0000 9954---0000 9956---0000 9958---0000 9960---0000 9962---0000 9964---0000 9966---0000 9968---0000 9970---0000 9972---0000 9974---0000 9976---0000 9978---0000 9980---0000 9982---0000 9984---0000 9986---0000 9988---0000 9990---0000 9992---0000 9994---0000 9996---0000 9998---0000 10000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m17.858s user 0m3.059s sys 0m0.017s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:46:15 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=7000, 9000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? 7000---0000 7002---0000 7004---0000 7006---0000 7008---0000 7010---0000 7012---0000 7014---0000 7016---0000 7018---0000 7020---0000 7022---0000 7024---0000 7026---0000 7028---0000 7030---0000 7032---0000 7034---0000 7036---0000 7038---0000 7040---0000 7042---0000 7044---0000 7046---0000 7048---0000 7050---0000 7052---0000 7054---0000 7056---0000 7058---0000 7060---0000 7062---0000 7064---0000 7066---0000 7068---0000 7070---0000 7072---0000 7074---0000 7076---0000 7078---0000 7080---0000 7082---0000 7084---0000 7086---0000 7088---0000 7090---0000 7092---0000 7094---0000 7096---0000 7098---0000 7100---0000 7102---0000 7104---0000 7106---0000 7108---0000 7110---0000 7112---0000 7114---0000 7116---0000 7118---0000 7120---0000 7122---0000 7124---0000 7126---0000 7128---0000 7130---0000 7132---0000 7134---0000 7136---0000 7138---0000 7140---0000 7142---0000 7144---0000 7146---0000 7148---0000 7150---0000 7152---0000 7154---0000 7156---0000 7158---0000 7160---0000 7162---0000 7164---0000 7166---0000 7168---0000 7170---0000 7172---0000 7174---0000 7176---0000 7178---0000 7180---0000 7182---0000 7184---0000 7186---0000 7188---0000 7190---0000 7192---0000 7194---0000 7196---0000 7198---0000 7200---0000 7202---0000 7204---0000 7206---0000 7208---0000 7210---0000 7212---0000 7214---0000 7216---0000 7218---0000 7220---0000 7222---0000 7224---0000 7226---0000 7228---0000 7230---0000 7232---0000 7234---0000 7236---0000 7238---0000 7240---0000 7242---0000 7244---0000 7246---0000 7248---0000 7250---0000 7252---0000 7254---0000 7256---0000 7258---0000 7260---0000 7262---0000 7264---0000 7266---0000 7268---0000 7270---0000 7272---0000 7274---0000 7276---0000 7278---0000 7280---0000 7282---0000 7284---0000 7286---0000 7288---0000 7290---0000 7292---0000 7294---0000 7296---0000 7298---0000 7300---0000 7302---0000 7304---0000 7306---0000 7308---0000 7310---0000 7312---0000 7314---0000 7316---0000 7318---0000 7320---0000 7322---0000 7324---0000 7326---0000 7328---0000 7330---0000 7332---0000 7334---0000 7336---0000 7338---0000 7340---0000 7342---0000 7344---0000 7346---0000 7348---0000 7350---0000 7352---0000 7354---0000 7356---0000 7358---0000 7360---0000 7362---0000 7364---0000 7366---0000 7368---0000 7370---0000 7372---0000 7374---0000 7376---0000 7378---0000 7380---0000 7382---0000 7384---0000 7386---0000 7388---0000 7390---0000 7392---0000 7394---0000 7396---0000 7398---0000 7400---0000 7402---0000 7404---0000 7406---0000 7408---0000 7410---0000 7412---0000 7414---0000 7416---0000 7418---0000 7420---0000 7422---0000 7424---0000 7426---0000 7428---0000 7430---0000 7432---0000 7434---0000 7436---0000 7438---0000 7440---0000 7442---0000 7444---0000 7446---0000 7448---0000 7450---0000 7452---0000 7454---0000 7456---0000 7458---0000 7460---0000 7462---0000 7464---0000 7466---0000 7468---0000 7470---0000 7472---0000 7474---0000 7476---0000 7478---0000 7480---0000 7482---0000 7484---0000 7486---0000 7488---0000 7490---0000 7492---0000 7494---0000 7496---0000 7498---0000 7500---0000 7502---0000 7504---0000 7506---0000 7508---0000 7510---0000 7512---0000 7514---0000 7516---0000 7518---0000 7520---0000 7522---0000 7524---0000 7526---0000 7528---0000 7530---0000 7532---0000 7534---0000 7536---0000 7538---0000 7540---0000 7542---0000 7544---0000 7546---0000 7548---0000 7550---0000 7552---0000 7554---0000 7556---0000 7558---0000 7560---0000 7562---0000 7564---0000 7566---0000 7568---0000 7570---0000 7572---0000 7574---0000 7576---0000 7578---0000 7580---0000 7582---0000 7584---0000 7586---0000 7588---0000 7590---0000 7592---0000 7594---0000 7596---0000 7598---0000 7600---0000 7602---0000 7604---0000 7606---0000 7608---0000 7610---0000 7612---0000 7614---0000 7616---0000 7618---0000 7620---0000 7622---0000 7624---0000 7626---0000 7628---0000 7630---0000 7632---0000 7634---0000 7636---0000 7638---0000 7640---0000 7642---0000 7644---0000 7646---0000 7648---0000 7650---0000 7652---0000 7654---0000 7656---0000 7658---0000 7660---0000 7662---0000 7664---0000 7666---0000 7668---0000 7670---0000 7672---0000 7674---0000 7676---0000 7678---0000 7680---0000 7682---0000 7684---0000 7686---0000 7688---0000 7690---0000 7692---0000 7694---0000 7696---0000 7698---0000 7700---0000 7702---0000 7704---0000 7706---0000 7708---0000 7710---0000 7712---0000 7714---0000 7716---0000 7718---0000 7720---0000 7722---0000 7724---0000 7726---0000 7728---0000 7730---0000 7732---0000 7734---0000 7736---0000 7738---0000 7740---0000 7742---0000 7744---0000 7746---0000 7748---0000 7750---0000 7752---0000 7754---0000 7756---0000 7758---0000 7760---0000 7762---0000 7764---0000 7766---0000 7768---0000 7770---0000 7772---0000 7774---0000 7776---0000 7778---0000 7780---0000 7782---0000 7784---0000 7786---0000 7788---0000 7790---0000 7792---0000 7794---0000 7796---0000 7798---0000 7800---0000 7802---0000 7804---0000 7806---0000 7808---0000 7810---0000 7812---0000 7814---0000 7816---0000 7818---0000 7820---0000 7822---0000 7824---0000 7826---0000 7828---0000 7830---0000 7832---0000 7834---0000 7836---0000 7838---0000 7840---0000 7842---0000 7844---0000 7846---0000 7848---0000 7850---0000 7852---0000 7854---0000 7856---0000 7858---0000 7860---0000 7862---0000 7864---0000 7866---0000 7868---0000 7870---0000 7872---0000 7874---0000 7876---0000 7878---0000 7880---0000 7882---0000 7884---0000 7886---0000 7888---0000 7890---0000 7892---0000 7894---0000 7896---0000 7898---0000 7900---0000 7902---0000 7904---0000 7906---0000 7908---0000 7910---0000 7912---0000 7914---0000 7916---0000 7918---0000 7920---0000 7922---0000 7924---0000 7926---0000 7928---0000 7930---0000 7932---0000 7934---0000 7936---0000 7938---0000 7940---0000 7942---0000 7944---0000 7946---0000 7948---0000 7950---0000 7952---0000 7954---0000 7956---0000 7958---0000 7960---0000 7962---0000 7964---0000 7966---0000 7968---0000 7970---0000 7972---0000 7974---0000 7976---0000 7978---0000 7980---0000 7982---0000 7984---0000 7986---0000 7988---0000 7990---0000 7992---0000 7994---0000 7996---0000 7998---0000 8000---0000 8002---0000 8004---0000 8006---0000 8008---0000 8010---0000 8012---0000 8014---0000 8016---0000 8018---0000 8020---0000 8022---0000 8024---0000 8026---0000 8028---0000 8030---0000 8032---0000 8034---0000 8036---0000 8038---0000 8040---0000 8042---0000 8044---0000 8046---0000 8048---0000 8050---0000 8052---0000 8054---0000 8056---0000 8058---0000 8060---0000 8062---0000 8064---0000 8066---0000 8068---0000 8070---0000 8072---0000 8074---0000 8076---0000 8078---0000 8080---0000 8082---0000 8084---0000 8086---0000 8088---0000 8090---0000 8092---0000 8094---0000 8096---0000 8098---0000 8100---0000 8102---0000 8104---0000 8106---0000 8108---0000 8110---0000 8112---0000 8114---0000 8116---0000 8118---0000 8120---0000 8122---0000 8124---0000 8126---0000 8128---0000 8130---0000 8132---0000 8134---0000 8136---0000 8138---0000 8140---0000 8142---0000 8144---0000 8146---0000 8148---0000 8150---0000 8152---0000 8154---0000 8156---0000 8158---0000 8160---0000 8162---0000 8164---0000 8166---0000 8168---0000 8170---0000 8172---0000 8174---0000 8176---0000 8178---0000 8180---0000 8182---0000 8184---0000 8186---0000 8188---0000 8190---0000 8192---0000 8194---0000 8196---0000 8198---0000 8200---0000 8202---0000 8204---0000 8206---0000 8208---0000 8210---0000 8212---0000 8214---0000 8216---0000 8218---0000 8220---0000 8222---0000 8224---0000 8226---0000 8228---0000 8230---0000 8232---0000 8234---0000 8236---0000 8238---0000 8240---0000 8242---0000 8244---0000 8246---0000 8248---0000 8250---0000 8252---0000 8254---0000 8256---0000 8258---0000 8260---0000 8262---0000 8264---0000 8266---0000 8268---0000 8270---0000 8272---0000 8274---0000 8276---0000 8278---0000 8280---0000 8282---0000 8284---0000 8286---0000 8288---0000 8290---0000 8292---0000 8294---0000 8296---0000 8298---0000 8300---0000 8302---0000 8304---0000 8306---0000 8308---0000 8310---0000 8312---0000 8314---0000 8316---0000 8318---0000 8320---0000 8322---0000 8324---0000 8326---0000 8328---0000 8330---0000 8332---0000 8334---0000 8336---0000 8338---0000 8340---0000 8342---0000 8344---0000 8346---0000 8348---0000 8350---0000 8352---0000 8354---0000 8356---0000 8358---0000 8360---0000 8362---0000 8364---0000 8366---0000 8368---0000 8370---0000 8372---0000 8374---0000 8376---0000 8378---0000 8380---0000 8382---0000 8384---0000 8386---0000 8388---0000 8390---0000 8392---0000 8394---0000 8396---0000 8398---0000 8400---0000 8402---0000 8404---0000 8406---0000 8408---0000 8410---0000 8412---0000 8414---0000 8416---0000 8418---0000 8420---0000 8422---0000 8424---0000 8426---0000 8428---0000 8430---0000 8432---0000 8434---0000 8436---0000 8438---0000 8440---0000 8442---0000 8444---0000 8446---0000 8448---0000 8450---0000 8452---0000 8454---0000 8456---0000 8458---0000 8460---0000 8462---0000 8464---0000 8466---0000 8468---0000 8470---0000 8472---0000 8474---0000 8476---0000 8478---0000 8480---0000 8482---0000 8484---0000 8486---0000 8488---0000 8490---0000 8492---0000 8494---0000 8496---0000 8498---0000 8500---0000 8502---0000 8504---0000 8506---0000 8508---0000 8510---0000 8512---0000 8514---0000 8516---0000 8518---0000 8520---0000 8522---0000 8524---0000 8526---0000 8528---0000 8530---0000 8532---0000 8534---0000 8536---0000 8538---0000 8540---0000 8542---0000 8544---0000 8546---0000 8548---0000 8550---0000 8552---0000 8554---0000 8556---0000 8558---0000 8560---0000 8562---0000 8564---0000 8566---0000 8568---0000 8570---0000 8572---0000 8574---0000 8576---0000 8578---0000 8580---0000 8582---0000 8584---0000 8586---0000 8588---0000 8590---0000 8592---0000 8594---0000 8596---0000 8598---0000 8600---0000 8602---0000 8604---0000 8606---0000 8608---0000 8610---0000 8612---0000 8614---0000 8616---0000 8618---0000 8620---0000 8622---0000 8624---0000 8626---0000 8628---0000 8630---0000 ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m24.849s user 0m4.415s sys 0m0.017s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:45:33 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=5630, 7000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? 5630---0000 5632---0000 5634---0000 5636---0000 5638---0000 5640---0000 5642---0000 5644---0000 5646---0000 5648---0000 5650---0000 5652---0000 5654---0000 5656---0000 5658---0000 5660---0000 5662---0000 5664---0000 5666---0000 5668---0000 5670---0000 5672---0000 5674---0000 5676---0000 5678---0000 5680---0000 5682---0000 5684---0000 5686---0000 5688---0000 5690---0000 5692---0000 5694---0000 5696---0000 5698---0000 5700---0000 5702---0000 5704---0000 5706---0000 5708---0000 5710---0000 5712---0000 5714---0000 5716---0000 5718---0000 5720---0000 5722---0000 5724---0000 5726---0000 5728---0000 5730---0000 5732---0000 5734---0000 5736---0000 5738---0000 5740---0000 5742---0000 5744---0000 5746---0000 5748---0000 5750---0000 5752---0000 5754---0000 5756---0000 5758---0000 5760---0000 5762---0000 5764---0000 5766---0000 5768---0000 5770---0000 5772---0000 5774---0000 5776---0000 5778---0000 5780---0000 5782---0000 5784---0000 5786---0000 5788---0000 5790---0000 5792---0000 5794---0000 5796---0000 5798---0000 5800---0000 5802---0000 5804---0000 5806---0000 5808---0000 5810---0000 5812---0000 5814---0000 5816---0000 5818---0000 5820---0000 5822---0000 5824---0000 5826---0000 5828---0000 5830---0000 5832---0000 5834---0000 5836---0000 5838---0000 5840---0000 5842---0000 5844---0000 5846---0000 5848---0000 5850---0000 5852---0000 5854---0000 5856---0000 5858---0000 5860---0000 5862---0000 5864---0000 5866---0000 5868---0000 5870---0000 5872---0000 5874---0000 5876---0000 5878---0000 5880---0000 5882---0000 5884---0000 5886---0000 5888---0000 5890---0000 5892---0000 5894---0000 5896---0000 5898---0000 5900---0000 5902---0000 5904---0000 5906---0000 5908---0000 5910---0000 5912---0000 5914---0000 5916---0000 5918---0000 5920---0000 5922---0000 5924---0000 5926---0000 5928---0000 5930---0000 5932---0000 5934---0000 5936---0000 5938---0000 5940---0000 5942---0000 5944---0000 5946---0000 5948---0000 5950---0000 5952---0000 5954---0000 5956---0000 5958---0000 5960---0000 5962---0000 5964---0000 5966---0000 5968---0000 5970---0000 5972---0000 5974---0000 5976---0000 5978---0000 5980---0000 5982---0000 5984---0000 5986---0000 5988---0000 5990---0000 5992---0000 5994---0000 5996---0000 5998---0000 6000---0000 6002---0000 6004---0000 6006---0000 6008---0000 6010---0000 6012---0000 6014---0000 6016---0000 6018---0000 6020---0000 6022---0000 6024---0000 6026---0000 6028---0000 6030---0000 6032---0000 6034---0000 6036---0000 6038---0000 6040---0000 6042---0000 6044---0000 6046---0000 6048---0000 6050---0000 6052---0000 6054---0000 6056---0000 6058---0000 6060---0000 6062---0000 6064---0000 6066---0000 6068---0000 6070---0000 6072---0000 6074---0000 6076---0000 6078---0000 6080---0000 6082---0000 6084---0000 6086---0000 6088---0000 6090---0000 6092---0000 6094---0000 6096---0000 6098---0000 6100---0000 6102---0000 6104---0000 6106---0000 6108---0000 6110---0000 6112---0000 6114---0000 6116---0000 6118---0000 6120---0000 6122---0000 6124---0000 6126---0000 6128---0000 6130---0000 6132---0000 6134---0000 6136---0000 6138---0000 6140---0000 6142---0000 6144---0000 6146---0000 6148---0000 6150---0000 6152---0000 6154---0000 6156---0000 6158---0000 6160---0000 6162---0000 6164---0000 6166---0000 6168---0000 6170---0000 6172---0000 6174---0000 6176---0000 6178---0000 6180---0000 6182---0000 6184---0000 6186---0000 6188---0000 6190---0000 6192---0000 6194---0000 6196---0000 6198---0000 6200---0000 6202---0000 6204---0000 6206---0000 6208---0000 6210---0000 6212---0000 6214---0000 6216---0000 6218---0000 6220---0000 6222---0000 6224---0000 6226---0000 6228---0000 6230---0000 6232---0000 6234---0000 6236---0000 6238---0000 6240---0000 6242---0000 6244---0000 6246---0000 6248---0000 6250---0000 6252---0000 6254---0000 6256---0000 6258---0000 6260---0000 6262---0000 6264---0000 6266---0000 6268---0000 6270---0000 6272---0000 6274---0000 6276---0000 6278---0000 6280---0000 6282---0000 6284---0000 6286---0000 6288---0000 6290---0000 6292---0000 6294---0000 6296---0000 6298---0000 6300---0000 6302---0000 6304---0000 6306---0000 6308---0000 6310---0000 6312---0000 6314---0000 6316---0000 6318---0000 6320---0000 6322---0000 6324---0000 6326---0000 6328---0000 6330---0000 6332---0000 6334---0000 6336---0000 6338---0000 6340---0000 6342---0000 6344---0000 6346---0000 6348---0000 6350---0000 6352---0000 6354---0000 6356---0000 6358---0000 6360---0000 6362---0000 6364---0000 6366---0000 6368---0000 6370---0000 6372---0000 6374---0000 6376---0000 6378---0000 6380---0000 6382---0000 6384---0000 6386---0000 6388---0000 6390---0000 6392---0000 6394---0000 6396---0000 6398---0000 6400---0000 6402---0000 6404---0000 6406---0000 6408---0000 6410---0000 6412---0000 6414---0000 6416---0000 6418---0000 6420---0000 6422---0000 6424---0000 6426---0000 6428---0000 6430---0000 6432---0000 6434---0000 6436---0000 6438---0000 6440---0000 6442---0000 6444---0000 6446---0000 6448---0000 6450---0000 6452---0000 6454---0000 6456---0000 6458---0000 6460---0000 6462---0000 6464---0000 6466---0000 6468---0000 6470---0000 6472---0000 6474---0000 6476---0000 6478---0000 6480---0000 6482---0000 6484---0000 6486---0000 6488---0000 6490---0000 6492---0000 6494---0000 6496---0000 6498---0000 6500---0000 6502---0000 6504---0000 6506---0000 6508---0000 6510---0000 6512---0000 6514---0000 6516---0000 6518---0000 6520---0000 6522---0000 6524---0000 6526---0000 6528---0000 6530---0000 6532---0000 6534---0000 6536---0000 6538---0000 6540---0000 6542---0000 6544---0000 6546---0000 6548---0000 6550---0000 6552---0000 6554---0000 6556---0000 6558---0000 6560---0000 6562---0000 6564---0000 6566---0000 6568---0000 6570---0000 6572---0000 6574---0000 6576---0000 6578---0000 6580---0000 6582---0000 6584---0000 6586---0000 6588---0000 6590---0000 6592---0000 6594---0000 6596---0000 6598---0000 6600---0000 6602---0000 6604---0000 6606---0000 6608---0000 6610---0000 6612---0000 6614---0000 6616---0000 6618---0000 6620---0000 6622---0000 6624---0000 6626---0000 6628---0000 6630---0000 6632---0000 6634---0000 6636---0000 6638---0000 6640---0000 6642---0000 6644---0000 6646---0000 6648---0000 6650---0000 6652---0000 6654---0000 6656---0000 6658---0000 6660---0000 6662---0000 6664---0000 6666---0000 6668---0000 6670---0000 6672---0000 6674---0000 6676---0000 6678---0000 6680---0000 6682---0000 6684---0000 6686---0000 6688---0000 6690---0000 6692---0000 6694---0000 6696---0000 6698---0000 6700---0000 6702---0000 6704---0000 6706---0000 6708---0000 6710---0000 6712---0000 6714---0000 6716---0000 6718---0000 6720---0000 6722---0000 6724---0000 6726---0000 6728---0000 6730---0000 6732---0000 6734---0000 6736---0000 6738---0000 6740---0000 6742---0000 6744---0000 6746---0000 6748---0000 6750---0000 6752---0000 6754---0000 6756---0000 6758---0000 6760---0000 6762---0000 6764---0000 6766---0000 6768---0000 6770---0000 6772---0000 6774---0000 6776---0000 6778---0000 6780---0000 6782---0000 6784---0000 6786---0000 6788---0000 6790---0000 6792---0000 6794---0000 6796---0000 6798---0000 6800---0000 6802---0000 6804---0000 6806---0000 6808---0000 6810---0000 6812---0000 6814---0000 6816---0000 6818---0000 6820---0000 6822---0000 6824---0000 6826---0000 6828---0000 6830---0000 6832---0000 6834---0000 6836---0000 6838---0000 6840---0000 6842---0000 6844---0000 6846---0000 6848---0000 6850---0000 6852---0000 6854---0000 6856---0000 6858---0000 6860---0000 6862---0000 6864---0000 6866---0000 6868---0000 6870---0000 6872---0000 6874---0000 6876---0000 6878---0000 6880---0000 6882---0000 6884---0000 6886---0000 6888---0000 6890---0000 6892---0000 6894---0000 6896---0000 6898---0000 6900---0000 6902---0000 6904---0000 6906---0000 6908---0000 6910---0000 6912---0000 6914---0000 6916---0000 6918---0000 6920---0000 6922---0000 6924---0000 6926---0000 6928---0000 6930---0000 6932---0000 6934---0000 6936---0000 6938---0000 6940---0000 6942---0000 6944---0000 6946---0000 6948---0000 6950---0000 6952---0000 6954---0000 6956---0000 6958---0000 6960---0000 6962---0000 6964---0000 6966---0000 6968---0000 6970---0000 6972---0000 6974---0000 6976---0000 6978---0000 6980---0000 6982---0000 6984---0000 6986---0000 6988---0000 6990---0000 6992---0000 6994---0000 6996---0000 6998---0000 7000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m16.644s user 0m2.973s sys 0m0.016s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:44:57 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=4000, 6000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? 4000---0000 4002---0000 4004---0000 4006---0000 4008---0000 4010---0000 4012---0000 4014---0000 4016---0000 4018---0000 4020---0000 4022---0000 4024---0000 4026---0000 4028---0000 4030---0000 4032---0000 4034---0000 4036---0000 4038---0000 4040---0000 4042---0000 4044---0000 4046---0000 4048---0000 4050---0000 4052---0000 4054---0000 4056---0000 4058---0000 4060---0000 4062---0000 4064---0000 4066---0000 4068---0000 4070---0000 4072---0000 4074---0000 4076---0000 4078---0000 4080---0000 4082---0000 4084---0000 4086---0000 4088---0000 4090---0000 4092---0000 4094---0000 4096---0000 4098---0000 4100---0000 4102---0000 4104---0000 4106---0000 4108---0000 4110---0000 4112---0000 4114---0000 4116---0000 4118---0000 4120---0000 4122---0000 4124---0000 4126---0000 4128---0000 4130---0000 4132---0000 4134---0000 4136---0000 4138---0000 4140---0000 4142---0000 4144---0000 4146---0000 4148---0000 4150---0000 4152---0000 4154---0000 4156---0000 4158---0000 4160---0000 4162---0000 4164---0000 4166---0000 4168---0000 4170---0000 4172---0000 4174---0000 4176---0000 4178---0000 4180---0000 4182---0000 4184---0000 4186---0000 4188---0000 4190---0000 4192---0000 4194---0000 4196---0000 4198---0000 4200---0000 4202---0000 4204---0000 4206---0000 4208---0000 4210---0000 4212---0000 4214---0000 4216---0000 4218---0000 4220---0000 4222---0000 4224---0000 4226---0000 4228---0000 4230---0000 4232---0000 4234---0000 4236---0000 4238---0000 4240---0000 4242---0000 4244---0000 4246---0000 4248---0000 4250---0000 4252---0000 4254---0000 4256---0000 4258---0000 4260---0000 4262---0000 4264---0000 4266---0000 4268---0000 4270---0000 4272---0000 4274---0000 4276---0000 4278---0000 4280---0000 4282---0000 4284---0000 4286---0000 4288---0000 4290---0000 4292---0000 4294---0000 4296---0000 4298---0000 4300---0000 4302---0000 4304---0000 4306---0000 4308---0000 4310---0000 4312---0000 4314---0000 4316---0000 4318---0000 4320---0000 4322---0000 4324---0000 4326---0000 4328---0000 4330---0000 4332---0000 4334---0000 4336---0000 4338---0000 4340---0000 4342---0000 4344---0000 4346---0000 4348---0000 4350---0000 4352---0000 4354---0000 4356---0000 4358---0000 4360---0000 4362---0000 4364---0000 4366---0000 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4700---0000 4702---0000 4704---0000 4706---0000 4708---0000 4710---0000 4712---0000 4714---0000 4716---0000 4718---0000 4720---0000 4722---0000 4724---0000 4726---0000 4728---0000 4730---0000 4732---0000 4734---0000 4736---0000 4738---0000 4740---0000 4742---0000 4744---0000 4746---0000 4748---0000 4750---0000 4752---0000 4754---0000 4756---0000 4758---0000 4760---0000 4762---0000 4764---0000 4766---0000 4768---0000 4770---0000 4772---0000 4774---0000 4776---0000 4778---0000 4780---0000 4782---0000 4784---0000 4786---0000 4788---0000 4790---0000 4792---0000 4794---0000 4796---0000 4798---0000 4800---0000 4802---0000 4804---0000 4806---0000 4808---0000 4810---0000 4812---0000 4814---0000 4816---0000 4818---0000 4820---0000 4822---0000 4824---0000 4826---0000 4828---0000 4830---0000 4832---0000 4834---0000 4836---0000 4838---0000 4840---0000 4842---0000 4844---0000 4846---0000 4848---0000 4850---0000 4852---0000 4854---0000 4856---0000 4858---0000 4860---0000 4862---0000 4864---0000 4866---0000 4868---0000 4870---0000 4872---0000 4874---0000 4876---0000 4878---0000 4880---0000 4882---0000 4884---0000 4886---0000 4888---0000 4890---0000 4892---0000 4894---0000 4896---0000 4898---0000 4900---0000 4902---0000 4904---0000 4906---0000 4908---0000 4910---0000 4912---0000 4914---0000 4916---0000 4918---0000 4920---0000 4922---0000 4924---0000 4926---0000 4928---0000 4930---0000 4932---0000 4934---0000 4936---0000 4938---0000 4940---0000 4942---0000 4944---0000 4946---0000 4948---0000 4950---0000 4952---0000 4954---0000 4956---0000 4958---0000 4960---0000 4962---0000 4964---0000 4966---0000 4968---0000 4970---0000 4972---0000 4974---0000 4976---0000 4978---0000 4980---0000 4982---0000 4984---0000 4986---0000 4988---0000 4990---0000 4992---0000 4994---0000 4996---0000 4998---0000 5000---0000 5002---0000 5004---0000 5006---0000 5008---0000 5010---0000 5012---0000 5014---0000 5016---0000 5018---0000 5020---0000 5022---0000 5024---0000 5026---0000 5028---0000 5030---0000 5032---0000 5034---0000 5036---0000 5038---0000 5040---0000 5042---0000 5044---0000 5046---0000 5048---0000 5050---0000 5052---0000 5054---0000 5056---0000 5058---0000 5060---0000 5062---0000 5064---0000 5066---0000 5068---0000 5070---0000 5072---0000 5074---0000 5076---0000 5078---0000 5080---0000 5082---0000 5084---0000 5086---0000 5088---0000 5090---0000 5092---0000 5094---0000 5096---0000 5098---0000 5100---0000 5102---0000 5104---0000 5106---0000 5108---0000 5110---0000 5112---0000 5114---0000 5116---0000 5118---0000 5120---0000 5122---0000 5124---0000 5126---0000 5128---0000 5130---0000 5132---0000 5134---0000 5136---0000 5138---0000 5140---0000 5142---0000 5144---0000 5146---0000 5148---0000 5150---0000 5152---0000 5154---0000 5156---0000 5158---0000 5160---0000 5162---0000 5164---0000 5166---0000 5168---0000 5170---0000 5172---0000 5174---0000 5176---0000 5178---0000 5180---0000 5182---0000 5184---0000 5186---0000 5188---0000 5190---0000 5192---0000 5194---0000 5196---0000 5198---0000 5200---0000 5202---0000 5204---0000 5206---0000 5208---0000 5210---0000 5212---0000 5214---0000 5216---0000 5218---0000 5220---0000 5222---0000 5224---0000 5226---0000 5228---0000 5230---0000 5232---0000 5234---0000 5236---0000 5238---0000 5240---0000 5242---0000 5244---0000 5246---0000 5248---0000 5250---0000 5252---0000 5254---0000 5256---0000 5258---0000 5260---0000 5262---0000 5264---0000 5266---0000 5268---0000 5270---0000 5272---0000 5274---0000 5276---0000 5278---0000 5280---0000 5282---0000 5284---0000 5286---0000 5288---0000 5290---0000 5292---0000 5294---0000 5296---0000 5298---0000 5300---0000 5302---0000 5304---0000 5306---0000 5308---0000 5310---0000 5312---0000 5314---0000 5316---0000 5318---0000 5320---0000 5322---0000 5324---0000 5326---0000 5328---0000 5330---0000 5332---0000 5334---0000 5336---0000 5338---0000 5340---0000 5342---0000 5344---0000 5346---0000 5348---0000 5350---0000 5352---0000 5354---0000 5356---0000 5358---0000 5360---0000 5362---0000 5364---0000 5366---0000 5368---0000 5370---0000 5372---0000 5374---0000 5376---0000 5378---0000 5380---0000 5382---0000 5384---0000 5386---0000 5388---0000 5390---0000 5392---0000 5394---0000 5396---0000 5398---0000 5400---0000 5402---0000 5404---0000 5406---0000 5408---0000 5410---0000 5412---0000 5414---0000 5416---0000 5418---0000 5420---0000 5422---0000 5424---0000 5426---0000 5428---0000 5430---0000 5432---0000 5434---0000 5436---0000 5438---0000 5440---0000 5442---0000 5444---0000 5446---0000 5448---0000 5450---0000 5452---0000 5454---0000 5456---0000 5458---0000 5460---0000 5462---0000 5464---0000 5466---0000 5468---0000 5470---0000 5472---0000 5474---0000 5476---0000 5478---0000 5480---0000 5482---0000 5484---0000 5486---0000 5488---0000 5490---0000 5492---0000 5494---0000 5496---0000 5498---0000 5500---0000 5502---0000 5504---0000 5506---0000 5508---0000 5510---0000 5512---0000 5514---0000 5516---0000 5518---0000 5520---0000 5522---0000 5524---0000 5526---0000 5528---0000 5530---0000 5532---0000 5534---0000 5536---0000 5538---0000 5540---0000 5542---0000 5544---0000 5546---0000 5548---0000 5550---0000 5552---0000 5554---0000 5556---0000 5558---0000 5560---0000 5562---0000 5564---0000 5566---0000 5568---0000 5570---0000 5572---0000 5574---0000 5576---0000 5578---0000 5580---0000 5582---0000 5584---0000 5586---0000 5588---0000 5590---0000 5592---0000 5594---0000 5596---0000 5598---0000 5600---0000 5602---0000 5604---0000 5606---0000 5608---0000 5610---0000 5612---0000 5614---0000 5616---0000 5618---0000 5620---0000 5622---0000 5624---0000 5626---0000 5628---0000 5630---0000 ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m8.480s user 0m4.227s sys 0m0.011s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:44:28 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=2630, 4000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? 2630---0000 2632---0000 2634---0000 2636---0000 2638---0000 2640---0000 2642---0000 2644---0000 2646---0000 2648---0000 2650---0000 2652---0000 2654---0000 2656---0000 2658---0000 2660---0000 2662---0000 2664---0000 2666---0000 2668---0000 2670---0000 2672---0000 2674---0000 2676---0000 2678---0000 2680---0000 2682---0000 2684---0000 2686---0000 2688---0000 2690---0000 2692---0000 2694---0000 2696---0000 2698---0000 2700---0000 2702---0000 2704---0000 2706---0000 2708---0000 2710---0000 2712---0000 2714---0000 2716---0000 2718---0000 2720---0000 2722---0000 2724---0000 2726---0000 2728---0000 2730---0000 2732---0000 2734---0000 2736---0000 2738---0000 2740---0000 2742---0000 2744---0000 2746---0000 2748---0000 2750---0000 2752---0000 2754---0000 2756---0000 2758---0000 2760---0000 2762---0000 2764---0000 2766---0000 2768---0000 2770---0000 2772---0000 2774---0000 2776---0000 2778---0000 2780---0000 2782---0000 2784---0000 2786---0000 2788---0000 2790---0000 2792---0000 2794---0000 2796---0000 2798---0000 2800---0000 2802---0000 2804---0000 2806---0000 2808---0000 2810---0000 2812---0000 2814---0000 2816---0000 2818---0000 2820---0000 2822---0000 2824---0000 2826---0000 2828---0000 2830---0000 2832---0000 2834---0000 2836---0000 2838---0000 2840---0000 2842---0000 2844---0000 2846---0000 2848---0000 2850---0000 2852---0000 2854---0000 2856---0000 2858---0000 2860---0000 2862---0000 2864---0000 2866---0000 2868---0000 2870---0000 2872---0000 2874---0000 2876---0000 2878---0000 2880---0000 2882---0000 2884---0000 2886---0000 2888---0000 2890---0000 2892---0000 2894---0000 2896---0000 2898---0000 2900---0000 2902---0000 2904---0000 2906---0000 2908---0000 2910---0000 2912---0000 2914---0000 2916---0000 2918---0000 2920---0000 2922---0000 2924---0000 2926---0000 2928---0000 2930---0000 2932---0000 2934---0000 2936---0000 2938---0000 2940---0000 2942---0000 2944---0000 2946---0000 2948---0000 2950---0000 2952---0000 2954---0000 2956---0000 2958---0000 2960---0000 2962---0000 2964---0000 2966---0000 2968---0000 2970---0000 2972---0000 2974---0000 2976---0000 2978---0000 2980---0000 2982---0000 2984---0000 2986---0000 2988---0000 2990---0000 2992---0000 2994---0000 2996---0000 2998---0000 3000---0000 3002---0000 3004---0000 3006---0000 3008---0000 3010---0000 3012---0000 3014---0000 3016---0000 3018---0000 3020---0000 3022---0000 3024---0000 3026---0000 3028---0000 3030---0000 3032---0000 3034---0000 3036---0000 3038---0000 3040---0000 3042---0000 3044---0000 3046---0000 3048---0000 3050---0000 3052---0000 3054---0000 3056---0000 3058---0000 3060---0000 3062---0000 3064---0000 3066---0000 3068---0000 3070---0000 3072---0000 3074---0000 3076---0000 3078---0000 3080---0000 3082---0000 3084---0000 3086---0000 3088---0000 3090---0000 3092---0000 3094---0000 3096---0000 3098---0000 3100---0000 3102---0000 3104---0000 3106---0000 3108---0000 3110---0000 3112---0000 3114---0000 3116---0000 3118---0000 3120---0000 3122---0000 3124---0000 3126---0000 3128---0000 3130---0000 3132---0000 3134---0000 3136---0000 3138---0000 3140---0000 3142---0000 3144---0000 3146---0000 3148---0000 3150---0000 3152---0000 3154---0000 3156---0000 3158---0000 3160---0000 3162---0000 3164---0000 3166---0000 3168---0000 3170---0000 3172---0000 3174---0000 3176---0000 3178---0000 3180---0000 3182---0000 3184---0000 3186---0000 3188---0000 3190---0000 3192---0000 3194---0000 3196---0000 3198---0000 3200---0000 3202---0000 3204---0000 3206---0000 3208---0000 3210---0000 3212---0000 3214---0000 3216---0000 3218---0000 3220---0000 3222---0000 3224---0000 3226---0000 3228---0000 3230---0000 3232---0000 3234---0000 3236---0000 3238---0000 3240---0000 3242---0000 3244---0000 3246---0000 3248---0000 3250---0000 3252---0000 3254---0000 3256---0000 3258---0000 3260---0000 3262---0000 3264---0000 3266---0000 3268---0000 3270---0000 3272---0000 3274---0000 3276---0000 3278---0000 3280---0000 3282---0000 3284---0000 3286---0000 3288---0000 3290---0000 3292---0000 3294---0000 3296---0000 3298---0000 3300---0000 3302---0000 3304---0000 3306---0000 3308---0000 3310---0000 3312---0000 3314---0000 3316---0000 3318---0000 3320---0000 3322---0000 3324---0000 3326---0000 3328---0000 3330---0000 3332---0000 3334---0000 3336---0000 3338---0000 3340---0000 3342---0000 3344---0000 3346---0000 3348---0000 3350---0000 3352---0000 3354---0000 3356---0000 3358---0000 3360---0000 3362---0000 3364---0000 3366---0000 3368---0000 3370---0000 3372---0000 3374---0000 3376---0000 3378---0000 3380---0000 3382---0000 3384---0000 3386---0000 3388---0000 3390---0000 3392---0000 3394---0000 3396---0000 3398---0000 3400---0000 3402---0000 3404---0000 3406---0000 3408---0000 3410---0000 3412---0000 3414---0000 3416---0000 3418---0000 3420---0000 3422---0000 3424---0000 3426---0000 3428---0000 3430---0000 3432---0000 3434---0000 3436---0000 3438---0000 3440---0000 3442---0000 3444---0000 3446---0000 3448---0000 3450---0000 3452---0000 3454---0000 3456---0000 3458---0000 3460---0000 3462---0000 3464---0000 3466---0000 3468---0000 3470---0000 3472---0000 3474---0000 3476---0000 3478---0000 3480---0000 3482---0000 3484---0000 3486---0000 3488---0000 3490---0000 3492---0000 3494---0000 3496---0000 3498---0000 3500---0000 3502---0000 3504---0000 3506---0000 3508---0000 3510---0000 3512---0000 3514---0000 3516---0000 3518---0000 3520---0000 3522---0000 3524---0000 3526---0000 3528---0000 3530---0000 3532---0000 3534---0000 3536---0000 3538---0000 3540---0000 3542---0000 3544---0000 3546---0000 3548---0000 3550---0000 3552---0000 3554---0000 3556---0000 3558---0000 3560---0000 3562---0000 3564---0000 3566---0000 3568---0000 3570---0000 3572---0000 3574---0000 3576---0000 3578---0000 3580---0000 3582---0000 3584---0000 3586---0000 3588---0000 3590---0000 3592---0000 3594---0000 3596---0000 3598---0000 3600---0000 3602---0000 3604---0000 3606---0000 3608---0000 3610---0000 3612---0000 3614---0000 3616---0000 3618---0000 3620---0000 3622---0000 3624---0000 3626---0000 3628---0000 3630---0000 3632---0000 3634---0000 3636---0000 3638---0000 3640---0000 3642---0000 3644---0000 3646---0000 3648---0000 3650---0000 3652---0000 3654---0000 3656---0000 3658---0000 3660---0000 3662---0000 3664---0000 3666---0000 3668---0000 3670---0000 3672---0000 3674---0000 3676---0000 3678---0000 3680---0000 3682---0000 3684---0000 3686---0000 3688---0000 3690---0000 3692---0000 3694---0000 3696---0000 3698---0000 3700---0000 3702---0000 3704---0000 3706---0000 3708---0000 3710---0000 3712---0000 3714---0000 3716---0000 3718---0000 3720---0000 3722---0000 3724---0000 3726---0000 3728---0000 3730---0000 3732---0000 3734---0000 3736---0000 3738---0000 3740---0000 3742---0000 3744---0000 3746---0000 3748---0000 3750---0000 3752---0000 3754---0000 3756---0000 3758---0000 3760---0000 3762---0000 3764---0000 3766---0000 3768---0000 3770---0000 3772---0000 3774---0000 3776---0000 3778---0000 3780---0000 3782---0000 3784---0000 3786---0000 3788---0000 3790---0000 3792---0000 3794---0000 3796---0000 3798---0000 3800---0000 3802---0000 3804---0000 3806---0000 3808---0000 3810---0000 3812---0000 3814---0000 3816---0000 3818---0000 3820---0000 3822---0000 3824---0000 3826---0000 3828---0000 3830---0000 3832---0000 3834---0000 3836---0000 3838---0000 3840---0000 3842---0000 3844---0000 3846---0000 3848---0000 3850---0000 3852---0000 3854---0000 3856---0000 3858---0000 3860---0000 3862---0000 3864---0000 3866---0000 3868---0000 3870---0000 3872---0000 3874---0000 3876---0000 3878---0000 3880---0000 3882---0000 3884---0000 3886---0000 3888---0000 3890---0000 3892---0000 3894---0000 3896---0000 3898---0000 3900---0000 3902---0000 3904---0000 3906---0000 3908---0000 3910---0000 3912---0000 3914---0000 3916---0000 3918---0000 3920---0000 3922---0000 3924---0000 3926---0000 3928---0000 3930---0000 3932---0000 3934---0000 3936---0000 3938---0000 3940---0000 3942---0000 3944---0000 3946---0000 3948---0000 3950---0000 3952---0000 3954---0000 3956---0000 3958---0000 3960---0000 3962---0000 3964---0000 3966---0000 3968---0000 3970---0000 3972---0000 3974---0000 3976---0000 3978---0000 3980---0000 3982---0000 3984---0000 3986---0000 3988---0000 3990---0000 3992---0000 3994---0000 3996---0000 3998---0000 4000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m16.353s user 0m2.881s sys 0m0.015s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:43:37 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=1000, 3000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? 1000---0000 1002---0000 1004---0000 1006---0000 1008---0000 1010---0000 1012---0000 1014---0000 1016---0000 1018---0000 1020---0000 1022---0000 1024---0000 1026---0000 1028---0000 1030---0000 1032---0000 1034---0000 1036---0000 1038---0000 1040---0000 1042---0000 1044---0000 1046---0000 1048---0000 1050---0000 1052---0000 1054---0000 1056---0000 1058---0000 1060---0000 1062---0000 1064---0000 1066---0000 1068---0000 1070---0000 1072---0000 1074---0000 1076---0000 1078---0000 1080---0000 1082---0000 1084---0000 1086---0000 1088---0000 1090---0000 1092---0000 1094---0000 1096---0000 1098---0000 1100---0000 1102---0000 1104---0000 1106---0000 1108---0000 1110---0000 1112---0000 1114---0000 1116---0000 1118---0000 1120---0000 1122---0000 1124---0000 1126---0000 1128---0000 1130---0000 1132---0000 1134---0000 1136---0000 1138---0000 1140---0000 1142---0000 1144---0000 1146---0000 1148---0000 1150---0000 1152---0000 1154---0000 1156---0000 1158---0000 1160---0000 1162---0000 1164---0000 1166---0000 1168---0000 1170---0000 1172---0000 1174---0000 1176---0000 1178---0000 1180---0000 1182---0000 1184---0000 1186---0000 1188---0000 1190---0000 1192---0000 1194---0000 1196---0000 1198---0000 1200---0000 1202---0000 1204---0000 1206---0000 1208---0000 1210---0000 1212---0000 1214---0000 1216---0000 1218---0000 1220---0000 1222---0000 1224---0000 1226---0000 1228---0000 1230---0000 1232---0000 1234---0000 1236---0000 1238---0000 1240---0000 1242---0000 1244---0000 1246---0000 1248---0000 1250---0000 1252---0000 1254---0000 1256---0000 1258---0000 1260---0000 1262---0000 1264---0000 1266---0000 1268---0000 1270---0000 1272---0000 1274---0000 1276---0000 1278---0000 1280---0000 1282---0000 1284---0000 1286---0000 1288---0000 1290---0000 1292---0000 1294---0000 1296---0000 1298---0000 1300---0000 1302---0000 1304---0000 1306---0000 1308---0000 1310---0000 1312---0000 1314---0000 1316---0000 1318---0000 1320---0000 1322---0000 1324---0000 1326---0000 1328---0000 1330---0000 1332---0000 1334---0000 1336---0000 1338---0000 1340---0000 1342---0000 1344---0000 1346---0000 1348---0000 1350---0000 1352---0000 1354---0000 1356---0000 1358---0000 1360---0000 1362---0000 1364---0000 1366---0000 1368---0000 1370---0000 1372---0000 1374---0000 1376---0000 1378---0000 1380---0000 1382---0000 1384---0000 1386---0000 1388---0000 1390---0000 1392---0000 1394---0000 1396---0000 1398---0000 1400---0000 1402---0000 1404---0000 1406---0000 1408---0000 1410---0000 1412---0000 1414---0000 1416---0000 1418---0000 1420---0000 1422---0000 1424---0000 1426---0000 1428---0000 1430---0000 1432---0000 1434---0000 1436---0000 1438---0000 1440---0000 1442---0000 1444---0000 1446---0000 1448---0000 1450---0000 1452---0000 1454---0000 1456---0000 1458---0000 1460---0000 1462---0000 1464---0000 1466---0000 1468---0000 1470---0000 1472---0000 1474---0000 1476---0000 1478---0000 1480---0000 1482---0000 1484---0000 1486---0000 1488---0000 1490---0000 1492---0000 1494---0000 1496---0000 1498---0000 1500---0000 1502---0000 1504---0000 1506---0000 1508---0000 1510---0000 1512---0000 1514---0000 1516---0000 1518---0000 1520---0000 1522---0000 1524---0000 1526---0000 1528---0000 1530---0000 1532---0000 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1866---0000 1868---0000 1870---0000 1872---0000 1874---0000 1876---0000 1878---0000 1880---0000 1882---0000 1884---0000 1886---0000 1888---0000 1890---0000 1892---0000 1894---0000 1896---0000 1898---0000 1900---0000 1902---0000 1904---0000 1906---0000 1908---0000 1910---0000 1912---0000 1914---0000 1916---0000 1918---0000 1920---0000 1922---0000 1924---0000 1926---0000 1928---0000 1930---0000 1932---0000 1934---0000 1936---0000 1938---0000 1940---0000 1942---0000 1944---0000 1946---0000 1948---0000 1950---0000 1952---0000 1954---0000 1956---0000 1958---0000 1960---0000 1962---0000 1964---0000 1966---0000 1968---0000 1970---0000 1972---0000 1974---0000 1976---0000 1978---0000 1980---0000 1982---0000 1984---0000 1986---0000 1988---0000 1990---0000 1992---0000 1994---0000 1996---0000 1998---0000 2000---0000 2002---0000 2004---0000 2006---0000 2008---0000 2010---0000 2012---0000 2014---0000 2016---0000 2018---0000 2020---0000 2022---0000 2024---0000 2026---0000 2028---0000 2030---0000 2032---0000 2034---0000 2036---0000 2038---0000 2040---0000 2042---0000 2044---0000 2046---0000 2048---0000 2050---0000 2052---0000 2054---0000 2056---0000 2058---0000 2060---0000 2062---0000 2064---0000 2066---0000 2068---0000 2070---0000 2072---0000 2074---0000 2076---0000 2078---0000 2080---0000 2082---0000 2084---0000 2086---0000 2088---0000 2090---0000 2092---0000 2094---0000 2096---0000 2098---0000 2100---0000 2102---0000 2104---0000 2106---0000 2108---0000 2110---0000 2112---0000 2114---0000 2116---0000 2118---0000 2120---0000 2122---0000 2124---0000 2126---0000 2128---0000 2130---0000 2132---0000 2134---0000 2136---0000 2138---0000 2140---0000 2142---0000 2144---0000 2146---0000 2148---0000 2150---0000 2152---0000 2154---0000 2156---0000 2158---0000 2160---0000 2162---0000 2164---0000 2166---0000 2168---0000 2170---0000 2172---0000 2174---0000 2176---0000 2178---0000 2180---0000 2182---0000 2184---0000 2186---0000 2188---0000 2190---0000 2192---0000 2194---0000 2196---0000 2198---0000 2200---0000 2202---0000 2204---0000 2206---0000 2208---0000 2210---0000 2212---0000 2214---0000 2216---0000 2218---0000 2220---0000 2222---0000 2224---0000 2226---0000 2228---0000 2230---0000 2232---0000 2234---0000 2236---0000 2238---0000 2240---0000 2242---0000 2244---0000 2246---0000 2248---0000 2250---0000 2252---0000 2254---0000 2256---0000 2258---0000 2260---0000 2262---0000 2264---0000 2266---0000 2268---0000 2270---0000 2272---0000 2274---0000 2276---0000 2278---0000 2280---0000 2282---0000 2284---0000 2286---0000 2288---0000 2290---0000 2292---0000 2294---0000 2296---0000 2298---0000 2300---0000 2302---0000 2304---0000 2306---0000 2308---0000 2310---0000 2312---0000 2314---0000 2316---0000 2318---0000 2320---0000 2322---0000 2324---0000 2326---0000 2328---0000 2330---0000 2332---0000 2334---0000 2336---0000 2338---0000 2340---0000 2342---0000 2344---0000 2346---0000 2348---0000 2350---0000 2352---0000 2354---0000 2356---0000 2358---0000 2360---0000 2362---0000 2364---0000 2366---0000 2368---0000 2370---0000 2372---0000 2374---0000 2376---0000 2378---0000 2380---0000 2382---0000 2384---0000 2386---0000 2388---0000 2390---0000 2392---0000 2394---0000 2396---0000 2398---0000 2400---0000 2402---0000 2404---0000 2406---0000 2408---0000 2410---0000 2412---0000 2414---0000 2416---0000 2418---0000 2420---0000 2422---0000 2424---0000 2426---0000 2428---0000 2430---0000 2432---0000 2434---0000 2436---0000 2438---0000 2440---0000 2442---0000 2444---0000 2446---0000 2448---0000 2450---0000 2452---0000 2454---0000 2456---0000 2458---0000 2460---0000 2462---0000 2464---0000 2466---0000 2468---0000 2470---0000 2472---0000 2474---0000 2476---0000 2478---0000 2480---0000 2482---0000 2484---0000 2486---0000 2488---0000 2490---0000 2492---0000 2494---0000 2496---0000 2498---0000 2500---0000 2502---0000 2504---0000 2506---0000 2508---0000 2510---0000 2512---0000 2514---0000 2516---0000 2518---0000 2520---0000 2522---0000 2524---0000 2526---0000 2528---0000 2530---0000 2532---0000 2534---0000 2536---0000 2538---0000 2540---0000 2542---0000 2544---0000 2546---0000 2548---0000 2550---0000 2552---0000 2554---0000 2556---0000 2558---0000 2560---0000 2562---0000 2564---0000 2566---0000 2568---0000 2570---0000 2572---0000 2574---0000 2576---0000 2578---0000 2580---0000 2582---0000 2584---0000 2586---0000 2588---0000 2590---0000 2592---0000 2594---0000 2596---0000 2598---0000 2600---0000 2602---0000 2604---0000 2606---0000 2608---0000 2610---0000 2612---0000 2614---0000 2616---0000 2618---0000 2620---0000 2622---0000 2624---0000 2626---0000 2628---0000 2630---0000 ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m7.931s user 0m4.057s sys 0m0.015s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:42:58 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m9.921s user 0m1.881s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:42:45 2006 Input: f=x^4+2*x^2-11 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 - 11 ? %2 = [x - 1, x^2 - 3, x^4 - 2*x^3 - 4*x^2 + 14*x - 11, x^4 + 2*x^2 - 11] ? ? %4 = [-1 1] [2 6] [3 2] [11 1] ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m10.100s user 0m1.876s sys 0m0.015s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:20:14 2006 Input: f=x^4+2*x^2-11 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 - 11 ? %2 = [x - 1, x^2 - 3, x^4 - 2*x^3 - 4*x^2 + 14*x - 11, x^4 + 2*x^2 - 11] ? ? %4 = [-1 1] [2 6] [3 2] [11 1] ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m10.009s user 0m1.877s sys 0m0.013s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:19:49 2006 Input: f=x^4+2*x^2+11 polred(f) nf=nfinit(f); factor(nf.disc) forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 11 ? %2 = [x - 1, x^2 + 10, x^4 - 20*x^2 + 1100, x^4 + 2*x^2 + 11] ? ? %4 = [2 10] [5 2] [11 1] ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m10.999s user 0m1.880s sys 0m0.016s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:19:11 2006 Input: f=x^4+2*x^2+11 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 11 ? %2 = [x - 1, x^2 + 10, x^4 - 20*x^2 + 1100, x^4 + 2*x^2 + 11] ? ? ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m10.187s user 0m1.878s sys 0m0.015s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:04:23 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=5000, 6000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 5000---0000 5002---0000 5004---0000 5006---0000 5008---0000 5010---0000 5012---0000 5014---0000 5016---0000 5018---0000 5020---0000 5022---0000 5024---0000 5026---0000 5028---0000 5030---0000 5032---0000 5034---0000 5036---0000 5038---0000 5040---0000 5042---0000 5044---0000 5046---0000 5048---0000 5050---0000 5052---0000 5054---0000 5056---0000 5058---0000 5060---0000 5062---0000 5064---0000 5066---0000 5068---0000 5070---0000 5072---0000 5074---0000 5076---0000 5078---0000 5080---0000 5082---0000 5084---0000 5086---0000 5088---0000 5090---0000 5092---0000 5094---0000 5096---0000 5098---0000 5100---0000 5102---0000 5104---0000 5106---0000 5108---0000 5110---0000 5112---0000 5114---0000 5116---0000 5118---0000 5120---0000 5122---0000 5124---0000 5126---0000 5128---0000 5130---0000 5132---0000 5134---0000 5136---0000 5138---0000 5140---0000 5142---0000 5144---0000 5146---0000 5148---0000 5150---0000 5152---0000 5154---0000 5156---0000 5158---0000 5160---0000 5162---0000 5164---0000 5166---0000 5168---0000 5170---0000 5172---0000 5174---0000 5176---0000 5178---0000 5180---0000 5182---0000 5184---0000 5186---0000 5188---0000 5190---0000 5192---0000 5194---0000 5196---0000 5198---0000 5200---0000 5202---0000 5204---0000 5206---0000 5208---0000 5210---0000 5212---0000 5214---0000 5216---0000 5218---0000 5220---0000 5222---0000 5224---0000 5226---0000 5228---0000 5230---0000 5232---0000 5234---0000 5236---0000 5238---0000 5240---0000 5242---0000 5244---0000 5246---0000 5248---0000 5250---0000 5252---0000 5254---0000 5256---0000 5258---0000 5260---0000 5262---0000 5264---0000 5266---0000 5268---0000 5270---0000 5272---0000 5274---0000 5276---0000 5278---0000 5280---0000 5282---0000 5284---0000 5286---0000 5288---0000 5290---0000 5292---0000 5294---0000 5296---0000 5298---0000 5300---0000 5302---0000 5304---0000 5306---0000 5308---0000 5310---0000 5312---0000 5314---0000 5316---0000 5318---0000 5320---0000 5322---0000 5324---0000 5326---0000 5328---0000 5330---0000 5332---0000 5334---0000 5336---0000 5338---0000 5340---0000 5342---0000 5344---0000 5346---0000 5348---0000 5350---0000 5352---0000 5354---0000 5356---0000 5358---0000 5360---0000 5362---0000 5364---0000 5366---0000 5368---0000 5370---0000 5372---0000 5374---0000 5376---0000 5378---0000 5380---0000 5382---0000 5384---0000 5386---0000 5388---0000 5390---0000 5392---0000 5394---0000 5396---0000 5398---0000 5400---0000 5402---0000 5404---0000 5406---0000 5408---0000 5410---0000 5412---0000 5414---0000 5416---0000 5418---0000 5420---0000 5422---0000 5424---0000 5426---0000 5428---0000 5430---0000 5432---0000 5434---0000 5436---0000 5438---0000 5440---0000 5442---0000 5444---0000 5446---0000 5448---0000 5450---0000 5452---0000 5454---0000 5456---0000 5458---0000 5460---0000 5462---0000 5464---0000 5466---0000 5468---0000 5470---0000 5472---0000 5474---0000 5476---0000 5478---0000 5480---0000 5482---0000 5484---0000 5486---0000 5488---0000 5490---0000 5492---0000 5494---0000 5496---0000 5498---0000 5500---0000 5502---0000 5504---0000 5506---0000 5508---0000 5510---0000 5512---0000 5514---0000 5516---0000 5518---0000 5520---0000 5522---0000 5524---0000 5526---0000 5528---0000 5530---0000 5532---0000 5534---0000 5536---0000 5538---0000 5540---0000 5542---0000 5544---0000 5546---0000 5548---0000 5550---0000 5552---0000 5554---0000 5556---0000 5558---0000 5560---0000 5562---0000 5564---0000 5566---0000 5568---0000 5570---0000 5572---0000 5574---0000 5576---0000 5578---0000 5580---0000 5582---0000 5584---0000 5586---0000 5588---0000 5590---0000 5592---0000 5594---0000 5596---0000 5598---0000 5600---0000 5602---0000 5604---0000 5606---0000 5608---0000 5610---0000 5612---0000 5614---0000 5616---0000 5618---0000 5620---0000 5622---0000 5624---0000 5626---0000 5628---0000 5630---0000 5632---0000 5634---0000 5636---0000 5638---0000 5640---0000 5642---0000 5644---0000 5646---0000 5648---0000 5650---0000 5652---0000 5654---0000 5656---0000 5658---0000 5660---0000 5662---0000 5664---0000 5666---0000 5668---0000 5670---0000 5672---0000 5674---0000 5676---0000 5678---0000 5680---0000 5682---0000 5684---0000 5686---0000 5688---0000 5690---0000 5692---0000 5694---0000 5696---0000 5698---0000 5700---0000 5702---0000 5704---0000 5706---0000 5708---0000 5710---0000 5712---0000 5714---0000 5716---0000 5718---0000 5720---0000 5722---0000 5724---0000 5726---0000 5728---0000 5730---0000 5732---0000 5734---0000 5736---0000 5738---0000 5740---0000 5742---0000 5744---0000 5746---0000 5748---0000 5750---0000 5752---0000 5754---0000 5756---0000 5758---0000 5760---0000 5762---0000 5764---0000 5766---0000 5768---0000 5770---0000 5772---0000 5774---0000 5776---0000 5778---0000 5780---0000 5782---0000 5784---0000 5786---0000 5788---0000 5790---0000 5792---0000 5794---0000 5796---0000 5798---0000 5800---0000 5802---0000 5804---0000 5806---0000 5808---0000 5810---0000 5812---0000 5814---0000 5816---0000 5818---0000 5820---0000 5822---0000 5824---0000 5826---0000 5828---0000 5830---0000 5832---0000 5834---0000 5836---0000 5838---0000 5840---0000 5842---0000 5844---0000 5846---0000 5848---0000 5850---0000 5852---0000 5854---0000 5856---0000 5858---0000 5860---0000 5862---0000 5864---0000 5866---0000 5868---0000 5870---0000 5872---0000 5874---0000 5876---0000 5878---0000 5880---0000 5882---0000 5884---0000 5886---0000 5888---0000 5890---0000 5892---0000 5894---0000 5896---0000 5898---0000 5900---0000 5902---0000 5904---0000 5906---0000 5908---0000 5910---0000 5912---0000 5914---0000 5916---0000 5918---0000 5920---0000 5922---0000 5924---0000 5926---0000 5928---0000 5930---0000 5932---0000 5934---0000 5936---0000 5938---0000 5940---0000 5942---0000 5944---0000 5946---0000 5948---0000 5950---0000 5952---0000 5954---0000 5956---0000 5958---0000 5960---0000 5962---0000 5964---0000 5966---0000 5968---0000 5970---0000 5972---0000 5974---0000 5976---0000 5978---0000 5980---0000 5982---0000 5984---0000 5986---0000 5988---0000 5990---0000 5992---0000 5994---0000 5996---0000 5998---0000 6000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m11.364s user 0m2.140s sys 0m0.014s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:03:51 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=4000, 5000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 4000---0000 4002---0000 4004---0000 4006---0000 4008---0000 4010---0000 4012---0000 4014---0000 4016---0000 4018---0000 4020---0000 4022---0000 4024---0000 4026---0000 4028---0000 4030---0000 4032---0000 4034---0000 4036---0000 4038---0000 4040---0000 4042---0000 4044---0000 4046---0000 4048---0000 4050---0000 4052---0000 4054---0000 4056---0000 4058---0000 4060---0000 4062---0000 4064---0000 4066---0000 4068---0000 4070---0000 4072---0000 4074---0000 4076---0000 4078---0000 4080---0000 4082---0000 4084---0000 4086---0000 4088---0000 4090---0000 4092---0000 4094---0000 4096---0000 4098---0000 4100---0000 4102---0000 4104---0000 4106---0000 4108---0000 4110---0000 4112---0000 4114---0000 4116---0000 4118---0000 4120---0000 4122---0000 4124---0000 4126---0000 4128---0000 4130---0000 4132---0000 4134---0000 4136---0000 4138---0000 4140---0000 4142---0000 4144---0000 4146---0000 4148---0000 4150---0000 4152---0000 4154---0000 4156---0000 4158---0000 4160---0000 4162---0000 4164---0000 4166---0000 4168---0000 4170---0000 4172---0000 4174---0000 4176---0000 4178---0000 4180---0000 4182---0000 4184---0000 4186---0000 4188---0000 4190---0000 4192---0000 4194---0000 4196---0000 4198---0000 4200---0000 4202---0000 4204---0000 4206---0000 4208---0000 4210---0000 4212---0000 4214---0000 4216---0000 4218---0000 4220---0000 4222---0000 4224---0000 4226---0000 4228---0000 4230---0000 4232---0000 4234---0000 4236---0000 4238---0000 4240---0000 4242---0000 4244---0000 4246---0000 4248---0000 4250---0000 4252---0000 4254---0000 4256---0000 4258---0000 4260---0000 4262---0000 4264---0000 4266---0000 4268---0000 4270---0000 4272---0000 4274---0000 4276---0000 4278---0000 4280---0000 4282---0000 4284---0000 4286---0000 4288---0000 4290---0000 4292---0000 4294---0000 4296---0000 4298---0000 4300---0000 4302---0000 4304---0000 4306---0000 4308---0000 4310---0000 4312---0000 4314---0000 4316---0000 4318---0000 4320---0000 4322---0000 4324---0000 4326---0000 4328---0000 4330---0000 4332---0000 4334---0000 4336---0000 4338---0000 4340---0000 4342---0000 4344---0000 4346---0000 4348---0000 4350---0000 4352---0000 4354---0000 4356---0000 4358---0000 4360---0000 4362---0000 4364---0000 4366---0000 4368---0000 4370---0000 4372---0000 4374---0000 4376---0000 4378---0000 4380---0000 4382---0000 4384---0000 4386---0000 4388---0000 4390---0000 4392---0000 4394---0000 4396---0000 4398---0000 4400---0000 4402---0000 4404---0000 4406---0000 4408---0000 4410---0000 4412---0000 4414---0000 4416---0000 4418---0000 4420---0000 4422---0000 4424---0000 4426---0000 4428---0000 4430---0000 4432---0000 4434---0000 4436---0000 4438---0000 4440---0000 4442---0000 4444---0000 4446---0000 4448---0000 4450---0000 4452---0000 4454---0000 4456---0000 4458---0000 4460---0000 4462---0000 4464---0000 4466---0000 4468---0000 4470---0000 4472---0000 4474---0000 4476---0000 4478---0000 4480---0000 4482---0000 4484---0000 4486---0000 4488---0000 4490---0000 4492---0000 4494---0000 4496---0000 4498---0000 4500---0000 4502---0000 4504---0000 4506---0000 4508---0000 4510---0000 4512---0000 4514---0000 4516---0000 4518---0000 4520---0000 4522---0000 4524---0000 4526---0000 4528---0000 4530---0000 4532---0000 4534---0000 4536---0000 4538---0000 4540---0000 4542---0000 4544---0000 4546---0000 4548---0000 4550---0000 4552---0000 4554---0000 4556---0000 4558---0000 4560---0000 4562---0000 4564---0000 4566---0000 4568---0000 4570---0000 4572---0000 4574---0000 4576---0000 4578---0000 4580---0000 4582---0000 4584---0000 4586---0000 4588---0000 4590---0000 4592---0000 4594---0000 4596---0000 4598---0000 4600---0000 4602---0000 4604---0000 4606---0000 4608---0000 4610---0000 4612---0000 4614---0000 4616---0000 4618---0000 4620---0000 4622---0000 4624---0000 4626---0000 4628---0000 4630---0000 4632---0000 4634---0000 4636---0000 4638---0000 4640---0000 4642---0000 4644---0000 4646---0000 4648---0000 4650---0000 4652---0000 4654---0000 4656---0000 4658---0000 4660---0000 4662---0000 4664---0000 4666---0000 4668---0000 4670---0000 4672---0000 4674---0000 4676---0000 4678---0000 4680---0000 4682---0000 4684---0000 4686---0000 4688---0000 4690---0000 4692---0000 4694---0000 4696---0000 4698---0000 4700---0000 4702---0000 4704---0000 4706---0000 4708---0000 4710---0000 4712---0000 4714---0000 4716---0000 4718---0000 4720---0000 4722---0000 4724---0000 4726---0000 4728---0000 4730---0000 4732---0000 4734---0000 4736---0000 4738---0000 4740---0000 4742---0000 4744---0000 4746---0000 4748---0000 4750---0000 4752---0000 4754---0000 4756---0000 4758---0000 4760---0000 4762---0000 4764---0000 4766---0000 4768---0000 4770---0000 4772---0000 4774---0000 4776---0000 4778---0000 4780---0000 4782---0000 4784---0000 4786---0000 4788---0000 4790---0000 4792---0000 4794---0000 4796---0000 4798---0000 4800---0000 4802---0000 4804---0000 4806---0000 4808---0000 4810---0000 4812---0000 4814---0000 4816---0000 4818---0000 4820---0000 4822---0000 4824---0000 4826---0000 4828---0000 4830---0000 4832---0000 4834---0000 4836---0000 4838---0000 4840---0000 4842---0000 4844---0000 4846---0000 4848---0000 4850---0000 4852---0000 4854---0000 4856---0000 4858---0000 4860---0000 4862---0000 4864---0000 4866---0000 4868---0000 4870---0000 4872---0000 4874---0000 4876---0000 4878---0000 4880---0000 4882---0000 4884---0000 4886---0000 4888---0000 4890---0000 4892---0000 4894---0000 4896---0000 4898---0000 4900---0000 4902---0000 4904---0000 4906---0000 4908---0000 4910---0000 4912---0000 4914---0000 4916---0000 4918---0000 4920---0000 4922---0000 4924---0000 4926---0000 4928---0000 4930---0000 4932---0000 4934---0000 4936---0000 4938---0000 4940---0000 4942---0000 4944---0000 4946---0000 4948---0000 4950---0000 4952---0000 4954---0000 4956---0000 4958---0000 4960---0000 4962---0000 4964---0000 4966---0000 4968---0000 4970---0000 4972---0000 4974---0000 4976---0000 4978---0000 4980---0000 4982---0000 4984---0000 4986---0000 4988---0000 4990---0000 4992---0000 4994---0000 4996---0000 4998---0000 5000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m4.262s user 0m2.114s sys 0m0.014s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:02:25 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=3000, 4000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 3000---0000 3002---0000 3004---0000 3006---0000 3008---0000 3010---0000 3012---0000 3014---0000 3016---0000 3018---0000 3020---0000 3022---0000 3024---0000 3026---0000 3028---0000 3030---0000 3032---0000 3034---0000 3036---0000 3038---0000 3040---0000 3042---0000 3044---0000 3046---0000 3048---0000 3050---0000 3052---0000 3054---0000 3056---0000 3058---0000 3060---0000 3062---0000 3064---0000 3066---0000 3068---0000 3070---0000 3072---0000 3074---0000 3076---0000 3078---0000 3080---0000 3082---0000 3084---0000 3086---0000 3088---0000 3090---0000 3092---0000 3094---0000 3096---0000 3098---0000 3100---0000 3102---0000 3104---0000 3106---0000 3108---0000 3110---0000 3112---0000 3114---0000 3116---0000 3118---0000 3120---0000 3122---0000 3124---0000 3126---0000 3128---0000 3130---0000 3132---0000 3134---0000 3136---0000 3138---0000 3140---0000 3142---0000 3144---0000 3146---0000 3148---0000 3150---0000 3152---0000 3154---0000 3156---0000 3158---0000 3160---0000 3162---0000 3164---0000 3166---0000 3168---0000 3170---0000 3172---0000 3174---0000 3176---0000 3178---0000 3180---0000 3182---0000 3184---0000 3186---0000 3188---0000 3190---0000 3192---0000 3194---0000 3196---0000 3198---0000 3200---0000 3202---0000 3204---0000 3206---0000 3208---0000 3210---0000 3212---0000 3214---0000 3216---0000 3218---0000 3220---0000 3222---0000 3224---0000 3226---0000 3228---0000 3230---0000 3232---0000 3234---0000 3236---0000 3238---0000 3240---0000 3242---0000 3244---0000 3246---0000 3248---0000 3250---0000 3252---0000 3254---0000 3256---0000 3258---0000 3260---0000 3262---0000 3264---0000 3266---0000 3268---0000 3270---0000 3272---0000 3274---0000 3276---0000 3278---0000 3280---0000 3282---0000 3284---0000 3286---0000 3288---0000 3290---0000 3292---0000 3294---0000 3296---0000 3298---0000 3300---0000 3302---0000 3304---0000 3306---0000 3308---0000 3310---0000 3312---0000 3314---0000 3316---0000 3318---0000 3320---0000 3322---0000 3324---0000 3326---0000 3328---0000 3330---0000 3332---0000 3334---0000 3336---0000 3338---0000 3340---0000 3342---0000 3344---0000 3346---0000 3348---0000 3350---0000 3352---0000 3354---0000 3356---0000 3358---0000 3360---0000 3362---0000 3364---0000 3366---0000 3368---0000 3370---0000 3372---0000 3374---0000 3376---0000 3378---0000 3380---0000 3382---0000 3384---0000 3386---0000 3388---0000 3390---0000 3392---0000 3394---0000 3396---0000 3398---0000 3400---0000 3402---0000 3404---0000 3406---0000 3408---0000 3410---0000 3412---0000 3414---0000 3416---0000 3418---0000 3420---0000 3422---0000 3424---0000 3426---0000 3428---0000 3430---0000 3432---0000 3434---0000 3436---0000 3438---0000 3440---0000 3442---0000 3444---0000 3446---0000 3448---0000 3450---0000 3452---0000 3454---0000 3456---0000 3458---0000 3460---0000 3462---0000 3464---0000 3466---0000 3468---0000 3470---0000 3472---0000 3474---0000 3476---0000 3478---0000 3480---0000 3482---0000 3484---0000 3486---0000 3488---0000 3490---0000 3492---0000 3494---0000 3496---0000 3498---0000 3500---0000 3502---0000 3504---0000 3506---0000 3508---0000 3510---0000 3512---0000 3514---0000 3516---0000 3518---0000 3520---0000 3522---0000 3524---0000 3526---0000 3528---0000 3530---0000 3532---0000 3534---0000 3536---0000 3538---0000 3540---0000 3542---0000 3544---0000 3546---0000 3548---0000 3550---0000 3552---0000 3554---0000 3556---0000 3558---0000 3560---0000 3562---0000 3564---0000 3566---0000 3568---0000 3570---0000 3572---0000 3574---0000 3576---0000 3578---0000 3580---0000 3582---0000 3584---0000 3586---0000 3588---0000 3590---0000 3592---0000 3594---0000 3596---0000 3598---0000 3600---0000 3602---0000 3604---0000 3606---0000 3608---0000 3610---0000 3612---0000 3614---0000 3616---0000 3618---0000 3620---0000 3622---0000 3624---0000 3626---0000 3628---0000 3630---0000 3632---0000 3634---0000 3636---0000 3638---0000 3640---0000 3642---0000 3644---0000 3646---0000 3648---0000 3650---0000 3652---0000 3654---0000 3656---0000 3658---0000 3660---0000 3662---0000 3664---0000 3666---0000 3668---0000 3670---0000 3672---0000 3674---0000 3676---0000 3678---0000 3680---0000 3682---0000 3684---0000 3686---0000 3688---0000 3690---0000 3692---0000 3694---0000 3696---0000 3698---0000 3700---0000 3702---0000 3704---0000 3706---0000 3708---0000 3710---0000 3712---0000 3714---0000 3716---0000 3718---0000 3720---0000 3722---0000 3724---0000 3726---0000 3728---0000 3730---0000 3732---0000 3734---0000 3736---0000 3738---0000 3740---0000 3742---0000 3744---0000 3746---0000 3748---0000 3750---0000 3752---0000 3754---0000 3756---0000 3758---0000 3760---0000 3762---0000 3764---0000 3766---0000 3768---0000 3770---0000 3772---0000 3774---0000 3776---0000 3778---0000 3780---0000 3782---0000 3784---0000 3786---0000 3788---0000 3790---0000 3792---0000 3794---0000 3796---0000 3798---0000 3800---0000 3802---0000 3804---0000 3806---0000 3808---0000 3810---0000 3812---0000 3814---0000 3816---0000 3818---0000 3820---0000 3822---0000 3824---0000 3826---0000 3828---0000 3830---0000 3832---0000 3834---0000 3836---0000 3838---0000 3840---0000 3842---0000 3844---0000 3846---0000 3848---0000 3850---0000 3852---0000 3854---0000 3856---0000 3858---0000 3860---0000 3862---0000 3864---0000 3866---0000 3868---0000 3870---0000 3872---0000 3874---0000 3876---0000 3878---0000 3880---0000 3882---0000 3884---0000 3886---0000 3888---0000 3890---0000 3892---0000 3894---0000 3896---0000 3898---0000 3900---0000 3902---0000 3904---0000 3906---0000 3908---0000 3910---0000 3912---0000 3914---0000 3916---0000 3918---0000 3920---0000 3922---0000 3924---0000 3926---0000 3928---0000 3930---0000 3932---0000 3934---0000 3936---0000 3938---0000 3940---0000 3942---0000 3944---0000 3946---0000 3948---0000 3950---0000 3952---0000 3954---0000 3956---0000 3958---0000 3960---0000 3962---0000 3964---0000 3966---0000 3968---0000 3970---0000 3972---0000 3974---0000 3976---0000 3978---0000 3980---0000 3982---0000 3984---0000 3986---0000 3988---0000 3990---0000 3992---0000 3994---0000 3996---0000 3998---0000 4000---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m4.178s user 0m2.098s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:01:59 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 200, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.461s user 0m0.346s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:01:40 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); for (A=2, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 2---0000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.009s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:01:18 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 500, 0, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? ? Goodbye! Errors/timing (if any): *** forstep: step equal to zero in forstep. Timing: real 0m0.040s user 0m0.008s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 03:00:36 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=-1000, 500, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? -1000---0000 -998---0000 -996---0000 -994---0000 -992---0000 -990---0000 -988---0000 -986---0000 -984---0000 -982---0000 -980---0000 -978---0000 -976---0000 -974---0000 -972---0000 -970---0000 -968---0000 -966---0000 -964---0000 -962---0000 -960---0000 -958---0000 -956---0000 -954---0000 -952---0000 -950---0000 -948---0000 -946---0000 -944---0000 -942---0000 -940---0000 -938---0000 -936---0000 -934---0000 -932---0000 -930---0000 -928---0000 -926---0000 -924---0000 -922---0000 -920---0000 -918---0000 -916---0000 -914---0000 -912---0000 -910---0000 -908---0000 -906---0000 -904---0000 -902---0000 -900---0000 -898---0000 -896---0000 -894---0000 -892---0000 -890---0000 -888---0000 -886---0000 -884---0000 -882---0000 -880---0000 -878---0000 -876---0000 -874---0000 -872---0000 -870---0000 -868---0000 -866---0000 -864---0000 -862---0000 -860---0000 -858---0000 -856---0000 -854---0000 -852---0000 -850---0000 -848---0000 -846---0000 -844---0000 -842---0000 -840---0000 -838---0000 -836---0000 -834---0000 -832---0000 -830---0000 -828---0000 -826---0000 -824---0000 -822---0000 -820---0000 -818---0000 -816---0000 -814---0000 -812---0000 -810---0000 -808---0000 -806---0000 -804---0000 -802---0000 -800---0000 -798---0000 -796---0000 -794---0000 -792---0000 -790---0000 -788---0000 -786---0000 -784---0000 -782---0000 -780---0000 -778---0000 -776---0000 -774---0000 -772---0000 -770---0000 -768---0000 -766---0000 -764---0000 -762---0000 -760---0000 -758---0000 -756---0000 -754---0000 -752---0000 -750---0000 -748---0000 -746---0000 -744---0000 -742---0000 -740---0000 -738---0000 -736---0000 -734---0000 -732---0000 -730---0000 -728---0000 -726---0000 -724---0000 -722---0000 -720---0000 -718---0000 -716---0000 -714---0000 -712---0000 -710---0000 -708---0000 -706---0000 -704---0000 -702---0000 -700---0000 -698---0000 -696---0000 -694---0000 -692---0000 -690---0000 -688---0000 -686---0000 -684---0000 -682---0000 -680---0000 -678---0000 -676---0000 -674---0000 -672---0000 -670---0000 -668---0000 -666---0000 -664---0000 -662---0000 -660---0000 -658---0000 -656---0000 -654---0000 -652---0000 -650---0000 -648---0000 -646---0000 -644---0000 -642---0000 -640---0000 -638---0000 -636---0000 -634---0000 -632---0000 -630---0000 -628---0000 -626---0000 -624---0000 -622---0000 -620---0000 -618---0000 -616---0000 -614---0000 -612---0000 -610---0000 -608---0000 -606---0000 -604---0000 -602---0000 -600---0000 -598---0000 -596---0000 -594---0000 -592---0000 -590---0000 -588---0000 -586---0000 -584---0000 -582---0000 -580---0000 -578---0000 -576---0000 -574---0000 -572---0000 -570---0000 -568---0000 -566---0000 -564---0000 -562---0000 -560---0000 -558---0000 -556---0000 -554---0000 -552---0000 -550---0000 -548---0000 -546---0000 -544---0000 -542---0000 -540---0000 -538---0000 -536---0000 -534---0000 -532---0000 -530---0000 -528---0000 -526---0000 -524---0000 -522---0000 -520---0000 -518---0000 -516---0000 -514---0000 -512---0000 -510---0000 -508---0000 -506---0000 -504---0000 -502---0000 -500---0000 -498---0000 -496---0000 -494---0000 -492---0000 -490---0000 -488---0000 -486---0000 -484---0000 -482---0000 -480---0000 -478---0000 -476---0000 -474---0000 -472---0000 -470---0000 -468---0000 -466---0000 -464---0000 -462---0000 -460---0000 -458---0000 -456---0000 -454---0000 -452---0000 -450---0000 -448---0000 -446---0000 -444---0000 -442---0000 -440---0000 -438---0000 -436---0000 -434---0000 -432---0000 -430---0000 -428---0000 -426---0000 -424---0000 -422---0000 -420---0000 -418---0000 -416---0000 -414---0000 -412---0000 -410---0000 -408---0000 -406---0000 -404---0000 -402---0000 -400---0000 -398---0000 -396---0000 -394---0000 -392---0000 -390---0000 -388---0000 -386---0000 -384---0000 -382---0000 -380---0000 -378---0000 -376---0000 -374---0000 -372---0000 -370---0000 -368---0000 -366---0000 -364---0000 -362---0000 -360---0000 -358---0000 -356---0000 -354---0000 -352---0000 -350---0000 -348---0000 -346---0000 -344---0000 -342---0000 -340---0000 -338---0000 -336---0000 -334---0000 -332---0000 -330---0000 -328---0000 -326---0000 -324---0000 -322---0000 -320---0000 -318---0000 -316---0000 -314---0000 -312---0000 -310---0000 -308---0000 -306---0000 -304---0000 -302---0000 -300---0000 -298---0000 -296---0000 -294---0000 -292---0000 -290---0000 -288---0000 -286---0000 -284---0000 -282---0000 -280---0000 -278---0000 -276---0000 -274---0000 -272---0000 -270---0000 -268---0000 -266---0000 -264---0000 -262---0000 -260---0000 -258---0000 -256---0000 -254---0000 -252---0000 -250---0000 -248---0000 -246---0000 -244---0000 -242---0000 -240---0000 -238---0000 -236---0000 -234---0000 -232---0000 -230---0000 -228---0000 -226---0000 -224---0000 -222---0000 -220---0000 -218---0000 -216---0000 -214---0000 -212---0000 -210---0000 -208---0000 -206---0000 -204---0000 -202---0000 -200---0000 -198---0000 -196---0000 -194---0000 -192---0000 -190---0000 -188---0000 -186---0000 -184---0000 -182---0000 -180---0000 -178---0000 -176---0000 -174---0000 -172---0000 -170---0000 -168---0000 -166---0000 -164---0000 -162---0000 -160---0000 -158---0000 -156---0000 -154---0000 -152---0000 -150---0000 -148---0000 -146---0000 -144---0000 -142---0000 -140---0000 -138---0000 -136---0000 -134---0000 -132---0000 -130---0000 -128---0000 -126---0000 -124---0000 -122---0000 -120---0000 -118---0000 -116---0000 -114---0000 -112---0000 -110---0000 -108---0000 -106---0000 -104---0000 -102---0000 -100---0000 -98---0000 -96---0000 -94---0000 -92---0000 -90---0000 -88---0000 -86---0000 -84---0000 -82---0000 -80---0000 -78---0000 -76---0000 -74---0000 -72---0000 -70---0000 -68---0000 -66---0000 -64---0000 -62---0000 -60---0000 -58---0000 -56---0000 -54---0000 -52---0000 -50---0000 -48---0000 -46---0000 -44---0000 -42---0000 -40---0000 -38---0000 -36---0000 -34---0000 -32---0000 -30---0000 -28---0000 -26---0000 -24---0000 -22---0000 -20---0000 -18---0000 -16---0000 -14---0000 -12---0000 -10---0000 -8---0000 -6---0000 -4---0000 -2---0000 ? Goodbye! Errors/timing (if any): *** nfinit: reducible polynomial in nfinit. Timing: real 0m11.060s user 0m1.878s sys 0m0.012s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 02:59:15 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=-1000, 0, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? -1000---0000 -998---0000 -996---0000 -994---0000 -992---0000 -990---0000 -988---0000 -986---0000 -984---0000 -982---0000 -980---0000 -978---0000 -976---0000 -974---0000 -972---0000 -970---0000 -968---0000 -966---0000 -964---0000 -962---0000 -960---0000 -958---0000 -956---0000 -954---0000 -952---0000 -950---0000 -948---0000 -946---0000 -944---0000 -942---0000 -940---0000 -938---0000 -936---0000 -934---0000 -932---0000 -930---0000 -928---0000 -926---0000 -924---0000 -922---0000 -920---0000 -918---0000 -916---0000 -914---0000 -912---0000 -910---0000 -908---0000 -906---0000 -904---0000 -902---0000 -900---0000 -898---0000 -896---0000 -894---0000 -892---0000 -890---0000 -888---0000 -886---0000 -884---0000 -882---0000 -880---0000 -878---0000 -876---0000 -874---0000 -872---0000 -870---0000 -868---0000 -866---0000 -864---0000 -862---0000 -860---0000 -858---0000 -856---0000 -854---0000 -852---0000 -850---0000 -848---0000 -846---0000 -844---0000 -842---0000 -840---0000 -838---0000 -836---0000 -834---0000 -832---0000 -830---0000 -828---0000 -826---0000 -824---0000 -822---0000 -820---0000 -818---0000 -816---0000 -814---0000 -812---0000 -810---0000 -808---0000 -806---0000 -804---0000 -802---0000 -800---0000 -798---0000 -796---0000 -794---0000 -792---0000 -790---0000 -788---0000 -786---0000 -784---0000 -782---0000 -780---0000 -778---0000 -776---0000 -774---0000 -772---0000 -770---0000 -768---0000 -766---0000 -764---0000 -762---0000 -760---0000 -758---0000 -756---0000 -754---0000 -752---0000 -750---0000 -748---0000 -746---0000 -744---0000 -742---0000 -740---0000 -738---0000 -736---0000 -734---0000 -732---0000 -730---0000 -728---0000 -726---0000 -724---0000 -722---0000 -720---0000 -718---0000 -716---0000 -714---0000 -712---0000 -710---0000 -708---0000 -706---0000 -704---0000 -702---0000 -700---0000 -698---0000 -696---0000 -694---0000 -692---0000 -690---0000 -688---0000 -686---0000 -684---0000 -682---0000 -680---0000 -678---0000 -676---0000 -674---0000 -672---0000 -670---0000 -668---0000 -666---0000 -664---0000 -662---0000 -660---0000 -658---0000 -656---0000 -654---0000 -652---0000 -650---0000 -648---0000 -646---0000 -644---0000 -642---0000 -640---0000 -638---0000 -636---0000 -634---0000 -632---0000 -630---0000 -628---0000 -626---0000 -624---0000 -622---0000 -620---0000 -618---0000 -616---0000 -614---0000 -612---0000 -610---0000 -608---0000 -606---0000 -604---0000 -602---0000 -600---0000 -598---0000 -596---0000 -594---0000 -592---0000 -590---0000 -588---0000 -586---0000 -584---0000 -582---0000 -580---0000 -578---0000 -576---0000 -574---0000 -572---0000 -570---0000 -568---0000 -566---0000 -564---0000 -562---0000 -560---0000 -558---0000 -556---0000 -554---0000 -552---0000 -550---0000 -548---0000 -546---0000 -544---0000 -542---0000 -540---0000 -538---0000 -536---0000 -534---0000 -532---0000 -530---0000 -528---0000 -526---0000 -524---0000 -522---0000 -520---0000 -518---0000 -516---0000 -514---0000 -512---0000 -510---0000 -508---0000 -506---0000 -504---0000 -502---0000 -500---0000 -498---0000 -496---0000 -494---0000 -492---0000 -490---0000 -488---0000 -486---0000 -484---0000 -482---0000 -480---0000 -478---0000 -476---0000 -474---0000 -472---0000 -470---0000 -468---0000 -466---0000 -464---0000 -462---0000 -460---0000 -458---0000 -456---0000 -454---0000 -452---0000 -450---0000 -448---0000 -446---0000 -444---0000 -442---0000 -440---0000 -438---0000 -436---0000 -434---0000 -432---0000 -430---0000 -428---0000 -426---0000 -424---0000 -422---0000 -420---0000 -418---0000 -416---0000 -414---0000 -412---0000 -410---0000 -408---0000 -406---0000 -404---0000 -402---0000 -400---0000 -398---0000 -396---0000 -394---0000 -392---0000 -390---0000 -388---0000 -386---0000 -384---0000 -382---0000 -380---0000 -378---0000 -376---0000 -374---0000 -372---0000 -370---0000 -368---0000 -366---0000 -364---0000 -362---0000 -360---0000 -358---0000 -356---0000 -354---0000 -352---0000 -350---0000 -348---0000 -346---0000 -344---0000 -342---0000 -340---0000 -338---0000 -336---0000 -334---0000 -332---0000 -330---0000 -328---0000 -326---0000 -324---0000 -322---0000 -320---0000 -318---0000 -316---0000 -314---0000 -312---0000 -310---0000 -308---0000 -306---0000 -304---0000 -302---0000 -300---0000 -298---0000 -296---0000 -294---0000 -292---0000 -290---0000 -288---0000 -286---0000 -284---0000 -282---0000 -280---0000 -278---0000 -276---0000 -274---0000 -272---0000 -270---0000 -268---0000 -266---0000 -264---0000 -262---0000 -260---0000 -258---0000 -256---0000 -254---0000 -252---0000 -250---0000 -248---0000 -246---0000 -244---0000 -242---0000 -240---0000 -238---0000 -236---0000 -234---0000 -232---0000 -230---0000 -228---0000 -226---0000 -224---0000 -222---0000 -220---0000 -218---0000 -216---0000 -214---0000 -212---0000 -210---0000 -208---0000 -206---0000 -204---0000 -202---0000 -200---0000 -198---0000 -196---0000 -194---0000 -192---0000 -190---0000 -188---0000 -186---0000 -184---0000 -182---0000 -180---0000 -178---0000 -176---0000 -174---0000 -172---0000 -170---0000 -168---0000 -166---0000 -164---0000 -162---0000 -160---0000 -158---0000 -156---0000 -154---0000 -152---0000 -150---0000 -148---0000 -146---0000 -144---0000 -142---0000 -140---0000 -138---0000 -136---0000 -134---0000 -132---0000 -130---0000 -128---0000 -126---0000 -124---0000 -122---0000 -120---0000 -118---0000 -116---0000 -114---0000 -112---0000 -110---0000 -108---0000 -106---0000 -104---0000 -102---0000 -100---0000 -98---0000 -96---0000 -94---0000 -92---0000 -90---0000 -88---0000 -86---0000 -84---0000 -82---0000 -80---0000 -78---0000 -76---0000 -74---0000 -72---0000 -70---0000 -68---0000 -66---0000 -64---0000 -62---0000 -60---0000 -58---0000 -56---0000 -54---0000 -52---0000 -50---0000 -48---0000 -46---0000 -44---0000 -42---0000 -40---0000 -38---0000 -36---0000 -34---0000 -32---0000 -30---0000 -28---0000 -26---0000 -24---0000 -22---0000 -20---0000 -18---0000 -16---0000 -14---0000 -12---0000 -10---0000 -8---0000 -6---0000 -4---0000 -2---0000 ? Goodbye! Errors/timing (if any): *** nfinit: reducible polynomial in nfinit. Timing: real 0m10.470s user 0m1.879s sys 0m0.012s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Thu Jul 27 02:58:28 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=1300, 3300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 1300---0000 1302---0000 1304---0000 1306---0000 1308---0000 1310---0000 1312---0000 1314---0000 1316---0000 1318---0000 1320---0000 1322---0000 1324---0000 1326---0000 1328---0000 1330---0000 1332---0000 1334---0000 1336---0000 1338---0000 1340---0000 1342---0000 1344---0000 1346---0000 1348---0000 1350---0000 1352---0000 1354---0000 1356---0000 1358---0000 1360---0000 1362---0000 1364---0000 1366---0000 1368---0000 1370---0000 1372---0000 1374---0000 1376---0000 1378---0000 1380---0000 1382---0000 1384---0000 1386---0000 1388---0000 1390---0000 1392---0000 1394---0000 1396---0000 1398---0000 1400---0000 1402---0000 1404---0000 1406---0000 1408---0000 1410---0000 1412---0000 1414---0000 1416---0000 1418---0000 1420---0000 1422---0000 1424---0000 1426---0000 1428---0000 1430---0000 1432---0000 1434---0000 1436---0000 1438---0000 1440---0000 1442---0000 1444---0000 1446---0000 1448---0000 1450---0000 1452---0000 1454---0000 1456---0000 1458---0000 1460---0000 1462---0000 1464---0000 1466---0000 1468---0000 1470---0000 1472---0000 1474---0000 1476---0000 1478---0000 1480---0000 1482---0000 1484---0000 1486---0000 1488---0000 1490---0000 1492---0000 1494---0000 1496---0000 1498---0000 1500---0000 1502---0000 1504---0000 1506---0000 1508---0000 1510---0000 1512---0000 1514---0000 1516---0000 1518---0000 1520---0000 1522---0000 1524---0000 1526---0000 1528---0000 1530---0000 1532---0000 1534---0000 1536---0000 1538---0000 1540---0000 1542---0000 1544---0000 1546---0000 1548---0000 1550---0000 1552---0000 1554---0000 1556---0000 1558---0000 1560---0000 1562---0000 1564---0000 1566---0000 1568---0000 1570---0000 1572---0000 1574---0000 1576---0000 1578---0000 1580---0000 1582---0000 1584---0000 1586---0000 1588---0000 1590---0000 1592---0000 1594---0000 1596---0000 1598---0000 1600---0000 1602---0000 1604---0000 1606---0000 1608---0000 1610---0000 1612---0000 1614---0000 1616---0000 1618---0000 1620---0000 1622---0000 1624---0000 1626---0000 1628---0000 1630---0000 1632---0000 1634---0000 1636---0000 1638---0000 1640---0000 1642---0000 1644---0000 1646---0000 1648---0000 1650---0000 1652---0000 1654---0000 1656---0000 1658---0000 1660---0000 1662---0000 1664---0000 1666---0000 1668---0000 1670---0000 1672---0000 1674---0000 1676---0000 1678---0000 1680---0000 1682---0000 1684---0000 1686---0000 1688---0000 1690---0000 1692---0000 1694---0000 1696---0000 1698---0000 1700---0000 1702---0000 1704---0000 1706---0000 1708---0000 1710---0000 1712---0000 1714---0000 1716---0000 1718---0000 1720---0000 1722---0000 1724---0000 1726---0000 1728---0000 1730---0000 1732---0000 1734---0000 1736---0000 1738---0000 1740---0000 1742---0000 1744---0000 1746---0000 1748---0000 1750---0000 1752---0000 1754---0000 1756---0000 1758---0000 1760---0000 1762---0000 1764---0000 1766---0000 1768---0000 1770---0000 1772---0000 1774---0000 1776---0000 1778---0000 1780---0000 1782---0000 1784---0000 1786---0000 1788---0000 1790---0000 1792---0000 1794---0000 1796---0000 1798---0000 1800---0000 1802---0000 1804---0000 1806---0000 1808---0000 1810---0000 1812---0000 1814---0000 1816---0000 1818---0000 1820---0000 1822---0000 1824---0000 1826---0000 1828---0000 1830---0000 1832---0000 1834---0000 1836---0000 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2170---0000 2172---0000 2174---0000 2176---0000 2178---0000 2180---0000 2182---0000 2184---0000 2186---0000 2188---0000 2190---0000 2192---0000 2194---0000 2196---0000 2198---0000 2200---0000 2202---0000 2204---0000 2206---0000 2208---0000 2210---0000 2212---0000 2214---0000 2216---0000 2218---0000 2220---0000 2222---0000 2224---0000 2226---0000 2228---0000 2230---0000 2232---0000 2234---0000 2236---0000 2238---0000 2240---0000 2242---0000 2244---0000 2246---0000 2248---0000 2250---0000 2252---0000 2254---0000 2256---0000 2258---0000 2260---0000 2262---0000 2264---0000 2266---0000 2268---0000 2270---0000 2272---0000 2274---0000 2276---0000 2278---0000 2280---0000 2282---0000 2284---0000 2286---0000 2288---0000 2290---0000 2292---0000 2294---0000 2296---0000 2298---0000 2300---0000 2302---0000 2304---0000 2306---0000 2308---0000 2310---0000 2312---0000 2314---0000 2316---0000 2318---0000 2320---0000 2322---0000 2324---0000 2326---0000 2328---0000 2330---0000 2332---0000 2334---0000 2336---0000 2338---0000 2340---0000 2342---0000 2344---0000 2346---0000 2348---0000 2350---0000 2352---0000 2354---0000 2356---0000 2358---0000 2360---0000 2362---0000 2364---0000 2366---0000 2368---0000 2370---0000 2372---0000 2374---0000 2376---0000 2378---0000 2380---0000 2382---0000 2384---0000 2386---0000 2388---0000 2390---0000 2392---0000 2394---0000 2396---0000 2398---0000 2400---0000 2402---0000 2404---0000 2406---0000 2408---0000 2410---0000 2412---0000 2414---0000 2416---0000 2418---0000 2420---0000 2422---0000 2424---0000 2426---0000 2428---0000 2430---0000 2432---0000 2434---0000 2436---0000 2438---0000 2440---0000 2442---0000 2444---0000 2446---0000 2448---0000 2450---0000 2452---0000 2454---0000 2456---0000 2458---0000 2460---0000 2462---0000 2464---0000 2466---0000 2468---0000 2470---0000 2472---0000 2474---0000 2476---0000 2478---0000 2480---0000 2482---0000 2484---0000 2486---0000 2488---0000 2490---0000 2492---0000 2494---0000 2496---0000 2498---0000 2500---0000 2502---0000 2504---0000 2506---0000 2508---0000 2510---0000 2512---0000 2514---0000 2516---0000 2518---0000 2520---0000 2522---0000 2524---0000 2526---0000 2528---0000 2530---0000 2532---0000 2534---0000 2536---0000 2538---0000 2540---0000 2542---0000 2544---0000 2546---0000 2548---0000 2550---0000 2552---0000 2554---0000 2556---0000 2558---0000 2560---0000 2562---0000 2564---0000 2566---0000 2568---0000 2570---0000 2572---0000 2574---0000 2576---0000 2578---0000 2580---0000 2582---0000 2584---0000 2586---0000 2588---0000 2590---0000 2592---0000 2594---0000 2596---0000 2598---0000 2600---0000 2602---0000 2604---0000 2606---0000 2608---0000 2610---0000 2612---0000 2614---0000 2616---0000 2618---0000 2620---0000 2622---0000 2624---0000 2626---0000 2628---0000 2630---0000 2632---0000 2634---0000 2636---0000 2638---0000 2640---0000 2642---0000 2644---0000 2646---0000 2648---0000 2650---0000 2652---0000 2654---0000 2656---0000 2658---0000 2660---0000 2662---0000 2664---0000 2666---0000 2668---0000 2670---0000 2672---0000 2674---0000 2676---0000 2678---0000 2680---0000 2682---0000 2684---0000 2686---0000 2688---0000 2690---0000 2692---0000 2694---0000 2696---0000 2698---0000 2700---0000 2702---0000 2704---0000 2706---0000 2708---0000 2710---0000 2712---0000 2714---0000 2716---0000 2718---0000 2720---0000 2722---0000 2724---0000 2726---0000 2728---0000 2730---0000 2732---0000 2734---0000 2736---0000 2738---0000 2740---0000 2742---0000 2744---0000 2746---0000 2748---0000 2750---0000 2752---0000 2754---0000 2756---0000 2758---0000 2760---0000 2762---0000 2764---0000 2766---0000 2768---0000 2770---0000 2772---0000 2774---0000 2776---0000 2778---0000 2780---0000 2782---0000 2784---0000 2786---0000 2788---0000 2790---0000 2792---0000 2794---0000 2796---0000 2798---0000 2800---0000 2802---0000 2804---0000 2806---0000 2808---0000 2810---0000 2812---0000 2814---0000 2816---0000 2818---0000 2820---0000 2822---0000 2824---0000 2826---0000 2828---0000 2830---0000 2832---0000 2834---0000 2836---0000 2838---0000 2840---0000 2842---0000 2844---0000 2846---0000 2848---0000 2850---0000 2852---0000 2854---0000 2856---0000 2858---0000 2860---0000 2862---0000 2864---0000 2866---0000 2868---0000 2870---0000 2872---0000 2874---0000 2876---0000 2878---0000 2880---0000 2882---0000 2884---0000 2886---0000 2888---0000 2890---0000 2892---0000 2894---0000 2896---0000 2898---0000 2900---0000 2902---0000 2904---0000 2906---0000 2908---0000 2910---0000 2912---0000 2914---0000 2916---0000 2918---0000 2920---0000 2922---0000 2924---0000 2926---0000 2928---0000 2930---0000 2932 ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m8.261s user 0m4.092s sys 0m0.017s '72.30.1' ************** PARI ***************** Host 72.30.129.123 (72.30.129.123) Time: Thu Jul 27 00:08:50 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.241s user 0m0.008s sys 0m0.004s '72.30.2' ************** PARI ***************** Host 72.30.226.160 (72.30.226.160) Time: Wed Jul 26 22:52:15 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.421s user 0m0.008s sys 0m0.008s '72.177.' ************** PARI ***************** Host 72.177.144.182 (72.177.144.182) Time: Wed Jul 26 10:23:50 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '72.177.' ************** PARI ***************** Host 72.177.144.182 (72.177.144.182) Time: Wed Jul 26 10:23:10 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.043s user 0m0.005s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:45:41 2006 Input: f=x^4+2*x^2+13 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=220, 1220, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 13 ? %2 = [x - 1, x^2 - x + 1, x^4 - 2*x^3 + 2*x^2 - x + 1, x^4 - x^3 - x^2 + x + 1] ? ? ? 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 1002---0000 1004---0000 1006---0000 1008---0000 1010---0000 1012---0000 1014---0000 1016---0000 1018---0000 1020---0000 1022---0000 1024---0000 1026---0000 1028---0000 1030---0000 1032---0000 1034---0000 1036---0000 1038---0000 1040---0000 1042---0000 1044---0000 1046---0000 1048---0000 1050---0000 1052---0000 1054---0000 1056---0000 1058---0000 1060---0000 1062---0000 1064---0000 1066---0000 1068---0000 1070---0000 1072---0000 1074---0000 1076---0000 1078---0000 1080---0000 1082---0000 1084---0000 1086---0000 1088---0000 1090---0000 1092---0000 1094---0000 1096---0000 1098---0000 1100---0000 1102---0000 1104---0000 1106---0000 1108---0000 1110---0000 1112---0000 1114---0000 1116---0000 1118---0000 1120---0000 1122---0000 1124---0000 1126---0000 1128---0000 1130---0000 1132---0000 1134---0000 1136---0000 1138---0000 1140---0000 1142---0000 1144---0000 1146---0000 1148---0000 1150---0000 1152---0000 1154---0000 1156---0000 1158---0000 1160---0000 1162---0000 1164---0000 1166---0000 1168---0000 1170---0000 1172---0000 1174---0000 1176---0000 1178---0000 1180---0000 1182---0000 1184---0000 1186---0000 1188---0000 1190---0000 1192---0000 1194---0000 1196---0000 1198---0000 1200---0000 1202---0000 1204---0000 1206---0000 1208---0000 1210---0000 1212---0000 1214---0000 1216---0000 1218---0000 1220---0000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m11.329s user 0m1.940s sys 0m0.011s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:45:09 2006 Input: f=x^4+2*x^2+13 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 220, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 13 ? %2 = [x - 1, x^2 - x + 1, x^4 - 2*x^3 + 2*x^2 - x + 1, x^4 - x^3 - x^2 + x + 1] ? ? ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m2.299s user 0m0.384s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:44:40 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=4932, 5300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 4932---0000 4934---0000 4936---0000 4938---0000 4940---0000 4942---0000 4944---0000 4946---0000 4948---0000 4950---0000 4952---0000 4954---0000 4956---0000 4958---0000 4960---0000 4962---0000 4964---0000 4966---0000 4968---0000 4970---0000 4972---0000 4974---0000 4976---0000 4978---0000 4980---0000 4982---0000 4984---0000 4986---0000 4988---0000 4990---0000 4992---0000 4994---0000 4996---0000 4998---0000 5000---0000 5002---0000 5004---0000 5006---0000 5008---0000 5010---0000 5012---0000 5014---0000 5016---0000 5018---0000 5020---0000 5022---0000 5024---0000 5026---0000 5028---0000 5030---0000 5032---0000 5034---0000 5036---0000 5038---0000 5040---0000 5042---0000 5044---0000 5046---0000 5048---0000 5050---0000 5052---0000 5054---0000 5056---0000 5058---0000 5060---0000 5062---0000 5064---0000 5066---0000 5068---0000 5070---0000 5072---0000 5074---0000 5076---0000 5078---0000 5080---0000 5082---0000 5084---0000 5086---0000 5088---0000 5090---0000 5092---0000 5094---0000 5096---0000 5098---0000 5100---0000 5102---0000 5104---0000 5106---0000 5108---0000 5110---0000 5112---0000 5114---0000 5116---0000 5118---0000 5120---0000 5122---0000 5124---0000 5126---0000 5128---0000 5130---0000 5132---0000 5134---0000 5136---0000 5138---0000 5140---0000 5142---0000 5144---0000 5146---0000 5148---0000 5150---0000 5152---0000 5154---0000 5156---0000 5158---0000 5160---0000 5162---0000 5164---0000 5166---0000 5168---0000 5170---0000 5172---0000 5174---0000 5176---0000 5178---0000 5180---0000 5182---0000 5184---0000 5186---0000 5188---0000 5190---0000 5192---0000 5194---0000 5196---0000 5198---0000 5200---0000 5202---0000 5204---0000 5206---0000 5208---0000 5210---0000 5212---0000 5214---0000 5216---0000 5218---0000 5220---0000 5222---0000 5224---0000 5226---0000 5228---0000 5230---0000 5232---0000 5234---0000 5236---0000 5238---0000 5240---0000 5242---0000 5244---0000 5246---0000 5248---0000 5250---0000 5252---0000 5254---0000 5256---0000 5258---0000 5260---0000 5262---0000 5264---0000 5266---0000 5268---0000 5270---0000 5272---0000 5274---0000 5276---0000 5278---0000 5280---0000 5282---0000 5284---0000 5286---0000 5288---0000 5290---0000 5292---0000 5294---0000 5296---0000 5298---0000 5300---0000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m1.603s user 0m0.783s sys 0m0.010s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:43:47 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=3300, 5300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 3300---0000 3302---0000 3304---0000 3306---0000 3308---0000 3310---0000 3312---0000 3314---0000 3316---0000 3318---0000 3320---0000 3322---0000 3324---0000 3326---0000 3328---0000 3330---0000 3332---0000 3334---0000 3336---0000 3338---0000 3340---0000 3342---0000 3344---0000 3346---0000 3348---0000 3350---0000 3352---0000 3354---0000 3356---0000 3358---0000 3360---0000 3362---0000 3364---0000 3366---0000 3368---0000 3370---0000 3372---0000 3374---0000 3376---0000 3378---0000 3380---0000 3382---0000 3384---0000 3386---0000 3388---0000 3390---0000 3392---0000 3394---0000 3396---0000 3398---0000 3400---0000 3402---0000 3404---0000 3406---0000 3408---0000 3410---0000 3412---0000 3414---0000 3416---0000 3418---0000 3420---0000 3422---0000 3424---0000 3426---0000 3428---0000 3430---0000 3432---0000 3434---0000 3436---0000 3438---0000 3440---0000 3442---0000 3444---0000 3446---0000 3448---0000 3450---0000 3452---0000 3454---0000 3456---0000 3458---0000 3460---0000 3462---0000 3464---0000 3466---0000 3468---0000 3470---0000 3472---0000 3474---0000 3476---0000 3478---0000 3480---0000 3482---0000 3484---0000 3486---0000 3488---0000 3490---0000 3492---0000 3494---0000 3496---0000 3498---0000 3500---0000 3502---0000 3504---0000 3506---0000 3508---0000 3510---0000 3512---0000 3514---0000 3516---0000 3518---0000 3520---0000 3522---0000 3524---0000 3526---0000 3528---0000 3530---0000 3532---0000 3534---0000 3536---0000 3538---0000 3540---0000 3542---0000 3544---0000 3546---0000 3548---0000 3550---0000 3552---0000 3554---0000 3556---0000 3558---0000 3560---0000 3562---0000 3564---0000 3566---0000 3568---0000 3570---0000 3572---0000 3574---0000 3576---0000 3578---0000 3580---0000 3582---0000 3584---0000 3586---0000 3588---0000 3590---0000 3592---0000 3594---0000 3596---0000 3598---0000 3600---0000 3602---0000 3604---0000 3606---0000 3608---0000 3610---0000 3612---0000 3614---0000 3616---0000 3618---0000 3620---0000 3622---0000 3624---0000 3626---0000 3628---0000 3630---0000 3632---0000 3634---0000 3636---0000 3638---0000 3640---0000 3642---0000 3644---0000 3646---0000 3648---0000 3650---0000 3652---0000 3654---0000 3656---0000 3658---0000 3660---0000 3662---0000 3664---0000 3666---0000 3668---0000 3670---0000 3672---0000 3674---0000 3676---0000 3678---0000 3680---0000 3682---0000 3684---0000 3686---0000 3688---0000 3690---0000 3692---0000 3694---0000 3696---0000 3698---0000 3700---0000 3702---0000 3704---0000 3706---0000 3708---0000 3710---0000 3712---0000 3714---0000 3716---0000 3718---0000 3720---0000 3722---0000 3724---0000 3726---0000 3728---0000 3730---0000 3732---0000 3734---0000 3736---0000 3738---0000 3740---0000 3742---0000 3744---0000 3746---0000 3748---0000 3750---0000 3752---0000 3754---0000 3756---0000 3758---0000 3760---0000 3762---0000 3764---0000 3766---0000 3768---0000 3770---0000 3772---0000 3774---0000 3776---0000 3778---0000 3780---0000 3782---0000 3784---0000 3786---0000 3788---0000 3790---0000 3792---0000 3794---0000 3796---0000 3798---0000 3800---0000 3802---0000 3804---0000 3806---0000 3808---0000 3810---0000 3812---0000 3814---0000 3816---0000 3818---0000 3820---0000 3822---0000 3824---0000 3826---0000 3828---0000 3830---0000 3832---0000 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4000---0000 4002---0000 4004---0000 4006---0000 4008---0000 4010---0000 4012---0000 4014---0000 4016---0000 4018---0000 4020---0000 4022---0000 4024---0000 4026---0000 4028---0000 4030---0000 4032---0000 4034---0000 4036---0000 4038---0000 4040---0000 4042---0000 4044---0000 4046---0000 4048---0000 4050---0000 4052---0000 4054---0000 4056---0000 4058---0000 4060---0000 4062---0000 4064---0000 4066---0000 4068---0000 4070---0000 4072---0000 4074---0000 4076---0000 4078---0000 4080---0000 4082---0000 4084---0000 4086---0000 4088---0000 4090---0000 4092---0000 4094---0000 4096---0000 4098---0000 4100---0000 4102---0000 4104---0000 4106---0000 4108---0000 4110---0000 4112---0000 4114---0000 4116---0000 4118---0000 4120---0000 4122---0000 4124---0000 4126---0000 4128---0000 4130---0000 4132---0000 4134---0000 4136---0000 4138---0000 4140---0000 4142---0000 4144---0000 4146---0000 4148---0000 4150---0000 4152---0000 4154---0000 4156---0000 4158---0000 4160---0000 4162---0000 4164---0000 4166---0000 4168---0000 4170---0000 4172---0000 4174---0000 4176---0000 4178---0000 4180---0000 4182---0000 4184---0000 4186---0000 4188---0000 4190---0000 4192---0000 4194---0000 4196---0000 4198---0000 4200---0000 4202---0000 4204---0000 4206---0000 4208---0000 4210---0000 4212---0000 4214---0000 4216---0000 4218---0000 4220---0000 4222---0000 4224---0000 4226---0000 4228---0000 4230---0000 4232---0000 4234---0000 4236---0000 4238---0000 4240---0000 4242---0000 4244---0000 4246---0000 4248---0000 4250---0000 4252---0000 4254---0000 4256---0000 4258---0000 4260---0000 4262---0000 4264---0000 4266---0000 4268---0000 4270---0000 4272---0000 4274---0000 4276---0000 4278---0000 4280---0000 4282---0000 4284---0000 4286---0000 4288---0000 4290---0000 4292---0000 4294---0000 4296---0000 4298---0000 4300---0000 4302---0000 4304---0000 4306---0000 4308---0000 4310---0000 4312---0000 4314---0000 4316---0000 4318---0000 4320---0000 4322---0000 4324---0000 4326---0000 4328---0000 4330---0000 4332---0000 4334---0000 4336---0000 4338---0000 4340---0000 4342---0000 4344---0000 4346---0000 4348---0000 4350---0000 4352---0000 4354---0000 4356---0000 4358---0000 4360---0000 4362---0000 4364---0000 4366---0000 4368---0000 4370---0000 4372---0000 4374---0000 4376---0000 4378---0000 4380---0000 4382---0000 4384---0000 4386---0000 4388---0000 4390---0000 4392---0000 4394---0000 4396---0000 4398---0000 4400---0000 4402---0000 4404---0000 4406---0000 4408---0000 4410---0000 4412---0000 4414---0000 4416---0000 4418---0000 4420---0000 4422---0000 4424---0000 4426---0000 4428---0000 4430---0000 4432---0000 4434---0000 4436---0000 4438---0000 4440---0000 4442---0000 4444---0000 4446---0000 4448---0000 4450---0000 4452---0000 4454---0000 4456---0000 4458---0000 4460---0000 4462---0000 4464---0000 4466---0000 4468---0000 4470---0000 4472---0000 4474---0000 4476---0000 4478---0000 4480---0000 4482---0000 4484---0000 4486---0000 4488---0000 4490---0000 4492---0000 4494---0000 4496---0000 4498---0000 4500---0000 4502---0000 4504---0000 4506---0000 4508---0000 4510---0000 4512---0000 4514---0000 4516---0000 4518---0000 4520---0000 4522---0000 4524---0000 4526---0000 4528---0000 4530---0000 4532---0000 4534---0000 4536---0000 4538---0000 4540---0000 4542---0000 4544---0000 4546---0000 4548---0000 4550---0000 4552---0000 4554---0000 4556---0000 4558---0000 4560---0000 4562---0000 4564---0000 4566---0000 4568---0000 4570---0000 4572---0000 4574---0000 4576---0000 4578---0000 4580---0000 4582---0000 4584---0000 4586---0000 4588---0000 4590---0000 4592---0000 4594---0000 4596---0000 4598---0000 4600---0000 4602---0000 4604---0000 4606---0000 4608---0000 4610---0000 4612---0000 4614---0000 4616---0000 4618---0000 4620---0000 4622---0000 4624---0000 4626---0000 4628---0000 4630---0000 4632---0000 4634---0000 4636---0000 4638---0000 4640---0000 4642---0000 4644---0000 4646---0000 4648---0000 4650---0000 4652---0000 4654---0000 4656---0000 4658---0000 4660---0000 4662---0000 4664---0000 4666---0000 4668---0000 4670---0000 4672---0000 4674---0000 4676---0000 4678---0000 4680---0000 4682---0000 4684---0000 4686---0000 4688---0000 4690---0000 4692---0000 4694---0000 4696---0000 4698---0000 4700---0000 4702---0000 4704---0000 4706---0000 4708---0000 4710---0000 4712---0000 4714---0000 4716---0000 4718---0000 4720---0000 4722---0000 4724---0000 4726---0000 4728---0000 4730---0000 4732---0000 4734---0000 4736---0000 4738---0000 4740---0000 4742---0000 4744---0000 4746---0000 4748---0000 4750---0000 4752---0000 4754---0000 4756---0000 4758---0000 4760---0000 4762---0000 4764---0000 4766---0000 4768---0000 4770---0000 4772---0000 4774---0000 4776---0000 4778---0000 4780---0000 4782---0000 4784---0000 4786---0000 4788---0000 4790---0000 4792---0000 4794---0000 4796---0000 4798---0000 4800---0000 4802---0000 4804---0000 4806---0000 4808---0000 4810---0000 4812---0000 4814---0000 4816---0000 4818---0000 4820---0000 4822---0000 4824---0000 4826---0000 4828---0000 4830---0000 4832---0000 4834---0000 4836---0000 4838---0000 4840---0000 4842---0000 4844---0000 4846---0000 4848---0000 4850---0000 4852---0000 4854---0000 4856---0000 4858---0000 4860---0000 4862---0000 4864---0000 4866---0000 4868---0000 4870---0000 4872---0000 4874---0000 4876---0000 4878---0000 4880---0000 4882---0000 4884---0000 4886---0000 4888---0000 4890---0000 4892---0000 4894---0000 4896---0000 4898---0000 4900---0000 4902---0000 4904---0000 4906---0000 4908---0000 4910---0000 4912---0000 4914---0000 4916---0000 4918---0000 4920---0000 4922---0000 4924---0000 4926---0000 4928---0000 4930---0000 4932 ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m8.477s user 0m4.207s sys 0m0.017s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:42:29 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=1300, 3300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 1300---0000 1302---0000 1304---0000 1306---0000 1308---0000 1310---0000 1312---0000 1314---0000 1316---0000 1318---0000 1320---0000 1322---0000 1324---0000 1326---0000 1328---0000 1330---0000 1332---0000 1334---0000 1336---0000 1338---0000 1340---0000 1342---0000 1344---0000 1346---0000 1348---0000 1350---0000 1352---0000 1354---0000 1356---0000 1358---0000 1360---0000 1362---0000 1364---0000 1366---0000 1368---0000 1370---0000 1372---0000 1374---0000 1376---0000 1378---0000 1380---0000 1382---0000 1384---0000 1386---0000 1388---0000 1390---0000 1392---0000 1394---0000 1396---0000 1398---0000 1400---0000 1402---0000 1404---0000 1406---0000 1408---0000 1410---0000 1412---0000 1414---0000 1416---0000 1418---0000 1420---0000 1422---0000 1424---0000 1426---0000 1428---0000 1430---0000 1432---0000 1434---0000 1436---0000 1438---0000 1440---0000 1442---0000 1444---0000 1446---0000 1448---0000 1450---0000 1452---0000 1454---0000 1456---0000 1458---0000 1460---0000 1462---0000 1464---0000 1466---0000 1468---0000 1470---0000 1472---0000 1474---0000 1476---0000 1478---0000 1480---0000 1482---0000 1484---0000 1486---0000 1488---0000 1490---0000 1492---0000 1494---0000 1496---0000 1498---0000 1500---0000 1502---0000 1504---0000 1506---0000 1508---0000 1510---0000 1512---0000 1514---0000 1516---0000 1518---0000 1520---0000 1522---0000 1524---0000 1526---0000 1528---0000 1530---0000 1532---0000 1534---0000 1536---0000 1538---0000 1540---0000 1542---0000 1544---0000 1546---0000 1548---0000 1550---0000 1552---0000 1554---0000 1556---0000 1558---0000 1560---0000 1562---0000 1564---0000 1566---0000 1568---0000 1570---0000 1572---0000 1574---0000 1576---0000 1578---0000 1580---0000 1582---0000 1584---0000 1586---0000 1588---0000 1590---0000 1592---0000 1594---0000 1596---0000 1598---0000 1600---0000 1602---0000 1604---0000 1606---0000 1608---0000 1610---0000 1612---0000 1614---0000 1616---0000 1618---0000 1620---0000 1622---0000 1624---0000 1626---0000 1628---0000 1630---0000 1632---0000 1634---0000 1636---0000 1638---0000 1640---0000 1642---0000 1644---0000 1646---0000 1648---0000 1650---0000 1652---0000 1654---0000 1656---0000 1658---0000 1660---0000 1662---0000 1664---0000 1666---0000 1668---0000 1670---0000 1672---0000 1674---0000 1676---0000 1678---0000 1680---0000 1682---0000 1684---0000 1686---0000 1688---0000 1690---0000 1692---0000 1694---0000 1696---0000 1698---0000 1700---0000 1702---0000 1704---0000 1706---0000 1708---0000 1710---0000 1712---0000 1714---0000 1716---0000 1718---0000 1720---0000 1722---0000 1724---0000 1726---0000 1728---0000 1730---0000 1732---0000 1734---0000 1736---0000 1738---0000 1740---0000 1742---0000 1744---0000 1746---0000 1748---0000 1750---0000 1752---0000 1754---0000 1756---0000 1758---0000 1760---0000 1762---0000 1764---0000 1766---0000 1768---0000 1770---0000 1772---0000 1774---0000 1776---0000 1778---0000 1780---0000 1782---0000 1784---0000 1786---0000 1788---0000 1790---0000 1792---0000 1794---0000 1796---0000 1798---0000 1800---0000 1802---0000 1804---0000 1806---0000 1808---0000 1810---0000 1812---0000 1814---0000 1816---0000 1818---0000 1820---0000 1822---0000 1824---0000 1826---0000 1828---0000 1830---0000 1832---0000 1834---0000 1836---0000 1838---0000 1840---0000 1842---0000 1844---0000 1846---0000 1848---0000 1850---0000 1852---0000 1854---0000 1856---0000 1858---0000 1860---0000 1862---0000 1864---0000 1866---0000 1868---0000 1870---0000 1872---0000 1874---0000 1876---0000 1878---0000 1880---0000 1882---0000 1884---0000 1886---0000 1888---0000 1890---0000 1892---0000 1894---0000 1896---0000 1898---0000 1900---0000 1902---0000 1904---0000 1906---0000 1908---0000 1910---0000 1912---0000 1914---0000 1916---0000 1918---0000 1920---0000 1922---0000 1924---0000 1926---0000 1928---0000 1930---0000 1932---0000 1934---0000 1936---0000 1938---0000 1940---0000 1942---0000 1944---0000 1946---0000 1948---0000 1950---0000 1952---0000 1954---0000 1956---0000 1958---0000 1960---0000 1962---0000 1964---0000 1966---0000 1968---0000 1970---0000 1972---0000 1974---0000 1976---0000 1978---0000 1980---0000 1982---0000 1984---0000 1986---0000 1988---0000 1990---0000 1992---0000 1994---0000 1996---0000 1998---0000 2000---0000 2002---0000 2004---0000 2006---0000 2008---0000 2010---0000 2012---0000 2014---0000 2016---0000 2018---0000 2020---0000 2022---0000 2024---0000 2026---0000 2028---0000 2030---0000 2032---0000 2034---0000 2036---0000 2038---0000 2040---0000 2042---0000 2044---0000 2046---0000 2048---0000 2050---0000 2052---0000 2054---0000 2056---0000 2058---0000 2060---0000 2062---0000 2064---0000 2066---0000 2068---0000 2070---0000 2072---0000 2074---0000 2076---0000 2078---0000 2080---0000 2082---0000 2084---0000 2086---0000 2088---0000 2090---0000 2092---0000 2094---0000 2096---0000 2098---0000 2100---0000 2102---0000 2104---0000 2106---0000 2108---0000 2110---0000 2112---0000 2114---0000 2116---0000 2118---0000 2120---0000 2122---0000 2124---0000 2126---0000 2128---0000 2130---0000 2132---0000 2134---0000 2136---0000 2138---0000 2140---0000 2142---0000 2144---0000 2146---0000 2148---0000 2150---0000 2152---0000 2154---0000 2156---0000 2158---0000 2160---0000 2162---0000 2164---0000 2166---0000 2168---0000 2170---0000 2172---0000 2174---0000 2176---0000 2178---0000 2180---0000 2182---0000 2184---0000 2186---0000 2188---0000 2190---0000 2192---0000 2194---0000 2196---0000 2198---0000 2200---0000 2202---0000 2204---0000 2206---0000 2208---0000 2210---0000 2212---0000 2214---0000 2216---0000 2218---0000 2220---0000 2222---0000 2224---0000 2226---0000 2228---0000 2230---0000 2232---0000 2234---0000 2236---0000 2238---0000 2240---0000 2242---0000 2244---0000 2246---0000 2248---0000 2250---0000 2252---0000 2254---0000 2256---0000 2258---0000 2260---0000 2262---0000 2264---0000 2266---0000 2268---0000 2270---0000 2272---0000 2274---0000 2276---0000 2278---0000 2280---0000 2282---0000 2284---0000 2286---0000 2288---0000 2290---0000 2292---0000 2294---0000 2296---0000 2298---0000 2300---0000 2302---0000 2304---0000 2306---0000 2308---0000 2310---0000 2312---0000 2314---0000 2316---0000 2318---0000 2320---0000 2322---0000 2324---0000 2326---0000 2328---0000 2330---0000 2332---0000 2334---0000 2336---0000 2338---0000 2340---0000 2342---0000 2344---0000 2346---0000 2348---0000 2350---0000 2352---0000 2354---0000 2356---0000 2358---0000 2360---0000 2362---0000 2364---0000 2366---0000 2368---0000 2370---0000 2372---0000 2374---0000 2376---0000 2378---0000 2380---0000 2382---0000 2384---0000 2386---0000 2388---0000 2390---0000 2392---0000 2394---0000 2396---0000 2398---0000 2400---0000 2402---0000 2404---0000 2406---0000 2408---0000 2410---0000 2412---0000 2414---0000 2416---0000 2418---0000 2420---0000 2422---0000 2424---0000 2426---0000 2428---0000 2430---0000 2432---0000 2434---0000 2436---0000 2438---0000 2440---0000 2442---0000 2444---0000 2446---0000 2448---0000 2450---0000 2452---0000 2454---0000 2456---0000 2458---0000 2460---0000 2462---0000 2464---0000 2466---0000 2468---0000 2470---0000 2472---0000 2474---0000 2476---0000 2478---0000 2480---0000 2482---0000 2484---0000 2486---0000 2488---0000 2490---0000 2492---0000 2494---0000 2496---0000 2498---0000 2500---0000 2502---0000 2504---0000 2506---0000 2508---0000 2510---0000 2512---0000 2514---0000 2516---0000 2518---0000 2520---0000 2522---0000 2524---0000 2526---0000 2528---0000 2530---0000 2532---0000 2534---0000 2536---0000 2538---0000 2540---0000 2542---0000 2544---0000 2546---0000 2548---0000 2550---0000 2552---0000 2554---0000 2556---0000 2558---0000 2560---0000 2562---0000 2564---0000 2566---0000 2568---0000 2570---0000 2572---0000 2574---0000 2576---0000 2578---0000 2580---0000 2582---0000 2584---0000 2586---0000 2588---0000 2590---0000 2592---0000 2594---0000 2596---0000 2598---0000 2600---0000 2602---0000 2604---0000 2606---0000 2608---0000 2610---0000 2612---0000 2614---0000 2616---0000 2618---0000 2620---0000 2622---0000 2624---0000 2626---0000 2628---0000 2630---0000 2632---0000 2634---0000 2636---0000 2638---0000 2640---0000 2642---0000 2644---0000 2646---0000 2648---0000 2650---0000 2652---0000 2654---0000 2656---0000 2658---0000 2660---0000 2662---0000 2664---0000 2666---0000 2668---0000 2670---0000 2672---0000 2674---0000 2676---0000 2678---0000 2680---0000 2682---0000 2684---0000 2686---0000 2688---0000 2690---0000 2692---0000 2694---0000 2696---0000 2698---0000 2700---0000 2702---0000 2704---0000 2706---0000 2708---0000 2710---0000 2712---0000 2714---0000 2716---0000 2718---0000 2720---0000 2722---0000 2724---0000 2726---0000 2728---0000 2730---0000 2732---0000 2734---0000 2736---0000 2738---0000 2740---0000 2742---0000 2744---0000 2746---0000 2748---0000 2750---0000 2752---0000 2754---0000 2756---0000 2758---0000 2760---0000 2762---0000 2764---0000 2766---0000 2768---0000 2770---0000 2772---0000 2774---0000 2776---0000 2778---0000 2780---0000 2782---0000 2784---0000 2786---0000 2788---0000 2790---0000 2792---0000 2794---0000 2796---0000 2798---0000 2800---0000 2802---0000 2804---0000 2806---0000 2808---0000 2810---0000 2812---0000 2814---0000 2816---0000 2818---0000 2820---0000 2822---0000 2824---0000 2826---0000 2828---0000 2830---0000 2832---0000 2834---0000 2836---0000 2838---0000 2840---0000 2842---0000 2844---0000 2846---0000 2848---0000 2850---0000 2852---0000 2854---0000 2856---0000 2858---0000 2860---0000 2862---0000 2864---0000 2866---0000 2868---0000 2870---0000 2872---0000 2874---0000 2876---0000 2878---0000 2880---0000 2882---0000 2884---0000 2886---0000 2888---0000 2890---0000 2892---0000 2894---0000 2896---0000 2898---0000 2900---0000 2902---0000 2904---0000 2906---0000 2908---0000 2910---0000 2912---0000 2914---0000 2916---0000 2918---0000 2920---0000 2922---0000 2924---0000 2926---0000 2928---0000 2930---0000 2932 ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m23.839s user 0m4.133s sys 0m0.029s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:41:42 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=300, 1300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 1002---0000 1004---0000 1006---0000 1008---0000 1010---0000 1012---0000 1014---0000 1016---0000 1018---0000 1020---0000 1022---0000 1024---0000 1026---0000 1028---0000 1030---0000 1032---0000 1034---0000 1036---0000 1038---0000 1040---0000 1042---0000 1044---0000 1046---0000 1048---0000 1050---0000 1052---0000 1054---0000 1056---0000 1058---0000 1060---0000 1062---0000 1064---0000 1066---0000 1068---0000 1070---0000 1072---0000 1074---0000 1076---0000 1078---0000 1080---0000 1082---0000 1084---0000 1086---0000 1088---0000 1090---0000 1092---0000 1094---0000 1096---0000 1098---0000 1100---0000 1102---0000 1104---0000 1106---0000 1108---0000 1110---0000 1112---0000 1114---0000 1116---0000 1118---0000 1120---0000 1122---0000 1124---0000 1126---0000 1128---0000 1130---0000 1132---0000 1134---0000 1136---0000 1138---0000 1140---0000 1142---0000 1144---0000 1146---0000 1148---0000 1150---0000 1152---0000 1154---0000 1156---0000 1158---0000 1160---0000 1162---0000 1164---0000 1166---0000 1168---0000 1170---0000 1172---0000 1174---0000 1176---0000 1178---0000 1180---0000 1182---0000 1184---0000 1186---0000 1188---0000 1190---0000 1192---0000 1194---0000 1196---0000 1198---0000 1200---0000 1202---0000 1204---0000 1206---0000 1208---0000 1210---0000 1212---0000 1214---0000 1216---0000 1218---0000 1220---0000 1222---0000 1224---0000 1226---0000 1228---0000 1230---0000 1232---0000 1234---0000 1236---0000 1238---0000 1240---0000 1242---0000 1244---0000 1246---0000 1248---0000 1250---0000 1252---0000 1254---0000 1256---0000 1258---0000 1260---0000 1262---0000 1264---0000 1266---0000 1268---0000 1270---0000 1272---0000 1274---0000 1276---0000 1278---0000 1280---0000 1282---0000 1284---0000 1286---0000 1288---0000 1290---0000 1292---0000 1294---0000 1296---0000 1298---0000 1300---0000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m8.800s user 0m1.952s sys 0m0.011s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:41:07 2006 Input: f=x^4+2*x^2+7 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 7 ? %2 = [x - 1, x^2 + 6, x^4 - 12*x^2 + 252, x^4 + 2*x^2 + 7] ? ? ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m2.148s user 0m0.532s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:40:24 2006 Input: f=x^4+2*x^2+1 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 2000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 1 ? ? ? ? 2---[-x^2 - 1, x^2 + 1]00[-x^2 + 1, x^2 - 1] 4---[-1/2*x^2 - 1, 1/2*x^2 + 1]00[-1/2*x^2 + 1, 1/2*x^2 - 1] 6---[-1/3*x^2 - 1, 1/3*x^2 + 1]00[-1/3*x^2 + 1, 1/3*x^2 - 1] 8---[-1/4*x^2 - 1, 1/4*x^2 + 1]00[-1/4*x^2 + 1, 1/4*x^2 - 1] 10---[-1/5*x^2 - 1, 1/5*x^2 + 1]00[-1/5*x^2 + 1, 1/5*x^2 - 1] 12---[-1/6*x^2 - 1, 1/6*x^2 + 1]00[-1/6*x^2 + 1, 1/6*x^2 - 1] 14---[-1/7*x^2 - 1, 1/7*x^2 + 1]00[-1/7*x^2 + 1, 1/7*x^2 - 1] 16---[-1/8*x^2 - 1, 1/8*x^2 + 1]00[-1/8*x^2 + 1, 1/8*x^2 - 1] 18---[-1/9*x^2 - 1, 1/9*x^2 + 1]00[-1/9*x^2 + 1, 1/9*x^2 - 1] 20---[-1/10*x^2 - 1, 1/10*x^2 + 1]00[-1/10*x^2 + 1, 1/10*x^2 - 1] 22---[-1/11*x^2 - 1, 1/11*x^2 + 1]00[-1/11*x^2 + 1, 1/11*x^2 - 1] 24---[-1/12*x^2 - 1, 1/12*x^2 + 1]00[-1/12*x^2 + 1, 1/12*x^2 - 1] 26---[-1/13*x^2 - 1, 1/13*x^2 + 1]00[-1/13*x^2 + 1, 1/13*x^2 - 1] 28---[-1/14*x^2 - 1, 1/14*x^2 + 1]00[-1/14*x^2 + 1, 1/14*x^2 - 1] 30---[-1/15*x^2 - 1, 1/15*x^2 + 1]00[-1/15*x^2 + 1, 1/15*x^2 - 1] 32---[-1/16*x^2 - 1, 1/16*x^2 + 1]00[-1/16*x^2 + 1, 1/16*x^2 - 1] 34---[-1/17*x^2 - 1, 1/17*x^2 + 1]00[-1/17*x^2 + 1, 1/17*x^2 - 1] 36---[-1/18*x^2 - 1, 1/18*x^2 + 1]00[-1/18*x^2 + 1, 1/18*x^2 - 1] 38---[-1/19*x^2 - 1, 1/19*x^2 + 1]00[-1/19*x^2 + 1, 1/19*x^2 - 1] 40---[-1/20*x^2 - 1, 1/20*x^2 + 1]00[-1/20*x^2 + 1, 1/20*x^2 - 1] 42---[-1/21*x^2 - 1, 1/21*x^2 + 1]00[-1/21*x^2 + 1, 1/21*x^2 - 1] 44---[-1/22*x^2 - 1, 1/22*x^2 + 1]00[-1/22*x^2 + 1, 1/22*x^2 - 1] 46---[-1/23*x^2 - 1, 1/23*x^2 + 1]00[-1/23*x^2 + 1, 1/23*x^2 - 1] 48---[-1/24*x^2 - 1, 1/24*x^2 + 1]00[-1/24*x^2 + 1, 1/24*x^2 - 1] 50---[-1/25*x^2 - 1, 1/25*x^2 + 1]00[-1/25*x^2 + 1, 1/25*x^2 - 1] 52---[-1/26*x^2 - 1, 1/26*x^2 + 1]00[-1/26*x^2 + 1, 1/26*x^2 - 1] 54---[-1/27*x^2 - 1, 1/27*x^2 + 1]00[-1/27*x^2 + 1, 1/27*x^2 - 1] 56---[-1/28*x^2 - 1, 1/28*x^2 + 1]00[-1/28*x^2 + 1, 1/28*x^2 - 1] 58---[-1/29*x^2 - 1, 1/29*x^2 + 1]00[-1/29*x^2 + 1, 1/29*x^2 - 1] 60---[-1/30*x^2 - 1, 1/30*x^2 + 1]00[-1/30*x^2 + 1, 1/30*x^2 - 1] 62---[-1/31*x^2 - 1, 1/31*x^2 + 1]00[-1/31*x^2 + 1, 1/31*x^2 - 1] 64---[-1/32*x^2 - 1, 1/32*x^2 + 1]00[-1/32*x^2 + 1, 1/32*x^2 - 1] 66---[-1/33*x^2 - 1, 1/33*x^2 + 1]00[-1/33*x^2 + 1, 1/33*x^2 - 1] 68---[-1/34*x^2 - 1, 1/34*x^2 + 1]00[-1/34*x^2 + 1, 1/34*x^2 - 1] 70---[-1/35*x^2 - 1, 1/35*x^2 + 1]00[-1/35*x^2 + 1, 1/35*x^2 - 1] 72---[-1/36*x^2 - 1, 1/36*x^2 + 1]00[-1/36*x^2 + 1, 1/36*x^2 - 1] 74---[-1/37*x^2 - 1, 1/37*x^2 + 1]00[-1/37*x^2 + 1, 1/37*x^2 - 1] 76---[-1/38*x^2 - 1, 1/38*x^2 + 1]00[-1/38*x^2 + 1, 1/38*x^2 - 1] 78---[-1/39*x^2 - 1, 1/39*x^2 + 1]00[-1/39*x^2 + 1, 1/39*x^2 - 1] 80---[-1/40*x^2 - 1, 1/40*x^2 + 1]00[-1/40*x^2 + 1, 1/40*x^2 - 1] 82---[-1/41*x^2 - 1, 1/41*x^2 + 1]00[-1/41*x^2 + 1, 1/41*x^2 - 1] 84---[-1/42*x^2 - 1, 1/42*x^2 + 1]00[-1/42*x^2 + 1, 1/42*x^2 - 1] 86---[-1/43*x^2 - 1, 1/43*x^2 + 1]00[-1/43*x^2 + 1, 1/43*x^2 - 1] 88---[-1/44*x^2 - 1, 1/44*x^2 + 1]00[-1/44*x^2 + 1, 1/44*x^2 - 1] 90---[-1/45*x^2 - 1, 1/45*x^2 + 1]00[-1/45*x^2 + 1, 1/45*x^2 - 1] 92---[-1/46*x^2 - 1, 1/46*x^2 + 1]00[-1/46*x^2 + 1, 1/46*x^2 - 1] 94---[-1/47*x^2 - 1, 1/47*x^2 + 1]00[-1/47*x^2 + 1, 1/47*x^2 - 1] 96---[-1/48*x^2 - 1, 1/48*x^2 + 1]00[-1/48*x^2 + 1, 1/48*x^2 - 1] 98---[-1/49*x^2 - 1, 1/49*x^2 + 1]00[-1/49*x^2 + 1, 1/49*x^2 - 1] 100---[-1/50*x^2 - 1, 1/50*x^2 + 1]00[-1/50*x^2 + 1, 1/50*x^2 - 1] 102---[-1/51*x^2 - 1, 1/51*x^2 + 1]00[-1/51*x^2 + 1, 1/51*x^2 - 1] 104---[-1/52*x^2 - 1, 1/52*x^2 + 1]00[-1/52*x^2 + 1, 1/52*x^2 - 1] 106---[-1/53*x^2 - 1, 1/53*x^2 + 1]00[-1/53*x^2 + 1, 1/53*x^2 - 1] 108---[-1/54*x^2 - 1, 1/54*x^2 + 1]00[-1/54*x^2 + 1, 1/54*x^2 - 1] 110---[-1/55*x^2 - 1, 1/55*x^2 + 1]00[-1/55*x^2 + 1, 1/55*x^2 - 1] 112---[-1/56*x^2 - 1, 1/56*x^2 + 1]00[-1/56*x^2 + 1, 1/56*x^2 - 1] 114---[-1/57*x^2 - 1, 1/57*x^2 + 1]00[-1/57*x^2 + 1, 1/57*x^2 - 1] 116---[-1/58*x^2 - 1, 1/58*x^2 + 1]00[-1/58*x^2 + 1, 1/58*x^2 - 1] 118---[-1/59*x^2 - 1, 1/59*x^2 + 1]00[-1/59*x^2 + 1, 1/59*x^2 - 1] 120---[-1/60*x^2 - 1, 1/60*x^2 + 1]00[-1/60*x^2 + 1, 1/60*x^2 - 1] 122---[-1/61*x^2 - 1, 1/61*x^2 + 1]00[-1/61*x^2 + 1, 1/61*x^2 - 1] 124---[-1/62*x^2 - 1, 1/62*x^2 + 1]00[-1/62*x^2 + 1, 1/62*x^2 - 1] 126---[-1/63*x^2 - 1, 1/63*x^2 + 1]00[-1/63*x^2 + 1, 1/63*x^2 - 1] 128---[-1/64*x^2 - 1, 1/64*x^2 + 1]00[-1/64*x^2 + 1, 1/64*x^2 - 1] 130---[-1/65*x^2 - 1, 1/65*x^2 + 1]00[-1/65*x^2 + 1, 1/65*x^2 - 1] 132---[-1/66*x^2 - 1, 1/66*x^2 + 1]00[-1/66*x^2 + 1, 1/66*x^2 - 1] 134---[-1/67*x^2 - 1, 1/67*x^2 + 1]00[-1/67*x^2 + 1, 1/67*x^2 - 1] 136---[-1/68*x^2 - 1, 1/68*x^2 + 1]00[-1/68*x^2 + 1, 1/68*x^2 - 1] 138---[-1/69*x^2 - 1, 1/69*x^2 + 1]00[-1/69*x^2 + 1, 1/69*x^2 - 1] 140---[-1/70*x^2 - 1, 1/70*x^2 + 1]00[-1/70*x^2 + 1, 1/70*x^2 - 1] 142---[-1/71*x^2 - 1, 1/71*x^2 + 1]00[-1/71*x^2 + 1, 1/71*x^2 - 1] 144---[-1/72*x^2 - 1, 1/72*x^2 + 1]00[-1/72*x^2 + 1, 1/72*x^2 - 1] 146---[-1/73*x^2 - 1, 1/73*x^2 + 1]00[-1/73*x^2 + 1, 1/73*x^2 - 1] 148---[-1/74*x^2 - 1, 1/74*x^2 + 1]00[-1/74*x^2 + 1, 1/74*x^2 - 1] 150---[-1/75*x^2 - 1, 1/75*x^2 + 1]00[-1/75*x^2 + 1, 1/75*x^2 - 1] 152---[-1/76*x^2 - 1, 1/76*x^2 + 1]00[-1/76*x^2 + 1, 1/76*x^2 - 1] 154---[-1/77*x^2 - 1, 1/77*x^2 + 1]00[-1/77*x^2 + 1, 1/77*x^2 - 1] 156---[-1/78*x^2 - 1, 1/78*x^2 + 1]00[-1/78*x^2 + 1, 1/78*x^2 - 1] 158---[-1/79*x^2 - 1, 1/79*x^2 + 1]00[-1/79*x^2 + 1, 1/79*x^2 - 1] 160---[-1/80*x^2 - 1, 1/80*x^2 + 1]00[-1/80*x^2 + 1, 1/80*x^2 - 1] 162---[-1/81*x^2 - 1, 1/81*x^2 + 1]00[-1/81*x^2 + 1, 1/81*x^2 - 1] 164---[-1/82*x^2 - 1, 1/82*x^2 + 1]00[-1/82*x^2 + 1, 1/82*x^2 - 1] 166---[-1/83*x^2 - 1, 1/83*x^2 + 1]00[-1/83*x^2 + 1, 1/83*x^2 - 1] 168---[-1/84*x^2 - 1, 1/84*x^2 + 1]00[-1/84*x^2 + 1, 1/84*x^2 - 1] 170---[-1/85*x^2 - 1, 1/85*x^2 + 1]00[-1/85*x^2 + 1, 1/85*x^2 - 1] 172---[-1/86*x^2 - 1, 1/86*x^2 + 1]00[-1/86*x^2 + 1, 1/86*x^2 - 1] 174---[-1/87*x^2 - 1, 1/87*x^2 + 1]00[-1/87*x^2 + 1, 1/87*x^2 - 1] 176---[-1/88*x^2 - 1, 1/88*x^2 + 1]00[-1/88*x^2 + 1, 1/88*x^2 - 1] 178---[-1/89*x^2 - 1, 1/89*x^2 + 1]00[-1/89*x^2 + 1, 1/89*x^2 - 1] 180---[-1/90*x^2 - 1, 1/90*x^2 + 1]00[-1/90*x^2 + 1, 1/90*x^2 - 1] 182---[-1/91*x^2 - 1, 1/91*x^2 + 1]00[-1/91*x^2 + 1, 1/91*x^2 - 1] 184---[-1/92*x^2 - 1, 1/92*x^2 + 1]00[-1/92*x^2 + 1, 1/92*x^2 - 1] 186---[-1/93*x^2 - 1, 1/93*x^2 + 1]00[-1/93*x^2 + 1, 1/93*x^2 - 1] 188---[-1/94*x^2 - 1, 1/94*x^2 + 1]00[-1/94*x^2 + 1, 1/94*x^2 - 1] 190---[-1/95*x^2 - 1, 1/95*x^2 + 1]00[-1/95*x^2 + 1, 1/95*x^2 - 1] 192---[-1/96*x^2 - 1, 1/96*x^2 + 1]00[-1/96*x^2 + 1, 1/96*x^2 - 1] 194---[-1/97*x^2 - 1, 1/97*x^2 + 1]00[-1/97*x^2 + 1, 1/97*x^2 - 1] 196---[-1/98*x^2 - 1, 1/98*x^2 + 1]00[-1/98*x^2 + 1, 1/98*x^2 - 1] 198---[-1/99*x^2 - 1, 1/99*x^2 + 1]00[-1/99*x^2 + 1, 1/99*x^2 - 1] 200---[-1/100*x^2 - 1, 1/100*x^2 + 1]00[-1/100*x^2 + 1, 1/100*x^2 - 1] 202---[-1/101*x^2 - 1, 1/101*x^2 + 1]00[-1/101*x^2 + 1, 1/101*x^2 - 1] 204---[-1/102*x^2 - 1, 1/102*x^2 + 1]00[-1/102*x^2 + 1, 1/102*x^2 - 1] 206---[-1/103*x^2 - 1, 1/103*x^2 + 1]00[-1/103*x^2 + 1, 1/103*x^2 - 1] 208---[-1/104*x^2 - 1, 1/104*x^2 + 1]00[-1/104*x^2 + 1, 1/104*x^2 - 1] 210---[-1/105*x^2 - 1, 1/105*x^2 + 1]00[-1/105*x^2 + 1, 1/105*x^2 - 1] 212---[-1/106*x^2 - 1, 1/106*x^2 + 1]00[-1/106*x^2 + 1, 1/106*x^2 - 1] 214---[-1/107*x^2 - 1, 1/107*x^2 + 1]00[-1/107*x^2 + 1, 1/107*x^2 - 1] 216---[-1/108*x^2 - 1, 1/108*x^2 + 1]00[-1/108*x^2 + 1, 1/108*x^2 - 1] 218---[-1/109*x^2 - 1, 1/109*x^2 + 1]00[-1/109*x^2 + 1, 1/109*x^2 - 1] 220---[-1/110*x^2 - 1, 1/110*x^2 + 1]00[-1/110*x^2 + 1, 1/110*x^2 - 1] 222---[-1/111*x^2 - 1, 1/111*x^2 + 1]00[-1/111*x^2 + 1, 1/111*x^2 - 1] 224---[-1/112*x^2 - 1, 1/112*x^2 + 1]00[-1/112*x^2 + 1, 1/112*x^2 - 1] 226---[-1/113*x^2 - 1, 1/113*x^2 + 1]00[-1/113*x^2 + 1, 1/113*x^2 - 1] 228---[-1/114*x^2 - 1, 1/114*x^2 + 1]00[-1/114*x^2 + 1, 1/114*x^2 - 1] 230---[-1/115*x^2 - 1, 1/115*x^2 + 1]00[-1/115*x^2 + 1, 1/115*x^2 - 1] 232---[-1/116*x^2 - 1, 1/116*x^2 + 1]00[-1/116*x^2 + 1, 1/116*x^2 - 1] 234---[-1/117*x^2 - 1, 1/117*x^2 + 1]00[-1/117*x^2 + 1, 1/117*x^2 - 1] 236---[-1/118*x^2 - 1, 1/118*x^2 + 1]00[-1/118*x^2 + 1, 1/118*x^2 - 1] 238---[-1/119*x^2 - 1, 1/119*x^2 + 1]00[-1/119*x^2 + 1, 1/119*x^2 - 1] 240---[-1/120*x^2 - 1, 1/120*x^2 + 1]00[-1/120*x^2 + 1, 1/120*x^2 - 1] 242---[-1/121*x^2 - 1, 1/121*x^2 + 1]00[-1/121*x^2 + 1, 1/121*x^2 - 1] 244---[-1/122*x^2 - 1, 1/122*x^2 + 1]00[-1/122*x^2 + 1, 1/122*x^2 - 1] 246---[-1/123*x^2 - 1, 1/123*x^2 + 1]00[-1/123*x^2 + 1, 1/123*x^2 - 1] 248---[-1/124*x^2 - 1, 1/124*x^2 + 1]00[-1/124*x^2 + 1, 1/124*x^2 - 1] 250---[-1/125*x^2 - 1, 1/125*x^2 + 1]00[-1/125*x^2 + 1, 1/125*x^2 - 1] 252---[-1/126*x^2 - 1, 1/126*x^2 + 1]00[-1/126*x^2 + 1, 1/126*x^2 - 1] 254---[-1/127*x^2 - 1, 1/127*x^2 + 1]00[-1/127*x^2 + 1, 1/127*x^2 - 1] 256---[-1/128*x^2 - 1, 1/128*x^2 + 1]00[-1/128*x^2 + 1, 1/128*x^2 - 1] 258---[-1/129*x^2 - 1, 1/129*x^2 + 1]00[-1/129*x^2 + 1, 1/129*x^2 - 1] 260---[-1/130*x^2 - 1, 1/130*x^2 + 1]00[-1/130*x^2 + 1, 1/130*x^2 - 1] 262---[-1/131*x^2 - 1, 1/131*x^2 + 1]00[-1/131*x^2 + 1, 1/131*x^2 - 1] 264---[-1/132*x^2 - 1, 1/132*x^2 + 1]00[-1/132*x^2 + 1, 1/132*x^2 - 1] 266---[-1/133*x^2 - 1, 1/133*x^2 + 1]00[-1/133*x^2 + 1, 1/133*x^2 - 1] 268---[-1/134*x^2 - 1, 1/134*x^2 + 1]00[-1/134*x^2 + 1, 1/134*x^2 - 1] 270---[-1/135*x^2 - 1, 1/135*x^2 + 1]00[-1/135*x^2 + 1, 1/135*x^2 - 1] 272---[-1/136*x^2 - 1, 1/136*x^2 + 1]00[-1/136*x^2 + 1, 1/136*x^2 - 1] 274---[-1/137*x^2 - 1, 1/137*x^2 + 1]00[-1/137*x^2 + 1, 1/137*x^2 - 1] 276---[-1/138*x^2 - 1, 1/138*x^2 + 1]00[-1/138*x^2 + 1, 1/138*x^2 - 1] 278---[-1/139*x^2 - 1, 1/139*x^2 + 1]00[-1/139*x^2 + 1, 1/139*x^2 - 1] 280---[-1/140*x^2 - 1, 1/140*x^2 + 1]00[-1/140*x^2 + 1, 1/140*x^2 - 1] 282---[-1/141*x^2 - 1, 1/141*x^2 + 1]00[-1/141*x^2 + 1, 1/141*x^2 - 1] 284---[-1/142*x^2 - 1, 1/142*x^2 + 1]00[-1/142*x^2 + 1, 1/142*x^2 - 1] 286---[-1/143*x^2 - 1, 1/143*x^2 + 1]00[-1/143*x^2 + 1, 1/143*x^2 - 1] 288---[-1/144*x^2 - 1, 1/144*x^2 + 1]00[-1/144*x^2 + 1, 1/144*x^2 - 1] 290---[-1/145*x^2 - 1, 1/145*x^2 + 1]00[-1/145*x^2 + 1, 1/145*x^2 - 1] 292---[-1/146*x^2 - 1, 1/146*x^2 + 1]00[-1/146*x^2 + 1, 1/146 ** WARNING: Output too long, hence truncated. Errors/timing (if any): *** polred: reducible polynomial in nfinit. *** nfinit: reducible polynomial in nfinit. *** incorrect type in disc: factor(nf.disc); ^------ Timing: real 0m43.529s user 0m7.442s sys 0m0.025s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:40:19 2006 Input: f=x^4+2*x^2+1 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 300, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + 2*x^2 + 1 ? ? ? ? 2---[-x^2 - 1, x^2 + 1]00[-x^2 + 1, x^2 - 1] 4---[-1/2*x^2 - 1, 1/2*x^2 + 1]00[-1/2*x^2 + 1, 1/2*x^2 - 1] 6---[-1/3*x^2 - 1, 1/3*x^2 + 1]00[-1/3*x^2 + 1, 1/3*x^2 - 1] 8---[-1/4*x^2 - 1, 1/4*x^2 + 1]00[-1/4*x^2 + 1, 1/4*x^2 - 1] 10---[-1/5*x^2 - 1, 1/5*x^2 + 1]00[-1/5*x^2 + 1, 1/5*x^2 - 1] 12---[-1/6*x^2 - 1, 1/6*x^2 + 1]00[-1/6*x^2 + 1, 1/6*x^2 - 1] 14---[-1/7*x^2 - 1, 1/7*x^2 + 1]00[-1/7*x^2 + 1, 1/7*x^2 - 1] 16---[-1/8*x^2 - 1, 1/8*x^2 + 1]00[-1/8*x^2 + 1, 1/8*x^2 - 1] 18---[-1/9*x^2 - 1, 1/9*x^2 + 1]00[-1/9*x^2 + 1, 1/9*x^2 - 1] 20---[-1/10*x^2 - 1, 1/10*x^2 + 1]00[-1/10*x^2 + 1, 1/10*x^2 - 1] 22---[-1/11*x^2 - 1, 1/11*x^2 + 1]00[-1/11*x^2 + 1, 1/11*x^2 - 1] 24---[-1/12*x^2 - 1, 1/12*x^2 + 1]00[-1/12*x^2 + 1, 1/12*x^2 - 1] 26---[-1/13*x^2 - 1, 1/13*x^2 + 1]00[-1/13*x^2 + 1, 1/13*x^2 - 1] 28---[-1/14*x^2 - 1, 1/14*x^2 + 1]00[-1/14*x^2 + 1, 1/14*x^2 - 1] 30---[-1/15*x^2 - 1, 1/15*x^2 + 1]00[-1/15*x^2 + 1, 1/15*x^2 - 1] 32---[-1/16*x^2 - 1, 1/16*x^2 + 1]00[-1/16*x^2 + 1, 1/16*x^2 - 1] 34---[-1/17*x^2 - 1, 1/17*x^2 + 1]00[-1/17*x^2 + 1, 1/17*x^2 - 1] 36---[-1/18*x^2 - 1, 1/18*x^2 + 1]00[-1/18*x^2 + 1, 1/18*x^2 - 1] 38---[-1/19*x^2 - 1, 1/19*x^2 + 1]00[-1/19*x^2 + 1, 1/19*x^2 - 1] 40---[-1/20*x^2 - 1, 1/20*x^2 + 1]00[-1/20*x^2 + 1, 1/20*x^2 - 1] 42---[-1/21*x^2 - 1, 1/21*x^2 + 1]00[-1/21*x^2 + 1, 1/21*x^2 - 1] 44---[-1/22*x^2 - 1, 1/22*x^2 + 1]00[-1/22*x^2 + 1, 1/22*x^2 - 1] 46---[-1/23*x^2 - 1, 1/23*x^2 + 1]00[-1/23*x^2 + 1, 1/23*x^2 - 1] 48---[-1/24*x^2 - 1, 1/24*x^2 + 1]00[-1/24*x^2 + 1, 1/24*x^2 - 1] 50---[-1/25*x^2 - 1, 1/25*x^2 + 1]00[-1/25*x^2 + 1, 1/25*x^2 - 1] 52---[-1/26*x^2 - 1, 1/26*x^2 + 1]00[-1/26*x^2 + 1, 1/26*x^2 - 1] 54---[-1/27*x^2 - 1, 1/27*x^2 + 1]00[-1/27*x^2 + 1, 1/27*x^2 - 1] 56---[-1/28*x^2 - 1, 1/28*x^2 + 1]00[-1/28*x^2 + 1, 1/28*x^2 - 1] 58---[-1/29*x^2 - 1, 1/29*x^2 + 1]00[-1/29*x^2 + 1, 1/29*x^2 - 1] 60---[-1/30*x^2 - 1, 1/30*x^2 + 1]00[-1/30*x^2 + 1, 1/30*x^2 - 1] 62---[-1/31*x^2 - 1, 1/31*x^2 + 1]00[-1/31*x^2 + 1, 1/31*x^2 - 1] 64---[-1/32*x^2 - 1, 1/32*x^2 + 1]00[-1/32*x^2 + 1, 1/32*x^2 - 1] 66---[-1/33*x^2 - 1, 1/33*x^2 + 1]00[-1/33*x^2 + 1, 1/33*x^2 - 1] 68---[-1/34*x^2 - 1, 1/34*x^2 + 1]00[-1/34*x^2 + 1, 1/34*x^2 - 1] 70---[-1/35*x^2 - 1, 1/35*x^2 + 1]00[-1/35*x^2 + 1, 1/35*x^2 - 1] 72---[-1/36*x^2 - 1, 1/36*x^2 + 1]00[-1/36*x^2 + 1, 1/36*x^2 - 1] 74---[-1/37*x^2 - 1, 1/37*x^2 + 1]00[-1/37*x^2 + 1, 1/37*x^2 - 1] 76---[-1/38*x^2 - 1, 1/38*x^2 + 1]00[-1/38*x^2 + 1, 1/38*x^2 - 1] 78---[-1/39*x^2 - 1, 1/39*x^2 + 1]00[-1/39*x^2 + 1, 1/39*x^2 - 1] 80---[-1/40*x^2 - 1, 1/40*x^2 + 1]00[-1/40*x^2 + 1, 1/40*x^2 - 1] 82---[-1/41*x^2 - 1, 1/41*x^2 + 1]00[-1/41*x^2 + 1, 1/41*x^2 - 1] 84---[-1/42*x^2 - 1, 1/42*x^2 + 1]00[-1/42*x^2 + 1, 1/42*x^2 - 1] 86---[-1/43*x^2 - 1, 1/43*x^2 + 1]00[-1/43*x^2 + 1, 1/43*x^2 - 1] 88---[-1/44*x^2 - 1, 1/44*x^2 + 1]00[-1/44*x^2 + 1, 1/44*x^2 - 1] 90---[-1/45*x^2 - 1, 1/45*x^2 + 1]00[-1/45*x^2 + 1, 1/45*x^2 - 1] 92---[-1/46*x^2 - 1, 1/46*x^2 + 1]00[-1/46*x^2 + 1, 1/46*x^2 - 1] 94---[-1/47*x^2 - 1, 1/47*x^2 + 1]00[-1/47*x^2 + 1, 1/47*x^2 - 1] 96---[-1/48*x^2 - 1, 1/48*x^2 + 1]00[-1/48*x^2 + 1, 1/48*x^2 - 1] 98---[-1/49*x^2 - 1, 1/49*x^2 + 1]00[-1/49*x^2 + 1, 1/49*x^2 - 1] 100---[-1/50*x^2 - 1, 1/50*x^2 + 1]00[-1/50*x^2 + 1, 1/50*x^2 - 1] 102---[-1/51*x^2 - 1, 1/51*x^2 + 1]00[-1/51*x^2 + 1, 1/51*x^2 - 1] 104---[-1/52*x^2 - 1, 1/52*x^2 + 1]00[-1/52*x^2 + 1, 1/52*x^2 - 1] 106---[-1/53*x^2 - 1, 1/53*x^2 + 1]00[-1/53*x^2 + 1, 1/53*x^2 - 1] 108---[-1/54*x^2 - 1, 1/54*x^2 + 1]00[-1/54*x^2 + 1, 1/54*x^2 - 1] 110---[-1/55*x^2 - 1, 1/55*x^2 + 1]00[-1/55*x^2 + 1, 1/55*x^2 - 1] 112---[-1/56*x^2 - 1, 1/56*x^2 + 1]00[-1/56*x^2 + 1, 1/56*x^2 - 1] 114---[-1/57*x^2 - 1, 1/57*x^2 + 1]00[-1/57*x^2 + 1, 1/57*x^2 - 1] 116---[-1/58*x^2 - 1, 1/58*x^2 + 1]00[-1/58*x^2 + 1, 1/58*x^2 - 1] 118---[-1/59*x^2 - 1, 1/59*x^2 + 1]00[-1/59*x^2 + 1, 1/59*x^2 - 1] 120---[-1/60*x^2 - 1, 1/60*x^2 + 1]00[-1/60*x^2 + 1, 1/60*x^2 - 1] 122---[-1/61*x^2 - 1, 1/61*x^2 + 1]00[-1/61*x^2 + 1, 1/61*x^2 - 1] 124---[-1/62*x^2 - 1, 1/62*x^2 + 1]00[-1/62*x^2 + 1, 1/62*x^2 - 1] 126---[-1/63*x^2 - 1, 1/63*x^2 + 1]00[-1/63*x^2 + 1, 1/63*x^2 - 1] 128---[-1/64*x^2 - 1, 1/64*x^2 + 1]00[-1/64*x^2 + 1, 1/64*x^2 - 1] 130---[-1/65*x^2 - 1, 1/65*x^2 + 1]00[-1/65*x^2 + 1, 1/65*x^2 - 1] 132---[-1/66*x^2 - 1, 1/66*x^2 + 1]00[-1/66*x^2 + 1, 1/66*x^2 - 1] 134---[-1/67*x^2 - 1, 1/67*x^2 + 1]00[-1/67*x^2 + 1, 1/67*x^2 - 1] 136---[-1/68*x^2 - 1, 1/68*x^2 + 1]00[-1/68*x^2 + 1, 1/68*x^2 - 1] 138---[-1/69*x^2 - 1, 1/69*x^2 + 1]00[-1/69*x^2 + 1, 1/69*x^2 - 1] 140---[-1/70*x^2 - 1, 1/70*x^2 + 1]00[-1/70*x^2 + 1, 1/70*x^2 - 1] 142---[-1/71*x^2 - 1, 1/71*x^2 + 1]00[-1/71*x^2 + 1, 1/71*x^2 - 1] 144---[-1/72*x^2 - 1, 1/72*x^2 + 1]00[-1/72*x^2 + 1, 1/72*x^2 - 1] 146---[-1/73*x^2 - 1, 1/73*x^2 + 1]00[-1/73*x^2 + 1, 1/73*x^2 - 1] 148---[-1/74*x^2 - 1, 1/74*x^2 + 1]00[-1/74*x^2 + 1, 1/74*x^2 - 1] 150---[-1/75*x^2 - 1, 1/75*x^2 + 1]00[-1/75*x^2 + 1, 1/75*x^2 - 1] 152---[-1/76*x^2 - 1, 1/76*x^2 + 1]00[-1/76*x^2 + 1, 1/76*x^2 - 1] 154---[-1/77*x^2 - 1, 1/77*x^2 + 1]00[-1/77*x^2 + 1, 1/77*x^2 - 1] 156---[-1/78*x^2 - 1, 1/78*x^2 + 1]00[-1/78*x^2 + 1, 1/78*x^2 - 1] 158---[-1/79*x^2 - 1, 1/79*x^2 + 1]00[-1/79*x^2 + 1, 1/79*x^2 - 1] 160---[-1/80*x^2 - 1, 1/80*x^2 + 1]00[-1/80*x^2 + 1, 1/80*x^2 - 1] 162---[-1/81*x^2 - 1, 1/81*x^2 + 1]00[-1/81*x^2 + 1, 1/81*x^2 - 1] 164---[-1/82*x^2 - 1, 1/82*x^2 + 1]00[-1/82*x^2 + 1, 1/82*x^2 - 1] 166---[-1/83*x^2 - 1, 1/83*x^2 + 1]00[-1/83*x^2 + 1, 1/83*x^2 - 1] 168---[-1/84*x^2 - 1, 1/84*x^2 + 1]00[-1/84*x^2 + 1, 1/84*x^2 - 1] 170---[-1/85*x^2 - 1, 1/85*x^2 + 1]00[-1/85*x^2 + 1, 1/85*x^2 - 1] 172---[-1/86*x^2 - 1, 1/86*x^2 + 1]00[-1/86*x^2 + 1, 1/86*x^2 - 1] 174---[-1/87*x^2 - 1, 1/87*x^2 + 1]00[-1/87*x^2 + 1, 1/87*x^2 - 1] 176---[-1/88*x^2 - 1, 1/88*x^2 + 1]00[-1/88*x^2 + 1, 1/88*x^2 - 1] 178---[-1/89*x^2 - 1, 1/89*x^2 + 1]00[-1/89*x^2 + 1, 1/89*x^2 - 1] 180---[-1/90*x^2 - 1, 1/90*x^2 + 1]00[-1/90*x^2 + 1, 1/90*x^2 - 1] 182---[-1/91*x^2 - 1, 1/91*x^2 + 1]00[-1/91*x^2 + 1, 1/91*x^2 - 1] 184---[-1/92*x^2 - 1, 1/92*x^2 + 1]00[-1/92*x^2 + 1, 1/92*x^2 - 1] 186---[-1/93*x^2 - 1, 1/93*x^2 + 1]00[-1/93*x^2 + 1, 1/93*x^2 - 1] 188---[-1/94*x^2 - 1, 1/94*x^2 + 1]00[-1/94*x^2 + 1, 1/94*x^2 - 1] 190---[-1/95*x^2 - 1, 1/95*x^2 + 1]00[-1/95*x^2 + 1, 1/95*x^2 - 1] 192---[-1/96*x^2 - 1, 1/96*x^2 + 1]00[-1/96*x^2 + 1, 1/96*x^2 - 1] 194---[-1/97*x^2 - 1, 1/97*x^2 + 1]00[-1/97*x^2 + 1, 1/97*x^2 - 1] 196---[-1/98*x^2 - 1, 1/98*x^2 + 1]00[-1/98*x^2 + 1, 1/98*x^2 - 1] 198---[-1/99*x^2 - 1, 1/99*x^2 + 1]00[-1/99*x^2 + 1, 1/99*x^2 - 1] 200---[-1/100*x^2 - 1, 1/100*x^2 + 1]00[-1/100*x^2 + 1, 1/100*x^2 - 1] 202---[-1/101*x^2 - 1, 1/101*x^2 + 1]00[-1/101*x^2 + 1, 1/101*x^2 - 1] 204---[-1/102*x^2 - 1, 1/102*x^2 + 1]00[-1/102*x^2 + 1, 1/102*x^2 - 1] 206---[-1/103*x^2 - 1, 1/103*x^2 + 1]00[-1/103*x^2 + 1, 1/103*x^2 - 1] 208---[-1/104*x^2 - 1, 1/104*x^2 + 1]00[-1/104*x^2 + 1, 1/104*x^2 - 1] 210---[-1/105*x^2 - 1, 1/105*x^2 + 1]00[-1/105*x^2 + 1, 1/105*x^2 - 1] 212---[-1/106*x^2 - 1, 1/106*x^2 + 1]00[-1/106*x^2 + 1, 1/106*x^2 - 1] 214---[-1/107*x^2 - 1, 1/107*x^2 + 1]00[-1/107*x^2 + 1, 1/107*x^2 - 1] 216---[-1/108*x^2 - 1, 1/108*x^2 + 1]00[-1/108*x^2 + 1, 1/108*x^2 - 1] 218---[-1/109*x^2 - 1, 1/109*x^2 + 1]00[-1/109*x^2 + 1, 1/109*x^2 - 1] 220---[-1/110*x^2 - 1, 1/110*x^2 + 1]00[-1/110*x^2 + 1, 1/110*x^2 - 1] 222---[-1/111*x^2 - 1, 1/111*x^2 + 1]00[-1/111*x^2 + 1, 1/111*x^2 - 1] 224---[-1/112*x^2 - 1, 1/112*x^2 + 1]00[-1/112*x^2 + 1, 1/112*x^2 - 1] 226---[-1/113*x^2 - 1, 1/113*x^2 + 1]00[-1/113*x^2 + 1, 1/113*x^2 - 1] 228---[-1/114*x^2 - 1, 1/114*x^2 + 1]00[-1/114*x^2 + 1, 1/114*x^2 - 1] 230---[-1/115*x^2 - 1, 1/115*x^2 + 1]00[-1/115*x^2 + 1, 1/115*x^2 - 1] 232---[-1/116*x^2 - 1, 1/116*x^2 + 1]00[-1/116*x^2 + 1, 1/116*x^2 - 1] 234---[-1/117*x^2 - 1, 1/117*x^2 + 1]00[-1/117*x^2 + 1, 1/117*x^2 - 1] 236---[-1/118*x^2 - 1, 1/118*x^2 + 1]00[-1/118*x^2 + 1, 1/118*x^2 - 1] 238---[-1/119*x^2 - 1, 1/119*x^2 + 1]00[-1/119*x^2 + 1, 1/119*x^2 - 1] 240---[-1/120*x^2 - 1, 1/120*x^2 + 1]00[-1/120*x^2 + 1, 1/120*x^2 - 1] 242---[-1/121*x^2 - 1, 1/121*x^2 + 1]00[-1/121*x^2 + 1, 1/121*x^2 - 1] 244---[-1/122*x^2 - 1, 1/122*x^2 + 1]00[-1/122*x^2 + 1, 1/122*x^2 - 1] 246---[-1/123*x^2 - 1, 1/123*x^2 + 1]00[-1/123*x^2 + 1, 1/123*x^2 - 1] 248---[-1/124*x^2 - 1, 1/124*x^2 + 1]00[-1/124*x^2 + 1, 1/124*x^2 - 1] 250---[-1/125*x^2 - 1, 1/125*x^2 + 1]00[-1/125*x^2 + 1, 1/125*x^2 - 1] 252---[-1/126*x^2 - 1, 1/126*x^2 + 1]00[-1/126*x^2 + 1, 1/126*x^2 - 1] 254---[-1/127*x^2 - 1, 1/127*x^2 + 1]00[-1/127*x^2 + 1, 1/127*x^2 - 1] 256---[-1/128*x^2 - 1, 1/128*x^2 + 1]00[-1/128*x^2 + 1, 1/128*x^2 - 1] 258---[-1/129*x^2 - 1, 1/129*x^2 + 1]00[-1/129*x^2 + 1, 1/129*x^2 - 1] 260---[-1/130*x^2 - 1, 1/130*x^2 + 1]00[-1/130*x^2 + 1, 1/130*x^2 - 1] 262---[-1/131*x^2 - 1, 1/131*x^2 + 1]00[-1/131*x^2 + 1, 1/131*x^2 - 1] 264---[-1/132*x^2 - 1, 1/132*x^2 + 1]00[-1/132*x^2 + 1, 1/132*x^2 - 1] 266---[-1/133*x^2 - 1, 1/133*x^2 + 1]00[-1/133*x^2 + 1, 1/133*x^2 - 1] 268---[-1/134*x^2 - 1, 1/134*x^2 + 1]00[-1/134*x^2 + 1, 1/134*x^2 - 1] 270---[-1/135*x^2 - 1, 1/135*x^2 + 1]00[-1/135*x^2 + 1, 1/135*x^2 - 1] 272---[-1/136*x^2 - 1, 1/136*x^2 + 1]00[-1/136*x^2 + 1, 1/136*x^2 - 1] 274---[-1/137*x^2 - 1, 1/137*x^2 + 1]00[-1/137*x^2 + 1, 1/137*x^2 - 1] 276---[-1/138*x^2 - 1, 1/138*x^2 + 1]00[-1/138*x^2 + 1, 1/138*x^2 - 1] 278---[-1/139*x^2 - 1, 1/139*x^2 + 1]00[-1/139*x^2 + 1, 1/139*x^2 - 1] 280---[-1/140*x^2 - 1, 1/140*x^2 + 1]00[-1/140*x^2 + 1, 1/140*x^2 - 1] 282---[-1/141*x^2 - 1, 1/141*x^2 + 1]00[-1/141*x^2 + 1, 1/141*x^2 - 1] 284---[-1/142*x^2 - 1, 1/142*x^2 + 1]00[-1/142*x^2 + 1, 1/142*x^2 - 1] 286---[-1/143*x^2 - 1, 1/143*x^2 + 1]00[-1/143*x^2 + 1, 1/143*x^2 - 1] 288---[-1/144*x^2 - 1, 1/144*x^2 + 1]00[-1/144*x^2 + 1, 1/144*x^2 - 1] 290---[-1/145*x^2 - 1, 1/145*x^2 + 1]00[-1/145*x^2 + 1, 1/145*x^2 - 1] 292---[-1/146*x^2 - 1, 1/146*x^2 + 1]00[-1/146*x^2 + 1, 1/146 ** WARNING: Output too long, hence truncated. Errors/timing (if any): *** polred: reducible polynomial in nfinit. *** nfinit: reducible polynomial in nfinit. *** incorrect type in disc: factor(nf.disc); ^------ Timing: real 0m2.068s user 0m1.024s sys 0m0.012s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:38:40 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 5000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 1002---0000 1004---0000 1006---0000 1008---0000 1010---0000 1012---0000 1014---0000 1016---0000 1018---0000 1020---0000 1022---0000 1024---0000 1026---0000 1028---0000 1030---0000 1032---0000 1034---0000 1036---0000 1038---0000 1040---0000 1042---0000 1044---0000 1046---0000 1048---0000 1050---0000 1052---0000 1054---0000 1056---0000 1058---0000 1060---0000 1062---0000 1064---0000 1066---0000 1068---0000 1070---0000 1072---0000 1074---0000 1076---0000 1078---0000 1080---0000 1082---0000 1084---0000 1086---0000 1088---0000 1090---0000 1092---0000 1094---0000 1096---0000 1098---0000 1100---0000 1102---0000 1104---0000 1106---0000 1108---0000 1110---0000 1112---0000 1114---0000 1116---0000 1118---0000 1120---0000 1122---0000 1124---0000 1126---0000 1128---0000 1130---0000 1132---0000 1134---0000 1136---0000 1138---0000 1140---0000 1142---0000 1144---0000 1146---0000 1148---0000 1150---0000 1152---0000 1154---0000 1156---0000 1158---0000 1160---0000 1162---0000 1164---0000 1166---0000 1168---0000 1170---0000 1172---0000 1174---0000 1176---0000 1178---0000 1180---0000 1182---0000 1184---0000 1186---0000 1188---0000 1190---0000 1192---0000 1194---0000 1196---0000 1198---0000 1200---0000 1202---0000 1204---0000 1206---0000 1208---0000 1210---0000 1212---0000 1214---0000 1216---0000 1218---0000 1220---0000 1222---0000 1224---0000 1226---0000 1228---0000 1230---0000 1232---0000 1234---0000 1236---0000 1238---0000 1240---0000 1242---0000 1244---0000 1246---0000 1248---0000 1250---0000 1252---0000 1254---0000 1256---0000 1258---0000 1260---0000 1262---0000 1264---0000 1266---0000 1268---0000 1270---0000 1272---0000 1274---0000 1276---0000 1278---0000 1280---0000 1282---0000 1284---0000 1286---0000 1288---0000 1290---0000 1292---0000 1294---0000 1296---0000 1298---0000 1300---0000 1302---0000 1304---0000 1306---0000 1308---0000 1310---0000 1312---0000 1314---0000 1316---0000 1318---0000 1320---0000 1322---0000 1324---0000 1326---0000 1328---0000 1330---0000 1332---0000 1334---0000 1336---0000 1338---0000 1340---0000 1342---0000 1344---0000 1346---0000 1348---0000 1350---0000 1352---0000 1354---0000 1356---0000 1358---0000 1360---0000 1362---0000 1364---0000 1366---0000 1368---0000 1370---0000 1372---0000 1374---0000 1376---0000 1378---0000 1380---0000 1382---0000 1384---0000 1386---0000 1388---0000 1390---0000 1392---0000 1394---0000 1396---0000 1398---0000 1400---0000 1402---0000 1404---0000 1406---0000 1408---0000 1410---0000 1412---0000 1414---0000 1416---0000 1418---0000 1420---0000 1422---0000 1424---0000 1426---0000 1428---0000 1430---0000 1432---0000 1434---0000 1436---0000 1438---0000 1440---0000 1442---0000 1444---0000 1446---0000 1448---0000 1450---0000 1452---0000 1454---0000 1456---0000 1458---0000 1460---0000 1462---0000 1464---0000 1466---0000 1468---0000 1470---0000 1472---0000 1474---0000 1476---0000 1478---0000 1480---0000 1482---0000 1484---0000 1486---0000 1488---0000 1490---0000 1492---0000 1494---0000 1496---0000 1498---0000 1500---0000 1502---0000 1504---0000 1506---0000 1508---0000 1510---0000 1512---0000 1514---0000 1516---0000 1518---0000 1520---0000 1522---0000 1524---0000 1526---0000 1528---0000 1530---0000 1532---0000 1534---0000 1536---0000 1538---0000 1540---0000 1542---0000 1544---0000 1546---0000 1548---0000 1550---0000 1552---0000 1554---0000 1556---0000 1558---0000 1560---0000 1562---0000 1564---0000 1566---0000 1568---0000 1570---0000 1572---0000 1574---0000 1576---0000 1578---0000 1580---0000 1582---0000 1584---0000 1586---0000 1588---0000 1590---0000 1592---0000 1594---0000 1596---0000 1598---0000 1600---0000 1602---0000 1604---0000 1606---0000 1608---0000 1610---0000 1612---0000 1614---0000 1616---0000 1618---0000 1620---0000 1622---0000 1624---0000 1626---0000 1628---0000 1630---0000 1632---0000 1634---0000 1636---0000 1638---0000 1640---0000 1642---0000 1644---0000 1646---0000 1648---0000 1650---0000 1652---0000 1654---0000 1656---0000 1658---0000 1660---0000 1662---0000 1664---0000 1666---0000 1668---0000 1670---0000 1672---0000 1674---0000 1676---0000 1678---0000 1680---0000 1682---0000 1684---0000 1686---0000 1688---0000 1690---0000 1692---0000 1694---0000 1696---0000 1698---0000 1700---0000 1702---0000 1704---0000 1706---0000 1708---0000 1710---0000 1712---0000 1714---0000 1716---0000 1718---0000 1720---0000 1722---0000 1724---0000 1726---0000 1728---0000 1730- ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m58.259s user 0m10.161s sys 0m0.038s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:38:39 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 2000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 1002---0000 1004---0000 1006---0000 1008---0000 1010---0000 1012---0000 1014---0000 1016---0000 1018---0000 1020---0000 1022---0000 1024---0000 1026---0000 1028---0000 1030---0000 1032---0000 1034---0000 1036---0000 1038---0000 1040---0000 1042---0000 1044---0000 1046---0000 1048---0000 1050---0000 1052---0000 1054---0000 1056---0000 1058---0000 1060---0000 1062---0000 1064---0000 1066---0000 1068---0000 1070---0000 1072---0000 1074---0000 1076---0000 1078---0000 1080---0000 1082---0000 1084---0000 1086---0000 1088---0000 1090---0000 1092---0000 1094---0000 1096---0000 1098---0000 1100---0000 1102---0000 1104---0000 1106---0000 1108---0000 1110---0000 1112---0000 1114---0000 1116---0000 1118---0000 1120---0000 1122---0000 1124---0000 1126---0000 1128---0000 1130---0000 1132---0000 1134---0000 1136---0000 1138---0000 1140---0000 1142---0000 1144---0000 1146---0000 1148---0000 1150---0000 1152---0000 1154---0000 1156---0000 1158---0000 1160---0000 1162---0000 1164---0000 1166---0000 1168---0000 1170---0000 1172---0000 1174---0000 1176---0000 1178---0000 1180---0000 1182---0000 1184---0000 1186---0000 1188---0000 1190---0000 1192---0000 1194---0000 1196---0000 1198---0000 1200---0000 1202---0000 1204---0000 1206---0000 1208---0000 1210---0000 1212---0000 1214---0000 1216---0000 1218---0000 1220---0000 1222---0000 1224---0000 1226---0000 1228---0000 1230---0000 1232---0000 1234---0000 1236---0000 1238---0000 1240---0000 1242---0000 1244---0000 1246---0000 1248---0000 1250---0000 1252---0000 1254---0000 1256---0000 1258---0000 1260---0000 1262---0000 1264---0000 1266---0000 1268---0000 1270---0000 1272---0000 1274---0000 1276---0000 1278---0000 1280---0000 1282---0000 1284---0000 1286---0000 1288---0000 1290---0000 1292---0000 1294---0000 1296---0000 1298---0000 1300---0000 1302---0000 1304---0000 1306---0000 1308---0000 1310---0000 1312---0000 1314---0000 1316---0000 1318---0000 1320---0000 1322---0000 1324---0000 1326---0000 1328---0000 1330---0000 1332---0000 1334---0000 1336---0000 1338---0000 1340---0000 1342---0000 1344---0000 1346---0000 1348---0000 1350---0000 1352---0000 1354---0000 1356---0000 1358---0000 1360---0000 1362---0000 1364---0000 1366---0000 1368---0000 1370---0000 1372---0000 1374---0000 1376---0000 1378---0000 1380---0000 1382---0000 1384---0000 1386---0000 1388---0000 1390---0000 1392---0000 1394---0000 1396---0000 1398---0000 1400---0000 1402---0000 1404---0000 1406---0000 1408---0000 1410---0000 1412---0000 1414---0000 1416---0000 1418---0000 1420---0000 1422---0000 1424---0000 1426---0000 1428---0000 1430---0000 1432---0000 1434---0000 1436---0000 1438---0000 1440---0000 1442---0000 1444---0000 1446---0000 1448---0000 1450---0000 1452---0000 1454---0000 1456---0000 1458---0000 1460---0000 1462---0000 1464---0000 1466---0000 1468---0000 1470---0000 1472---0000 1474---0000 1476---0000 1478---0000 1480---0000 1482---0000 1484---0000 1486---0000 1488---0000 1490---0000 1492---0000 1494---0000 1496---0000 1498---0000 1500---0000 1502---0000 1504---0000 1506---0000 1508---0000 1510---0000 1512---0000 1514---0000 1516---0000 1518---0000 1520---0000 1522---0000 1524---0000 1526---0000 1528---0000 1530---0000 1532---0000 1534---0000 1536---0000 1538---0000 1540---0000 1542---0000 1544---0000 1546---0000 1548---0000 1550---0000 1552---0000 1554---0000 1556---0000 1558---0000 1560---0000 1562---0000 1564---0000 1566---0000 1568---0000 1570---0000 1572---0000 1574---0000 1576---0000 1578---0000 1580---0000 1582---0000 1584---0000 1586---0000 1588---0000 1590---0000 1592---0000 1594---0000 1596---0000 1598---0000 1600---0000 1602---0000 1604---0000 1606---0000 1608---0000 1610---0000 1612---0000 1614---0000 1616---0000 1618---0000 1620---0000 1622---0000 1624---0000 1626---0000 1628---0000 1630---0000 1632---0000 1634---0000 1636---0000 1638---0000 1640---0000 1642---0000 1644---0000 1646---0000 1648---0000 1650---0000 1652---0000 1654---0000 1656---0000 1658---0000 1660---0000 1662---0000 1664---0000 1666---0000 1668---0000 1670---0000 1672---0000 1674---0000 1676---0000 1678---0000 1680---0000 1682---0000 1684---0000 1686---0000 1688---0000 1690---0000 1692---0000 1694---0000 1696---0000 1698---0000 1700---0000 1702---0000 1704---0000 1706---0000 1708---0000 1710---0000 1712---0000 1714---0000 1716---0000 1718---0000 1720---0000 1722---0000 1724---0000 1726---0000 1728---0000 1730- ** WARNING: Output too long, hence truncated. Errors/timing (if any): Timing: real 0m7.730s user 0m3.852s sys 0m0.011s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:37:22 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=0, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** nfinit: reducible polynomial in nfinit. Timing: real 0m0.016s user 0m0.007s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:36:48 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 1000, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 102---0000 104---0000 106---0000 108---0000 110---0000 112---0000 114---0000 116---0000 118---0000 120---0000 122---0000 124---0000 126---0000 128---0000 130---0000 132---0000 134---0000 136---0000 138---0000 140---0000 142---0000 144---0000 146---0000 148---0000 150---0000 152---0000 154---0000 156---0000 158---0000 160---0000 162---0000 164---0000 166---0000 168---0000 170---0000 172---0000 174---0000 176---0000 178---0000 180---0000 182---0000 184---0000 186---0000 188---0000 190---0000 192---0000 194---0000 196---0000 198---0000 200---0000 202---0000 204---0000 206---0000 208---0000 210---0000 212---0000 214---0000 216---0000 218---0000 220---0000 222---0000 224---0000 226---0000 228---0000 230---0000 232---0000 234---0000 236---0000 238---0000 240---0000 242---0000 244---0000 246---0000 248---0000 250---0000 252---0000 254---0000 256---0000 258---0000 260---0000 262---0000 264---0000 266---0000 268---0000 270---0000 272---0000 274---0000 276---0000 278---0000 280---0000 282---0000 284---0000 286---0000 288---0000 290---0000 292---0000 294---0000 296---0000 298---0000 300---0000 302---0000 304---0000 306---0000 308---0000 310---0000 312---0000 314---0000 316---0000 318---0000 320---0000 322---0000 324---0000 326---0000 328---0000 330---0000 332---0000 334---0000 336---0000 338---0000 340---0000 342---0000 344---0000 346---0000 348---0000 350---0000 352---0000 354---0000 356---0000 358---0000 360---0000 362---0000 364---0000 366---0000 368---0000 370---0000 372---0000 374---0000 376---0000 378---0000 380---0000 382---0000 384---0000 386---0000 388---0000 390---0000 392---0000 394---0000 396---0000 398---0000 400---0000 402---0000 404---0000 406---0000 408---0000 410---0000 412---0000 414---0000 416---0000 418---0000 420---0000 422---0000 424---0000 426---0000 428---0000 430---0000 432---0000 434---0000 436---0000 438---0000 440---0000 442---0000 444---0000 446---0000 448---0000 450---0000 452---0000 454---0000 456---0000 458---0000 460---0000 462---0000 464---0000 466---0000 468---0000 470---0000 472---0000 474---0000 476---0000 478---0000 480---0000 482---0000 484---0000 486---0000 488---0000 490---0000 492---0000 494---0000 496---0000 498---0000 500---0000 502---0000 504---0000 506---0000 508---0000 510---0000 512---0000 514---0000 516---0000 518---0000 520---0000 522---0000 524---0000 526---0000 528---0000 530---0000 532---0000 534---0000 536---0000 538---0000 540---0000 542---0000 544---0000 546---0000 548---0000 550---0000 552---0000 554---0000 556---0000 558---0000 560---0000 562---0000 564---0000 566---0000 568---0000 570---0000 572---0000 574---0000 576---0000 578---0000 580---0000 582---0000 584---0000 586---0000 588---0000 590---0000 592---0000 594---0000 596---0000 598---0000 600---0000 602---0000 604---0000 606---0000 608---0000 610---0000 612---0000 614---0000 616---0000 618---0000 620---0000 622---0000 624---0000 626---0000 628---0000 630---0000 632---0000 634---0000 636---0000 638---0000 640---0000 642---0000 644---0000 646---0000 648---0000 650---0000 652---0000 654---0000 656---0000 658---0000 660---0000 662---0000 664---0000 666---0000 668---0000 670---0000 672---0000 674---0000 676---0000 678---0000 680---0000 682---0000 684---0000 686---0000 688---0000 690---0000 692---0000 694---0000 696---0000 698---0000 700---0000 702---0000 704---0000 706---0000 708---0000 710---0000 712---0000 714---0000 716---0000 718---0000 720---0000 722---0000 724---0000 726---0000 728---0000 730---0000 732---0000 734---0000 736---0000 738---0000 740---0000 742---0000 744---0000 746---0000 748---0000 750---0000 752---0000 754---0000 756---0000 758---0000 760---0000 762---0000 764---0000 766---0000 768---0000 770---0000 772---0000 774---0000 776---0000 778---0000 780---0000 782---0000 784---0000 786---0000 788---0000 790---0000 792---0000 794---0000 796---0000 798---0000 800---0000 802---0000 804---0000 806---0000 808---0000 810---0000 812---0000 814---0000 816---0000 818---0000 820---0000 822---0000 824---0000 826---0000 828---0000 830---0000 832---0000 834---0000 836---0000 838---0000 840---0000 842---0000 844---0000 846---0000 848---0000 850---0000 852---0000 854---0000 856---0000 858---0000 860---0000 862---0000 864---0000 866---0000 868---0000 870---0000 872---0000 874---0000 876---0000 878---0000 880---0000 882---0000 884---0000 886---0000 888---0000 890---0000 892---0000 894---0000 896---0000 898---0000 900---0000 902---0000 904---0000 906---0000 908---0000 910---0000 912---0000 914---0000 916---0000 918---0000 920---0000 922---0000 924---0000 926---0000 928---0000 930---0000 932---0000 934---0000 936---0000 938---0000 940---0000 942---0000 944---0000 946---0000 948---0000 950---0000 952---0000 954---0000 956---0000 958---0000 960---0000 962---0000 964---0000 966---0000 968---0000 970---0000 972---0000 974---0000 976---0000 978---0000 980---0000 982---0000 984---0000 986---0000 988---0000 990---0000 992---0000 994---0000 996---0000 998---0000 1000---0000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m9.311s user 0m1.881s sys 0m0.011s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:36:27 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,"---",nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 2---0000 4---0000 6---0000 8---0000 10---0000 12---0000 14---0000 16---0000 18---0000 20---0000 22---0000 24---0000 26---0000 28---0000 30---0000 32---0000 34---0000 36---0000 38---0000 40---0000 42---0000 44---0000 46---0000 48---0000 50---0000 52---0000 54---0000 56---0000 58---0000 60---0000 62---0000 64---0000 66---0000 68---0000 70---0000 72---0000 74---0000 76---0000 78---0000 80---0000 82---0000 84---0000 86---0000 88---0000 90---0000 92---0000 94---0000 96---0000 98---0000 100---0000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.174s user 0m0.171s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:36:18 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,---,nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: ...;nfisisom(f,g1);print(A,---,nfisisom(f,g1),nf ^-------------------- Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:36:06 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,/t,nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: ...);nfisisom(f,g1);print(A,/t,nfisisom(f,g1),nf ^-------------------- Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:35:59 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,t,nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 2t0000 4t0000 6t0000 8t0000 10t0000 12t0000 14t0000 16t0000 18t0000 20t0000 22t0000 24t0000 26t0000 28t0000 30t0000 32t0000 34t0000 36t0000 38t0000 40t0000 42t0000 44t0000 46t0000 48t0000 50t0000 52t0000 54t0000 56t0000 58t0000 60t0000 62t0000 64t0000 66t0000 68t0000 70t0000 72t0000 74t0000 76t0000 78t0000 80t0000 82t0000 84t0000 86t0000 88t0000 90t0000 92t0000 94t0000 96t0000 98t0000 100t0000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.174s user 0m0.168s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:35:50 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,t,nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 2t0000 4t0000 6t0000 8t0000 10t0000 12t0000 14t0000 16t0000 18t0000 20t0000 22t0000 24t0000 26t0000 28t0000 30t0000 32t0000 34t0000 36t0000 38t0000 40t0000 42t0000 44t0000 46t0000 48t0000 50t0000 52t0000 54t0000 56t0000 58t0000 60t0000 62t0000 64t0000 66t0000 68t0000 70t0000 72t0000 74t0000 76t0000 78t0000 80t0000 82t0000 84t0000 86t0000 88t0000 90t0000 92t0000 94t0000 96t0000 98t0000 100t0000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.900s user 0m0.171s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:35:36 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(A,nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000 220000 240000 260000 280000 300000 320000 340000 360000 380000 400000 420000 440000 460000 480000 500000 520000 540000 560000 580000 600000 620000 640000 660000 680000 700000 720000 740000 760000 780000 800000 820000 840000 860000 880000 900000 920000 940000 960000 980000 1000000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.174s user 0m0.169s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:35:23 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(nfisisom(f,g1), nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.177s user 0m0.166s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:34:59 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2); forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); print(nfisisom(f,g2),nfisisom(f,g3),nfisisom(f,g4))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.273s user 0m0.165s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:34:10 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2); forstep (A=2, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); nfisisom(f,g2);nfisisom(f,g3);nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.173s user 0m0.167s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:33:51 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2); forstep (A=0, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); nfisisom(f,g2);nfisisom(f,g3);nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? ? ? Goodbye! Errors/timing (if any): *** nfinit: reducible polynomial in nfinit. Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:33:37 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2); forstep (A=1, 100, 2, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); nfisisom(f,g2);nfisisom(f,g3);nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? ? ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. Timing: real 0m0.057s user 0m0.010s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:13:56 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2); for (A=1, 5, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); nfisisom(f,g2);nfisisom(f,g3);nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? ? ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:13:44 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2); for (A=1, 5, g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4);factor(nf1.disc);factor(nf2.disc);factor(nf3.disc);factor(nf4.disc);nfisisom(f,g1); nfisisom(f,g2);nfisisom(f,g3);nfisisom(f,g4)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? ? ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. Timing: real 0m0.022s user 0m0.009s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:12:53 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i); g1=x^4+A*x^2+A^2/2); for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.016s user 0m0.007s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:12:14 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, (print(i), g1=x^4+A*x^2+A^2/2)); for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: for(i=1,19,(print(i) *** ,g1=x^4+A*x^2+A^2/2) ^-------------------- *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:11:46 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i), g1=x^4+A*x^2+A^2/2); for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: for(i=1,19,print(i) *** ,g1=x^4+A*x^2+A^2/2) ^-------------------- *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.098s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:11:40 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i), g1=x^4+A*x^2+A^2/2); for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: for(i=1,19,print(i) *** ,g1=x^4+A*x^2+A^2/2) ^-------------------- *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:11:34 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i), g1=x^4+A*x^2+A^2/2,); for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: for(i=1,19,print(i) *** ,g1=x^4+A*x^2+A^2/2, ^-------------------- *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.039s user 0m0.007s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:11:16 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (i=1, 19, print(i)); for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:10:25 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1), nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:09:50 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2,g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1)nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.014s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:09:17 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); for (A=1, 5, g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2,g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2,nf1=nfinit(g1),nf2=nfinit(g2),nf3=nfinit(g3),nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1)nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.016s user 0m0.008s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:07:49 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for (A=1, 5 ,g1=x^4+A*x^2+A^2/2,g2=x^4-A*x^2-A^2/2,g3=x^4+A*x^2-A^2/2,g4=x^4-A*x^2+A^2/2,nf1=nfinit(g1),nf2=nfinit(g2),nf3=nfinit(g3),nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1)nfisisom(f,g2)nfisisom(f,g3),nfisisom(f,g4)) } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.077s user 0m0.009s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:07:29 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for (A=1, 5 ,g1=x^4+A*x^2+A^2/2,g2=x^4-A*x^2-A^2/2,g3=x^4+A*x^2-A^2/2,g4=x^4-A*x^2+A^2/2,nf1=nfinit(g1),nf2=nfinit(g2),nf3=nfinit(g3),nf4=nfinit(g4),factor(nf1.disc),factor(nf2.disc),factor(nf3.disc),factor(nf4.disc),nfisisom(f,g1)nfisisom(f,g2)nfisisom(f,g3)nfisisom(f,g4)) } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.052s user 0m0.007s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:03:22 2006 Input: for (i=1, 19, print(i)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? Goodbye! Errors/timing (if any): Timing: real 0m0.055s user 0m0.007s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:03:08 2006 Input: for (i=1, 19, 2, print(i)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: for(i=1,19,2,print(i)); ^----------- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:03:00 2006 Input: for (i=1, 19, print(i)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:02:55 2006 Input: for (i=1, 19, print(i)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:02:48 2006 Input: for (i=1, 19, print(i)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ? Goodbye! Errors/timing (if any): Timing: real 0m0.098s user 0m0.010s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:01:37 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for (A=1, 5 ,g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4), factor(nf1.disc), factor(nf2.disc), factor(nf3.disc), factor(nf4.disc), nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4)) } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.099s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:01:31 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for (A=1, 5 , g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4), factor(nf1.disc), factor(nf2.disc), factor(nf3.disc), factor(nf4.disc), nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4)) } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:01:27 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for (A=1, 5 , g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4), factor(nf1.disc), factor(nf2.disc), factor(nf3.disc), factor(nf4.disc), nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4)) } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.013s user 0m0.010s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:01:14 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for (A=1, 5 , g1=x^4+A*x^2+A^2/2, g2=x^4-A*x^2-A^2/2, g3=x^4+A*x^2-A^2/2, g4=x^4-A*x^2+A^2/2, nf1=nfinit(g1), nf2=nfinit(g2), nf3=nfinit(g3), nf4=nfinit(g4), factor(nf1.disc), factor(nf2.disc), factor(nf3.disc), factor(nf4.disc), nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4)) } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(A=1,5,g1=x^4+A*x^2+A^2/2 *** ,g2=x^4-A*x^2-A^2/2, ^-------------------- Timing: real 0m0.016s user 0m0.008s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:00:39 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for (A=1, 5 , g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4)) } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(nf4.disc);nfisisom(f,g1) *** nfisisom(f,g2)nfisis ^-------------------- Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 08:00:21 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for (A=1, 5 , g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) ) /*1*/ } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(nf4.disc);nfisisom(f,g1) *** nfisisom(f,g2)nfisis ^-------------------- Timing: real 0m0.038s user 0m0.007s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:57:53 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for ( /*1*/ A=1, 5 , g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) ) /*1*/ } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(nf4.disc);nfisisom(f,g1) *** nfisisom(f,g2)nfisis ^-------------------- Timing: real 0m0.014s user 0m0.005s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:57:24 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for ( /*1*/ A=1, 5 , ( /*2*/ g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) ) /*2*/ ) /*1*/ } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...A=1,5,(g1=x^4+A*x^2+A^2/2 *** ;g2=x^4-A*x^2-A^2/2; ^-------------------- Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:57:14 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for ( /*1*/ A=1, n , ( /*2*/ g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) ) /*2*/ ) /*1*/ } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...A=1,n,(g1=x^4+A*x^2+A^2/2 *** ;g2=x^4-A*x^2-A^2/2; ^-------------------- Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:56:50 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); {for ( /*1*/ A=1, n ,if ( /*2*/ k[count],a1 = length(k[count]);nf=nfinit(k[count][a1]);print(factor(nf.disc)) g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) ) /*2*/ ) /*1*/ } Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...]);print(factor(nf.disc)) *** g1=x^4+A*x^2+A^2/2;g ^-------------------- Timing: real 0m0.015s user 0m0.010s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:41:24 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc); A=212; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.038s user 0m0.015s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:41:02 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=212; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:40:56 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=210; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.012s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:40:47 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=208; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.011s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:27:43 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=206; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.008s sys 0m0.010s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:27:31 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=204; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.014s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:27:24 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=202; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:27:17 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=200; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:27:09 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=198; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.015s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:27:02 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=196; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.104s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:26:56 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=194; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:26:47 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=192; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:26:39 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=190; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.012s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:26:28 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=188; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:26:03 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=186; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 186*x^2 + 17298 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:25:52 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=184; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 184*x^2 + 16928 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.010s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:25:44 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=182; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 182*x^2 + 16562 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:25:37 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=180; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 180*x^2 + 16200 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.069s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:25:27 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=178; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 178*x^2 + 15842 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:24:43 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=176; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 176*x^2 + 15488 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:24:35 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=174; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 174*x^2 + 15138 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.012s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:24:27 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=172; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 172*x^2 + 14792 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.046s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:24:19 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=170; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 170*x^2 + 14450 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.102s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:24:11 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=168; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 168*x^2 + 14112 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.009s sys 0m0.011s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:24:02 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=166; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 166*x^2 + 13778 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:23:53 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=164; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 164*x^2 + 13448 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.074s user 0m0.014s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:23:45 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=162; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 162*x^2 + 13122 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.094s user 0m0.014s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:23:35 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=160; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 160*x^2 + 12800 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:23:28 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=158; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 158*x^2 + 12482 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:23:19 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=156; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 156*x^2 + 12168 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.050s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:23:11 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=154; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 154*x^2 + 11858 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.393s user 0m0.013s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:22:40 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=152; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 152*x^2 + 11552 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:22:32 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=150; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 150*x^2 + 11250 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.052s user 0m0.012s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:22:21 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=148; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 148*x^2 + 10952 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:22:13 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=146; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 146*x^2 + 10658 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.010s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:22:02 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=144; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 144*x^2 + 10368 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:21:55 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=142; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 142*x^2 + 10082 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.014s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:21:48 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=140; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 140*x^2 + 9800 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:21:38 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=138; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 138*x^2 + 9522 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:21:29 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=136; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 136*x^2 + 9248 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:21:22 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=134; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 134*x^2 + 8978 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.094s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:20:57 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=132; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 132*x^2 + 8712 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.100s user 0m0.014s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:20:45 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=130; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 130*x^2 + 8450 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.014s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:20:38 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=128; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 128*x^2 + 8192 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:20:26 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=124; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 124*x^2 + 7688 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.082s user 0m0.012s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:20:19 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=122; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 122*x^2 + 7442 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:20:11 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=120; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 120*x^2 + 7200 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.098s user 0m0.014s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:20:03 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=118; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 118*x^2 + 6962 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:19:55 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=116; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 116*x^2 + 6728 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.015s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:19:48 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=115; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 115*x^2 + 13225/2 ? ? ? ? ? ? ? ? ? ? ? ? %10 = 0 ? %11 = 0 ? %12 = 0 ? %13 = 0 ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. *** nfinit: polynomial not in Z[X] in nfinit. *** nfinit: polynomial not in Z[X] in nfinit. *** nfinit: polynomial not in Z[X] in nfinit. *** incorrect type in disc: factor(nf1.disc); ^------ *** incorrect type in disc: factor(nf2.disc); ^------ *** incorrect type in disc: factor(nf3.disc); ^------ *** incorrect type in disc: factor(nf4.disc); ^------ Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:19:40 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=114; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 114*x^2 + 6498 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.011s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:19:32 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=112; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 112*x^2 + 6272 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:19:24 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=110; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 110*x^2 + 6050 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:19:15 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=108; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 108*x^2 + 5832 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.062s user 0m0.011s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:19:07 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=106; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 106*x^2 + 5618 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.013s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:18:59 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=104; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 104*x^2 + 5408 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:18:47 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=102; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 102*x^2 + 5202 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:18:38 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=102; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc) nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 102*x^2 + 5202 ? ? ? ? ? ? ? ? ? ? ? %17 = [2 9] [3 2] [17 2] ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:18:27 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=102; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc) nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? ? %6 = x^4 + 102*x^2 + 5202 ? ? ? ? ? ? ? ? ? ? ? %17 = [2 9] [3 2] [17 2] ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.015s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:18:09 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=100; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc) nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? ? %6 = x^4 + 100*x^2 + 5000 ? ? ? ? ? ? ? ? ? ? ? %17 = [2 9] ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:17:31 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=100; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc) nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 100*x^2 + 5000 ? ? ? ? ? ? ? ? ? ? ? %17 = [2 9] ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:17:20 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=100; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1) nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 100*x^2 + 5000 ? ? ? ? %10 = [x^4 + 100*x^2 + 5000, [0, 2], 512, 125000, [[1, 3.761581922631320025 E-39 + 1.0000000000000000000000000000000000000*I, -1.0986841134678099660398011952406783785 - 0.45508986056222734130435775782246856961*I, -0.45508986056222734130435775782246856961 + 1.0986841134678099660398011952406783785*I; 1, 3.761581922631320025 E-39 + 1.0000000000000000000000000000000000000*I, 1.0986841134678099660398011952406783785 + 0.45508986056222734130435775782246856961*I, 0.45508986056222734130435775782246856961 - 1.0986841134678099660398011952406783785*I], [1, 1.0000000000000000000000000000000000000, -1.5537739740300373073441589530631469482, 0.64359425290558262473544343741820980893; 1, -1.0000000000000000000000000000000000000, -0.64359425290558262473544343741820980892, -1.5537739740300373073441589530631469482; 1, 1.0000000000000000000000000000000000000, 1.5537739740300373073441589530631469482, -0.64359425290558262473544343741820980893; 1, -1.0000000000000000000000000000000000000, 0.64359425290558262473544343741820980892, 1.5537739740300373073441589530631469482], 0, [4, 0, 0, 0; 0, -4, 0, 0; 0, 0, 4, 4; 0, 0, 4, -4], [8, 4, 0, 0; 0, 4, 0, 0; 0, 0, 4, 0; 0, 0, 0, 4], [2, 0, 0, 0; 0, -2, 0, 0; 0, 0, 1, 1; 0, 0, 1, -1], [2, [0, 0, 2, 0; 0, 0, 0, -2; 1, 1, 0, 0; 1, -1, 0, 0]]], [3.2179712645279131236772171870910490446 + 7.7688698701501865367207947653157347408*I, -3.2179712645279131236772171870910490446 - 7.7688698701501865367207947653157347408*I], [1, 1/50*x^2 + 1, 1/500*x^3, 1/500*x^3 + 1/5*x], [1, 0, -50, 0; 0, 0, 50, 0; 0, -5, 0, 500; 0, 5, 0, 0], [1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 1, -1; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, -1; 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0]] ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:17:12 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=100; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 100*x^2 + 5000 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:17:02 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=98; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 98*x^2 + 4802 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:16:52 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=96; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 96*x^2 + 4608 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.090s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:16:45 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=94; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 94*x^2 + 4418 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:16:37 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=92; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 92*x^2 + 4232 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.068s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:16:29 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=90; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 90*x^2 + 4050 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:16:21 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=88; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 88*x^2 + 3872 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:16:08 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=86; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %6 = x^4 + 86*x^2 + 3698 ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.009s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:15:58 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=84; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.012s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:15:49 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=82; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:15:39 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=80; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:15:33 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=78; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.094s user 0m0.009s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:15:25 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=76; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.012s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:15:16 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=74; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:15:09 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=72; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:15:02 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=70; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:14:54 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=68; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:14:47 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=66; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.014s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:14:40 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=64; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:14:33 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=62; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.014s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:14:24 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=60; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:14:16 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=58; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.040s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:14:07 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=56; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:13:58 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=54; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:13:52 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=52; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.007s sys 0m0.010s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:13:44 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=50; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:13:35 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=48; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:13:28 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=46; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:13:20 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=44; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.014s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:13:14 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=42; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:13:06 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=40; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:12:54 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=38; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.112s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:12:47 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=36; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.010s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:12:40 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=34; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.009s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:12:34 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=32; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.009s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:12:24 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=30; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.081s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:12:15 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A-30; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. *** nfinit: polynomial not in Z[X] in nfinit. *** nfinit: polynomial not in Z[X] in nfinit. *** nfinit: polynomial not in Z[X] in nfinit. *** incorrect type in disc: factor(nf1.disc); ^------ *** incorrect type in disc: factor(nf2.disc); ^------ *** incorrect type in disc: factor(nf3.disc); ^------ *** incorrect type in disc: factor(nf4.disc); ^------ *** nfisisom: polynomial not in Z[X] in nsiso0. *** nfisisom: polynomial not in Z[X] in nsiso0. *** nfisisom: polynomial not in Z[X] in nsiso0. *** nfisisom: polynomial not in Z[X] in nsiso0. Timing: real 0m0.014s user 0m0.010s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:12:04 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=28; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:11:56 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=26; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.038s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:11:49 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=24; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.012s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:11:39 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=22; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.331s user 0m0.016s sys 0m0.002s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:11:33 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=21; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %10 = 0 ? %11 = 0 ? %12 = 0 ? %13 = 0 ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. *** nfinit: polynomial not in Z[X] in nfinit. *** nfinit: polynomial not in Z[X] in nfinit. *** nfinit: polynomial not in Z[X] in nfinit. *** incorrect type in disc: factor(nf1.disc); ^------ *** incorrect type in disc: factor(nf2.disc); ^------ *** incorrect type in disc: factor(nf3.disc); ^------ *** incorrect type in disc: factor(nf4.disc); ^------ Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:11:24 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=20; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:11:14 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=18; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.010s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:11:05 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=16; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.008s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:10:56 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=14; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.111s user 0m0.013s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:10:28 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=14; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc) factor(nf2.disc) factor(nf3.disc) factor(nf4.disc) nfisisom(f,g1); nfisisom(f,g2); nfisisom(f,g3); nfisisom(f,g4); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? %14 = [2 9] [7 2] ? %15 = [-1 1] [2 9] [3 2] [7 2] ? %16 = [-1 1] [2 9] [3 2] [7 2] ? %17 = [2 9] [7 2] ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.014s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:10:03 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=14; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc) factor(nf2.disc) factor(nf3.disc) factor(nf4.disc) nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? %14 = [2 9] [7 2] ? %15 = [-1 1] [2 9] [3 2] [7 2] ? %16 = [-1 1] [2 9] [3 2] [7 2] ? %17 = [2 9] [7 2] ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.011s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:09:49 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=12; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc) factor(nf2.disc) factor(nf3.disc) factor(nf4.disc) nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? %14 = [2 9] [3 2] ? %15 = [-1 1] [2 9] [3 2] ? %16 = [-1 1] [2 9] [3 2] ? %17 = [2 9] [3 2] ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.035s user 0m0.009s sys 0m0.010s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:09:29 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=12; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc) factor(nf3.disc); factor(nf4.disc) nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? %15 = [-1 1] [2 9] [3 2] ? ? %17 = [2 9] [3 2] ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.058s user 0m0.013s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:09:18 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=12; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.010s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:09:09 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=10; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:09:01 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=8; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:08:51 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=6; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.013s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:08:44 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-6; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.273s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:08:34 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-4; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:08:27 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-2; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g3); nf4=nfinit(g4); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.064s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:08:08 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-44; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2) nf3=nfinit(g3); nf4=nfinit(g4) factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? %11 = [x^4 + 44*x^2 - 968, [2, 1], -557568, 968, [[1, 1.7320508075688772935274463415058723669, -5.4820214230936429485194608254230802233, -4.0131182098855872672625221821856992525; 1, 1.7320508075688772935274463415058723669, 5.4820214230936429485194608254230802233, 4.0131182098855872672625221821856992525; 1, -1.7320508075688772935274463415058723669 + 0.E-39*I, 0.E-38 + 2.8377030999133172580306931790731170238*I, 0.E-38 - 7.7527490457588849041629151053839403122*I], [1, 1.7320508075688772935274463415058723669, -5.4820214230936429485194608254230802233, -4.0131182098855872672625221821856992525; 1, 1.7320508075688772935274463415058723669, 5.4820214230936429485194608254230802233, 4.0131182098855872672625221821856992525; 1, -1.7320508075688772935274463415058723669, 2.8377030999133172580306931790731170238, -7.7527490457588849041629151053839403122; 1, -1.7320508075688772935274463415058723669, -2.8377030999133172580306931790731170238, 7.7527490457588849041629151053839403122], 0, [4, 0, 0, 0; 0, 12, 0, 0; 0, 0, 44, 88; 0, 0, 88, -88], [-264, -132, 0, 0; 0, -44, 0, 0; 0, 0, -12, -4; 0, 0, 0, -4], [-66, 0, 0, 0; 0, -22, 0, 0; 0, 0, -2, -2; 0, 0, -2, 1], [66, [0, 0, 66, 66; 0, 0, 44, 22; 4, 6, 0, 0; 1, 3, 0, 0]]], [-4.0131182098855872672625221821856992525, 4.0131182098855872672625221821856992525, 0.E-38 - 7.7527490457588849041629151053839403122*I], [1, 1/22*x^2 + 1, 1/44*x^3 + x, x], [1, 0, -22, 0; 0, 0, 22, 0; 0, 0, 0, 44; 0, 1, 0, -44], [1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 11, 22, 0, 0, 22, -22; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 22; 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 2, 0, 0; 0, 0, 0, 1, 0, 0, 1, -1, 0, 1, 0, 0, 1, -1, 0, 0]] ? ? %13 = [x^4 + 44*x^2 + 968, [0, 2], 61952, 968, [[1, 0.E-39 + 1.0000000000000000000000000000000000000*I, -1.5093623133800654055633752499315538832 + 3.6439229674969835685280960709955670516*I, 3.6439229674969835685280960709955670515 + 1.5093623133800654055633752499315538832*I; 1, 0.E-39 + 1.0000000000000000000000000000000000000*I, 1.5093623133800654055633752499315538832 - 3.6439229674969835685280960709955670516*I, -3.6439229674969835685280960709955670515 - 1.5093623133800654055633752499315538832*I], [1, 1.0000000000000000000000000000000000000, 2.1345606541169181629647208210640131683, 5.1532852808770489740914713209271209347; 1, -1.0000000000000000000000000000000000000, -5.1532852808770489740914713209271209347, 2.1345606541169181629647208210640131683; 1, 1.0000000000000000000000000000000000000, -2.1345606541169181629647208210640131683, -5.1532852808770489740914713209271209347; 1, -1.0000000000000000000000000000000000000, 5.1532852808770489740914713209271209347, -2.1345606541169181629647208210640131683], 0, [4, 0, 0, 0; 0, -4, 0, 0; 0, 0, -44, -44; 0, 0, -44, 44], [88, 44, 0, 0; 0, 44, 0, 0; 0, 0, 4, 0; 0, 0, 0, 4], [22, 0, 0, 0; 0, -22, 0, 0; 0, 0, -1, -1; 0, 0, -1, 1], [22, [0, 0, -22, 0; 0, 0, 0, 22; 1, 1, 0, 0; 1, -1, 0, 0]]], [2.1345606541169181629647208210640131683 + 5.1532852808770489740914713209271209347*I, -2.1345606541169181629647208210640131683 - 5.1532852808770489740914713209271209347*I], [1, 1/22*x^2 + 1, 1/44*x^3 + x, -1/44*x^3], [1, 0, -22, 0; 0, 0, 22, 0; 0, 1, 0, 0; 0, 1, 0, -44], [1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -11, -11, 0, 0, -11, 11; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, -11, 11, 0, 0, 11, 11; 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0]] ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.061s user 0m0.012s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:07:56 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-44; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.363s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:07:48 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-14; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:07:40 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-12; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.042s user 0m0.014s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:07:34 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-10; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:07:25 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-8; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.008s sys 0m0.010s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:07:17 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-6; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.035s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:07:11 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-4; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:07:05 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-2; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:06:57 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=-2; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.010s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:06:45 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=44; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? ? ? ? ? ? ? ? ? ? ? ? ? ? %18 = 0 ? %19 = 0 ? %20 = 0 ? %21 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.064s user 0m0.014s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:06:26 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=42; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.018s user 0m0.009s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:06:18 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=40; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:06:10 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=38; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.097s user 0m0.014s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:06:01 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=36; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.018s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:05:53 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=34; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.107s user 0m0.014s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:05:47 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=32; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.017s user 0m0.009s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:05:40 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=30; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.037s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:05:32 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=28; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:05:24 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=26; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.075s user 0m0.015s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:05:16 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=24; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.017s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:05:10 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=22; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.017s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:05:02 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=20; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.018s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:04:52 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=18; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.093s user 0m0.010s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:04:44 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=16; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.016s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:04:35 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=14; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.017s user 0m0.009s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:04:28 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=12; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.018s user 0m0.011s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:04:18 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=10; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.032s user 0m0.013s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:04:09 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=8; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.047s user 0m0.009s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:04:02 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=6; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.295s user 0m0.015s sys 0m0.003s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:03:54 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=4; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.019s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:03:23 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=2; g1=x^4+A*x^2+A^2/2; g2=x^4-A*x^2-A^2/2; g3=x^4+A*x^2-A^2/2; g4=x^4-A*x^2+A^2/2; nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc); factor(nf2.disc); factor(nf3.disc); factor(nf4.disc); nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.154s user 0m0.011s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:02:48 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=20; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2-A^2/2 g3=x^4+A*x^2-A^2/2 g4=x^4-A*x^2+A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); nf3=nfinit(g1); nf4=nfinit(g2); factor(nf1.disc) factor(nf2.disc) factor(nf3.disc) factor(nf4.disc) nfisisom(f,g1) nfisisom(f,g2) nfisisom(f,g3) nfisisom(f,g4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 20*x^2 + 200 ? %6 = x^4 - 20*x^2 - 200 ? %7 = x^4 + 20*x^2 - 200 ? %8 = x^4 - 20*x^2 + 200 ? ? ? ? ? %13 = [2 9] [5 2] ? %14 = [-1 1] [2 9] [3 2] [5 2] ? %15 = [2 9] [5 2] ? %16 = [-1 1] [2 9] [3 2] [5 2] ? %17 = 0 ? %18 = 0 ? %19 = 0 ? %20 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.044s user 0m0.013s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 07:00:15 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=20; g1=x^4+A*x^2+A^2/2 g2=x^4-A*x^2+A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 20*x^2 + 200 ? %6 = x^4 - 20*x^2 + 200 ? ? ? %9 = [2 9] [5 2] ? %10 = [2 9] [5 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.099s user 0m0.013s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:59:58 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=20; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2+A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 20*x^2 + 200 ? %6 = x^4 + 20*x^2 + 200 ? ? ? %9 = [2 9] [5 2] ? %10 = [2 9] [5 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.089s user 0m0.009s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:59:43 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=20; g1=x^4+A*x^2+A^2/2 g2=x^4=A*x^2+A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 20*x^2 + 200 ? ? ? ? %8 = [2 9] [5 2] ? %9 = [;] ? %10 = 0 ? %11 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- *** unexpected character: g2=x^4=A*x^2+A^2/2 ^------------ Timing: real 0m0.019s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:58:59 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=20; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 20*x^2 + 200 ? %6 = x^4 + 20*x^2 - 200 ? ? ? %9 = [2 9] [5 2] ? %10 = [-1 1] [2 9] [3 2] [5 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.083s user 0m0.012s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:58:45 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=18; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 18*x^2 + 162 ? %6 = x^4 + 18*x^2 - 162 ? ? ? %9 = [2 9] ? %10 = [-1 1] [2 9] [3 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.039s user 0m0.010s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:58:37 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=16; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 16*x^2 + 128 ? %6 = x^4 + 16*x^2 - 128 ? ? ? %9 = [2 9] ? %10 = [-1 1] [2 9] [3 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.053s user 0m0.007s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:58:27 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=14; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 14*x^2 + 98 ? %6 = x^4 + 14*x^2 - 98 ? ? ? %9 = [2 9] [7 2] ? %10 = [-1 1] [2 9] [3 2] [7 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.068s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:58:19 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=12; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 12*x^2 + 72 ? %6 = x^4 + 12*x^2 - 72 ? ? ? %9 = [2 9] [3 2] ? %10 = [-1 1] [2 9] [3 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.065s user 0m0.008s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:58:10 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=10; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 10*x^2 + 50 ? %6 = x^4 + 10*x^2 - 50 ? ? ? %9 = [2 9] [5 2] ? %10 = [-1 1] [2 9] [3 2] [5 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.248s user 0m0.008s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:58:01 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=8; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 8*x^2 + 32 ? %6 = x^4 + 8*x^2 - 32 ? ? ? %9 = [2 9] ? %10 = [-1 1] [2 9] [3 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.045s user 0m0.009s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:57:51 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=6; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 6*x^2 + 18 ? %6 = x^4 + 6*x^2 - 18 ? ? ? %9 = [2 9] [3 2] ? %10 = [-1 1] [2 9] [3 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.041s user 0m0.007s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:57:40 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=4; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 4*x^2 + 8 ? %6 = x^4 + 4*x^2 - 8 ? ? ? %9 = [2 9] ? %10 = [-1 1] [2 9] [3 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.055s user 0m0.009s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:57:25 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=2; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); nf2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 2*x^2 + 2 ? %6 = x^4 + 2*x^2 - 2 ? ? ? %9 = [2 9] ? %10 = [-1 1] [2 9] [3 2] ? %11 = 0 ? %12 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.017s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:57:05 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=2; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g1); n2=nfinit(g2); factor(nf1.disc) factor(nf2.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 2*x^2 + 2 ? %6 = x^4 + 2*x^2 - 2 ? ? ? %9 = [2 9] ? ? %10 = 0 ? %11 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- *** incorrect type in disc: factor(nf2.disc) ^----- Timing: real 0m0.386s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:56:23 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=2; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g1) nfisisom(f,g2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 2*x^2 + 2 ? %6 = x^4 + 2*x^2 - 2 ? ? %8 = [;] ? %9 = 0 ? %10 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.087s user 0m0.010s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:56:06 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=2; g1=x^4+A*x^2+A^2/2 g2=x^4+A*x^2-A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 2*x^2 + 2 ? %6 = x^4 + 2*x^2 - 2 ? ? %8 = [;] ? %9 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.014s user 0m0.011s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:55:01 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=2; g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 2*x^2 + 2 ? ? %7 = [2 9] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.051s user 0m0.013s sys 0m0.002s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:54:52 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-2; g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 - 2*x^2 + 2 ? ? %7 = [2 9] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.443s user 0m0.006s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:54:45 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-24; g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 - 24*x^2 + 288 ? ? %7 = [2 9] [3 2] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.208s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:54:37 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-24; g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 - 24*x^2 + 288 ? ? %7 = [2 9] [3 2] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.234s user 0m0.011s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:54:27 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=24; g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + 24*x^2 + 288 ? ? %7 = [2 9] [3 2] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:54:08 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=24; g=x^4+x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + x^2 + 288 ? ? %7 = [2 5] [1151 2] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:54:01 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-24; g=x^4+x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + x^2 + 288 ? ? %7 = [2 5] [1151 2] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.016s user 0m0.007s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:53:53 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-22; g=x^4+x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + x^2 + 242 ? ? %7 = [2 3] [967 2] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.278s user 0m0.010s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:53:44 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=22; g=x^4+x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + x^2 + 242 ? ? %7 = [2 3] [967 2] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.123s user 0m0.005s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:53:39 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=22; g=x^4+x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + x^2 + 242 ? ? %7 = [2 3] [967 2] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.015s user 0m0.008s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:53:28 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-22; g=x^4+x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + x^2 + 242 ? ? %7 = [2 3] [967 2] ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.107s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:53:16 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-22; g=x^4+x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + x^2 + 242 ? ? ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.015s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:53:08 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-2; g=x^4+x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + x^2 + 2 ? ? ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.060s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:52:57 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-4; g=x^4+x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? %5 = x^4 + x^2 + 8 ? ? ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.015s user 0m0.009s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:52:44 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-6; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.015s user 0m0.009s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:52:36 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-8; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.014s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:52:29 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-10; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.015s user 0m0.010s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:52:22 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-12; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.354s user 0m0.009s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:52:16 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-14; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.102s user 0m0.008s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:52:09 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-16; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:52:02 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); fact6r(nf.disc); A=-18; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %8 = 0 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: fact6r(nf.disc); ^------- Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:51:53 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-18; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.007s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:51:45 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=-20; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.087s user 0m0.011s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:51:32 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=20; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:51:25 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=18; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.040s user 0m0.007s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:51:16 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=16; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.075s user 0m0.010s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:51:08 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=14; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.092s user 0m0.011s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:51:01 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=12; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:50:51 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=10; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:50:41 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=8; g=x^4+x^2+A^2/2;; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.423s user 0m0.007s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:50:27 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=8; g=x^4-6; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = [-x, x] ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:50:01 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc); A=8; g=x^4+A*x^2+A^2/2; nf1=nfinit(g); factor(nf1.disc); nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? ? ? ? ? ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.056s user 0m0.012s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:49:44 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=8 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 8 ? %6 = x^4 + 8*x^2 + 32 ? ? %8 = [2 9] ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:49:24 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=6 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 6 ? %6 = x^4 + 6*x^2 + 18 ? ? %8 = [2 9] [3 2] ? %9 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.011s sys 0m0.004s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:49:18 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=6 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 6 ? %6 = x^4 + 6*x^2 + 18 ? ? %8 = [2 9] [3 2] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.009s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:49:04 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=5 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 5 ? %6 = x^4 + 5*x^2 + 25/2 ? ? ? ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. *** incorrect type in disc: factor(nf1.disc) ^----- Timing: real 0m0.060s user 0m0.007s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:48:51 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) A=5 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 5 ? %6 = x^4 + 5*x^2 + 25/2 ? ? ? ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. *** incorrect type in disc: factor(nf1.disc) ^----- Timing: real 0m0.016s user 0m0.008s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:48:32 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=5 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 5 ? %6 = x^4 + 5*x^2 + 25/2 ? ? ? ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. *** incorrect type in disc: factor(nf1.disc) ^----- Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:48:16 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=4 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 4 ? %6 = x^4 + 4*x^2 + 8 ? ? %8 = [2 9] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.179s user 0m0.010s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:48:06 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=3 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 3 ? %6 = x^4 + 3*x^2 + 9/2 ? ? ? ? Goodbye! Errors/timing (if any): *** nfinit: polynomial not in Z[X] in nfinit. *** incorrect type in disc: factor(nf1.disc) ^----- Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:47:40 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=2 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) nfisisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 2 ? %6 = x^4 + 2*x^2 + 2 ? ? %8 = [2 9] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.051s user 0m0.012s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:47:18 2006 Input: f=x^4-6 polred(f); nf=nfinit(f); factor(nf.disc) A=2 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) isisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 2 ? %6 = x^4 + 2*x^2 + 2 ? ? %8 = [2 9] ? ? Goodbye! Errors/timing (if any): *** obsolete function: isisom(f,g); ^------------ For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: isisom(x,y) ===> nfisisom(x,y) nfisisom(x,y): as nfisincl but tests whether x is isomorphic to y. Timing: real 0m0.117s user 0m0.009s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:47:00 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) A=2 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) isisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 2 ? %6 = x^4 + 2*x^2 + 2 ? ? %8 = [2 9] ? ? Goodbye! Errors/timing (if any): *** obsolete function: isisom(f,g); ^------------ For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: isisom(x,y) ===> nfisisom(x,y) nfisisom(x,y): as nfisincl but tests whether x is isomorphic to y. Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:46:43 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) A=2 g=x^4+A*x^2+A^2/2 nf1=nfinit(g); factor(nf1.disc) isincl(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 2 ? %6 = x^4 + 2*x^2 + 2 ? ? %8 = [2 9] ? ? Goodbye! Errors/timing (if any): *** obsolete function: isincl(f,g); ^------------ For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: isincl(x,y) ===> nfisincl(x,y) nfisincl(x,y): tests whether the number field x is isomorphic to a subfield of y (where x and y are either polynomials or number fields as output by nfinit). Return 0 if not, and otherwise all the isomorphisms. If y is a number field, a faster algorithm is used. Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:45:35 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) A=2 g=x^4+A*x^2+A^2/2 isincl(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 2 ? %6 = x^4 + 2*x^2 + 2 ? ? Goodbye! Errors/timing (if any): *** obsolete function: isincl(f,g); ^------------ For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: isincl(x,y) ===> nfisincl(x,y) nfisincl(x,y): tests whether the number field x is isomorphic to a subfield of y (where x and y are either polynomials or number fields as output by nfinit). Return 0 if not, and otherwise all the isomorphisms. If y is a number field, a faster algorithm is used. Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:45:14 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) A=2 g=x^4+A*x^2+A^2/2 isisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 2 ? %6 = x^4 + 2*x^2 + 2 ? ? Goodbye! Errors/timing (if any): *** obsolete function: isisom(f,g); ^------------ For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: isisom(x,y) ===> nfisisom(x,y) nfisisom(x,y): as nfisincl but tests whether x is isomorphic to y. Timing: real 0m0.079s user 0m0.010s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:45:02 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) A=1 g=x^4+A*x^2+A^2/2 isisom(f,g); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? %5 = 1 ? %6 = x^4 + x^2 + 1/2 ? ? Goodbye! Errors/timing (if any): *** obsolete function: isisom(f,g); ^------------ For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: isisom(x,y) ===> nfisisom(x,y) nfisisom(x,y): as nfisincl but tests whether x is isomorphic to y. Timing: real 0m0.067s user 0m0.006s sys 0m0.007s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:42:14 2006 Input: f=x^4-6 polred(f) nf=nfinit(f); factor(nf.disc) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? ? %4 = [-1 1] [2 11] [3 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.065s user 0m0.011s sys 0m0.005s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:41:47 2006 Input: f=x^4-6 polred(f) nf=nfinit(f) nf.disc Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? %3 = [x^4 - 6, [2, 1], -55296, 1, [[1, -1.5650845800732873165844854991586898098, 2.4494897427831780981972840747058913920, -3.8336586254776348551320958309633386020; 1, 1.5650845800732873165844854991586898098, 2.4494897427831780981972840747058913920, 3.8336586254776348551320958309633386020; 1, 0.E-38 - 1.5650845800732873165844854991586898098*I, -2.4494897427831780981972840747058913920 + 0.E-38*I, 0.E-37 + 3.8336586254776348551320958309633386020*I], [1, -1.5650845800732873165844854991586898098, 2.4494897427831780981972840747058913920, -3.8336586254776348551320958309633386020; 1, 1.5650845800732873165844854991586898098, 2.4494897427831780981972840747058913920, 3.8336586254776348551320958309633386020; 1, -1.5650845800732873165844854991586898098, -2.4494897427831780981972840747058913920, 3.8336586254776348551320958309633386020; 1, 1.5650845800732873165844854991586898098, -2.4494897427831780981972840747058913920, -3.8336586254776348551320958309633386020], 0, [4, 0, 0, 0; 0, 0, 0, 24; 0, 0, 24, 0; 0, 24, 0, 0], [24, 0, 0, 0; 0, 24, 0, 0; 0, 0, 24, 0; 0, 0, 0, 4], [-6, 0, 0, 0; 0, 0, 0, -1; 0, 0, -1, 0; 0, -1, 0, 0], [6, [0, 0, 0, 6; 1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0]]], [-1.5650845800732873165844854991586898098, 1.5650845800732873165844854991586898098, 0.E-38 - 1.5650845800732873165844854991586898098*I], [1, x, x^2, x^3], [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 0, 6, 0, 0; 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0; 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 6; 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0]] ? %4 = -55296 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.005s sys 0m0.008s '193.170' ************** PARI ***************** Host 193.170.37.83 (193.170.37.83) Time: Wed Jul 26 06:38:55 2006 Input: f=x^4-6 polred(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 - 6 ? %2 = [x - 1, x^2 - 6, x^4 - 216, x^4 - 6] ? Goodbye! Errors/timing (if any): Timing: real 0m0.142s user 0m0.009s sys 0m0.009s '72.30.1' ************** PARI ***************** Host 72.30.131.199 (72.30.131.199) Time: Wed Jul 26 05:14:49 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.103s user 0m0.004s sys 0m0.007s '80.36.9' ************** PARI ***************** Host 80.36.96.104 (80.36.96.104) Time: Wed Jul 26 04:36:04 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.042s user 0m0.010s sys 0m0.003s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Wed Jul 26 03:54:54 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.207s user 0m0.007s sys 0m0.005s '61.246.' ************** PARI ***************** Host 61.246.151.223 (61.246.151.223) Time: Tue Jul 25 23:13:51 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.707s user 0m0.007s sys 0m0.008s '68.42.0' ************** PARI ***************** Host 68.42.0.194 (68.42.0.194) Time: Tue Jul 25 19:06:38 2006 Input: 163.205 x log10(36.5 + 46.5 – 15.5) – 97.684 x log10(60) – 78.387= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: xlog10(36.5+46.515.5)97.684xlog10(60)78.387=. *** unknown function or error in formal parameters: 163.205 *** xlog10(36.5+46.515.5 ^-------------------- Timing: real 0m0.110s user 0m0.006s sys 0m0.006s '68.238.' ************** PARI ***************** Host 68.238.95.250 (68.238.95.250) Time: Tue Jul 25 18:57:33 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '68.238.' ************** PARI ***************** Host 68.238.95.250 (68.238.95.250) Time: Tue Jul 25 18:57:26 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '71.107.' ************** PARI ***************** Host 71.107.11.162 (71.107.11.162) Time: Tue Jul 25 11:39:56 2006 Input: 13divided by 211 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = dividedby211 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: dividedby211. Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '68.3.25' ************** PARI ***************** Host 68.3.255.90 (68.3.255.90) Time: Tue Jul 25 09:37:47 2006 Input: 355/40 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71/8 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '82.3.11' ************** PARI ***************** Host 82.3.119.241 (82.3.119.241) Time: Tue Jul 25 05:54:42 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.180 (134.76.82.180) Time: Tue Jul 25 03:22:03 2006 Input: e=ellinit([0,0,0,0,-11^17]); factor(ellglobalred(e)[1]) factor(e.disc) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [2 2] [3 3] [11 2] ? %3 = [-1 1] [2 4] [3 3] [11 34] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '134.76.' ************** PARI ***************** Host 134.76.82.180 (134.76.82.180) Time: Tue Jul 25 03:21:51 2006 Input: e=ellinit([0,0,0,0,-11^17]); factor(ellglobalred(e)[1]) e.disc Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [2 2] [3 3] [11 2] ? %3 = -110365933803306864286040400568060990512 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '134.76.' ************** PARI ***************** Host 134.76.82.180 (134.76.82.180) Time: Tue Jul 25 03:19:59 2006 Input: e=ellinit([0,0,0,0,-11^17]); factor(ellglobalred(e)[1]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [2 2] [3 3] [11 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.180 (134.76.82.180) Time: Tue Jul 25 03:17:23 2006 Input: e=ellinit([0,0,0,-889,11^7]); factor(ellglobalred(e)[1]) e.c4 e.j e Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [2 4] [29 1] [84017 1] [4208197067 1] ? %3 = 42672 ? %4 = -4856339190528/10253242696366031 ? %5 = [0, 0, 0, -889, 19487171, 0, -1778, 77948684, -790321, 42672, -16836915744, -164051883141856496, -4856339190528/10253242696366031, [-270.20277986293979247624839699180734070, 135.10138993146989623812419849590367035 - 232.09514575760783533338793980997212795*I, 135.10138993146989623812419849590367035 + 232.09514575760783533338793980997212795*I]~, 0.25675192542122520606233702175134539177, -0.12837596271061260303116851087567269588 + 0.073931596105245620496114662347600232939*I, -21.219736618399018488603469510838682856, 10.609868309199509244301734755419341428 - 18.346120065090502369024160253262708027*I, 0.018982079649486167464146454267069478279] ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.002s '134.76.' ************** PARI ***************** Host 134.76.82.180 (134.76.82.180) Time: Tue Jul 25 03:17:08 2006 Input: e=ellinit([0,0,0,0,11^7]); factor(ellglobalred(e)[1]) e.c4 e.j e Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [2 4] [3 3] [11 2] ? %3 = 0 ? %4 = 0 ? %5 = [0, 0, 0, 0, 19487171, 0, 0, 77948684, 0, 0, -16836915744, -164051928107960112, 0, [-269.10159095888717806100896858338102078, 134.55079547944358903050448429169051039 + 233.04881396920511266557247053075664850*I, 134.55079547944358903050448429169051039 - 233.04881396920511266557247053075664850*I]~, 0.25642923832450672651956603972861282501, -0.12821461916225336325978301986430641250 + 0.074024744887372329104082094358979742342*I, -21.219881665041094945371208085615038980, 10.609940832520547472685604042807519490 - 18.376956587225220519437540828473337000*I, 0.018982108948634809819292170949530388106] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '134.76.' ************** PARI ***************** Host 134.76.82.180 (134.76.82.180) Time: Tue Jul 25 03:16:22 2006 Input: e=ellinit([0,0,0,0,11^7]); factor(ellglobalred(e)[1]) e.c4 e.j Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [2 4] [3 3] [11 2] ? %3 = 0 ? %4 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.180 (134.76.82.180) Time: Tue Jul 25 03:14:30 2006 Input: e=ellinit([0,0,0,0,11^7]); factor(ellglobalred(e)[1]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [2 4] [3 3] [11 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.096s user 0m0.005s sys 0m0.009s '137.193' ************** PARI ***************** Host 137.193.61.27 (137.193.61.27) Time: Tue Jul 25 03:10:34 2006 Input: 8+5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 13 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '63.241.' ************** PARI ***************** Host 63.241.61.7 (63.241.61.7) Time: Mon Jul 24 22:40:08 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))}ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1617 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: ss(60). Timing: real 0m0.024s user 0m0.007s sys 0m0.007s '72.30.2' ************** PARI ***************** Host 72.30.226.223 (72.30.226.223) Time: Mon Jul 24 20:38:42 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '69.153.' ************** PARI ***************** Host 69.153.68.164 (69.153.68.164) Time: Mon Jul 24 18:40:05 2006 Input: -3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '75.3.15' ************** PARI ***************** Host 75.3.153.31 (75.3.153.31) Time: Mon Jul 24 18:33:37 2006 Input: -1/6+5/6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2/3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.047s user 0m0.005s sys 0m0.007s '199.91.' ************** PARI ***************** Host 199.91.33.254 (199.91.33.254) Time: Mon Jul 24 14:28:37 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '199.91.' ************** PARI ***************** Host 199.91.33.254 (199.91.33.254) Time: Mon Jul 24 14:28:28 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:13:50 2006 Input: p=43 q=79 n=p*q e=p+q h=q-p a=2 x=(a^(h*h)) / n g=Mod((a^(h*h)), n) Mod(p*x, n) Mod(-1*(g-1), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 79 ? %3 = 3397 ? %4 = 122 ? %5 = 36 ? %6 = 2 ? %7 = 1364188488619052116466105100188265419717379653273741532242786693992101715597506680981060248106739195555665885784215520253232226795300253192439713838619337787037991503054663889161182688006843079127591737170026798935139113651083474222050508981461091652957942433095504472118187338632823518614811421165606509195698926020610034372011417336379206274761103883598061489450479872973957125731659022336/3397 ? %8 = Mod(1460, 3397) ? %9 = Mod(0, 3397) ? %10 = Mod(3, 43) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:13:32 2006 Input: p=43 q=79 n=p*q e=p+q h=q-p a=17 x=(a^(h*h)) / n g=Mod((a^(h*h)), n) Mod(p*x, n) Mod(-1*(g-1), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 79 ? %3 = 3397 ? %4 = 122 ? %5 = 36 ? %6 = 17 ? %7 = 45898881902230086977008023085916961541815117623689130740904824776533559669194060851416144585018762202477517028290707846663584926325663405357533068224069461994481866198087722267263547713252969528336288682644846039976108304777267408108919737394031674717215599101643532476586721703718659903733211550424739299016656840392339854866942146104015514234730950387483253604366918343888794721553105602112012886818089195059935334735406110472510759971984334640176462525387539456719696024474770282733758923194387905544871614348609927825150234892973603182406795191294207509448549395834252963575522943864736878805925993888165756092444451635073670473562866201092130186340627849882024910598620588365169942575069502169854669277645588419550795349617154674172435761920523437820854684825668256644709722514058493852530675307845834464449988160922693197629230312660149307097509901338261705858084130332051634496451896344752591272453693118427665363868618629423815734263425228535406641068782589246414713897670527226029828635200211843872351475618555679376428476061300534550845571242514199756464411458862263778642740302375725365466183738523469357827777448414600784466724300748777290989194243974939747913178191631114146194846879904250322713542108792780545658883326584240159827102242354180809264261395666216265527978227408879577449029429561901620458138683359486376273198964247785750187165433821888065346088886816373224148567324758675307712551978391988792095159092037763693917870269814697330854299143367146839752649854934716353195472499687855010271328291637764835054222384207209021913398471282371367195124689775931327316806682881/3397 ? %8 = Mod(575, 3397) ? %9 = Mod(0, 3397) ? %10 = Mod(28, 43) ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.009s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:12:39 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^(h*h)) / n g=Mod((a^(h*h)), n) Mod(p*x, n) Mod(-1*(g-1), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? %8 = Mod(6895, 10793) ? %9 = Mod(0, 10793) ? %10 = Mod(29, 43) ? Goodbye! Errors/timing (if any): Timing: real 0m0.211s user 0m0.151s sys 0m0.060s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:12:31 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^(h*h)) / n g=Mod((a^(h*h)), n) Mod(p*x, n) Mod((g-1), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? %8 = Mod(6895, 10793) ? %9 = Mod(0, 10793) ? %10 = Mod(14, 43) ? Goodbye! Errors/timing (if any): Timing: real 0m0.205s user 0m0.147s sys 0m0.059s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:12:15 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^(h*h)) / n g=Mod((a^(h*h)), n) Mod(p*x, n) Mod(-1*(g-1), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? %8 = Mod(6895, 10793) ? %9 = Mod(0, 10793) ? %10 = Mod(29, 43) ? Goodbye! Errors/timing (if any): Timing: real 0m0.205s user 0m0.132s sys 0m0.073s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:12:06 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^(h*h)) / n g=Mod((a^(h*h)), n) Mod(p*x, n) Mod(-1*(g-1), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? %8 = Mod(6895, 10793) ? %9 = Mod(0, 10793) ? %10 = Mod(3899, 10793) ? Goodbye! Errors/timing (if any): Timing: real 0m0.205s user 0m0.145s sys 0m0.060s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:11:37 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^(h*h)) / n g=Mod((a^(h*h)), n) Mod(p*x, n) Mod((g-1), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? %8 = Mod(6895, 10793) ? %9 = Mod(0, 10793) ? %10 = Mod(6894, 10793) ? Goodbye! Errors/timing (if any): Timing: real 0m0.210s user 0m0.143s sys 0m0.068s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:11:11 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^(h*h)) / n g=Mod((a^(h*h)), n) Mod(p*x, n) Mod(-1*(g-1), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? %8 = Mod(6895, 10793) ? %9 = Mod(0, 10793) ? %10 = Mod(3899, 10793) ? Goodbye! Errors/timing (if any): Timing: real 0m0.223s user 0m0.147s sys 0m0.060s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:10:50 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^(h*h)) / n g=Mod((a^(h*h)), n) Mod(p*x, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? %8 = Mod(6895, 10793) ? %9 = Mod(0, 10793) ? Goodbye! Errors/timing (if any): Timing: real 0m0.211s user 0m0.144s sys 0m0.068s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:09:55 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^(h*h)) / n g=Mod((a^(h*h)), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? %8 = Mod(6895, 10793) ? Goodbye! Errors/timing (if any): Timing: real 0m0.210s user 0m0.156s sys 0m0.053s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:09:29 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^(h*h)) / n g=Mod((a^(h*h)) / n, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? %8 = Mod(0, 10793) ? Goodbye! Errors/timing (if any): Timing: real 0m0.211s user 0m0.138s sys 0m0.074s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:08:44 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^((h)*(h))) / n g=Mod((a^((h)*(h))) / n, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? %8 = Mod(0, 10793) ? Goodbye! Errors/timing (if any): Timing: real 0m0.264s user 0m0.131s sys 0m0.081s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:07:23 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^((h)*(h))) / n Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? %7 = 1387185401267822509924759255297292885804433274300386345030683365755856554164294480232262571778968780024860079407669388921233980137027507877839700198748264927484292334741828053300815150976158655656213571613796604392820704096821678169572747819286632039828436103256749601201006269095900339995836605336691896532928488558382080623833584701636960250656591737267560929788654008664946714908777700777223068816400042896391063669331801065990788824063604937495039495637818134908746258562161235362047486721679013422572314918970917210961277956232017738891205581920314496300269413322120618284929589780007311518776567394209668191180641985096128927135849953974812947151489884084719586623158191775760536806858042885375033670728202881232392872240600994041238501542345238032568866447257084663755986727629612522001095617502334947739021516140716834105291657513885311131364860490068841001636219374618521893173392620227773980811536735805642602844355109845673075616432584935272255987757443154878200356088006004263237794075696571636001133113175334131701489431433009495454457592964007257381372302678475496639202198036713246981352332852264845066617308226786879397377267263226702870836729116952885398065575325182324365882886855284213971535926515087376457532860647517570498763369635115889300140712120239630505957561387748872291667831800031569383349545939109505985606205489756617552288995710202414329155875435428966280007896974426700259946674766598952101813672378324255642119879626986100348692373281137555902818698601473534260237683313511446283584806873989020892629521306199650462150824395045212181528713011014420340528846159967895529466158939355400303688155536441463459610340808384852885448423916030847852447053417076986657543691779334587771148881759227403563232340372537652579683881122519296450500062094997304816854092348814225263417023537076435204165278111073660828555638194107100432010597326625044795956850215905560749288616141972649127075864504359032024812131595647856185286420829471735119240617488153588560327748851278210373327370435211270490272702456881185800153161605963046634004056722853297976159850995758621443183440260868659428304623206127339816288159688063106076116831464594847795565974873849704703482040307548511851772052757993548485254454335662229527876005052780746694290753882519829371430172554347641415620601518244902223053653222609006252931285367362823945711411593475561222443269226181803384881654890419331904943298592060996494231252182177887360616211711606449308990501196764535708893730777601850342991553868296923840044231207282693145413297336574367919316501111113362810417691559169108887716584494861539845439716655409199546982875342603217858281201008176020548486874994064803236341135876682323017101871265138955385320502874356600951497854078658027851666798939001368302299322727411050776201778661691958852910661568072958766717339211700337500640224421492285573861028100165056209705372564956546625196900524912389637716708247744870070788356444727578957644667729616312667500572898057387183185073603478883880484902219126174324610215605389481762057058100716218186902800759032661461209063426007794341853123551563297941611240986092285816266532160604003132605368808840327632308138810724810327318787311146661263677[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.202s user 0m0.132s sys 0m0.071s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:07:10 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^((n-1)*(n-1))) / n Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 20364 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.103s user 0m20.600s sys 0m0.431s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:06:40 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^((n-1)*(n-1))) / p Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 20355 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.123s user 0m20.584s sys 0m0.445s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:06:15 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^((n-1)*(n-1))) / p Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 20344 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.345s user 0m20.468s sys 0m0.562s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:06:15 2006 Input: p=43 q=251 n=p*q e=p+q h=q-p a=17 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 10793 ? %4 = 294 ? %5 = 208 ? %6 = 17 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:05:45 2006 Input: P=43 q=251 n=p*q Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 251*p ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:05:37 2006 Input: P=43; q=251; n=p*q; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:05:31 2006 Input: P=43 q=251 n=p*q; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:05:25 2006 Input: P=43 q=251 n=p*q Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 251*p ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.003s sys 0m0.009s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:04:58 2006 Input: P=43 q=251 n=p*q e=p+q h=q-p a=17 x=(a^((n-1)*(n-1))) / p Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 251*p ? %4 = p + 251 ? %5 = -p + 251 ? %6 = 17 ? %7 = 17.000000000000000000000000000000000000*p^-1 - 24178.642678175748028849528428929261854 + 20228736.178431694885440087994107421648*p - 12467444727.271974325493802370832327495*p^2 + 6238394713630.1666842720705640085846837*p^3 - 2664692180589515.0220741632053507666505*p^4 + 1002827991814119709.3237607641069529220*p^5 - 339652170943518224477.07253192773747608*p^6 + 105134782472266759163697.31051215304037*p^7 - 30086998600969158543176295.881292507845*p^8 + 8032405231654233844599969060.2770886535*p^9 - 2015004362774387974242834215406.1100560*p^10 + 477781603549259438278453683177587.10415*p^11 - 107605648694695217196207934613330594.67*p^12 + 23114866841254664064004610624222882372.*p^13 - 4.7526568506817171410932884741988588531 E39*p^14 + O(p^15) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 24 12:04:38 2006 Input: P=43 q=251 n=p*q e=p+q h=q-p a=17 x=a^((n-1)*(n-1)) / p Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 43 ? %2 = 251 ? %3 = 251*p ? %4 = p + 251 ? %5 = -p + 251 ? %6 = 17 ? %7 = 17.000000000000000000000000000000000000*p^-1 - 24178.642678175748028849528428929261854 + 20228736.178431694885440087994107421648*p - 12467444727.271974325493802370832327495*p^2 + 6238394713630.1666842720705640085846837*p^3 - 2664692180589515.0220741632053507666505*p^4 + 1002827991814119709.3237607641069529220*p^5 - 339652170943518224477.07253192773747608*p^6 + 105134782472266759163697.31051215304037*p^7 - 30086998600969158543176295.881292507845*p^8 + 8032405231654233844599969060.2770886535*p^9 - 2015004362774387974242834215406.1100560*p^10 + 477781603549259438278453683177587.10415*p^11 - 107605648694695217196207934613330594.67*p^12 + 23114866841254664064004610624222882372.*p^13 - 4.7526568506817171410932884741988588531 E39*p^14 + O(p^15) ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.009s sys 0m0.004s '169.229' ************** PARI ***************** Host 169.229.137.154 (169.229.137.154) Time: Mon Jul 24 11:45:31 2006 Input: f1 = 'alt=sin(t)' f2 = 'azm=sin(t)*cos(p)' eqn=maxima([f1,f2]) s = eqn.solve('[p,t]'); s Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: f1='alt=sin(t)' ^-------- *** unexpected character: f2='azm=sin(t)*cos(p)' ^--------------- *** unknown function or error in formal parameters: eqn=maxima([f1,f2]) ^--------------- *** Warning: unused characters: ('[p,t]');s. *** unknown member function: s=eqn.solve('[p,t]');s ^---------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '67.11.2' ************** PARI ***************** Host 67.11.212.178 (67.11.212.178) Time: Mon Jul 24 09:26:22 2006 Input: 20 * .30 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6.0000000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '67.11.2' ************** PARI ***************** Host 67.11.212.178 (67.11.212.178) Time: Mon Jul 24 09:26:11 2006 Input: 20 x .30 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x.30. *** unknown member function: 20x.30 ^-- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Mon Jul 24 09:11:54 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '169.237' ************** PARI ***************** Host 169.237.30.114 (169.237.30.114) Time: Mon Jul 24 09:07:17 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '70.31.1' ************** PARI ***************** Host 70.31.199.89 (70.31.199.89) Time: Mon Jul 24 06:37:32 2006 Input: (4m + 5)2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: (4m+5)2 ^----- Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:28:36 2006 Input: q(d)=quadclassunit(nfinit(x^2-d).disc); q(3) q(5) q(15) q(19) ?quadclassunit ?4 ?qfbclassno ?qfbhclassno Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [1, [], [], 1.3169578969248167086250463473079684440] ? %2 = [1, [], [], 0.48121182505960344749775891342436842314] ? %3 = [2, [2], [Qfb(2, 6, -3, 0.E-57)], 2.0634370688955605467272811726201318715] ? %4 = [1, [], [], 5.8289369669789265547345668575229095390] ? quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group and the regulator of the quadratic field of discriminant D. If flag is non-null (and D>0), compute the narrow class group. See manual for the optional technical parameters. ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental ispower isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primepi primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint zncoppersmith znlog znorder znprimroot znstar ? qfbclassno(x,{flag=0}): class number of discriminant x using Shanks's method by default. If (optional) flag is set to 1, use Euler products. ? qfbhclassno(x): Hurwitz-Kronecker class number of x>0. ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:27:19 2006 Input: q(d)=quadclassunit(nfinit(x^2-d).disc); q(3) q(5) q(15) q(19) ?quadclassunit ?4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [1, [], [], 1.3169578969248167086250463473079684440] ? %2 = [1, [], [], 0.48121182505960344749775891342436842314] ? %3 = [2, [2], [Qfb(2, 6, -3, 0.E-57)], 2.0634370688955605467272811726201318715] ? %4 = [1, [], [], 5.8289369669789265547345668575229095390] ? quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group and the regulator of the quadratic field of discriminant D. If flag is non-null (and D>0), compute the narrow class group. See manual for the optional technical parameters. ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental ispower isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primepi primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint zncoppersmith znlog znorder znprimroot znstar ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.008s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:26:37 2006 Input: q(d)=quadclassunit(nfinit(x^2-d).disc); q(3) q(5) q(15) q(19) ?quadclassunit Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [1, [], [], 1.3169578969248167086250463473079684440] ? %2 = [1, [], [], 0.48121182505960344749775891342436842314] ? %3 = [2, [2], [Qfb(2, 6, -3, 0.E-57)], 2.0634370688955605467272811726201318715] ? %4 = [1, [], [], 5.8289369669789265547345668575229095390] ? quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group and the regulator of the quadratic field of discriminant D. If flag is non-null (and D>0), compute the narrow class group. See manual for the optional technical parameters. ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.009s sys 0m0.007s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:26:17 2006 Input: q(d)=quadclassunit(nfinit(x^2-d).disc); q(3) q(5) q(15) q(19) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [1, [], [], 1.3169578969248167086250463473079684440] ? %2 = [1, [], [], 0.48121182505960344749775891342436842314] ? %3 = [2, [2], [Qfb(2, 6, -3, 0.E-57)], 2.0634370688955605467272811726201318715] ? %4 = [1, [], [], 5.8289369669789265547345668575229095390] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.010s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:25:38 2006 Input: q(d)=quadclassunit(nfinit(x^2-d).disc); q(5) q(-5) q(-163) q(-167) q(11) q(12) q(13) q(14) q(15) q(16) q(17) q(18) q(19) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [1, [], [], 0.48121182505960344749775891342436842314] ? %2 = [2, [2], [Qfb(3, -2, 2)], 1] ? %3 = [1, [], [], 1] ? %4 = [11, [11], [Qfb(2, 1, 21)], 1] ? %5 = [1, [], [], 2.9932228461263808979126677137741829131] ? %6 = [1, [], [], 1.3169578969248167086250463473079684440] ? %7 = [1, [], [], 1.1947632172871093041119308285190905235] ? %8 = [1, [], [], 3.4000844141133395007001872142448670645] ? %9 = [2, [2], [Qfb(2, 6, -3, 0.E-57)], 2.0634370688955605467272811726201318715] ? ? %10 = [1, [], [], 2.0947125472611012942448228460655286535] ? %11 = [1, [], [], 0.88137358701954302523260932497979230902] ? %12 = [1, [], [], 5.8289369669789265547345668575229095390] ? ? Goodbye! Errors/timing (if any): *** nfinit: reducible polynomial in nfinit. Timing: real 0m0.020s user 0m0.014s sys 0m0.006s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:24:53 2006 Input: q(d)=quadclassunit(nfinit(x^2-d).disc); q(5) q(-5) q(-163) q(-167) q(11) q(12) q(13) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [1, [], [], 0.48121182505960344749775891342436842314] ? %2 = [2, [2], [Qfb(3, -2, 2)], 1] ? %3 = [1, [], [], 1] ? %4 = [11, [11], [Qfb(2, 1, 21)], 1] ? %5 = [1, [], [], 2.9932228461263808979126677137741829131] ? %6 = [1, [], [], 1.3169578969248167086250463473079684440] ? %7 = [1, [], [], 1.1947632172871093041119308285190905235] ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.007s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:24:10 2006 Input: q(d)=quadclassunit(nfinit(x^2-d).disc); q(13) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [1, [], [], 1.1947632172871093041119308285190905235] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:22:37 2006 Input: p=x^2-13; nf=nfinit(p); factor(nf.disc); ?4 ?quadclassunit quadclassunit(13) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental ispower isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primepi primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint zncoppersmith znlog znorder znprimroot znstar ? quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group and the regulator of the quadratic field of discriminant D. If flag is non-null (and D>0), compute the narrow class group. See manual for the optional technical parameters. ? %4 = [1, [], [], 1.1947632172871093041119308285190905235] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:21:55 2006 Input: p=x^2-13; nf=nfinit(p); factor(nf.disc); ?4 ?quadclassunit Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental ispower isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primepi primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint zncoppersmith znlog znorder znprimroot znstar ? quadclassunit(D,{flag=0},{tech=[]}): compute the structure of the class group and the regulator of the quadratic field of discriminant D. If flag is non-null (and D>0), compute the narrow class group. See manual for the optional technical parameters. ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:20:15 2006 Input: p=x^2-13; nf=nfinit(p); factor(nf.disc); ?4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental ispower isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primepi primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint zncoppersmith znlog znorder znprimroot znstar ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:19:54 2006 Input: p=x^2-13; nf=nfinit(p); factor(nf.disc); ? Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Help topics: for a list of relevant subtopics, type ?n for n in 0: user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:17:26 2006 Input: p=x^2-13; nf=nfinit(p); factor(nf.disc); ?6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? bnfcertify bnfclassunit bnfclgp bnfdecodemodule bnfinit bnfisintnorm bnfisnorm bnfisprincipal bnfissunit bnfisunit bnfmake bnfnarrow bnfreg bnfsignunit bnfsunit bnfunit bnrL1 bnrclass bnrclassno bnrclassnolist bnrconductor bnrconductorofchar bnrdisc bnrdisclist bnrinit bnrisconductor bnrisprincipal bnrrootnumber bnrstark dirzetak factornf galoisexport galoisfixedfield galoisidentify galoisinit galoisisabelian galoispermtopol galoissubcyclo galoissubfields galoissubgroups idealadd idealaddtoone idealappr idealchinese idealcoprime idealdiv idealfactor idealhnf idealintersect idealinv ideallist ideallistarch ideallog idealmin idealmul idealnorm idealpow idealprimedec idealprincipal idealred idealstar idealtwoelt idealval ideleprincipal matalgtobasis matbasistoalg modreverse newtonpoly nfalgtobasis nfbasis nfbasistoalg nfdetint nfdisc nfeltdiv nfeltdiveuc nfeltdivmodpr nfeltdivrem nfeltmod nfeltmul nfeltmulmodpr nfeltpow nfeltpowmodpr nfeltreduce nfeltreducemodpr nfeltval nffactor nffactormod nfgaloisapply nfgaloisconj nfhilbert nfhnf nfhnfmod nfinit nfisideal nfisincl nfisisom nfkermodpr nfmodprinit nfnewprec nfroots nfrootsof1 nfsnf nfsolvemodpr nfsubfields polcompositum polgalois polred polredabs polredord poltschirnhaus rnfalgtobasis rnfbasis rnfbasistoalg rnfcharpoly rnfconductor rnfdedekind rnfdet rnfdisc rnfeltabstorel rnfeltdown rnfeltreltoabs rnfeltup rnfequation rnfhnfbasis rnfidealabstorel rnfidealdown rnfidealhnf rnfidealmul rnfidealnormabs rnfidealnormrel rnfidealreltoabs rnfidealtwoelt rnfidealup rnfinit rnfisfree rnfisnorm rnfisnorminit rnfkummer rnflllgram rnfnormgroup rnfpolred rnfpolredabs rnfpseudobasis rnfsteinitz subgrouplist zetak zetakinit ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:16:50 2006 Input: p=x^2-13; nf=nfinit(p); factor(nf.disc) ? Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %3 = [13 1] ? Help topics: for a list of relevant subtopics, type ?n for n in 0: user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '134.76.' ************** PARI ***************** Host 134.76.82.172 (134.76.82.172) Time: Mon Jul 24 05:16:25 2006 Input: p=x^2-13; nf=nfinit(p); factor(nf.disc) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %3 = [13 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.123s user 0m0.010s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.110.15 (72.30.110.15) Time: Sun Jul 23 21:06:21 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.053s user 0m0.008s sys 0m0.003s '69.199.' ************** PARI ***************** Host 69.199.89.124 (69.199.89.124) Time: Sun Jul 23 18:55:26 2006 Input: log(0.7, 0.028)= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: log(0.7,0.028)= ^-------- Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '68.65.1' ************** PARI ***************** Host 68.65.144.232 (68.65.144.232) Time: Sun Jul 23 17:18:48 2006 Input: 2052/160 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 513/40 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '130.13.' ************** PARI ***************** Host 130.13.101.118 (130.13.101.118) Time: Sun Jul 23 12:18:36 2006 Input: p=282174488599599500573849980909 q=671998030559713968361666935769 phi=p*q p1=sqrt(phi) r=phi-p1*p1 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 282174488599599500573849980909 ? %2 = 671998030559713968361666935769 ? %3 = 189620700613125325959116839007395234454467716598457179234021 ? %4 = 435454590759042665485476994260.29417462 ? %5 = 0.E21 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '72.30.9' ************** PARI ***************** Host 72.30.98.145 (72.30.98.145) Time: Sun Jul 23 12:07:03 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.027s user 0m0.007s sys 0m0.004s '65.54.1' ************** PARI ***************** Host 65.54.188.53 (65.54.188.53) Time: Sun Jul 23 11:07:14 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '74.129.' ************** PARI ***************** Host 74.129.80.7 (74.129.80.7) Time: Sun Jul 23 10:32:31 2006 Input: 251 - 121 + 441 - 340 + 130 - 113 + 409 - 253 + 130 - 181 + 297 - 149 + 081 - 088 + 467 - 059 + 306 - 229 + 345 - 351 + 117 - 047 + 353 - 216 + 401 - 147 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1434 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '74.129.' ************** PARI ***************** Host 74.129.80.7 (74.129.80.7) Time: Sun Jul 23 10:32:18 2006 Input: 251 - 121 + 441 - 340 + 130 - 113 + 409 - 253 + 130 - 181 + 297 - 149 + 081 - 088 + 467 - 059 + 306 - 229 + 345 - 351 + 117 - 047 + 353 - 216 + 401 - 147 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1434 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:46:24 2006 Input: [1,0;1,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0] [2 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:46:11 2006 Input: [1,1;0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 2] [0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:45:52 2006 Input: [1,0;0,0]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0] [0 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:45:38 2006 Input: [1,1;0,0]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1] [0 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:44:22 2006 Input: [1,1,0;0,1,1;1,0,1]^5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [11 10 11] [11 11 10] [10 11 11] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:43:48 2006 Input: [1,1,0;0,1,1;1,0,1]^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5 5 6] [6 5 5] [5 6 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:42:51 2006 Input: [1,1,0;0,1,1;1,0,1]^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 3] [3 2 3] [3 3 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:42:42 2006 Input: [1,1,0;0,1,1;1,0,1]^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 2 1] [1 1 2] [2 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '210.56.' ************** PARI ***************** Host 210.56.15.19 (210.56.15.19) Time: Sun Jul 23 09:42:24 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:40:56 2006 Input: [1,0,1;0,1,1;1,1,0]^7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [43 42 43] [42 43 43] [43 43 42] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:40:19 2006 Input: [1,0,1;0,1,1;1,1,0]^6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [22 21 21] [21 22 21] [21 21 22] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:39:29 2006 Input: [1,0,1;0,1,1;1,1,0]^5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [11 10 11] [10 11 11] [11 11 10] ? Goodbye! Errors/timing (if any): Timing: real 0m0.032s user 0m0.006s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:38:16 2006 Input: [1,0,1;0,1,1;1,1,0]*[1,0,1;0,1,1;1,1,0]*[1,0,1;0,1,1;1,1,0]*[1,0,1;0,1,1;1,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [6 5 5] [5 6 5] [5 5 6] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:36:38 2006 Input: [1,0,1;0,1,1;1,1,0]*[1,0,1;0,1,1;1,1,0]*[1,0,1;0,1,1;1,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 2 3] [2 3 3] [3 3 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sun Jul 23 09:34:04 2006 Input: [1,1,1,1;0,2,1,0;1,0,1,2;1,1,1,1]*[1,0,0,1;0,0,1,1;1,1,0,0;0,1,1,0] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 2 2 2] [1 1 2 2] [2 3 2 1] [2 2 2 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.006s sys 0m0.006s '67.33.2' ************** PARI ***************** Host 67.33.205.137 (67.33.205.137) Time: Sun Jul 23 09:11:54 2006 Input: 39.54+10.00+3.74+1.69+1.29+3.36+8.51+5.31+39.88+20.00+6.72+4.49+4.12+6.40+3.18+1.67+10.00+7.89+5.00+3.45+10.03+3.74+8.92-5.55 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 203.38000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.284s user 0m0.008s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sun Jul 23 07:21:12 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.106s user 0m0.009s sys 0m0.003s '72.30.1' ************** PARI ***************** Host 72.30.102.206 (72.30.102.206) Time: Sun Jul 23 01:55:51 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.120s user 0m0.003s sys 0m0.010s '72.30.1' ************** PARI ***************** Host 72.30.129.123 (72.30.129.123) Time: Sat Jul 22 20:48:42 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.051s user 0m0.006s sys 0m0.011s '72.30.2' ************** PARI ***************** Host 72.30.226.223 (72.30.226.223) Time: Sat Jul 22 14:44:05 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 22 10:30:12 2006 Input: [1,0,0;1,1,0;1,1,1]*[1,0,0;1,1,0;1,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [2 1 0] [3 2 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 22 09:49:46 2006 Input: [1,0,0;1,1,0;1,1,1]*[1,0,0;1,1,0;1,1,1]*[1,0,0;1,1,0;1,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [3 1 0] [6 3 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 22 09:47:52 2006 Input: [1,0,0;1,1,0;1,1,1]*[1,0,0;1,1,0;1,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [2 1 0] [3 2 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 22 09:47:34 2006 Input: [1,0,0;1,1,0;1,1,1]*[1,0,0;1,1,;1,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: ...;1,1,0;1,1,1]*[1,0,0;1,1,;1,1,1] ^------- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 22 09:46:44 2006 Input: [1,0,0;1,1,1;1,1,1]*[1,0,0;1,1,1;1,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [3 2 2] [3 2 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Sat Jul 22 09:46:29 2006 Input: [1,0,0;1,1,1,;1,1,1]*[1,0,0;1,1,1;1,1,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ';' instead of: [1,0,0;1,1,1,;1,1,1]*[1,0,0;1,1, ^-------------------- Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sat Jul 22 06:10:38 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.003s sys 0m0.008s '72.30.9' ************** PARI ***************** Host 72.30.98.26 (72.30.98.26) Time: Sat Jul 22 03:24:42 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Fri Jul 21 20:25:34 2006 Input: [1, 0, 1;1, 1,0;0, 1, 1]*[1, 0, 1;1, 1,0;0, 1, 1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1 2] [2 1 1] [1 2 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Fri Jul 21 20:25:17 2006 Input: {[1, 0, 1;1, 1,0;0, 1, 1]}*{[1, 0, 1;1, 1,0;0, 1, 1]} Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** sorry, embedded braces (in parser) is not yet implemented. Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Fri Jul 21 20:24:32 2006 Input: [1, 0, 1;1, 1,0;0, 1, 1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 1] [1 1 0] [0 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Fri Jul 21 20:19:39 2006 Input: [2,2;3,4;6,5] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 2] [3 4] [6 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Fri Jul 21 20:18:55 2006 Input: [2,1]*[2,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** forbidden multiplication t_VEC * t_VEC. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Fri Jul 21 20:18:34 2006 Input: [2,1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Fri Jul 21 20:00:55 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.045s user 0m0.024s sys 0m0.006s '24.250.' ************** PARI ***************** Host 24.250.16.34 (24.250.16.34) Time: Fri Jul 21 17:39:17 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.193' ************** PARI ***************** Host 128.193.221.253 (128.193.221.253) Time: Fri Jul 21 17:01:13 2006 Input: log ( 27 * 54 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7.2848209125686034577887035429933307959 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Fri Jul 21 16:06:17 2006 Input: y= t*(x+2) (169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110))/(x+2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = t*x + 2*t ? ? %2 = ((256*t^2 - 416*t + 169)*x^2 + (1024*t^2 - 770*t - 291)*x + (1024*t^2 + 124*t - 94))/(220*x + 440) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Fri Jul 21 16:05:03 2006 Input: x = t*(y+2) (169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110))/(y+2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (y + 2)*t ? ? %2 = (169/220*y + 169/110)*t^2 + (-104/55*y - 291/220)*t + ((128*y^2 + 31*y - 47)/(110*y + 220)) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Fri Jul 21 16:04:06 2006 Input: x = t*(y+2) (169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (y + 2)*t ? ? %2 = (169/220*y^2 + 169/55*y + 169/55)*t^2 + (-104/55*y^2 - 1123/220*y - 291/110)*t + (64/55*y^2 + 31/110*y - 47/110) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Fri Jul 21 16:03:49 2006 Input: x = t*(y+2) (169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110))/(x+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (y + 2)*t ? ? %2 = ((169*y^2 + 676*y + 676)*t^2 + (-416*y^2 - 1123*y - 582)*t + (256*y^2 + 62*y - 94))/((220*y + 440)*t + 220) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Fri Jul 21 15:55:58 2006 Input: y = t*x + t -1 (169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110))/(x+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = t*x + (t - 1) ? ? %2 = ((256*t^2 - 416*t + 169)*x^2 + (512*t^2 - 866*t + 125)*x + (256*t^2 - 450*t + 100))/(220*x + 220) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Fri Jul 21 15:55:41 2006 Input: y = t*x + t -1 169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110)(x+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = t*x + (t - 1) ? ? %2 = x + 1 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (x+1). Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Fri Jul 21 15:54:52 2006 Input: y = t*x +t -1 169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = t*x + (t - 1) ? ? %2 = (64/55*t^2 - 104/55*t + 169/220)*x^2 + (128/55*t^2 - 433/110*t + 25/44)*x + (64/55*t^2 - 45/22*t + 5/11) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Fri Jul 21 15:54:10 2006 Input: c = 1/55 (3/2*x - y + 1/2)*(1/2*x - y -1) + c * (x + 3*y -2)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1/55 ? ? %2 = 169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '70.34.1' ************** PARI ***************** Host 70.34.176.199 (70.34.176.199) Time: Fri Jul 21 15:29:41 2006 Input: 6892 ÷ 5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 68925 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 15:08:53 2006 Input: c = 1/55 (3/2*x - y + 1/2)*(1/2*x - y -1) + c * (x + 3*y -2)^2 (6*c-2)^2 - 4*(c+3/4)*(9*c +1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1/55 ? ? %2 = 169/220*x^2 + (-104/55*y - 291/220)*x + (64/55*y^2 + 31/110*y - 47/110) ? ? %3 = 0 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 15:08:06 2006 Input: (3/2*x - y + 1/2)*(1/2*x - y -1) + c * (x + 3*y -2)^2 (6*c-2)^2 - 4*(c+3/4)*(9*c +1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (c + 3/4)*x^2 + ((6*c - 2)*y + (-4*c - 5/4))*x + ((9*c + 1)*y^2 + (-12*c + 1/2)*y + (4*c - 1/2)) ? ? %2 = -55*c + 1 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 15:04:02 2006 Input: (3/2*x - y + 1/2)*(1/2*x - y -1) + c * (x + 3*y -2)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (c + 3/4)*x^2 + ((6*c - 2)*y + (-4*c - 5/4))*x + ((9*c + 1)*y^2 + (-12*c + 1/2)*y + (4*c - 1/2)) ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.002s sys 0m0.011s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 15:03:09 2006 Input: 3/2*x - y + 1/2)*(1/2*x - y -1) + c * (x + 3*y -2)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 3/2*x + (-y + 1/2) ? ? ? ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: )*(1/2*x-y-1)+c*(x+3*y-2)^2. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:38:09 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) t = 9/2 ((2*t^2 - 3*t + 3)*(4*t -1)- (4*t - 3)*(2*t^2-t-6) )/(2*t^2 - 3*t + 3)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = 9/2 ? %3 = 1/15 ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.004s sys 0m0.012s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:27:09 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) y = (6*t^2 - 3*t - 18)/(6*t^2 - 9*t + 9) x = t*(y+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? %2 = (2*t^2 - t - 6)/(2*t^2 - 3*t + 3) ? ? ? %3 = (4*t^3 - 4*t^2 - 3*t)/(2*t^2 - 3*t + 3) ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:26:32 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) y = (6*t^2 - 3*t - 18)/(6*t^2 - 9*t + 9) (6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18)/(y+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? %2 = (2*t^2 - t - 6)/(2*t^2 - 3*t + 3) ? ? ? %3 = ((12*t^2 - 18*t + 18)/(4*t^2 - 4*t - 3))*x^2 + ((-24*t^2 + 18*t + 45)/(4*t^2 - 4*t - 3))*x + ((-18*t^2 + 45*t - 108)/(2*t^2 - 3*t + 3)) ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:26:19 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) y = (6*t^2 - 3*t - 18)/(6*t^2 - 9*t + 9) x = t*(y+1) (6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18)/(y+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? %2 = (2*t^2 - t - 6)/(2*t^2 - 3*t + 3) ? ? ? %3 = (4*t^3 - 4*t^2 - 3*t)/(2*t^2 - 3*t + 3) ? ? %4 = 12*t^2 - 6*t - 36 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:17:19 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) x = t*(y+1) (6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18)/(y+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t*y + t ? ? %3 = (6*t^2 - 9*t + 9)*y + (6*t^2 - 3*t - 18) ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:16:15 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) x = t*(y+1) (6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t*y + t ? ? %3 = (6*t^2 - 9*t + 9)*y^2 + (12*t^2 - 12*t - 9)*y + (6*t^2 - 3*t - 18) ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:16:09 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) x = t*(y+1) (6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18)/(y+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t*y + t ? ? %3 = (6*t^2 - 9*t + 9)*y + (6*t^2 - 3*t - 18) ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:15:29 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) x = t*(y+1) 6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t*y + t ? ? %3 = (6*t^2 - 9*t + 9)*y^2 + (12*t^2 - 12*t - 9)*y + (6*t^2 - 3*t - 18) ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:15:22 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) x = t*(y+x) 6*x^2 - 9*y*x - 3*x + 9*y^2 - 9*y - 18 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t*x + t*y ? ? %3 = 6*t^2*x^2 + ((12*t^2 - 9*t)*y - 3*t)*x + ((6*t^2 - 9*t + 9)*y^2 + (-3*t - 9)*y - 18) ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:09:28 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) y = (t*x + 1) 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t*x + 1 ? ? %3 = (9*t^2 - 9*t + 6)*x^2 + (9*t - 12)*x - 18 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:07:42 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) y = (t*x + t)/(x+1) 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ((9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18))/(x +1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t ? ? %3 = 6*x^2 + (-9*t - 3)*x + (9*t^2 - 9*t - 18) ? ? ? %4 = ((9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18))/(x + 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:07:21 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) y = (t*x + t) 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ((9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18))/(x +1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t*x + t ? %3 = (9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18) ? ? ? %4 = ((9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18))/(x + 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:05:39 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) y = (t*x + t) 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t*x + t ? %3 = (9*t^2 - 9*t + 6)*x^2 + (18*t^2 - 18*t - 3)*x + (9*t^2 - 9*t - 18) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:04:40 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) y = (t*x - t) 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ((9*t^2 - 9*t + 6)*x^2 + (-18*t^2 - 3)*x + (9*t^2 + 9*t - 18))/(x +1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t*x - t ? %3 = (9*t^2 - 9*t + 6)*x^2 + (-18*t^2 - 3)*x + (9*t^2 + 9*t - 18) ? ? ? %4 = ((9*t^2 - 9*t + 6)*x^2 + (-18*t^2 - 3)*x + (9*t^2 + 9*t - 18))/(x + 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:03:16 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) y = (t*x - t) 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = t*x - t ? %3 = (9*t^2 - 9*t + 6)*x^2 + (-18*t^2 - 3)*x + (9*t^2 + 9*t - 18) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 14:02:18 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) y = (tx - t) 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? ? %2 = tx - t ? %3 = 6*x^2 + (-9*tx + (9*t - 3))*x + (9*tx^2 + (-18*t - 9)*tx + (9*t^2 + 9*t - 18)) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 13:49:26 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) 81 - 4*6*(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? %2 = -135 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 13:48:40 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) 81 - 4*6*(-3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? %2 = 153 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 13:47:28 2006 Input: //x = 3 //y = 1 (x - 2*y - 2)*( x - y +2) + (1/4)*( -2*x - y -1)*(-1*x - y +2) 81 - 4*6*(-3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 3/2*x^2 + (-9/4*y - 3/4)*x + (9/4*y^2 - 9/4*y - 9/2) ? ? %2 = 153 ? Goodbye! Errors/timing (if any): *** unexpected character: //x=3 ^----- *** unexpected character: //y=1 ^----- Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 13:47:12 2006 Input: //x = 3 //y = 1 (x - 2*y - 2)*( x - y +2) + c*( -2*x - y -1)*(-1*x - y +2) 81 - 4*6*(-3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = (2*c + 1)*x^2 + ((3*c - 3)*y - 3*c)*x + ((c + 2)*y^2 + (-c - 2)*y + (-2*c - 4)) ? ? %2 = 153 ? Goodbye! Errors/timing (if any): *** unexpected character: //x=3 ^----- *** unexpected character: //y=1 ^----- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 13:46:35 2006 Input: x = 3 y = 1 (x - 2*y - 2)*( x - y +2) + c*( -2*x - y -1)*(-1*x - y +2) 81 - 4*6*(-3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? %2 = 1 ? ? %3 = 16*c - 4 ? ? %4 = 153 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 13:43:38 2006 Input: (x - 2*y - 2)*( x - y +2) + 1/4*(y + 2*x +1)*(y+x-2) 81 - 4*6*(-3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3/2*x^2 + (-9/4*y - 3/4)*x + (9/4*y^2 - 9/4*y - 9/2) ? ? %2 = 153 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 13:43:12 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) 81 - 4*6*(-3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? ? %2 = 153 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 13:42:19 2006 Input: 4*(x - 2*y - 2)*( x - y +2) + (y + 2*x +1)*(y+x-2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6*x^2 + (-9*y - 3)*x + (9*y^2 - 9*y - 18) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 13:42:05 2006 Input: 4*(x - 2*y - 2)( x - y +2) + (y + 2*x +1)(y+x-2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x + (y - 2) ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (x-y+2)+(y+2*x+1)(y+x-2). Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '65.64.1' ************** PARI ***************** Host 65.64.103.23 (65.64.103.23) Time: Fri Jul 21 12:55:57 2006 Input: 6+2+1+9+7= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 6+2+1+9+7= ^- Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.88 (68.142.249.88) Time: Fri Jul 21 11:08:16 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.087s user 0m0.005s sys 0m0.010s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:58:15 2006 Input: //a3 = 1 36/84 t = 2 a0 = 3/7 a1 = -9/2*a0 a2 = 1 - 27*a0 - 8*(-9/2*a0) a3 = -29/2*a0 + 8 a4 = -7 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 3/7 ? %2 = 2 ? ? %3 = 3/7 ? %4 = -27/14 ? %5 = 34/7 ? %6 = 25/14 ? %7 = -7 ? %8 = 0 ? %9 = 0 ? %10 = 0 ? ? %11 = 480/7 ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:57:35 2006 Input: //a3 = 1 36/84 t = 2 //a0 = //a1 = -9/2*a0 a2 = 1 - 27*a0 - 8*(-9/2*a0) a3 = -29/2*a0 + 8 a4 = -7 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 3/7 ? %2 = 2 ? ? ? %3 = 9*a0 + 1 ? %4 = -29/2*a0 + 8 ? %5 = -7 ? %6 = 0 ? %7 = 0 ? %8 = 0 ? ? %9 = -36*a0 + 84 ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=-9/2*a0 ^----------------- Timing: real 0m0.036s user 0m0.009s sys 0m0.003s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:55:38 2006 Input: //a3 = 1 t = 2 //a0 = //a1 = -9/2*a0 a2 = 1 - 27*a0 - 8*(-9/2*a0) a3 = -29/2*a0 + 8 a4 = -7 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 2 ? ? ? %2 = 9*a0 + 1 ? %3 = -29/2*a0 + 8 ? %4 = -7 ? %5 = 0 ? %6 = 0 ? %7 = 0 ? ? %8 = -36*a0 + 84 ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=-9/2*a0 ^----------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:41:53 2006 Input: //a3 = 1 t = 1 //a0 = //a1 = -9/2*a0 a2 = 1 - 27*a0 - 8*(-9/2*a0) a3 = -29/2*a0 + 8 a4 = -7 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1 ? ? ? %2 = 9*a0 + 1 ? %3 = -29/2*a0 + 8 ? %4 = -7 ? %5 = 0 ? %6 = 0 ? %7 = 0 ? ? %8 = 16 ? ? ? ? %9 = 283/2*a0 + (27*a1 + 20) ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=-9/2*a0 ^----------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:36:39 2006 Input: //a3 = 1 t = 1 //a0 = //a1 = -9/2*a0 a2 = 1 - 27*a0 - 8*(-9/2*a0) //a3 = 0 a4 = -7 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1 ? ? ? %2 = 9*a0 + 1 ? ? %3 = -7 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = 29/2*a0 + (a3 + 8) ? ? ? ? %8 = 156*a0 + (a3 + (27*a1 + 12)) ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=-9/2*a0 ^----------------- *** unexpected character: //a3=0 ^------ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:35:29 2006 Input: //a3 = 1 t = 1 //a0 = //a1 = -9/2*a0 a2 = 1 - 27*a0 - 8*(-9/2*a0) //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1 ? ? ? %2 = 9*a0 + 1 ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = 29/2*a0 + (a3 + 8) ? ? %8 = 156*a0 + (a3 + (27*a1 + 12)) ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=-9/2*a0 ^----------------- *** unexpected character: //a3=0 ^------ Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:35:16 2006 Input: //a3 = 1 t = 1 //a0 = a1 = -9/2*a0 a2 = 1 - 27*a0 - 8*(-9/2*a0) //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1 ? ? ? %2 = 9*a0 + 1 ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = 29/2*a0 + (a3 + 8) ? ? %8 = 156*a0 + (a3 + (27*a1 + 12)) ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=a1=-9/2*a0 ^--------------- *** unexpected character: //a3=0 ^------ Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:34:42 2006 Input: //a3 = 1 t = 1 //a0 = a1 = -9/2*a0 a2 = 1 - 27*a0 - 8*(-9/2*a0) //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1 ? ? ? %2 = 9*a0 + 1 ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = 136*a0 + (27*a1 + (a3 + 8)) ? ? %8 = 156*a0 + (27*a1 + (a3 + 12)) ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=a1=-9/2*a0 ^--------------- *** unexpected character: //a3=0 ^------ Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:33:54 2006 Input: //a3 = 1 t = 1 //a0 = a1 = -9/2*a0 a2 = 1 - 27*a0 - 8*a1 //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + (-9/2*a0)*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1 ? ? ? %2 = -27*a0 + (-8*a1 + 1) ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = -547/2*a0 + (-64*a1 + (a3 + 8)) ? ? %8 = -276*a0 + (-69*a1 + (a3 + 12)) ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=a1=-9/2*a0 ^--------------- *** unexpected character: //a3=0 ^------ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:32:45 2006 Input: //a3 = 1 t = 1 //a0 = a1 = -9/2*a0 a2 = 1 - 27*a0 - 8*a1 //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1 ? ? ? %2 = -27*a0 + (-8*a1 + 1) ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = -152*a0 + (-37*a1 + (a3 + 8)) ? ? %8 = -276*a0 + (-69*a1 + (a3 + 12)) ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=a1=-9/2*a0 ^--------------- *** unexpected character: //a3=0 ^------ Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:32:00 2006 Input: //a3 = 1 t = 1 //a0 = a1 = (-9/2)*a0 a2 = 1 - 27*a0 - 8*a1 //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1 ? ? ? %2 = -27*a0 + (-8*a1 + 1) ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = -152*a0 + (-37*a1 + (a3 + 8)) ? ? %8 = -276*a0 + (-69*a1 + (a3 + 12)) ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=a1=(-9/2)*a0 ^----------------- *** unexpected character: //a3=0 ^------ Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:28:24 2006 Input: //a3 = 1 t = 0 //a0 = //a1 = 0 a2 = 1 - 27*a0 - 8*a1 //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 3*(1 - 27*a0 - 8*a1) *(t+1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 0 ? ? ? %2 = -27*a0 + (-8*a1 + 1) ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = 1 ? ? %8 = -54*a0 + (-12*a1 + 3) ? ? ? %9 = -81*a0 + (-24*a1 + 3) ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=0 ^----------- *** unexpected character: //a3=0 ^------ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:28:09 2006 Input: //a3 = 1 t = 0 //a0 = //a1 = 0 a2 = 1 - 27*a0 - 8*a1 //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 3*(1 - 27*a0 - 8a1) *(t+1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 0 ? ? ? %2 = -27*a0 + (-8*a1 + 1) ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = 1 ? ? %8 = -54*a0 + (-12*a1 + 3) ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=0 ^----------- *** unexpected character: //a3=0 ^------ *** expected character: ')' instead of: 3*(1-27*a0-8a1)*(t+1)^2 ^----------- Timing: real 0m0.032s user 0m0.007s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:27:42 2006 Input: //a3 = 1 t = 0 //a0 = //a1 = 0 a2 = 1 - 27a0 - 8a1 //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 3*(1 - 27a0 - 8a1) *(t+1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 0 ? ? ? %2 = a1 ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = 27*a0 + (8*a1 - 26) ? ? %8 = 27*a0 + (12*a1 - 78) ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=0 ^----------- *** Warning: unused characters: a0-8a1. *** unexpected character: //a3=0 ^------ *** expected character: ')' instead of: 3*(1-27a0-8a1)*(t+1)^2 ^--------------- Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:26:53 2006 Input: //a3 = 1 t = 0 //a0 = //a1 = 0 a2 = 1 - 27a0 - 8a1 //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 3*a2 *(t+1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 0 ? ? ? %2 = a1 ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = 27*a0 + (8*a1 - 26) ? ? %8 = 27*a0 + (12*a1 - 78) ? ? ? %9 = -78 ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=0 ^----------- *** Warning: unused characters: a0-8a1. *** unexpected character: //a3=0 ^------ Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:24:17 2006 Input: //a3 = 1 t = 0 //a0 = //a1 = 0 a2 = 1 - 27a0 - 8a1 //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 0 ? ? ? %2 = a1 ? ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? ? %7 = 27*a0 + (8*a1 - 26) ? ? %8 = 27*a0 + (12*a1 - 78) ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=0 ^----------- *** Warning: unused characters: a0-8a1. *** unexpected character: //a3=0 ^------ Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:23:32 2006 Input: //a3 = 1 t = 0 //a0 = //a1 = 0 //a2 = 0 //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 3*a0*(t+3)^2 + 3*a1*(t+2)^2 + 3*a2 *(t+1)^2 + a3*(t-0)^3 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 0 ? ? ? ? ? %2 = 0 ? %3 = 0 ? %4 = 0 ? %5 = 0 ? ? %6 = 27*a0 + (8*a1 + a2) ? ? %7 = 27*a0 + (12*a1 + 3*a2) ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=0 ^----------- *** unexpected character: //a2=0 ^------ *** unexpected character: //a3=0 ^------ Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:21:53 2006 Input: //a3 = 1 t = 0 //a0 = //a1 = 0 //a2 = 0 //a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 0 ? ? ? ? ? %2 = 0 ? %3 = 0 ? %4 = 0 ? %5 = 0 ? ? %6 = 27*a0 + (8*a1 + a2) ? ? %7 = a1 ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=1 ^------ *** unexpected character: //a0=//a1=0 ^----------- *** unexpected character: //a2=0 ^------ *** unexpected character: //a3=0 ^------ Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:20:35 2006 Input: a3 = 1 //a0 = a1 = 0 a2 = 0 a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 //a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? ? ? %2 = 0 ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? %7 = 0 ? ? %8 = (t^3 + 9*t^2 + 27*t + 27)*a0 + (a1*t^3 + 6*a1*t^2 + 12*a1*t + 8*a1) ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a0=a1=0 ^--------- *** unexpected character: //a1+a2*2*t+3*a3*t^2 ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Fri Jul 21 10:20:18 2006 Input: a3 = 1 a0 = 1 a1 = 0 a2 = 0 a3 = 0 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0*(t+3)^3 + a1*(t+2)^3 + a2 *(t+1)^3 + a3*(t-0)^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 //a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? ? %2 = 1 ? %3 = 0 ? %4 = 0 ? %5 = 0 ? %6 = 0 ? %7 = 0 ? %8 = 0 ? %9 = 0 ? ? %10 = t^3 + 9*t^2 + 27*t + 27 ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //a1+a2*2*t+3*a3*t^2 ^-------------------- Timing: real 0m0.071s user 0m0.005s sys 0m0.009s '24.179.' ************** PARI ***************** Host 24.179.14.186 (24.179.14.186) Time: Fri Jul 21 09:13:10 2006 Input: 21,478,350*33,780 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 21 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: ,478,350*33,780. Timing: real 0m0.053s user 0m0.005s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.132.102 (72.30.132.102) Time: Fri Jul 21 08:22:13 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '63.241.' ************** PARI ***************** Host 63.241.61.7 (63.241.61.7) Time: Fri Jul 21 05:39:51 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.023s sys 0m0.007s '139.179' ************** PARI ***************** Host 139.179.137.109 (139.179.137.109) Time: Fri Jul 21 05:23:09 2006 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.103.19 (72.30.103.19) Time: Fri Jul 21 02:23:36 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '206.127' ************** PARI ***************** Host 206.127.2.114 (206.127.2.114) Time: Fri Jul 21 01:41:12 2006 Input: (3x^3)-(x^2)-(15x)+5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: (3x^3)-(x^2)-(15x)+5 ^------------------ Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.127' ************** PARI ***************** Host 206.127.2.114 (206.127.2.114) Time: Fri Jul 21 01:40:50 2006 Input: (3x^3)-(x^2)-(15x)+5=0 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: (3x^3)-(x^2)-(15x)+5=0 ^-------------------- Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Fri Jul 21 01:03:33 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.024s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Fri Jul 21 00:25:34 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '72.30.1' ************** PARI ***************** Host 72.30.133.210 (72.30.133.210) Time: Thu Jul 20 23:26:18 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Thu Jul 20 22:35:55 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.047s user 0m0.005s sys 0m0.006s '72.30.9' ************** PARI ***************** Host 72.30.99.77 (72.30.99.77) Time: Thu Jul 20 21:56:02 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.111s user 0m0.010s sys 0m0.008s '69.231.' ************** PARI ***************** Host 69.231.67.105 (69.231.67.105) Time: Thu Jul 20 20:26:44 2006 Input: 79 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 79 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:49:12 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) Mod(a^e,n) Mod(a^(n+1),n) l=Mod(a^(h^2),n) Mod(l^a, n) Mod(l^a, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? %13 = Mod(52196, 57403) ? %14 = Mod(52196, 57403) ? %15 = Mod(17124, 57403) ? %16 = Mod(27399, 57403) ? %17 = Mod(136, 137) ? Goodbye! Errors/timing (if any): Timing: real 0m0.042s user 0m0.040s sys 0m0.002s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:49:00 2006 Input: p=37 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) Mod(a^e,n) Mod(a^(n+1),n) l=Mod(a^(h^2),n) Mod(l^a, n) Mod(l^a, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 419 ? %3 = 15503 ? %4 = 456 ? %5 = 382 ? %6 = 41 ? %7 = Mod(34, 37) ? %8 = Mod(34, 37) ? %9 = Mod(2809, 15503) ? %10 = Mod(4511, 15503) ? %11 = Mod(34, 37) ? %12 = Mod(34, 37) ? %13 = Mod(2024, 15503) ? %14 = Mod(2024, 15503) ? %15 = Mod(6186, 15503) ? %16 = Mod(6003, 15503) ? %17 = Mod(9, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.043s user 0m0.039s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:48:16 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) Mod(a^e,n) Mod(a^(n+1),n) l=Mod(a^(h^2),n) Mod(l^a, n) Mod(l^a, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? %13 = Mod(52196, 57403) ? %14 = Mod(52196, 57403) ? %15 = Mod(17124, 57403) ? %16 = Mod(27399, 57403) ? %17 = Mod(136, 137) ? Goodbye! Errors/timing (if any): Timing: real 0m0.043s user 0m0.037s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:47:37 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) Mod(a^e,n) Mod(a^(n+1),n) l=Mod(a^(h^2),n) Mod(a^l, n) Mod(a^l, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? %13 = Mod(52196, 57403) ? %14 = Mod(52196, 57403) ? %15 = Mod(17124, 57403) ? ? ? Goodbye! Errors/timing (if any): *** forbidden multiplication t_REAL * t_INTMOD. *** forbidden multiplication t_REAL * t_INTMOD. Timing: real 0m0.043s user 0m0.038s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:22:42 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) Mod(a^e,n) Mod(a^(n+1),n) l=Mod(a^(h^2),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? ? %13 = Mod(52196, 57403) ? %14 = Mod(52196, 57403) ? %15 = Mod(17124, 57403) ? Goodbye! Errors/timing (if any): Timing: real 0m0.042s user 0m0.036s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:22:31 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) l=Mod(a^e,n) Mod(a^(n+1),n) l=Mod(a^(h^2),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? ? %13 = Mod(52196, 57403) ? %14 = Mod(52196, 57403) ? %15 = Mod(17124, 57403) ? Goodbye! Errors/timing (if any): Timing: real 0m0.043s user 0m0.036s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:22:05 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) l=Mod(a^e,n) Mod(a^(n+1),n) Mod(a^((n-1)^2),n) Mod(a^(h^2),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? ? %13 = Mod(52196, 57403) ? %14 = Mod(52196, 57403) ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 16123 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m28.672s user 0m20.512s sys 0m0.522s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:21:52 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) l=Mod(a^e,n) Mod(a^(n+1),n) Mod(a^((n-1)^2),n) Mod(a^(h^2),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? ? %13 = Mod(52196, 57403) ? %14 = Mod(52196, 57403) ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 16119 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m28.936s user 0m20.461s sys 0m0.578s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:19:31 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) l=Mod(a^e,n) Mod(a^(n+1),n) Mod(a^(h^2),n) Mod(a^(h^2),p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? ? %13 = Mod(52196, 57403) ? %14 = Mod(52196, 57403) ? %15 = Mod(17124, 57403) ? %16 = Mod(136, 137) ? Goodbye! Errors/timing (if any): Timing: real 0m0.053s user 0m0.046s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:19:14 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) l=Mod(a^e,n) Mod(a^(n+1),n) Mod(m^(h^2),n) Mod(m^(h^2),p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? ? %13 = Mod(52196, 57403) ? %14 = Mod(52196, 57403) ? %15 = Mod(48362, 57403) ? %16 = Mod(1, 137) ? Goodbye! Errors/timing (if any): Timing: real 0m0.032s user 0m0.027s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:18:18 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) l=Mod(a^e,n) Mod(a^(n+1),n) Mod(m^h,n) Mod(m^h,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? ? %13 = Mod(52196, 57403) ? %14 = Mod(52196, 57403) ? %15 = Mod(15343, 57403) ? %16 = Mod(136, 137) ? Goodbye! Errors/timing (if any): Timing: real 0m0.050s user 0m0.028s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:15:26 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.020s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:14:39 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) Mod(que,n) Mod(m,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? %13 = Mod(28396, 57403) ? %14 = Mod(20998, 57403) ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.017s sys 0m0.009s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:14:17 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) que=Mod(a^h,n) m=Mod(a^(n-1),n) Mod(que,p) Mod(m,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? %11 = Mod(37, 137) ? %12 = Mod(37, 137) ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.019s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:13:44 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 Mod(a^h,p) Mod(a^(n-1),p) Mod(a^h,n) Mod(a^(n-1),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? %7 = Mod(37, 137) ? %8 = Mod(37, 137) ? %9 = Mod(28396, 57403) ? %10 = Mod(20998, 57403) ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.023s sys 0m0.002s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jul 20 19:13:30 2006 Input: p=137 q=419 n=p*q e=p+q h=q-p a=41 mod(a^h,p) mod(a^(n-1),p) mod(a^h,n) mod(a^(n-1),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 137 ? %2 = 419 ? %3 = 57403 ? %4 = 556 ? %5 = 282 ? %6 = 41 ? ? ? ? ? Goodbye! Errors/timing (if any): *** obsolete function: mod(a^h,p) ^---------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: mod(a^(n-1),p) ^-------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: mod(a^h,n) ^---------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: mod(a^(n-1),n) ^-------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.031s user 0m0.005s sys 0m0.006s '63.199.' ************** PARI ***************** Host 63.199.242.110 (63.199.242.110) Time: Thu Jul 20 17:40:11 2006 Input: 333^(1/6) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2.6327363651586554792281444498210712531 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '63.199.' ************** PARI ***************** Host 63.199.242.110 (63.199.242.110) Time: Thu Jul 20 17:39:46 2006 Input: 1.91293^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6.9999870156307569999999999999999999999 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '63.199.' ************** PARI ***************** Host 63.199.242.110 (63.199.242.110) Time: Thu Jul 20 17:39:25 2006 Input: 7^(1/3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1.9129311827723891011991168395487602829 ? Goodbye! Errors/timing (if any): Timing: real 0m0.087s user 0m0.005s sys 0m0.006s '68.73.1' ************** PARI ***************** Host 68.73.123.250 (68.73.123.250) Time: Thu Jul 20 15:13:36 2006 Input: 31 * 31 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 961 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Thu Jul 20 15:04:18 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.038s user 0m0.006s sys 0m0.006s '72.30.9' ************** PARI ***************** Host 72.30.98.35 (72.30.98.35) Time: Thu Jul 20 14:59:11 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.148s user 0m0.025s sys 0m0.008s '195.112' ************** PARI ***************** Host 195.112.44.172 (195.112.44.172) Time: Thu Jul 20 13:08:08 2006 Input: DirichletGroup(20) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: DirichletGroup(20) ^------------------ Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '138.162' ************** PARI ***************** Host 138.162.5.12 (138.162.5.12) Time: Thu Jul 20 09:33:53 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '208.54.' ************** PARI ***************** Host 208.54.94.73 (208.54.94.73) Time: Thu Jul 20 08:12:49 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.251.155 (68.142.251.155) Time: Thu Jul 20 06:24:49 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.010s sys 0m0.002s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Thu Jul 20 02:55:14 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.066s user 0m0.006s sys 0m0.009s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Thu Jul 20 02:43:21 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '129.217' ************** PARI ***************** Host 129.217.4.64 (129.217.4.64) Time: Thu Jul 20 02:13:25 2006 Input: 12000! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1201858406751094813215537862229413579273903778819871509781937698530038350660860169670917371878152953448126096270928257528762029090464991491076442906109525418045467519792725373198536354301858453253846165195884935721164436213505153722760122056793086146140905433159473067748531674800236644754708239931069034241296663953338927096775251375029665424008771069634452986894902622957878834581870518862710573293627105221942614088527635926932398344032949842161644969853918449341240708119783886434362219851357290562966666105006287400515466950853748185151637476631407136164092451450025703570632794085427076382136807103101966488567634804715767206079288231734866173361080038077977602168094101167976673856833209964261177857055872793240166881327686111541877999904012889743561036361655983541476096196638459905407459395925871680045369295198360303076468230606297056864947387260231992171519443686692238802735289613296859967770839283263403806385209112168372142293253662281712714495704459907641566305808111352873610453046172363915674399945257285698908699657142585503488495196837565280149793042480811970338804942507273426741834641076044494523665417337436990883431542844969718525209724183471945174759947180279586329694782666848422167638419490229463830545367926262011688150634911635610939838446115823846213359251061555047211817135057012771136047458679916266381752610547815807579377682191473292496800208703700515673596366788785158748151866312551170360471417673866041244849690269491617684455163010206719285101844946768817465854897763361742331376939693720799411394822064175584141397983128027579566456816219796068779500188112072489098109919082756265307945040329208001984233420336499058141509467427088478556323722870712482892044523282899294135422935244125676123349312017047923070858868902817791302059265230569604798628355893345570295954687258691289343421370547561835601212354894510113855172164223742887955106787739330026149589382135847175306705548238306702310024707479558036404066282278669025905150070262103680183123694185414659339459748832669124924280245365198626654805750377769079111161268905199670388519325457357799002112841179008342483409618850135047574281110795388595683003077802351065244551300757071706050356977798620602479359144117344123774225069550262059126922141853452194569248510850905986323885856892760864357500075373968548984931058807388261363117077893331085322598490397497246191300447394799013063388036987931085468278826236511216212942874265386988220673529482541533633235535431545571452620978548092772518060236716644822529963314595647273386361565894921793481157813682928823947226944897617211730724928507616597083945381726055844938261571369510797612966640393069503548216213079022638787122859347632343871969616838286298140195222789325898866514950645873310283352239785750676185784532017718919374610494867137021634811726883381821571548639992187486546956814724833222136466745526632234485914231245030406482619752076076954125629297107274899730116441138406955253196139029162811650331688727340149451116062073149640127650336308177330022521701054222470762226042541696968100263888044022668931744100022913733213976440275222168948266084762525618856825000145165748358360040257782942254414393986427281116537307737738353209993[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.164s user 0m0.102s sys 0m0.054s '129.217' ************** PARI ***************** Host 129.217.4.64 (129.217.4.64) Time: Thu Jul 20 02:13:10 2006 Input: 1200! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 63507890863456767124026223135865363993920361927048401849732641593094118304334664838518489279761202858110442656198961423888337785958374054395875090008179394602121729048755527506222388620438398012556615061940909904115015164483186340282667999681601237310950712039020066375755766076440811303940538840103890741951917564190561275396873204122937083746098640414588850116107225675520412584415359155103495655208534054658149146203739758027326003354866456731097561086620889903717246818807490131678158299401901235057514328881677204150054888001843870188616756694468379677033228639349974219800691760236674808772459147849761319772233349285258185354881462706759016416844508026593468378544952254302304068325633905800617846092173316334920423976973219453332902616477256306327233355305287468380745909208415980513577159243876582648875144838454034618802839634184994308400967856236366107563273185702779295861081100580569890291839403080692152562549750464518941296615589072961901445867101610266912853288908304184351248084449986727837714164724886934713403840928394071581648559037175552279054765268191336562999918827853842984694855922999162907679561931097787771324637893456823082524179018246504955405803121771121360752264414781039718455098118457351815525441962553663917394824907930942411732997508709279776658345871568600666174624864566227235992187598660130953640936345350873339744682415089563501119516442999676532779307108492176925439731860347372511112433604790992759325197681339726349322054878255119874625965850196940660648685990671210212572225564228346159053754713667934756177880507837712524591347066833930606771513277248914447108453842428044821209156242191481316239948456314071437111282270756494813443336707372525017024678559199590515860360962136467183581351799081925904581530470013515629221769984825958416224944982867113744499809912183809641523923237883957287541972186804232110652653006828947123647231393100716154785438044926596489481061404444949958850342025214038700582411675847296195285368313134928856220726124462351334098415059073275239953735718425086123827271757497468773885713767925771130546617686545287963633612898691413349119011210341661317374809835898724194978360650558823413986166888783608735534361048197825992486540004672367499044204531085976637277941222039312514997381320707709813267213844400528265917241905520030567187527121305903232698469502319828288497642071789544559470672876896682816986176852553613912123976135208540633191577134212923764719883260091745561140753211368159375154389149276613870478944559132118639123292629448861220166692668795869998815536697843168702435154762819119055700781916899847331952260368608062686678197902264191722301178373738543720223581116366378070649868986724225640819288848872888236573440404740650405057575066492961346462735749115329710082527101393654163731209311139319445720303577449977552535888706315264756010489543514382828926003274237925093166062460951592960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '129.217' ************** PARI ***************** Host 129.217.4.64 (129.217.4.64) Time: Thu Jul 20 02:12:39 2006 Input: 120! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6689502913449127057588118054090372586752746333138029810295671352301633557244962989366874165271984981308157637893214090552534408589408121859898481114389650005964960521256960000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.034s user 0m0.008s sys 0m0.003s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Wed Jul 19 22:37:04 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.081s user 0m0.004s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Wed Jul 19 21:54:32 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.048s user 0m0.024s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 21:02:50 2006 Input: a3 = 1 t = 4 a0 = 1 a1 = -3 a2 = 2 - a3 a3 = 1 a4 = -4*a3 - 3 a5 = 14*a3 + 14 a6 = -52*a3 - 52 a7 = 194*a3 + 195 a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? %2 = 4 ? ? %3 = 1 ? %4 = -3 ? %5 = 1 ? %6 = 1 ? %7 = -7 ? %8 = 28 ? %9 = -104 ? %10 = 389 ? ? %11 = 0 ? ? %12 = -112 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.003s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 21:02:23 2006 Input: a3 = 1 t = 3 a0 = 1 a1 = -3 a2 = 2 - a3 a3 = 1 a4 = -4*a3 - 3 a5 = 14*a3 + 14 a6 = -52*a3 - 52 a7 = 0 a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? %2 = 3 ? ? %3 = 1 ? %4 = -3 ? %5 = 1 ? %6 = 1 ? %7 = -7 ? %8 = 28 ? %9 = -104 ? %10 = 0 ? ? %11 = 0 ? ? %12 = 30 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 21:01:31 2006 Input: a3 = 1 t = 2 a0 = 1 a1 = -3 a2 = 2 - a3 a3 = 1 a4 = -4*a3 - 3 a5 = 14*a3 + 14 a6 = -52*a3 - 52 a7 = 0 a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? %2 = 2 ? ? %3 = 1 ? %4 = -3 ? %5 = 1 ? %6 = 1 ? %7 = -7 ? %8 = 28 ? %9 = -104 ? %10 = 0 ? ? %11 = 104 ? ? %12 = -320 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 21:00:12 2006 Input: a3 = 1 t = 2 a0 = 1 a1 = -3 a2 = 2 - a3 a3 = 1 a4 = -4*a3 - 3 a5 = 14*a3 + 14 a6 = 0 a7 = 0 a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? %2 = 2 ? ? %3 = 1 ? %4 = -3 ? %5 = 1 ? %6 = 1 ? %7 = -7 ? %8 = 28 ? %9 = 0 ? %10 = 0 ? ? %11 = 0 ? ? %12 = -8 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:59:33 2006 Input: a3 = 1 t = 1 a0 = 1 a1 = -3 a2 = 2 - a3 a3 = 1 a4 = -4*a3 - 3 a5 = 0 a6 = 0 a7 = 0 a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? %2 = 1 ? ? %3 = 1 ? %4 = -3 ? %5 = 1 ? %6 = 1 ? %7 = -7 ? %8 = 0 ? %9 = 0 ? %10 = 0 ? ? %11 = 0 ? ? %12 = 2 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:58:58 2006 Input: a3 = 1 t = 0 a0 = 1 a1 = -3 a2 = 2 - a3 a3 = 1 a4 = 0 a5 = 0 a6 = 0 a7 = 0 a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? %2 = 0 ? ? %3 = 1 ? %4 = -3 ? %5 = 1 ? %6 = 1 ? %7 = 0 ? %8 = 0 ? %9 = 0 ? %10 = 0 ? ? %11 = 1 ? ? %12 = -3 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.009s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:43:17 2006 Input: a3 = 1 a0 = 1 a1 = -3 a2 = 2 - a3 a3 = 1 a4 = -4*a3 - 3 a5 = 14*a3 + 14 a6 = -52*a3 - 52 a7 = 194*a3 + 195 a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? ? %2 = 1 ? %3 = -3 ? %4 = 1 ? %5 = 1 ? %6 = -7 ? %7 = 28 ? %8 = -104 ? %9 = 389 ? ? %10 = 307*t^3 - 3878*t^2 + 16176*t - 22304 ? ? %11 = 921*t^2 - 7756*t + 16176 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:42:56 2006 Input: a3 = 1 a0 = 1 a1 = -3 a2 = 2 - a3 a4 = -4*a3 - 3 a5 = 14*a3 + 14 a6 = -52*a3 - 52 a7 = 194*a3 + 195 a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? ? %2 = 1 ? %3 = -3 ? %4 = 1 ? %5 = -7 ? %6 = 28 ? %7 = -104 ? %8 = 389 ? ? %9 = 307*t^3 - 3878*t^2 + 16176*t - 22304 ? ? %10 = 921*t^2 - 7756*t + 16176 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:41:56 2006 Input: //a3 = -206/209 t = 5 a0 = 1 a1 = -3 a2 = 2 - a3 a4 = -4*a3 - 3 a5 = 14*a3 + 14 a6 = -52*a3 - 52 a7 = 194*a3 + 195 a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 -3 + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +(-52*a3-52)*(t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 5 ? %2 = 1 ? %3 = -3 ? %4 = -a3 + 2 ? %5 = -4*a3 - 3 ? %6 = 14*a3 + 14 ? %7 = -52*a3 - 52 ? %8 = 194*a3 + 195 ? ? %9 = 1 ? ? %10 = 209*a3 + 212 ? ? ? %11 = 12 ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=-206/209 ^------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:41:30 2006 Input: //a3 = -206/209 a0 = 1 a1 = -3 a2 = 2 - a3 a4 = -4*a3 - 3 a5 = 14*a3 + 14 a6 = -52*a3 - 52 a7 = 194*a3 + 195 a0 + a1*t + a2 * t^2 + a3* t^3 + a4*(t-1)^3 + a5*(t-2)^3 + a6*(t-3)^3 + a7*(t-4)^3 a1 + a2 * 2*t + 3*a3* t^2 + 3*a4*(t-1)^2 + 3*a5*(t-2)^2 + 3*a6*(t-3)^2 + 3*a7*(t-4)^2 -3 + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +(-52*a3-52)*(t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1 ? %2 = -3 ? %3 = -a3 + 2 ? %4 = -4*a3 - 3 ? %5 = 14*a3 + 14 ? %6 = -52*a3 - 52 ? %7 = 194*a3 + 195 ? ? %8 = (153*t^3 - 1933*t^2 + 8064*t - 11120)*a3 + (154*t^3 - 1945*t^2 + 8112*t - 11184) ? ? %9 = (459*t^2 - 3866*t + 8064)*a3 + (462*t^2 - 3890*t + 8112) ? ? ? %10 = (153*t^3 - 1933*t^2 + 8064*t - 11120)*a3 + (154*t^3 - 1945*t^2 + 8115*t - 11188) ? Goodbye! Errors/timing (if any): *** unexpected character: //a3=-206/209 ^------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:34:17 2006 Input: a3 = -206/209 - 3 + 2*(2 - a3) * t + 3*a3* t^2 + 3*(-4*a3-3)*(t-1)^2 + 3*(14*a3+14)*(t-2)^2 +3*(-52*a3-52)*(t-3)^2 + 3*(194*a3+194)*(t-4)^2 (3-209)/209 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -206/209 ? %2 = 1377/209*t^2 - 11598/209*t + 24192/209 ? ? ? %3 = -206/209 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:32:48 2006 Input: t = 5 - 3 + 2*(2 - a3) * t + 3*a3* t^2 + 3*(-4*a3-3)*(t-1)^2 + 3*(14*a3+14)*(t-2)^2 +3*(-52*a3-52)*(t-3)^2 + 3*(194*a3+194)*(t-4)^2 (3-209)/209 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? %2 = 209*a3 + 209 ? ? ? %3 = -206/209 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:30:45 2006 Input: t = 5 - 3 + 2*(2 - a3) * t + 3*a3* t^2 + 3*(-4*a3-3)*(t-1)^2 + 3*(14*a3+14)*(t-2)^2 +3*(-52*a3-52)*(t-3)^2 + 3*(194*a3+194)*(t-4)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? %2 = 209*a3 + 209 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:28:31 2006 Input: t = 5 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +(-52*a3-52)*(t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? %2 = -194*a3 + (a7 - 194) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:20:36 2006 Input: t = 5 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +(-51*a3-52)*(t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? %2 = -186*a3 + (a7 - 194) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:20:14 2006 Input: t = 4 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +(-51*a3-52)*(t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = a3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '69.180.' ************** PARI ***************** Host 69.180.5.21 (69.180.5.21) Time: Wed Jul 19 20:20:09 2006 Input: 251 - 121 + 441 - 340 + 130 - 113 + 409 - 253 + 130 - 181 + 297 - 149 + 081 - 088 + 467 - 059 + 306 - 229 + 345 - 351 + 117 - 047 + 353 - 216 + 401 - 147 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1434 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:15:28 2006 Input: t = 4 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (14*a3+14)*(t-2)^3 +a6*(t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = 52*a3 + (a6 + 52) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:14:36 2006 Input: t = 4 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (a5)*(t-2)^3 +a6*(t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = -60*a3 + (8*a5 + (a6 - 60)) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:07:03 2006 Input: t = 3 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3-3)*(t-1)^3 + (a5)*(t-2)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? %2 = -14*a3 + (a5 - 14) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:04:00 2006 Input: t = 4 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3+3)*(t-1)^3 + (14*a3-34)*(t-2)^3 + (-52*a3-170) * (t-3)^3 + a7*(t-4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = -340 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 20:02:36 2006 Input: t = 4 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3+3)*(t-1)^3 + (14*a3-34)*(t-2)^3 + a6 * (t-3)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = 52*a3 + (a6 - 170) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 19:59:25 2006 Input: t = 3 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + (-4*a3+3)*(t-1)^3 + a5*(t-2)^3 + a6 * (t-3)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? %2 = -14*a3 + (a5 + 34) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 19:52:07 2006 Input: t = 2 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + a4*(t-1)^3 a3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2 ? %2 = 4*a3 + (a4 + 3) ? ? %3 = a3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 19:51:52 2006 Input: t = 2 1 - 3*t + (2 - a3) * t^2 + a3* t^3 + a4*(t-1)^3 + Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2 ? ? Goodbye! Errors/timing (if any): *** unexpected character: ...3)*t^2+a3*t^3+a4*(t-1)^3+ ^ Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 19:46:22 2006 Input: t = 5 1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4*a3)*(t-1)^3 + (14*a3 + 116)*(t-2)^3 + (-52*a3 - 610)*(t -3)^3 + a7*(t- 4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? %2 = -194*a3 + (a7 - 2438) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 19:46:13 2006 Input: t = 4 1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4*a3)*(t-1)^3 + (14*a3 + 116)*(t-2)^3 + (-52*a3 - 610)*(t -3)^3 + a7*(t- 4)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 19:38:10 2006 Input: t = 4 1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4*a3)*(t-1)^3 + (14*a3 + 116)*(t-2)^3 + a6*(t -3)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = 52*a3 + (a6 + 610) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 19:31:35 2006 Input: t = 3 1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4*a3)*(t-1)^3 + (a5)*(t-2)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? %2 = -14*a3 + (a5 - 116) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 19:31:03 2006 Input: t = 3 1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4*a3)*(t-1)^3 + (86*a3+44)*(t-2)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? %2 = 72*a3 - 72 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 19:09:01 2006 Input: t = 3 1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4)*a3*(t-1)^3 + a5*(t-2)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? %2 = -86*a3 + (a5 - 44) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 19:08:43 2006 Input: 1 - 3*t+ ( -4 - a3) * t^2 + a3* t^3 + (-9-4)*a3*(t-1)^3 + a5*(t-2)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (-12*a3 + a5)*t^3 + (38*a3 + (-6*a5 - 4))*t^2 + (-39*a3 + (12*a5 - 3))*t + (13*a3 + (-8*a5 + 1)) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 18:40:54 2006 Input: (t-1)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = t^3 - 3*t^2 + 3*t - 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.051s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 18:40:46 2006 Input: (t-1)^-1 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1/(t - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 18:40:28 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Wed Jul 19 17:53:59 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.048s user 0m0.010s sys 0m0.002s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Wed Jul 19 17:45:47 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '217.191' ************** PARI ***************** Host 217.191.224.235 (217.191.224.235) Time: Wed Jul 19 17:17:33 2006 Input: 2+3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '217.191' ************** PARI ***************** Host 217.191.224.235 (217.191.224.235) Time: Wed Jul 19 17:17:23 2006 Input: 2+pi Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = pi + 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '217.191' ************** PARI ***************** Host 217.191.224.235 (217.191.224.235) Time: Wed Jul 19 17:17:05 2006 Input: e Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = e ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '217.191' ************** PARI ***************** Host 217.191.224.235 (217.191.224.235) Time: Wed Jul 19 17:16:47 2006 Input: n 100 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = n100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '217.191' ************** PARI ***************** Host 217.191.224.235 (217.191.224.235) Time: Wed Jul 19 17:16:06 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 16:20:46 2006 Input: g = [ 1, -1, 0, 3, -2] m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28, 0, 2,0, 2 ] q = m^(-1) g*q Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, -1, 0, 3, -2] ? ? %2 = [0 2 0 0 0] [1 -1 1 1 4] [2 0 0 -1/2 1] [-2 1 1 1/4 1] [-28 0 2 0 2] ? ? %3 = [-11/222 -1/111 1/37 10/111 -3/74] [1/2 0 0 0 0] [-109/111 -40/111 3/37 178/111 -9/74] [14/37 16/37 -48/37 -12/37 -2/37] [32/111 26/111 11/37 -38/111 2/37] ? ? %4 = [1/111, 91/111, -165/37, -22/111, -23/74] ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 16:20:40 2006 Input: g = [ 1, -1, 0, 3, -2] m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28, 0, 2,0, 2 ] q = m^(-1) g*g Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, -1, 0, 3, -2] ? ? %2 = [0 2 0 0 0] [1 -1 1 1 4] [2 0 0 -1/2 1] [-2 1 1 1/4 1] [-28 0 2 0 2] ? ? %3 = [-11/222 -1/111 1/37 10/111 -3/74] [1/2 0 0 0 0] [-109/111 -40/111 3/37 178/111 -9/74] [14/37 16/37 -48/37 -12/37 -2/37] [32/111 26/111 11/37 -38/111 2/37] ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** forbidden multiplication t_VEC * t_VEC. Timing: real 0m0.023s user 0m0.007s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 16:18:32 2006 Input: g = [ 1, -1, 0, 3, -2] m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28, 0, 2,0, 2 ] m^(-1)*g Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, -1, 0, 3, -2] ? ? %2 = [0 2 0 0 0] [1 -1 1 1 4] [2 0 0 -1/2 1] [-2 1 1 1/4 1] [-28 0 2 0 2] ? ? ? ? Goodbye! Errors/timing (if any): *** impossible multiplication t_MAT * t_VEC. Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 16:14:35 2006 Input: m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28, 0, 2,0, 2 ] m^(-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0 2 0 0 0] [1 -1 1 1 4] [2 0 0 -1/2 1] [-2 1 1 1/4 1] [-28 0 2 0 2] ? ? %2 = [-11/222 -1/111 1/37 10/111 -3/74] [1/2 0 0 0 0] [-109/111 -40/111 3/37 178/111 -9/74] [14/37 16/37 -48/37 -12/37 -2/37] [32/111 26/111 11/37 -38/111 2/37] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.049s user 0m0.007s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 16:14:18 2006 Input: m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28 0, 2, 0, 2 ] m^(-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1/m ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...1;-2,1,1,1/4,1;-280,2,0,2] ^- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 16:14:02 2006 Input: m = [ 0, 2, 0, 0, 0;1,-1, 1, 1, 4;2, 0, 0, -1/2, 1;-2, 1,1, 1/4, 1;-28 0, 2, 0, 2] m^(-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1/m ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...1;-2,1,1,1/4,1;-280,2,0,2] ^- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 16:13:24 2006 Input: m = [ 0, 2, 0, 0, 0; 1,-1, 1, 1, 4; 2, 0, 0, -1/2, 1; -2, 1,1, 1/4, 1; -28 0, 2, 0, 2] m^(-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %4 = -280 ? ? %5 = 1/m ? ? Goodbye! Errors/timing (if any): *** unexpected character: m=[0,2,0,0,0; ^ *** Warning: unused characters: ,-1,1,1,4;. *** Warning: unused characters: ,0,0,-1/2,1;. *** Warning: unused characters: ,1,1,1/4,1;. *** Warning: unused characters: ,2,0,2]. Timing: real 0m0.059s user 0m0.006s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 16:09:01 2006 Input: m = [ 0, 2, 0, 0, 0; 1,-1, 1, 1, 4;] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: m=[0,2,0,0,0;1,-1,1,1,4;] ^- Timing: real 0m0.012s user 0m0.008s sys 0m0.002s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 19 16:07:47 2006 Input: m = [ 0, 2, 0, 0, 0; 1,-1, 1, 1, 4] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1 ? ? Goodbye! Errors/timing (if any): *** unexpected character: m=[0,2,0,0,0; ^ *** Warning: unused characters: ,-1,1,1,4]. Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '201.34.' ************** PARI ***************** Host 201.34.91.89 (201.34.91.89) Time: Wed Jul 19 13:08:24 2006 Input: b=1 c=2 a^2=b^2+c^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 2 ? ? Goodbye! Errors/timing (if any): *** unexpected character: a^2=b^2+c^2 ^-------- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.110.15 (72.30.110.15) Time: Wed Jul 19 11:35:23 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '212.128' ************** PARI ***************** Host 212.128.170.213 (212.128.170.213) Time: Wed Jul 19 08:40:59 2006 Input: exp(1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2.7182818284590452353602874713526624978 ? Goodbye! Errors/timing (if any): Timing: real 0m0.028s user 0m0.006s sys 0m0.007s '212.117' ************** PARI ***************** Host 212.117.127.210 (212.117.127.210) Time: Wed Jul 19 06:58:48 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.035s user 0m0.008s sys 0m0.005s '203.160' ************** PARI ***************** Host 203.160.1.47 (203.160.1.47) Time: Wed Jul 19 06:58:31 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '203.160' ************** PARI ***************** Host 203.160.1.47 (203.160.1.47) Time: Wed Jul 19 06:58:25 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '212.117' ************** PARI ***************** Host 212.117.127.210 (212.117.127.210) Time: Wed Jul 19 06:53:16 2006 Input: 9*(3/2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 27/2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Wed Jul 19 04:20:15 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.024s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:45:33 2006 Input: E = ellinit([0,0,0,5,10]); E.disc E.j Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = -51200 ? %3 = 270 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:40:02 2006 Input: E = ellinit([0,0,0,5,10]); E.disc E.b2 E.b4 E.b6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = -51200 ? %3 = 0 ? %4 = 10 ? %5 = 40 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.003s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:30:17 2006 Input: E = ellinit([0,0,0,5,10]); E.disc Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = -51200 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.006s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:29:51 2006 Input: E = ellinit([0,0,0,5,10]); E.delta Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** unknown member function: E.delta ^----- Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:20:59 2006 Input: E = ellinit([0,0,0,5,10]); ellbil(E, [1,4], [1,4]) ellan(E,20) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269291 ? %3 = [1, 0, -3, 0, 0, 0, 2, 0, 6, 0, -1, 0, -4, 0, 0, 0, -5, 0, -1, 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:16:04 2006 Input: E = ellinit([0,0,0,5,10]); ellbil(E, [1,4], [1,4]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 0.12837506294605086906217592378339269291 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:15:15 2006 Input: E = ellinit([0,0,0,5,10]); ellbil(E, (1,4), (1,4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ellbil(E,(1,4),(1,4)) ^---------- Timing: real 0m0.014s user 0m0.010s sys 0m0.004s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:14:13 2006 Input: E = ellinit([0,0,0,5,10]); P = (1,4); ellbil(E, P, P) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: P=(1,4); ^---- *** ellbil: bad argument for an elliptic curve related function Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:12:19 2006 Input: E = ellinit([0,0,0,5,10]); ellminimalmodel(E) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [0, 0, 0, 5, 10, 0, 10, 40, -25, -240, -8640, -51200, 270, [-1.4233183447530720839637549246282910396, 0.71165917237653604198187746231414551980 - 2.5533069405935058319433718225821719402*I, 0.71165917237653604198187746231414551980 + 2.5533069405935058319433718225821719402*I]~, 2.5292107620580267572591609417786962829, -1.2646053810290133786295804708893481415 + 0.90405376585134445817384638151563273959*I, -1.8391281983676645395951280657774160868 + 7.792038177385329417 E-39*I, 0.91956409918383226979756403288870804342 - 1.8995109064371664100222636546513616911*I, 2.2865425140703078042026374234384580468] ? Goodbye! Errors/timing (if any): Timing: real 0m0.034s user 0m0.007s sys 0m0.005s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:10:58 2006 Input: E = ellinit([0,0,0,5,10]); ellgenerators(E); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: ellgenerators(E); ^- Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:10:47 2006 Input: E = ellinit([0,0,0,5,10]); ellgenerators(E) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: ellgenerators(E) ^ Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:09:18 2006 Input: E = ellinit([0,0,0,5,10]); ellan(E,20) ellgenerators(E) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [1, 0, -3, 0, 0, 0, 2, 0, 6, 0, -1, 0, -4, 0, 0, 0, -5, 0, -1, 0] ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: ellgenerators(E) ^ Timing: real 0m0.017s user 0m0.006s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:03:15 2006 Input: E = ellinit([0,0,0,5,10]); ellan(E,20) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [1, 0, -3, 0, 0, 0, 2, 0, 6, 0, -1, 0, -4, 0, 0, 0, -5, 0, -1, 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:02:32 2006 Input: E = ellinit([0,0,0,5,10]); ellak(E,1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:02:27 2006 Input: E = ellinit([0,0,0,5,10]); ellak(E,1); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:00:48 2006 Input: E = ellinit([0,0,0,5,10]); E.a4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 03:00:29 2006 Input: E = ellinit([0,0,0,5,10]); E.a4; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 02:59:58 2006 Input: E = ellinit([0,0,0,5,10]); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.073s user 0m0.009s sys 0m0.006s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 02:59:46 2006 Input: E = ellinit([0,0,05,10]); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** ellinit: bad argument for an elliptic curve related function Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '141.20.' ************** PARI ***************** Host 141.20.50.145 (141.20.50.145) Time: Wed Jul 19 02:59:24 2006 Input: E = ellinit([0,0,05,10]); E.ellminimalmodel; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** ellinit: bad argument for an elliptic curve related function *** unknown member function: E.ellminimalmodel; ^---------------- Timing: real 0m0.046s user 0m0.004s sys 0m0.007s '72.30.9' ************** PARI ***************** Host 72.30.98.145 (72.30.98.145) Time: Wed Jul 19 02:54:28 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.044s user 0m0.004s sys 0m0.008s '68.9.91' ************** PARI ***************** Host 68.9.91.53 (68.9.91.53) Time: Tue Jul 18 18:48:07 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '68.124.' ************** PARI ***************** Host 68.124.160.207 (68.124.160.207) Time: Tue Jul 18 17:57:09 2006 Input: negative nine minus negative forty eight Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = negativenineminusnegativefortyeight ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '137.30.' ************** PARI ***************** Host 137.30.109.12 (137.30.109.12) Time: Tue Jul 18 16:01:34 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Tue Jul 18 14:56:35 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '67.51.1' ************** PARI ***************** Host 67.51.134.174 (67.51.134.174) Time: Tue Jul 18 14:31:34 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Tue Jul 18 14:12:40 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Tue Jul 18 14:06:47 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.036s user 0m0.005s sys 0m0.007s '155.229' ************** PARI ***************** Host 155.229.77.1 (155.229.77.1) Time: Tue Jul 18 13:55:44 2006 Input: x+5 ____ x+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x + 5 ? ? %2 = x + 2 ? Goodbye! Errors/timing (if any): *** unexpected character: ____ ^---- Timing: real 0m0.031s user 0m0.007s sys 0m0.006s '68.189.' ************** PARI ***************** Host 68.189.248.100 (68.189.248.100) Time: Tue Jul 18 12:36:02 2006 Input: leg8 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = leg8 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '68.189.' ************** PARI ***************** Host 68.189.248.100 (68.189.248.100) Time: Tue Jul 18 12:34:35 2006 Input: leg8 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = leg8 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '68.189.' ************** PARI ***************** Host 68.189.248.100 (68.189.248.100) Time: Tue Jul 18 12:33:19 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.189.' ************** PARI ***************** Host 68.189.248.100 (68.189.248.100) Time: Tue Jul 18 12:33:16 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.88 (68.142.249.88) Time: Tue Jul 18 11:39:33 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.143s user 0m0.005s sys 0m0.008s '72.30.2' ************** PARI ***************** Host 72.30.226.223 (72.30.226.223) Time: Tue Jul 18 11:13:29 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.066s user 0m0.006s sys 0m0.006s '65.106.' ************** PARI ***************** Host 65.106.182.67 (65.106.182.67) Time: Tue Jul 18 09:37:10 2006 Input: 3+4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '65.106.' ************** PARI ***************** Host 65.106.182.67 (65.106.182.67) Time: Tue Jul 18 09:37:00 2006 Input: 3+4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '72.30.1' ************** PARI ***************** Host 72.30.129.123 (72.30.129.123) Time: Tue Jul 18 03:36:50 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.008s sys 0m0.003s '68.142.' ************** PARI ***************** Host 68.142.251.86 (68.142.251.86) Time: Tue Jul 18 02:58:38 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.051s user 0m0.008s sys 0m0.005s '71.132.' ************** PARI ***************** Host 71.132.130.250 (71.132.130.250) Time: Tue Jul 18 01:03:57 2006 Input: print gap('SymmetricGroup(5)') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printgap('SymmetricGroup(5)') ^----- Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '71.132.' ************** PARI ***************** Host 71.132.130.250 (71.132.130.250) Time: Tue Jul 18 01:03:37 2006 Input: print gap('SymmetricGroup(7)') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printgap('SymmetricGroup(7)') ^----- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Tue Jul 18 00:10:53 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.024s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Mon Jul 17 23:25:54 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '71.131.' ************** PARI ***************** Host 71.131.60.92 (71.131.60.92) Time: Mon Jul 17 21:49:37 2006 Input: 436/3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 436/3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '152.163' ************** PARI ***************** Host 152.163.100.68 (152.163.100.68) Time: Mon Jul 17 19:05:54 2006 Input: y=x+3 3x+y=11 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x + 3 ? %2 = x + 11 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x+y=11. Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '152.163' ************** PARI ***************** Host 152.163.100.68 (152.163.100.68) Time: Mon Jul 17 19:05:38 2006 Input: y=x+3 3x+y=11 solve for x and y Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x + 3 ? %2 = solveforxandy ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x+y=11solveforxandy. Timing: real 0m0.021s user 0m0.003s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.160 (68.142.249.160) Time: Mon Jul 17 18:14:39 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.155 (68.142.251.155) Time: Mon Jul 17 17:55:23 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Mon Jul 17 17:09:06 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.031s user 0m0.025s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.131.199 (72.30.131.199) Time: Mon Jul 17 14:46:11 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.005s '195.93.' ************** PARI ***************** Host 195.93.21.40 (195.93.21.40) Time: Mon Jul 17 14:20:24 2006 Input: 8! + (112 + 1)2 + 53 + 72 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 127 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: 2+53+72. Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Mon Jul 17 14:19:50 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.023s user 0m0.006s sys 0m0.011s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Mon Jul 17 13:35:45 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:30:35 2006 Input: factor(3446457653424234237543333333333333745645645646346456456456534535345) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 1801 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.041s user 0m20.966s sys 0m0.032s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:30:10 2006 Input: factor(344645765342423423754745645645646346456456456534535345) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5 1] [101 1] [666637 1] [86385313930118357381 1] [11850924690911985200827577 1] ? Goodbye! Errors/timing (if any): Timing: real 0m1.207s user 0m1.169s sys 0m0.036s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:30:06 2006 Input: factor(344645765754745645645646346456456456534535345) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5 1] [5313541 1] [16746739 1] [774619909288243940476642329731 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.047s user 0m0.009s sys 0m0.008s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:30:03 2006 Input: factor(34464576575476346456456456534535345) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [5 1] [11 2] [331 1] [599 1] [10155599789 1] [9430526152364143 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.027s user 0m0.016s sys 0m0.012s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:29:59 2006 Input: factor(344645765754763534535345) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5 1] [839 1] [2111 1] [38918200284085861 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:29:53 2006 Input: factor(15) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [5 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:29:46 2006 Input: factor(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:29:33 2006 Input: 1000! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:29:29 2006 Input: 100! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:29:21 2006 Input: 5^70 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 8470329472543003390683225006796419620513916015625 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:29:05 2006 Input: 5^7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 78125 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '129.6.5' ************** PARI ***************** Host 129.6.54.202 (129.6.54.202) Time: Mon Jul 17 13:29:00 2006 Input: 5**5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 5**5 ^-- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '67.11.2' ************** PARI ***************** Host 67.11.212.178 (67.11.212.178) Time: Mon Jul 17 13:10:41 2006 Input: 24.50 - 7.30 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 17.200000000000000000000000000000000000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.054s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Mon Jul 17 12:25:15 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.162s user 0m0.004s sys 0m0.007s '59.144.' ************** PARI ***************** Host 59.144.61.43 (59.144.61.43) Time: Mon Jul 17 11:10:45 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '66.117.' ************** PARI ***************** Host 66.117.135.200 (66.117.135.200) Time: Mon Jul 17 10:19:23 2006 Input: factor(2^257-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 447 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.002s user 0m20.984s sys 0m0.015s '66.117.' ************** PARI ***************** Host 66.117.135.200 (66.117.135.200) Time: Mon Jul 17 10:16:24 2006 Input: factor(2^256-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [5 1] [17 1] [257 1] [641 1] [65537 1] [274177 1] [6700417 1] [67280421310721 1] [59649589127497217 1] [5704689200685129054721 1] ? Goodbye! Errors/timing (if any): Timing: real 0m4.543s user 0m4.488s sys 0m0.054s '66.117.' ************** PARI ***************** Host 66.117.135.200 (66.117.135.200) Time: Mon Jul 17 10:15:58 2006 Input: factor(2^512-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 431 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.010s user 0m20.985s sys 0m0.014s '66.117.' ************** PARI ***************** Host 66.117.135.200 (66.117.135.200) Time: Mon Jul 17 10:14:33 2006 Input: factor(2^1024-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 424 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.018s user 0m20.995s sys 0m0.005s '66.117.' ************** PARI ***************** Host 66.117.135.200 (66.117.135.200) Time: Mon Jul 17 10:12:25 2006 Input: factor(2^128-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [5 1] [17 1] [257 1] [641 1] [65537 1] [274177 1] [6700417 1] [67280421310721 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.083s user 0m0.014s sys 0m0.008s '129.70.' ************** PARI ***************** Host 129.70.6.104 (129.70.6.104) Time: Mon Jul 17 09:56:07 2006 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Mon Jul 17 09:46:42 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Mon Jul 17 09:38:22 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(2*n), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Mod(que^p, p) Mod(a^(n-p^2), p) Mod(a^(n-1), p) Mod(m,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? %10 = Mod(28, 29) ? %11 = Mod(28, 29) ? %12 = Mod(28, 29) ? %13 = Mod(28, 29) ? Goodbye! Errors/timing (if any): Timing: real 0m0.089s user 0m0.008s sys 0m0.005s '160.127' ************** PARI ***************** Host 160.127.130.244 (160.127.130.244) Time: Mon Jul 17 08:32:53 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '160.127' ************** PARI ***************** Host 160.127.130.244 (160.127.130.244) Time: Mon Jul 17 08:32:49 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.057s user 0m0.007s sys 0m0.005s '24.5.3.' ************** PARI ***************** Host 24.5.3.178 (24.5.3.178) Time: Mon Jul 17 07:59:40 2006 Input: how fast is 3.7 miles in 10 minutes Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown member function: howfastis3.7milesin10minutes ^----------------- Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Mon Jul 17 06:08:15 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.038s user 0m0.025s sys 0m0.007s '71.141.' ************** PARI ***************** Host 71.141.7.214 (71.141.7.214) Time: Mon Jul 17 01:07:40 2006 Input: 1+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '65.54.1' ************** PARI ***************** Host 65.54.188.55 (65.54.188.55) Time: Mon Jul 17 00:28:53 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Sun Jul 16 19:41:05 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '69.254.' ************** PARI ***************** Host 69.254.237.192 (69.254.237.192) Time: Sun Jul 16 19:19:35 2006 Input: 2x(x+4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x + 4 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x(x+4). Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '70.136.' ************** PARI ***************** Host 70.136.153.167 (70.136.153.167) Time: Sun Jul 16 19:11:05 2006 Input: 30/100= /10 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 30/100=/10 ^---- Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '144.136' ************** PARI ***************** Host 144.136.148.49 (144.136.148.49) Time: Sun Jul 16 17:56:28 2006 Input: 0.14 = (2 * ( 1 + g )) / 28.40 ) + g Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 0.14=(2*(1+g))/28.40)+g ^------------------- Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '144.136' ************** PARI ***************** Host 144.136.148.49 (144.136.148.49) Time: Sun Jul 16 17:56:25 2006 Input: 0.14 = (2 * ( 1 + g )) / 28.40 ) + g Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 0.14=(2*(1+g))/28.40)+g ^------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Sun Jul 16 17:18:00 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.065s user 0m0.007s sys 0m0.004s '65.4.78' ************** PARI ***************** Host 65.4.78.160 (65.4.78.160) Time: Sun Jul 16 16:58:27 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '65.4.78' ************** PARI ***************** Host 65.4.78.160 (65.4.78.160) Time: Sun Jul 16 16:58:06 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Sun Jul 16 16:26:58 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.077s user 0m0.003s sys 0m0.009s '213.39.' ************** PARI ***************** Host 213.39.225.238 (213.39.225.238) Time: Sun Jul 16 15:27:18 2006 Input: print maxima('tan(x)').integrate('x') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printmaxima('tan *** (x)').integrate('x') ^-------------------- Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '68.237.' ************** PARI ***************** Host 68.237.44.80 (68.237.44.80) Time: Sun Jul 16 10:08:30 2006 Input: 2006-1986 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 20 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.004s sys 0m0.008s '58.177.' ************** PARI ***************** Host 58.177.16.108 (58.177.16.108) Time: Sun Jul 16 10:03:16 2006 Input: 2222 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2222 ? Goodbye! Errors/timing (if any): Timing: real 0m0.302s user 0m0.005s sys 0m0.010s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Sun Jul 16 03:10:22 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '24.175.' ************** PARI ***************** Host 24.175.221.215 (24.175.221.215) Time: Sun Jul 16 00:57:13 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.86 (68.142.251.86) Time: Sun Jul 16 00:32:44 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.067s user 0m0.007s sys 0m0.005s '69.153.' ************** PARI ***************** Host 69.153.130.47 (69.153.130.47) Time: Sun Jul 16 00:24:19 2006 Input: 18*8/100 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 36/25 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.005s '75.16.5' ************** PARI ***************** Host 75.16.53.248 (75.16.53.248) Time: Sat Jul 15 23:06:19 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '70.160.' ************** PARI ***************** Host 70.160.63.32 (70.160.63.32) Time: Sat Jul 15 20:24:40 2006 Input: zeta(1.5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2.6123753486854883433485675679240716306 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '70.160.' ************** PARI ***************** Host 70.160.63.32 (70.160.63.32) Time: Sat Jul 15 20:24:08 2006 Input: zeta(3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1.2020569031595942853997381615114499908 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '70.160.' ************** PARI ***************** Host 70.160.63.32 (70.160.63.32) Time: Sat Jul 15 20:23:49 2006 Input: zeta(3/2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2.6123753486854883433485675679240716306 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '70.160.' ************** PARI ***************** Host 70.160.63.32 (70.160.63.32) Time: Sat Jul 15 20:23:36 2006 Input: zeta(4/3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3.6009377504588624212922075784754112775 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '70.160.' ************** PARI ***************** Host 70.160.63.32 (70.160.63.32) Time: Sat Jul 15 20:22:37 2006 Input: zeta(2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1.6449340668482264364724151666460251892 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '70.160.' ************** PARI ***************** Host 70.160.63.32 (70.160.63.32) Time: Sat Jul 15 20:22:28 2006 Input: z(2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: z(2) ^---- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '70.160.' ************** PARI ***************** Host 70.160.63.32 (70.160.63.32) Time: Sat Jul 15 20:22:16 2006 Input: s(2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: s(2) ^---- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.38.2' ************** PARI ***************** Host 68.38.238.116 (68.38.238.116) Time: Sat Jul 15 16:53:14 2006 Input: 36x+8x^3+4x^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^2 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x+8x^3+4x^2. Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '74.237.' ************** PARI ***************** Host 74.237.92.222 (74.237.92.222) Time: Sat Jul 15 16:51:48 2006 Input: 2x > -6 and x - 4 < 3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x>-6andx-4<3. *** incorrect type in comparison. Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '205.188' ************** PARI ***************** Host 205.188.117.12 (205.188.117.12) Time: Sat Jul 15 16:21:27 2006 Input: (2x + 1)(x - 2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: (2x+1)(x-2) ^--------- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '205.188' ************** PARI ***************** Host 205.188.117.12 (205.188.117.12) Time: Sat Jul 15 16:14:10 2006 Input: 3x^2 (4x^2 - 2x + 3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x^2(4x^2-2x+3). *** expected character: ')' instead of: 3x^2(4x^2-2x+3) ^--------- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Sat Jul 15 15:30:06 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.025s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Sat Jul 15 15:04:58 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '205.188' ************** PARI ***************** Host 205.188.117.12 (205.188.117.12) Time: Sat Jul 15 14:43:55 2006 Input: 3^2 * (6 - 4) + 8 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 26 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.003s sys 0m0.009s '68.142.' ************** PARI ***************** Host 68.142.249.88 (68.142.249.88) Time: Sat Jul 15 11:40:09 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.077s user 0m0.009s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Sat Jul 15 10:21:42 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.370s user 0m0.008s sys 0m0.012s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Sat Jul 15 06:08:42 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '72.30.2' ************** PARI ***************** Host 72.30.226.223 (72.30.226.223) Time: Sat Jul 15 04:39:53 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '72.30.1' ************** PARI ***************** Host 72.30.102.206 (72.30.102.206) Time: Sat Jul 15 03:53:34 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.155 (68.142.251.155) Time: Sat Jul 15 03:43:37 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.051s user 0m0.007s sys 0m0.006s '72.30.9' ************** PARI ***************** Host 72.30.98.26 (72.30.98.26) Time: Sat Jul 15 02:31:03 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.075s user 0m0.009s sys 0m0.003s '72.30.1' ************** PARI ***************** Host 72.30.110.15 (72.30.110.15) Time: Sat Jul 15 01:23:13 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.053s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Fri Jul 14 23:40:06 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.292s user 0m0.007s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Fri Jul 14 17:20:38 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.023s user 0m0.006s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Fri Jul 14 16:11:45 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.111s user 0m0.027s sys 0m0.004s '70.231.' ************** PARI ***************** Host 70.231.174.162 (70.231.174.162) Time: Fri Jul 14 15:14:22 2006 Input: 2406.20+1000+145.47 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3551.6700000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.086s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:52:27 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(2*n), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Mod(que^p, p) Mod(a^(n-p^2), p) Mod(a^(n-1), p) Mod(m,p) Mod(a^n-m*a,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? %10 = Mod(28, 29) ? %11 = Mod(28, 29) ? %12 = Mod(28, 29) ? %13 = Mod(28, 29) ? %14 = Mod(0, 2987) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:52:22 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(2*n), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Mod(que^p, p) Mod(a^(n-p^2), p) Mod(a^(n-1), p) Mod(m,p) Mod(a^n-m*a) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? %10 = Mod(28, 29) ? %11 = Mod(28, 29) ? %12 = Mod(28, 29) ? %13 = Mod(28, 29) ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: Mod(a^n-m*a) ^- Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:49:58 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(2*n), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Mod(que^p, p) Mod(a^(n-p^2), p) Mod(a^(n-1), p) Mod(m,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? %10 = Mod(28, 29) ? %11 = Mod(28, 29) ? %12 = Mod(28, 29) ? %13 = Mod(28, 29) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.010s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:48:29 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(2*n), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Mod(que^p, p) Mod(a^(n-p^2), p) Mod(m,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? %10 = Mod(28, 29) ? %11 = Mod(28, 29) ? %12 = Mod(28, 29) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:48:09 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(2*n), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Mod(que^p, p) Mod(a^(n-p^2), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? %10 = Mod(28, 29) ? %11 = Mod(28, 29) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:48:05 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(2*n), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Mod(que^p, p) Mod(a^(n-p^2), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? %10 = Mod(28, 29) ? %11 = Mod(1913, 2987) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:47:38 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(2*n), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Mod(que^p, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? %10 = Mod(28, 29) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:46:12 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(2*n), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:45:58 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(n+n-1-1), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(668, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:45:17 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(n-1+q+p), n) Mod((que*m)*(a^(2*p)),n) Mod(m*m*a^2, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(2783, 2987) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:45:09 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(n-1+q+p), n) Mod((que*m)*(a^(2*p)),n) Mod(que*m*a^2, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? %9 = Mod(1681, 2987) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:44:30 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(n-1+q+p), n) Mod((que*m)*(a^(2*p)),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(2783, 2987) ? %8 = Mod(2783, 2987) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:43:42 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(n-1+q+p), n) Mod((que*m)^(2*p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(2783, 2987) ? %8 = Mod(1, 2987) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:43:28 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(a^(n+1+q+p), n) Mod((que*m)^(2*p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? %7 = Mod(581, 2987) ? %8 = Mod(1, 2987) ? Goodbye! Errors/timing (if any): Timing: real 0m0.081s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:42:07 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:41:54 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), p) Mod(m,p) Mod(q,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(28, 29) ? %7 = Mod(28, 29) ? %8 = Mod(16, 29) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:41:27 2006 Input: p=29 q=103 n=p*q a=41 m=Mod(a^(n-1), n) que=Mod(a^(q-p), n) Mod(m,p) Mod(q,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = Mod(840, 2987) ? %6 = Mod(985, 2987) ? %7 = Mod(28, 29) ? %8 = Mod(16, 29) ? Goodbye! Errors/timing (if any): Timing: real 0m0.046s user 0m0.004s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:41:00 2006 Input: p=29 q=103 n=p*q a=41 mod(23,3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? ? ? Goodbye! Errors/timing (if any): *** obsolete function: mod(23,3) ^--------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:40:40 2006 Input: p=29 q=103 n=p*q a=41 3 mod 4 m=mod(a^(n-1), n) que=(a^(q-p), n) mod(m,p) mod(q,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? %5 = mod4 ? ? ? ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: mod4. *** obsolete function: m=mod(a^(n-1),n) ^-------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** expected character: ')' instead of: que=(a^(q-p),n) ^--- *** obsolete function: mod(m,p) ^-------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: mod(q,p) ^-------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:40:32 2006 Input: p=29 q=103 n=p*q a=41 mod(3,4) m=mod(a^(n-1), n) que=(a^(q-p), n) mod(m,p) mod(q,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** obsolete function: mod(3,4) ^-------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: m=mod(a^(n-1),n) ^-------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** expected character: ')' instead of: que=(a^(q-p),n) ^--- *** obsolete function: mod(m,p) ^-------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: mod(q,p) ^-------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jul 14 13:40:06 2006 Input: p=29 q=103 n=p*q a=41 m=mod(a^(n-1), n) que=(a^(q-p), n) mod(m,p) mod(q,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29 ? %2 = 103 ? %3 = 2987 ? %4 = 41 ? ? ? ? ? Goodbye! Errors/timing (if any): *** obsolete function: m=mod(a^(n-1),n) ^-------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** expected character: ')' instead of: que=(a^(q-p),n) ^--- *** obsolete function: mod(m,p) ^-------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. *** obsolete function: mod(q,p) ^-------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.274s user 0m0.007s sys 0m0.005s '69.120.' ************** PARI ***************** Host 69.120.87.24 (69.120.87.24) Time: Fri Jul 14 12:58:15 2006 Input: 20% of 680 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Fri Jul 14 11:47:22 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.041s user 0m0.008s sys 0m0.004s '70.242.' ************** PARI ***************** Host 70.242.126.117 (70.242.126.117) Time: Fri Jul 14 11:16:27 2006 Input: (-5)(-7) + (-16) = Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (-7)+(-16)=. *** unexpected character: (-5)(-7)+(-16)= ^- Timing: real 0m0.015s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Fri Jul 14 10:54:37 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.128s user 0m0.024s sys 0m0.010s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Fri Jul 14 09:44:02 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.123 (72.30.129.123) Time: Fri Jul 14 09:31:15 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.062s user 0m0.009s sys 0m0.004s '134.157' ************** PARI ***************** Host 134.157.51.244 (134.157.51.244) Time: Fri Jul 14 08:40:21 2006 Input: WeberPolynomial(-23) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: WeberPolynomial(-23) ^-------------------- Timing: real 0m0.011s user 0m0.005s sys 0m0.008s '67.81.7' ************** PARI ***************** Host 67.81.74.206 (67.81.74.206) Time: Fri Jul 14 07:30:43 2006 Input: 85*6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 510 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Fri Jul 14 07:16:15 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.421s user 0m0.005s sys 0m0.007s '70.156.' ************** PARI ***************** Host 70.156.112.148 (70.156.112.148) Time: Fri Jul 14 02:29:24 2006 Input: 15 divided by 2000 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = dividedby2000 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: dividedby2000. Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Fri Jul 14 00:27:44 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.132.102 (72.30.132.102) Time: Thu Jul 13 23:01:43 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '63.241.' ************** PARI ***************** Host 63.241.61.7 (63.241.61.7) Time: Thu Jul 13 22:26:43 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.289s user 0m0.008s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.103.19 (72.30.103.19) Time: Thu Jul 13 18:17:13 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.089s user 0m0.008s sys 0m0.004s '24.128.' ************** PARI ***************** Host 24.128.232.126 (24.128.232.126) Time: Thu Jul 13 16:05:40 2006 Input: 251 - 121 + 441 - 340 + 130 - 113 + 409 - 253 + 130 - 181 + 297 - 149 + 081 - 088 + 467 - 059 + 306 - 229 + 345 - 351 + 117 - 047 + 353 - 216 + 401 - 147 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1434 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '68.112.' ************** PARI ***************** Host 68.112.125.227 (68.112.125.227) Time: Thu Jul 13 15:38:24 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Thu Jul 13 14:22:07 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '70.255.' ************** PARI ***************** Host 70.255.191.218 (70.255.191.218) Time: Thu Jul 13 12:39:49 2006 Input: .99*8.25% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '70.255.' ************** PARI ***************** Host 70.255.191.218 (70.255.191.218) Time: Thu Jul 13 12:39:14 2006 Input: 69.98*8.255 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 577.68490000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Thu Jul 13 11:40:48 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.092s user 0m0.025s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Thu Jul 13 10:29:03 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.091s user 0m0.004s sys 0m0.009s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Thu Jul 13 04:11:17 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.100' ************** PARI ***************** Host 192.100.124.219 (192.100.124.219) Time: Thu Jul 13 03:04:04 2006 Input: 400 * 365 * 24 * 3600 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 12614400000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Thu Jul 13 01:52:42 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.110.15 (72.30.110.15) Time: Wed Jul 12 22:29:41 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '140.113' ************** PARI ***************** Host 140.113.39.164 (140.113.39.164) Time: Wed Jul 12 22:09:03 2006 Input: bnfinit(x^3-3*x+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [[;], matrix(0,7), [0.63094472420204595128127987751932688856 + 3.1415926535897932384626433832795028842*I, -0.42663208937288892044892126428188617938; -1.0575768135749348717302011418012130679 - 3.526483052466862524 E-38*I, -0.63094472420204595128127987751932688856 + 3.1415926535897932384626433832795028842*I; 0.42663208937288892044892126428188617933 - 3.526483052466862524 E-38*I, 1.0575768135749348717302011418012130679 + 6.2831853071795864769252867665590057684*I], [0.85799451593316733192199611882579324859, -1.2204603890856085808709303861598036910, 1.0516765170267134156367984292707246396 + 3.1415926535897932384626433832795028842*I, -1.1256810251846538820076540128803599710, 1.1977232321836442310625727580907780402, 1.2344843013216846492932682004210429839, -2.2861608183483980649300666296917676235 + 3.1415926535897932384626433832795028842*I; -1.2204603890856085808709303861598036910 + 3.1415926535897932384626433832795028842*I, 0.36246587315244124894893426733401044243 + 3.1415926535897932384626433832795028842*I, -1.0242713699443061623675068746531138465 + 3.1415926535897932384626433832795028842*I, 0.98947260196521586145274827072206616482, -1.8881038354187483628196860422959597757 + 3.1415926535897932384626433832795028842*I, -1.0634771101231563278236038543317014962 + 3.1415926535897932384626433832795028842*I, 2.0877484800674624901911107289848153426; 0.36246587315244124894893426733401044243, 0.85799451593316733192199611882579324860 + 3.1415926535897932384626433832795028842*I, -0.027405147082407253269291554617610793163, 0.13620842321943802055490574215829380614, 0.69038060323510413175711328420518173555 + 3.1415926535897932384626433832795028842*I, -0.17100719119852832146966434608934148777 + 3.1415926535897932384626433832795028842*I, 0.19841233828093557473895590070695228092 + 3.1415926535897932384626433832795028842*I], [[17, [3, 1, 0]~, 1, 1, [8, -7, 5; -3, 9, -4; 1, -3, 7]], [17, [-7, 1, 0]~, 1, 1, [-3, 13, -5; 7, -2, 6; 1, 7, -4]], [19, [-7, 1, 0]~, 1, 1, [-9, 13, -5; 7, -8, 6; 1, 7, -10]], [3, [1, 1, 0]~, 3, 1, [0, -3, 3; -1, 1, -2; 1, -1, -1]], [17, [4, 1, 0]~, 1, 1, [-2, -9, 6; -4, -1, -5; 1, -4, -3]], [19, [-3, 1, 0]~, 1, 1, [8, 5, -1; 3, 9, 2; 1, 3, 7]], [19, [-9, 1, 0]~, 1, 1, [4, 17, -7; 9, 5, 8; 1, 9, 3]]], 0, [x^3 - 3*x + 1, [3, 0], 81, 1, [[1, -1.8793852415718167681082185546494629399, 1.5320888862379560704047853011108333479; 1, 0.34729635533386069770343325353862959200, -1.8793852415718167681082185546494629399; 1, 1.5320888862379560704047853011108333479, 0.34729635533386069770343325353862959201], [1, -1.8793852415718167681082185546494629399, 1.5320888862379560704047853011108333479; 1, 0.34729635533386069770343325353862959200, -1.8793852415718167681082185546494629399; 1, 1.5320888862379560704047853011108333479, 0.34729635533386069770343325353862959201], 0, [3, 0, 0; 0, 6, -3; 0, -3, 6], [9, 3, 3; 0, 3, 0; 0, 0, 3], [3, 0, 0; 0, 2, 1; 0, 1, 2], [3, [0, -3, 3; -1, 1, -2; 1, -1, -1]]], [-1.8793852415718167681082185546494629399, 0.34729635533386069770343325353862959200, 1.5320888862379560704047853011108333479], [1, x, x^2 - 2], [1, 0, 2; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 2, -1, 0, -1, 2; 0, 1, 0, 1, 0, 1, 0, 1, -1; 0, 0, 1, 0, 1, 0, 1, 0, -1]], [[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.108s user 0m0.011s sys 0m0.003s '140.113' ************** PARI ***************** Host 140.113.39.164 (140.113.39.164) Time: Wed Jul 12 22:08:44 2006 Input: bnf(x^3-3*x+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: bnf(x^3-3*x+1) ^--------- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '140.113' ************** PARI ***************** Host 140.113.39.164 (140.113.39.164) Time: Wed Jul 12 22:07:34 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '137.82.' ************** PARI ***************** Host 137.82.188.68 (137.82.188.68) Time: Wed Jul 12 21:50:49 2006 Input: 2+2 factor (90) print gp(`ellinit([1,2,3,4,5])`).j factor (813920471395793875981074098312758937409123871932) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = [2 1] [3 2] [5 1] ? ? %3 = [2 2] [3 1] [139 1] [439 1] [479 1] [118269313 1] [19620669291651032127963049537783 1] ? Goodbye! Errors/timing (if any): *** unexpected character: printgp(`ellinit([1,2,3,4,5] ^-------------------- Timing: real 0m0.025s user 0m0.020s sys 0m0.005s '137.82.' ************** PARI ***************** Host 137.82.188.68 (137.82.188.68) Time: Wed Jul 12 21:49:56 2006 Input: 2+2 factor (90) print gp(`ellinit([1,2,3,4,5])`).j factor (81392047139579387598107409831275893740912387193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = [2 1] [3 2] [5 1] ? ? %3 = [19 1] [241 1] [17775070351513297138700023985865012828327667 1] ? Goodbye! Errors/timing (if any): *** unexpected character: printgp(`ellinit([1,2,3,4,5] ^-------------------- Timing: real 0m0.050s user 0m0.010s sys 0m0.004s '137.82.' ************** PARI ***************** Host 137.82.188.68 (137.82.188.68) Time: Wed Jul 12 21:49:17 2006 Input: 2+2 factor (90) print gp(`ellinit([1,2,3,4,5])`).j Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = [2 1] [3 2] [5 1] ? ? Goodbye! Errors/timing (if any): *** unexpected character: printgp(`ellinit([1,2,3,4,5] ^-------------------- Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '137.82.' ************** PARI ***************** Host 137.82.188.68 (137.82.188.68) Time: Wed Jul 12 21:46:11 2006 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.86 (68.142.251.86) Time: Wed Jul 12 21:43:46 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.040s user 0m0.007s sys 0m0.004s '72.30.9' ************** PARI ***************** Host 72.30.99.77 (72.30.99.77) Time: Wed Jul 12 20:44:12 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.154s user 0m0.008s sys 0m0.006s '24.48.1' ************** PARI ***************** Host 24.48.127.53 (24.48.127.53) Time: Wed Jul 12 20:04:32 2006 Input: 2^20100 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5045600325728943754639415960323361600171717389128648170285446537790139092022413184446871295280139768874799336583615862530712776373179302160661403818439187821664388190341184717279749863761124869580569967577474221995687941234527007218267028650377627355497197592525049358415914726293942898627985869466947873898043016688799306912815483595083501875769105725501311026087442993944535276524333822867390630953511504035238454005900298946871573354801766179500058320270062568025185390414082781738607082717107810947125542987701210092607347537510086962259802696299130230667362643458424378635528132051983260404127030825396255332506962190825248994458998212850496759467330053610127116465286325943144702466187215344174724752036425156682886050668002000187470606414264577085424670586132417982614195521191019801385275627345908951492574159621925631611145153277616640871798342384657977920865130512522988636960949971743788001769099739971140792597464015294976983095494472895933622302169643286731293399566025798222964344609167128738188078210305943922404135639104306677718947898403572438791850243756061413336097475941995004717368373582123451932836286731906601520262971823323709392467454084774562469934402259011854550383775670240989737133962322852097468547051547177572520512892931949534532404530493970161698146681049834812472984601421200151729858603757517859114426997504968320597178027517049789911329534974491989755960482766136373381395636788077693025438254938790274525059873461546062539199225890163115888965211062604726595366397295860339657293075881163456664657433865218864019687083307923814922690692447921805517037434337242525794783317022038171290801260366858253801097560302342031966162233713013755880287012648854346775693209500252964647007280001698493043447547376403832962967938402041609470521680717283638330167037970017941425541873750917262585756390780208441706832598565996570394782601338681667703924694035101678176487423014973038409636318766134252433928216986234009683903524494266030839210213598567525354513488420022819237892411705462251503210916595093495370541230349496036118053344135612373656880024081361883165025512705396020737495977497506074241370415841674999253752238224232630130686630273997939544329237590893457436449048590874204957803953215366875211462315697813908683046606367950342892415890812629574434906254114704295972471412303243282584386318091019559153545707248098969696754502228012713502777760477647779083992220864281495375040295418205397790353599512878388705999549690493788335855374270041478260841185487921910345751282207184059589778670185668623196952762298073224336097135238228126937279304379112556116126435023884835942849012819727325636682228790969593780127764905990561152718183583377721676046955008130291062349665532814975192134072299338575403230038769840781184454524747638881227563707278138261917498377619244423582082477498500230675590784264625303545098867551155331103908299021791904689458134835810737242482655488182144091915915578827103992880432068163933450603544983606320714844930184655509021554230329773972369261139297872135036577653148196200910884051833268753612119423480747859643502926207338358211764607062668234146724793066587631277523191424920351070308264953339333150274246053642883011412[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.076s user 0m0.006s sys 0m0.008s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Wed Jul 12 15:49:52 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.134s user 0m0.027s sys 0m0.007s '24.210.' ************** PARI ***************** Host 24.210.169.118 (24.210.169.118) Time: Wed Jul 12 15:34:16 2006 Input: 167-25= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 167-25= ^- Timing: real 0m0.029s user 0m0.007s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Wed Jul 12 12:29:12 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '68.36.1' ************** PARI ***************** Host 68.36.137.236 (68.36.137.236) Time: Wed Jul 12 11:23:54 2006 Input: 16/.04= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 16/.04= ^- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.88 (68.142.249.88) Time: Wed Jul 12 11:11:43 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.156s user 0m0.004s sys 0m0.012s '84.49.1' ************** PARI ***************** Host 84.49.109.118 (84.49.109.118) Time: Wed Jul 12 09:05:49 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '84.49.1' ************** PARI ***************** Host 84.49.109.118 (84.49.109.118) Time: Wed Jul 12 09:05:45 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.063s user 0m0.005s sys 0m0.007s '152.133' ************** PARI ***************** Host 152.133.7.1 (152.133.7.1) Time: Wed Jul 12 07:50:36 2006 Input: 33709+9946+950+1620 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 46225 ? Goodbye! Errors/timing (if any): Timing: real 0m0.382s user 0m0.004s sys 0m0.008s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Wed Jul 12 06:25:36 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.112s user 0m0.006s sys 0m0.007s '72.30.9' ************** PARI ***************** Host 72.30.98.35 (72.30.98.35) Time: Wed Jul 12 02:58:44 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.025s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Wed Jul 12 02:48:44 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.052s user 0m0.025s sys 0m0.004s '72.30.2' ************** PARI ***************** Host 72.30.226.223 (72.30.226.223) Time: Wed Jul 12 01:19:35 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.129.123 (72.30.129.123) Time: Tue Jul 11 23:10:00 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '67.79.7' ************** PARI ***************** Host 67.79.74.113 (67.79.74.113) Time: Tue Jul 11 20:45:11 2006 Input: log 38 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = log38 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Tue Jul 11 19:58:34 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '72.30.9' ************** PARI ***************** Host 72.30.98.145 (72.30.98.145) Time: Tue Jul 11 19:29:57 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.53.9' ************** PARI ***************** Host 71.53.93.81 (71.53.93.81) Time: Tue Jul 11 18:37:26 2006 Input: 5% ot a 1000 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Tue Jul 11 17:56:11 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.032s user 0m0.008s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Tue Jul 11 17:17:17 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.063s user 0m0.008s sys 0m0.005s '70.137.' ************** PARI ***************** Host 70.137.64.90 (70.137.64.90) Time: Tue Jul 11 14:20:58 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Tue Jul 11 14:08:55 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.083s user 0m0.006s sys 0m0.007s '72.155.' ************** PARI ***************** Host 72.155.5.89 (72.155.5.89) Time: Tue Jul 11 13:28:41 2006 Input: 113-61 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 52 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Tue Jul 11 13:11:26 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.062s user 0m0.006s sys 0m0.005s '71.137.' ************** PARI ***************** Host 71.137.137.69 (71.137.137.69) Time: Tue Jul 11 13:03:12 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.138s user 0m0.005s sys 0m0.008s '68.41.1' ************** PARI ***************** Host 68.41.126.191 (68.41.126.191) Time: Tue Jul 11 12:21:27 2006 Input: 2+2= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 2+2= ^- Timing: real 0m0.018s user 0m0.005s sys 0m0.006s '130.36.' ************** PARI ***************** Host 130.36.62.126 (130.36.62.126) Time: Tue Jul 11 09:30:43 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.041s user 0m0.007s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Tue Jul 11 07:35:33 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.078s user 0m0.007s sys 0m0.004s '199.203' ************** PARI ***************** Host 199.203.96.62 (199.203.96.62) Time: Tue Jul 11 07:17:59 2006 Input: 5! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 120 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '199.203' ************** PARI ***************** Host 199.203.96.62 (199.203.96.62) Time: Tue Jul 11 07:17:46 2006 Input: 2**4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 2**4 ^-- Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '199.203' ************** PARI ***************** Host 199.203.96.62 (199.203.96.62) Time: Tue Jul 11 07:17:32 2006 Input: 2+3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.358s user 0m0.006s sys 0m0.008s '200.204' ************** PARI ***************** Host 200.204.108.79 (200.204.108.79) Time: Tue Jul 11 06:08:34 2006 Input: ibase=16 obase=16 Mod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utput: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 16 ? %2 = 16 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: Mod(5317347400B3E6842996D15F22CA11 ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '200.204' ************** PARI ***************** Host 200.204.108.79 (200.204.108.79) Time: Tue Jul 11 06:06:48 2006 Input: Mod(112, 3)^3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 3) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '128.119' ************** PARI ***************** Host 128.119.68.160 (128.119.68.160) Time: Mon Jul 10 22:32:11 2006 Input: factor(2^1024+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 4107 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.069s user 0m20.989s sys 0m0.010s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Mon Jul 10 20:19:44 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.024s sys 0m0.005s '67.182.' ************** PARI ***************** Host 67.182.215.139 (67.182.215.139) Time: Mon Jul 10 19:04:43 2006 Input: 20.99+134.99+9.69+79.99+14.99+29.99+20.00 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 310.64000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.120s user 0m0.006s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Mon Jul 10 18:41:19 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.025s sys 0m0.004s '68.106.' ************** PARI ***************** Host 68.106.131.65 (68.106.131.65) Time: Mon Jul 10 18:27:39 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '74.226.' ************** PARI ***************** Host 74.226.77.57 (74.226.77.57) Time: Mon Jul 10 15:44:55 2006 Input: Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '200.204' ************** PARI ***************** Host 200.204.108.79 (200.204.108.79) Time: Mon Jul 10 13:21:38 2006 Input: Mod(5,3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2, 3) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '200.204' ************** PARI ***************** Host 200.204.108.79 (200.204.108.79) Time: Mon Jul 10 13:21:16 2006 Input: mod(5,3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** obsolete function: mod(5,3) ^-------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.038s user 0m0.007s sys 0m0.005s '200.204' ************** PARI ***************** Host 200.204.108.79 (200.204.108.79) Time: Mon Jul 10 13:20:47 2006 Input: Mod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utput: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: Mod(5317347400B3E6842996D15F22CA11 ^-------------------- Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '200.204' ************** PARI ***************** Host 200.204.108.79 (200.204.108.79) Time: Mon Jul 10 13:19:44 2006 Input: 5317347400B3E6842996D15F22CA1110DB177DA2A612F115A7811FEB5B94C61E8C59606867AE8028AA413D5F9CBCD7868E92281ADA00263D4795D67314EB7DE3DCA3480FEF5C65623A1C3D7B38199DD57C07C0F688EF268D2C3B16C365880589DB6DC43768B488EFE0C48210835B16B04E6EF7B3694E250A439CA9D15F778984 ^010001 mod CFD28744CB536392A75955A82653E8B3F50C24B88F179A0F866217C4A287F4A498ABBC0A037FBD0BEE8A46863E19AAF4D6BBAF54E5CB8EB12146E8C8ECB86CCDDBF705DFFD0A8941B2EA76DFD259BDD2B7F897B66631918FEC53D111099286C9AEDBA9F5A558CB6603CEE7CFC4BAEFB25965930CBDDCB0A1434BA417B89C41F3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = modCFD28744CB536392A75955A82653E8B3F50C24B88F179A0F866217C4A287F4A498ABBC0A037FBD0BEE8A46863E19AAF4D6BBAF54E5CB8EB12146E8C8ECB86CCDDBF705DFFD0A8941B2EA76DFD259BDD2B7F897B66631918FEC53D111099286C9AEDBA9F5A558CB6603CEE7CFC4BAEFB25965930CBDDCB0A1434BA417B89C41F3 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: B3E6842996D15F22CA1110DB177DA2A612F115A7811FEB5B94C61E8C59606867AE8028AA413D5F9CBCD7868E92281ADA00263D4795D67314EB7DE3[+++]. Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '18.4.1.' ************** PARI ***************** Host 18.4.1.76 (18.4.1.76) Time: Mon Jul 10 13:16:14 2006 Input: 1+1 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '81.155.' ************** PARI ***************** Host 81.155.179.202 (81.155.179.202) Time: Mon Jul 10 13:15:32 2006 Input: -2x-11<7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x-11<7. *** incorrect type in comparison. Timing: real 0m0.013s user 0m0.005s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.131.227 (72.30.131.227) Time: Mon Jul 10 13:07:24 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '83.36.1' ************** PARI ***************** Host 83.36.129.228 (83.36.129.228) Time: Mon Jul 10 12:46:57 2006 Input: integrate(1+x^2,x,0,%pi) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '83.36.1' ************** PARI ***************** Host 83.36.129.228 (83.36.129.228) Time: Mon Jul 10 12:15:06 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '216.153' ************** PARI ***************** Host 216.153.251.12 (216.153.251.12) Time: Mon Jul 10 11:21:41 2006 Input: factor (8) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.003s sys 0m0.008s '216.153' ************** PARI ***************** Host 216.153.251.12 (216.153.251.12) Time: Mon Jul 10 11:16:48 2006 Input: factor (2345) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [5 1] [7 1] [67 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Mon Jul 10 11:14:40 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 11:01:38 2006 Input: M=x^3-x^2-2*x+1; -bezout(c*x^2+b*x+a,M)[1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = ((2*c^2 + (-b + a)*c - b^2)/(c^3 + (2*b + 6*a)*c^2 + (-b^2 + a*b + 5*a^2)*c + (-b^3 - 2*a*b^2 + a^2*b + a^3)))*x^2 + ((-c^2 + b*c + (b^2 + a*b))/(c^3 + (2*b + 6*a)*c^2 + (-b^2 + a*b + 5*a^2)*c + (-b^3 - 2*a*b^2 + a^2*b + a^3)))*x + ((-5*c^2 + (b - 5*a)*c + (2*b^2 - a*b - a^2))/(c^3 + (2*b + 6*a)*c^2 + (-b^2 + a*b + 5*a^2)*c + (-b^3 - 2*a*b^2 + a^2*b + a^3))) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 11:01:05 2006 Input: M=x^3-x^2-2*x+1; bezout(c*x^2+b*x+a,M) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [((-2*c^2 + (b - a)*c + b^2)/(c^3 + (2*b + 6*a)*c^2 + (-b^2 + a*b + 5*a^2)*c + (-b^3 - 2*a*b^2 + a^2*b + a^3)))*x^2 + ((c^2 - b*c + (-b^2 - a*b))/(c^3 + (2*b + 6*a)*c^2 + (-b^2 + a*b + 5*a^2)*c + (-b^3 - 2*a*b^2 + a^2*b + a^3)))*x + ((5*c^2 + (-b + 5*a)*c + (-2*b^2 + a*b + a^2))/(c^3 + (2*b + 6*a)*c^2 + (-b^2 + a*b + 5*a^2)*c + (-b^3 - 2*a*b^2 + a^2*b + a^3))), ((2*c^3 + (-b + a)*c^2 - b^2*c)/(c^3 + (2*b + 6*a)*c^2 + (-b^2 + a*b + 5*a^2)*c + (-b^3 - 2*a*b^2 + a^2*b + a^3)))*x + ((c^3 + (2*b + a)*c^2 + (-b^2 + 2*a*b)*c - b^3)/(c^3 + (2*b + 6*a)*c^2 + (-b^2 + a*b + 5*a^2)*c + (-b^3 - 2*a*b^2 + a^2*b + a^3))), 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:54:19 2006 Input: M=x^3-x^2-2*x+1; bezout(c*x^2,M) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [-2/c*x^2 + 1/c*x + 5/c, 2*x + 1, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.008s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:53:44 2006 Input: M=x^3-x^2-2*x+1; bezout(a,M) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [1/a, 0, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:53:18 2006 Input: M=x^3-x^2-2*x+1; bezout(bezout(a,M)[1]+x,M) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [-a^3/(a^3 + 2*a^2 - a - 1)*x^2 + ((a^3 + a^2)/(a^3 + 2*a^2 - a - 1))*x + ((2*a^3 - a^2 - a)/(a^3 + 2*a^2 - a - 1)), a^3/(a^3 + 2*a^2 - a - 1), 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:52:59 2006 Input: M=x^3-x^2-2*x+1; bezout(bezout(a,M)[1]+(a-2)*x,M) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [((-a^5 + 4*a^4 - 4*a^3)/(a^6 - 6*a^5 + 14*a^4 - 16*a^3 + 7*a^2 + 2*a - 1))*x^2 + ((a^5 - 4*a^4 + 5*a^3 - 2*a^2)/(a^6 - 6*a^5 + 14*a^4 - 16*a^3 + 7*a^2 + 2*a - 1))*x + ((2*a^5 - 8*a^4 + 7*a^3 + 2*a^2 - a)/(a^6 - 6*a^5 + 14*a^4 - 16*a^3 + 7*a^2 + 2*a - 1)), (a^6 - 6*a^5 + 12*a^4 - 8*a^3)/(a^6 - 6*a^5 + 14*a^4 - 16*a^3 + 7*a^2 + 2*a - 1), 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:52:34 2006 Input: M=x^3-x^2-2*x+1; bezout(bezout(a,M)[1]+a*x,M) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = [-a^5/(a^6 + 2*a^4 - a^2 - 1)*x^2 + ((a^5 + a^3)/(a^6 + 2*a^4 - a^2 - 1))*x + ((2*a^5 - a^3 - a)/(a^6 + 2*a^4 - a^2 - 1)), a^6/(a^6 + 2*a^4 - a^2 - 1), 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:51:12 2006 Input: M=x^3-x^2-2*x+1; bezout(a,M)[1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = 1/a ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:35:02 2006 Input: M=x^3-x^2-2*x+1; bezout(a+c*x^2,M)[1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = ((-c*a - 2*c^2)/(a^3 + 5*c*a^2 + 6*c^2*a + c^3))*x^2 + c^2/(a^3 + 5*c*a^2 + 6*c^2*a + c^3)*x + ((a^2 + 5*c*a + 5*c^2)/(a^3 + 5*c*a^2 + 6*c^2*a + c^3)) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:33:51 2006 Input: M=x^3-x^2-2*x+1; bezout(bezout(a+c*x^2,M)[1]+2*x,M)[1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = ((-4*a^3 - 20*c*a^2 + (-24*c^2 + 2*c)*a + (-4*c^3 - c))/(8*a^3 + (40*c + 8)*a^2 + (48*c^2 + 36*c - 2)*a + (8*c^3 + 44*c^2 - 8*c - 1)))*x^2 + ((4*a^3 + (20*c + 2)*a^2 + (24*c^2 + 8*c)*a + (4*c^3 + 10*c^2))/(8*a^3 + (40*c + 8)*a^2 + (48*c^2 + 36*c - 2)*a + (8*c^3 + 44*c^2 - 8*c - 1)))*x + ((8*a^3 + (40*c - 2)*a^2 + (48*c^2 - 12*c - 1)*a + (8*c^3 - 6*c^2))/(8*a^3 + (40*c + 8)*a^2 + (48*c^2 + 36*c - 2)*a + (8*c^3 + 44*c^2 - 8*c - 1))) ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:28:09 2006 Input: M=x^3-x^2-2*x+1; bezout(bezout(a+b*x+c*x^2,M)[1]+2*x,M)[1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = ((4*a^3 + (4*b + 20*c)*a^2 + (-8*b^2 + (4*c - 4)*b + (24*c^2 - 2*c))*a + (-4*b^3 + (-4*c - 2)*b^2 + (8*c^2 - 2*c)*b + (4*c^3 + c)))/(-8*a^3 + (-8*b + (-40*c - 8))*a^2 + (16*b^2 + (-8*c + 4)*b + (-48*c^2 - 36*c + 2))*a + (8*b^3 + (8*c + 24)*b^2 + (-16*c^2 + 16*c + 10)*b + (-8*c^3 - 44*c^2 + 8*c + 1))))*x^2 + ((-4*a^3 + (-4*b + (-20*c - 2))*a^2 + (8*b^2 + (-4*c + 2)*b + (-24*c^2 - 8*c))*a + (4*b^3 + (4*c + 6)*b^2 + (-8*c^2 + 4*c + 1)*b + (-4*c^3 - 10*c^2)))/(-8*a^3 + (-8*b + (-40*c - 8))*a^2 + (16*b^2 + (-8*c + 4)*b + (-48*c^2 - 36*c + 2))*a + (8*b^3 + (8*c + 24)*b^2 + (-16*c^2 + 16*c + 10)*b + (-8*c^3 - 44*c^2 + 8*c + 1))))*x + ((-8*a^3 + (-8*b + (-40*c + 2))*a^2 + (16*b^2 + (-8*c + 10)*b + (-48*c^2 + 12*c + 1))*a + (8*b^3 + (8*c + 2)*b^2 + (-16*c^2 + 4*c)*b + (-8*c^3 + 6*c^2)))/(-8*a^3 + (-8*b + (-40*c - 8))*a^2 + (16*b^2 + (-8*c + 4)*b + (-48*c^2 - 36*c + 2))*a + (8*b^3 + (8*c + 24)*b^2 + (-16*c^2 + 16*c + 10)*b + (-8*c^3 - 44*c^2 + 8*c + 1)))) ? Goodbye! Errors/timing (if any): Timing: real 0m0.853s user 0m0.849s sys 0m0.004s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:27:37 2006 Input: M=x^3-x^2-2*x+1; bezout(bezout(a+b*x+c*x^2,M)[1]+x,M)[1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = ((a^3 + (b + 5*c)*a^2 + (-2*b^2 + (c - 2)*b + (6*c^2 - c))*a + (-b^3 + (-c - 1)*b^2 + (2*c^2 - c)*b + (c^3 + c)))/(-a^3 + (-b + (-5*c - 2))*a^2 + (2*b^2 + (-c + 1)*b + (-6*c^2 - 9*c + 1))*a + (b^3 + (c + 6)*b^2 + (-2*c^2 + 4*c + 5)*b + (-c^3 - 11*c^2 + 4*c + 1))))*x^2 + ((-a^3 + (-b + (-5*c - 1))*a^2 + (2*b^2 + (-c + 1)*b + (-6*c^2 - 4*c))*a + (b^3 + (c + 3)*b^2 + (-2*c^2 + 2*c + 1)*b + (-c^3 - 5*c^2)))/(-a^3 + (-b + (-5*c - 2))*a^2 + (2*b^2 + (-c + 1)*b + (-6*c^2 - 9*c + 1))*a + (b^3 + (c + 6)*b^2 + (-2*c^2 + 4*c + 5)*b + (-c^3 - 11*c^2 + 4*c + 1))))*x + ((-2*a^3 + (-2*b + (-10*c + 1))*a^2 + (4*b^2 + (-2*c + 5)*b + (-12*c^2 + 6*c + 1))*a + (2*b^3 + (2*c + 1)*b^2 + (-4*c^2 + 2*c)*b + (-2*c^3 + 3*c^2)))/(-a^3 + (-b + (-5*c - 2))*a^2 + (2*b^2 + (-c + 1)*b + (-6*c^2 - 9*c + 1))*a + (b^3 + (c + 6)*b^2 + (-2*c^2 + 4*c + 5)*b + (-c^3 - 11*c^2 + 4*c + 1)))) ? Goodbye! Errors/timing (if any): Timing: real 0m0.910s user 0m0.869s sys 0m0.008s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:26:01 2006 Input: bezout(a+b*x+c*x^2,x^3-x^2-2*x+1)[1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-c*a + (b^2 + c*b - 2*c^2))/(a^3 + (b + 5*c)*a^2 + (-2*b^2 + c*b + 6*c^2)*a + (-b^3 - c*b^2 + 2*c^2*b + c^3)))*x^2 + ((-b*a + (-b^2 - c*b + c^2))/(a^3 + (b + 5*c)*a^2 + (-2*b^2 + c*b + 6*c^2)*a + (-b^3 - c*b^2 + 2*c^2*b + c^3)))*x + ((a^2 + (b + 5*c)*a + (-2*b^2 - c*b + 5*c^2))/(a^3 + (b + 5*c)*a^2 + (-2*b^2 + c*b + 6*c^2)*a + (-b^3 - c*b^2 + 2*c^2*b + c^3))) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 10 10:24:23 2006 Input: bezout(a+b*x+c*x^2,x^3-x^2-2*x+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [((-c*a + (b^2 + c*b - 2*c^2))/(a^3 + (b + 5*c)*a^2 + (-2*b^2 + c*b + 6*c^2)*a + (-b^3 - c*b^2 + 2*c^2*b + c^3)))*x^2 + ((-b*a + (-b^2 - c*b + c^2))/(a^3 + (b + 5*c)*a^2 + (-2*b^2 + c*b + 6*c^2)*a + (-b^3 - c*b^2 + 2*c^2*b + c^3)))*x + ((a^2 + (b + 5*c)*a + (-2*b^2 - c*b + 5*c^2))/(a^3 + (b + 5*c)*a^2 + (-2*b^2 + c*b + 6*c^2)*a + (-b^3 - c*b^2 + 2*c^2*b + c^3))), ((c^2*a + (-c*b^2 - c^2*b + 2*c^3))/(a^3 + (b + 5*c)*a^2 + (-2*b^2 + c*b + 6*c^2)*a + (-b^3 - c*b^2 + 2*c^2*b + c^3)))*x + (((2*c*b + c^2)*a + (-b^3 - c*b^2 + 2*c^2*b + c^3))/(a^3 + (b + 5*c)*a^2 + (-2*b^2 + c*b + 6*c^2)*a + (-b^3 - c*b^2 + 2*c^2*b + c^3))), 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.059s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Mon Jul 10 08:47:45 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.056s user 0m0.009s sys 0m0.004s '71.162.' ************** PARI ***************** Host 71.162.154.246 (71.162.154.246) Time: Mon Jul 10 08:28:08 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.063s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.160 (68.142.249.160) Time: Mon Jul 10 07:35:43 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.407s user 0m0.006s sys 0m0.015s '63.241.' ************** PARI ***************** Host 63.241.61.7 (63.241.61.7) Time: Mon Jul 10 06:34:31 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.067s user 0m0.005s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Mon Jul 10 05:57:25 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.075s user 0m0.008s sys 0m0.005s '84.3.10' ************** PARI ***************** Host 84.3.102.13 (84.3.102.13) Time: Mon Jul 10 05:20:20 2006 Input: gap('SymmetricGroup(7)') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: gap('SymmetricGroup(7)') ^----- Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '84.3.10' ************** PARI ***************** Host 84.3.102.13 (84.3.102.13) Time: Mon Jul 10 05:19:44 2006 Input: print gap('SymmetricGroup(7)') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printgap('SymmetricGroup(7)') ^----- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '84.3.10' ************** PARI ***************** Host 84.3.102.13 (84.3.102.13) Time: Mon Jul 10 05:18:52 2006 Input: print maxima('tan(x)').integrate('x') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printmaxima('tan *** (x)').integrate('x') ^-------------------- Timing: real 0m0.038s user 0m0.004s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.108 (68.142.249.108) Time: Mon Jul 10 00:56:37 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.024s sys 0m0.006s '66.112.' ************** PARI ***************** Host 66.112.49.90 (66.112.49.90) Time: Mon Jul 10 00:25:59 2006 Input: 204/60 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 17/5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Sun Jul 9 21:39:20 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.024s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Sun Jul 9 21:27:31 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.080s user 0m0.007s sys 0m0.005s '71.8.21' ************** PARI ***************** Host 71.8.215.121 (71.8.215.121) Time: Sun Jul 9 19:22:06 2006 Input: Find the deritave of the function: f(x)= e^4x Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = x ? Goodbye! Errors/timing (if any): *** Warning: unused characters: :. *** unexpected character: ...dthederitaveofthefunction: ^- *** Warning: unused characters: x. Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '74.32.1' ************** PARI ***************** Host 74.32.186.126 (74.32.186.126) Time: Sun Jul 9 17:24:01 2006 Input: (3/x-1)/(x/x^2-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (-x + 3)/(-x + 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.096s user 0m0.007s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Sun Jul 9 16:52:56 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.027s user 0m0.004s sys 0m0.008s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sun Jul 9 13:40:14 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.054s user 0m0.006s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.102.206 (72.30.102.206) Time: Sun Jul 9 13:05:51 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.250.13 (68.142.250.13) Time: Sun Jul 9 11:05:20 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.123 (72.30.129.123) Time: Sun Jul 9 10:17:30 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '69.248.' ************** PARI ***************** Host 69.248.69.127 (69.248.69.127) Time: Sun Jul 9 10:08:21 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '213.36.' ************** PARI ***************** Host 213.36.148.25 (213.36.148.25) Time: Sun Jul 9 10:02:31 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.88 (68.142.249.88) Time: Sun Jul 9 09:28:18 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.077s user 0m0.010s sys 0m0.003s '69.248.' ************** PARI ***************** Host 69.248.69.127 (69.248.69.127) Time: Sun Jul 9 09:16:25 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '69.248.' ************** PARI ***************** Host 69.248.69.127 (69.248.69.127) Time: Sun Jul 9 08:52:56 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.045s user 0m0.007s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Sun Jul 9 07:19:06 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.267s user 0m0.007s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Sun Jul 9 05:34:52 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Sun Jul 9 04:19:59 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.051s user 0m0.007s sys 0m0.006s '69.213.' ************** PARI ***************** Host 69.213.136.125 (69.213.136.125) Time: Sun Jul 9 04:19:36 2006 Input: .650*500= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: .650*500= ^- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.132.102 (72.30.132.102) Time: Sun Jul 9 04:13:11 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.103.19 (72.30.103.19) Time: Sun Jul 9 03:35:47 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '72.30.9' ************** PARI ***************** Host 72.30.98.26 (72.30.98.26) Time: Sun Jul 9 02:56:14 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Sun Jul 9 01:38:27 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.028s user 0m0.025s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.86 (68.142.251.86) Time: Sun Jul 9 01:15:17 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.054s user 0m0.002s sys 0m0.010s '70.246.' ************** PARI ***************** Host 70.246.77.191 (70.246.77.191) Time: Sat Jul 8 22:00:39 2006 Input: (34 + x)^5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^5 + 170*x^4 + 11560*x^3 + 393040*x^2 + 6681680*x + 45435424 ? Goodbye! Errors/timing (if any): Timing: real 0m0.108s user 0m0.006s sys 0m0.007s '82.55.2' ************** PARI ***************** Host 82.55.247.120 (82.55.247.120) Time: Sat Jul 8 12:24:00 2006 Input: X^2+X+4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = X^2 + X + 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '82.55.2' ************** PARI ***************** Host 82.55.247.120 (82.55.247.120) Time: Sat Jul 8 12:23:35 2006 Input: X^2+X+4=0 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: X^2+X+4=0 ^-- Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '82.55.2' ************** PARI ***************** Host 82.55.247.120 (82.55.247.120) Time: Sat Jul 8 12:23:04 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.054s user 0m0.007s sys 0m0.006s '67.20.2' ************** PARI ***************** Host 67.20.24.148 (67.20.24.148) Time: Sat Jul 8 08:27:04 2006 Input: 3.25+3.25+5.50+5.95+6.5= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 3.25+3.25+5.50+5.95+6.5= ^- Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.131.227 (72.30.131.227) Time: Sat Jul 8 08:17:29 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.049s user 0m0.007s sys 0m0.006s '165.21.' ************** PARI ***************** Host 165.21.154.15 (165.21.154.15) Time: Sat Jul 8 06:54:50 2006 Input: print maxima('tan(x)').integrate('x') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printmaxima('tan *** (x)').integrate('x') ^-------------------- Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sat Jul 8 06:46:31 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Sat Jul 8 04:53:54 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.025s sys 0m0.005s '72.30.9' ************** PARI ***************** Host 72.30.98.145 (72.30.98.145) Time: Sat Jul 8 02:15:36 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.005s sys 0m0.006s '66.27.1' ************** PARI ***************** Host 66.27.112.147 (66.27.112.147) Time: Fri Jul 7 22:00:54 2006 Input: factor(1234567) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [127 1] [9721 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.110.15 (72.30.110.15) Time: Fri Jul 7 19:48:27 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.101.' ************** PARI ***************** Host 65.101.90.83 (65.101.90.83) Time: Fri Jul 7 18:58:13 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '68.9.50' ************** PARI ***************** Host 68.9.50.27 (68.9.50.27) Time: Fri Jul 7 18:01:49 2006 Input: gp('factor(234234);3*3*3*3') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: gp('factor(234234);3*3*3*3') ^------------------ Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.9.50' ************** PARI ***************** Host 68.9.50.27 (68.9.50.27) Time: Fri Jul 7 18:00:32 2006 Input: factor(234234) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 2] [7 1] [11 1] [13 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '68.9.50' ************** PARI ***************** Host 68.9.50.27 (68.9.50.27) Time: Fri Jul 7 18:00:11 2006 Input: pari.factor(234234) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (234234). *** unknown member function: pari.factor(234234) ^-------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.9.50' ************** PARI ***************** Host 68.9.50.27 (68.9.50.27) Time: Fri Jul 7 18:00:01 2006 Input: factor(234234) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 2] [7 1] [11 1] [13 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.9.50' ************** PARI ***************** Host 68.9.50.27 (68.9.50.27) Time: Fri Jul 7 17:59:50 2006 Input: factor(234234) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 2] [7 1] [11 1] [13 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Fri Jul 7 16:13:37 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.026s user 0m0.005s sys 0m0.006s '72.30.9' ************** PARI ***************** Host 72.30.99.77 (72.30.99.77) Time: Fri Jul 7 15:40:55 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.117s user 0m0.006s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.251.155 (68.142.251.155) Time: Fri Jul 7 15:05:08 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.55 (68.142.249.55) Time: Fri Jul 7 14:52:53 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Fri Jul 7 12:45:36 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Fri Jul 7 12:43:42 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.217s user 0m0.025s sys 0m0.006s '69.40.4' ************** PARI ***************** Host 69.40.43.242 (69.40.43.242) Time: Fri Jul 7 12:42:00 2006 Input: -.90+.84 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -0.059999999999999999999999999999999999999 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '71.75.9' ************** PARI ***************** Host 71.75.98.12 (71.75.98.12) Time: Fri Jul 7 12:09:40 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '131.137' ************** PARI ***************** Host 131.137.245.198 (131.137.245.198) Time: Fri Jul 7 10:30:48 2006 Input: 30000*262 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7860000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Fri Jul 7 10:16:05 2006 Input: Mod(x^2+2*x+4,2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Mod: incorrect type in Rg_to_Fl. Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Fri Jul 7 10:15:39 2006 Input: Mod(x^2+2x+4,2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: Mod(x^2+2x+4,2) ^------ Timing: real 0m0.016s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 09:08:12 2006 Input: gcd(4248-2646,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 09:06:28 2006 Input: Mod(187*205,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4248, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 09:06:08 2006 Input: Mod(2*(3^3)*(7^2),34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2646, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 09:05:29 2006 Input: Mod((2*(3^3)*(7^2))^2,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(13481, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 09:05:03 2006 Input: Mod((2*(3^2)*(7^2))^2,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(28010, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 09:04:43 2006 Input: Mod((2*3^2*7^2)^2,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(28010, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 09:04:17 2006 Input: Mod((187*205)^2,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(13481, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 09:02:16 2006 Input: factor((3+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 2] [7 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 09:01:54 2006 Input: factor((21+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 4] [7 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:59:49 2006 Input: Mod(2*3^3*7^2,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2646, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:58:34 2006 Input: Mod(7938*882,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(13481, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:57:58 2006 Input: Mod(((2^2)*(3^6)*(7^4)),34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(13481, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:57:08 2006 Input: Mod(((2^2)*(3^6)*(7^4))^2,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(19564, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.010s sys 0m0.001s '192.156' ************** PARI ***************** Host 192.156.14.34 (192.156.14.34) Time: Fri Jul 7 08:57:02 2006 Input: 4075/4076 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4075/4076 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:56:47 2006 Input: Mod(((2^2)*(3^4)*(7^4))^2,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(13708, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:56:25 2006 Input: Mod((2^2*3^4*7^4)^2,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(13708, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.009s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:55:44 2006 Input: Mod((7938*882)^2,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(19564, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:55:29 2006 Input: Mod(7938*882,34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(13481, 34087) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:45:44 2006 Input: (3+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 882 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:41:55 2006 Input: (21+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7938 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '204.210' ************** PARI ***************** Host 204.210.46.89 (204.210.46.89) Time: Fri Jul 7 08:41:48 2006 Input: 20*x = 24 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 480 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '204.210' ************** PARI ***************** Host 204.210.46.89 (204.210.46.89) Time: Fri Jul 7 08:41:22 2006 Input: 20x = 24 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 24 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x=24. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:40:54 2006 Input: factor((21+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 4] [7 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:39:05 2006 Input: factor((16+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 4] [73 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:37:04 2006 Input: factor((17+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [7 1] [11 1] [41 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:36:53 2006 Input: factor((18+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [2239 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:36:37 2006 Input: factor((19+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 1] [1187 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:36:26 2006 Input: factor((20+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [7529 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:35:31 2006 Input: factor((-20+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [3 2] [17 1] [47 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:35:16 2006 Input: factor((-19+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [2 1] [47 1] [73 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:34:59 2006 Input: factor((-18+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [3 1] [7 1] [311 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:34:34 2006 Input: factor((-17+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [2 1] [3 1] [1033 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:33:59 2006 Input: factor((-16+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [11 1] [13 1] [41 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:27:59 2006 Input: factor((-15+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [2 1] [3 2] [307 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:25:08 2006 Input: factor((-14+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [3 1] [7 1] [13 1] [19 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:24:56 2006 Input: factor((-13+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [2 1] [2423 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:24:30 2006 Input: factor((-12+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [3 1] [19 1] [79 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:23:55 2006 Input: factor((-11+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [2 1] [3 3] [7 1] [11 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:23:17 2006 Input: factor((11+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [11 1] [179 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:22:56 2006 Input: factor((12+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 2] [13 1] [37 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:22:46 2006 Input: factor((13+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 1] [787 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:22:25 2006 Input: factor((14+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [7 1] [17 1] [43 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:22:11 2006 Input: factor((15+184)^2-34087) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 1] [919 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:21:44 2006 Input: (15+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5514 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:21:36 2006 Input: (14+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5117 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:21:27 2006 Input: (13+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4722 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:21:15 2006 Input: (12+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4329 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:20:42 2006 Input: (11+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3938 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:04:30 2006 Input: factor(2013) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [11 1] [61 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:04:12 2006 Input: factor(2394) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 2] [7 1] [19 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:03:55 2006 Input: factor(2777) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2777 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:03:28 2006 Input: factor(3162) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 1] [17 1] [31 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:02:48 2006 Input: factor(3549) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [7 1] [13 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:02:25 2006 Input: factor(-2403) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [3 3] [89 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:02:13 2006 Input: factor(-2758) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [2 1] [7 1] [197 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:02:00 2006 Input: factor(-3111) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [3 1] [17 1] [61 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:01:41 2006 Input: factor(-3462) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [2 1] [3 1] [577 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:01:26 2006 Input: factor(-3811) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [37 1] [103 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:01:02 2006 Input: (-10+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -3811 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:00:52 2006 Input: (-9+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -3462 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:00:44 2006 Input: (-8+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -3111 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 08:00:27 2006 Input: (-7+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -2758 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:58:53 2006 Input: (-6+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -2403 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:58:33 2006 Input: (10+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3549 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:58:24 2006 Input: (9+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3162 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:58:12 2006 Input: (8+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2777 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:58:04 2006 Input: (7+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2394 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:57:51 2006 Input: (6+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2013 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:36:55 2006 Input: factor(-2046) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [2 1] [3 1] [11 1] [31 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:36:40 2006 Input: factor(-1687) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [7 1] [241 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:36:22 2006 Input: factor(-1326) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [2 1] [3 1] [13 1] [17 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:36:07 2006 Input: factor(-963) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [3 2] [107 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:35:42 2006 Input: factor(-598) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-1 1] [2 1] [13 1] [23 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:35:22 2006 Input: (-1+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -598 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:35:14 2006 Input: (-2+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -963 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:35:05 2006 Input: (-3+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1326 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:34:57 2006 Input: (-4+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1687 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:34:38 2006 Input: (-5+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -2046 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:34:16 2006 Input: (-5+184)^2-3408 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 28633 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:34:02 2006 Input: (-4+184)^2-3408 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 28992 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:33:50 2006 Input: (-3+184)^2-3408 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29353 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:33:41 2006 Input: (-2+184)^2-3408 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 29716 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:33:25 2006 Input: (-1+184)^2-3408 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 30081 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:31:41 2006 Input: factor(1634) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [19 1] [43 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:31:21 2006 Input: factor(1257) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [3 1] [419 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:29:57 2006 Input: factor(882) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 2] [7 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:29:46 2006 Input: factor(509) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [509 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:29:35 2006 Input: factor(138) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 1] [3 1] [23 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.085s user 0m0.009s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:29:09 2006 Input: (5+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1634 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:28:58 2006 Input: (4+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1257 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:27:18 2006 Input: (3+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 882 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:27:04 2006 Input: (2+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 509 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:26:30 2006 Input: (1+184)^2-34087 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 138 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:21:02 2006 Input: exp(2.9747)^.5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4.4253527818769446198762720333182236501 ? Goodbye! Errors/timing (if any): Timing: real 0m0.099s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:20:50 2006 Input: (exp(2.9747)^.5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: (exp(2.9747)^.5 ^ Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:20:30 2006 Input: (exp^2.9747)^.5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: (exp^2.9747)^.5 ^----------- Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:18:44 2006 Input: (exp^((log(34087)*log(log(34087)))^.5)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: (exp^((log(34087)*log(lo ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 07:18:34 2006 Input: (exp^((log(34087)*log(log(34087)))^.5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...087)*log(log(34087)))^.5) ^ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.131.199 (72.30.131.199) Time: Fri Jul 7 06:40:32 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.049s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 06:37:15 2006 Input: gcd(13446,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 06:36:51 2006 Input: Mod(6089^41^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(13447, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.98 (209.184.114.98) Time: Fri Jul 7 06:36:38 2006 Input: gcd(6088,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:36:25 2006 Input: Mod(6120^39^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(6089, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:36:12 2006 Input: gcd(6119,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:36:01 2006 Input: Mod(456^37^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(6120, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:35:50 2006 Input: gcd(455,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:35:34 2006 Input: Mod(2468^31^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(456, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.005s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:35:19 2006 Input: gcd(2467,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.008s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:35:01 2006 Input: Mod(982^29^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2468, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:34:47 2006 Input: gcd(981,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:34:36 2006 Input: Mod(5519^27^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(982, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:34:19 2006 Input: gcd(5518,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:34:05 2006 Input: Mod(8160^23^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(5519, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:33:39 2006 Input: gcd(8159,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:33:21 2006 Input: Mod(5058^19^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(8160, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:32:59 2006 Input: gcd(5057,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:32:47 2006 Input: gcd(4236,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:32:38 2006 Input: gcd(8310,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:32:31 2006 Input: gcd(2965,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:32:18 2006 Input: gcd(10734,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.008s sys 0m0.009s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:32:08 2006 Input: gcd(11050,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:32:00 2006 Input: gcd(11051,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:31:53 2006 Input: gcd(4908,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:31:36 2006 Input: Mod(4237^17^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(5058, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:27:38 2006 Input: Mod(8311^13^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4237, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:27:34 2006 Input: Mod(8311^13^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4237, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:27:20 2006 Input: gcd(8311,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:27:08 2006 Input: Mod(2966^11^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(8311, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:26:47 2006 Input: gcd(2966,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:26:28 2006 Input: Mod(10735^7^4,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2966, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:26:09 2006 Input: gcd(10735,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:25:56 2006 Input: Mod(11051^5^5,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(10735, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:25:33 2006 Input: gcd(11051,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:25:17 2006 Input: Mod(4909^3^8,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(11051, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.010s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:24:53 2006 Input: gcd(4909,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:22:06 2006 Input: Mod(2^2^13,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4909, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:10:33 2006 Input: Mod(6245^3^8,13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1365, 13193) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:10:06 2006 Input: Mod(2^2^13,13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(6245, 13193) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:09:29 2006 Input: Mod(2^3^8,13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(3356, 13193) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:09:17 2006 Input: Mod(2^2^13,13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(6245, 13193) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:09:07 2006 Input: Mod(2^2^13),13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: Mod(2^2^13),13193) ^-------- Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:08:20 2006 Input: Mod(2^(13^3),13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(8745, 13193) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:02:11 2006 Input: Mod((2^13)^3,13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7743, 13193) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:01:58 2006 Input: Mod(2^(13^3),13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(8745, 13193) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:01:49 2006 Input: Mod(2^13^3,13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(8745, 13193) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:00:47 2006 Input: gcd(8744,13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:00:28 2006 Input: Mod(2^13^3,13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(8745, 13193) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Fri Jul 7 06:00:08 2006 Input: mod(2^13^3,13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** obsolete function: mod(2^13^3,13193) ^----------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.026s user 0m0.008s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Fri Jul 7 02:29:30 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.009s sys 0m0.003s '72.30.9' ************** PARI ***************** Host 72.30.98.35 (72.30.98.35) Time: Fri Jul 7 01:21:58 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.023s sys 0m0.009s '66.249.' ************** PARI ***************** Host 66.249.65.112 (66.249.65.112) Time: Fri Jul 7 00:15:43 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '67.161.' ************** PARI ***************** Host 67.161.106.93 (67.161.106.93) Time: Thu Jul 6 23:07:34 2006 Input: 45*23 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1035 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Thu Jul 6 22:55:13 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Thu Jul 6 22:37:22 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.049s user 0m0.006s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Thu Jul 6 22:23:05 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.009s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Thu Jul 6 22:02:10 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.160 (68.142.249.160) Time: Thu Jul 6 19:17:14 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '136.152' ************** PARI ***************** Host 136.152.180.19 (136.152.180.19) Time: Thu Jul 6 17:52:22 2006 Input: A=[2, 3, 4; 2 ,4 ,5] matrank(A) v = matker(A) v * 2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 4] [2 4 5] ? %2 = 2 ? %3 = [-1/2] [-1] [1] ? %4 = [-1] [-2] [2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '136.152' ************** PARI ***************** Host 136.152.180.19 (136.152.180.19) Time: Thu Jul 6 17:52:00 2006 Input: A=[2, 3, 4; 2 ,4 ,5] matrank(A) matker(A) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 4] [2 4 5] ? %2 = 2 ? %3 = [-1/2] [-1] [1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.004s '136.152' ************** PARI ***************** Host 136.152.180.19 (136.152.180.19) Time: Thu Jul 6 17:51:25 2006 Input: A=[2, 3, 4; 2 ,4 ,5] matrank(A) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 4] [2 4 5] ? %2 = 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.057s user 0m0.008s sys 0m0.005s '136.152' ************** PARI ***************** Host 136.152.180.19 (136.152.180.19) Time: Thu Jul 6 17:51:01 2006 Input: A=[2, 3, 4; 2 ,4 ,5] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 4] [2 4 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '136.152' ************** PARI ***************** Host 136.152.180.19 (136.152.180.19) Time: Thu Jul 6 17:50:46 2006 Input: A=[2, 3, 4; 2 ,4 ,5]; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '136.152' ************** PARI ***************** Host 136.152.180.19 (136.152.180.19) Time: Thu Jul 6 17:50:34 2006 Input: A=[2, 3, 4; 2 ,4 ,5] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3 4] [2 4 5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '136.152' ************** PARI ***************** Host 136.152.180.19 (136.152.180.19) Time: Thu Jul 6 17:50:21 2006 Input: A=[2 3 4; 2 4 5] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [234] [245] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '69.235.' ************** PARI ***************** Host 69.235.23.161 (69.235.23.161) Time: Thu Jul 6 17:44:22 2006 Input: 23-4x=27 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 27 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x=27. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Thu Jul 6 16:37:34 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.025s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Thu Jul 6 16:15:28 2006 Input: ((p0 + B*(p1 - p0))/(pw0 + B*(pw1 - pw0)) - p0/pw0) * pw1*pw0/(p1*pw0 - pw1*p0) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = pw1*B/((-pw0 + pw1)*B + pw0) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Thu Jul 6 16:15:18 2006 Input: ((p0 + B*(p1 - p0))/(pw0 + B*(pw1 - pw0)) - p0/pw0) * pw1*pw0 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -pw1^2*B/((-pw0 + pw1)*B + pw0)*p0 + pw1*pw0*p1*B/((-pw0 + pw1)*B + pw0) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Thu Jul 6 16:14:39 2006 Input: ((p0 + B*(p1 - p0))/(pw0 + B*(pw1 - pw0)) - p0/pw0) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -pw1/pw0*B/((-pw0 + pw1)*B + pw0)*p0 + p1*B/((-pw0 + pw1)*B + pw0) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Thu Jul 6 16:14:19 2006 Input: (p0 + B*(p1 - p0))/(pw0 + B*(pw1 - pw0)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-B + 1)/((-pw0 + pw1)*B + pw0))*p0 + p1*B/((-pw0 + pw1)*B + pw0) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Thu Jul 6 16:12:03 2006 Input: ((p0 + B*(p1 - p0))/(pw0 + B*(pw1 - pw0)) - p0/pw0) * pw1*pw0/(p1*pw0 - pw1*p0) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = pw1*B/((-pw0 + pw1)*B + pw0) ? Goodbye! Errors/timing (if any): Timing: real 0m0.032s user 0m0.005s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Thu Jul 6 16:11:26 2006 Input: ((p0 + B*(p1 - p0)/(pw0 + B*(pw1 - pw0)) - p0/pw0) * pw1*pw0/(p1*pw0 - pw1*p0) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...)*pw1*pw0/(p1*pw0-pw1*p0) ^ Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:09:57 2006 Input: factor(13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [83 1] [167 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:09:04 2006 Input: gcd(10509,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:08:49 2006 Input: Mod(2^51^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(10511, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:08:34 2006 Input: gcd(3947,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:08:22 2006 Input: Mod(2^49^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(3948, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:07:22 2006 Input: gcd(12047,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:07:09 2006 Input: Mod(2^47^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(12048, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:06:59 2006 Input: gcd(6042,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:06:44 2006 Input: Mod(2^43^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(6043, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:06:35 2006 Input: gcd(5476,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:06:21 2006 Input: Mod(2^41^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(5477, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:06:09 2006 Input: gcd(12018,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:05:55 2006 Input: Mod(2^39^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(12019, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:05:42 2006 Input: gcd(6756,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:05:30 2006 Input: Mod(2^37^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(6757, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:05:11 2006 Input: gcd(8352,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:04:57 2006 Input: Mod(2^31^2,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(8353, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:04:38 2006 Input: gcd(11986,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:04:26 2006 Input: Mod(2^29^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(11987, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:04:16 2006 Input: gcd(588,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:04:02 2006 Input: Mod(2^27^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(589, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:03:53 2006 Input: gcd(12363,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:03:42 2006 Input: Mod(2^23^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(12364, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:03:32 2006 Input: gcd(6942,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:03:16 2006 Input: Mod(2^19^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(6943, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:03:02 2006 Input: gcd(5916,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:02:50 2006 Input: Mod(2^17^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(5917, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:02:38 2006 Input: gcd(1897,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:02:25 2006 Input: Mod(2^13^3,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1898, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:02:10 2006 Input: gcd(8864,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:01:56 2006 Input: Mod(2^11^4,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(8865, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:01:34 2006 Input: gcd(9762,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:01:19 2006 Input: Mod(2^7^5,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(9763, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:00:59 2006 Input: gcd(2971,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.010s sys 0m0.002s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:00:48 2006 Input: Mod(2^5^6,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2972, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:00:26 2006 Input: gcd(588,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 15:00:15 2006 Input: Mod(2^3^9,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(589, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:59:47 2006 Input: gcd(7862,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:59:25 2006 Input: Mod(2^2^14,13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7863, 13861) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:57:16 2006 Input: Factor(13861) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: Factor(13861) ^------------- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:54:06 2006 Input: gcd(14315,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:53:54 2006 Input: Mod(7^83^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(14316, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:53:41 2006 Input: gcd(18145,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:53:27 2006 Input: Mod(7^79^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(18146, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:53:10 2006 Input: gcd(4261,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:52:56 2006 Input: Mod(7^73^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4261, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:52:41 2006 Input: gcd(3969,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:52:19 2006 Input: Mod(7^71^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(3970, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:52:06 2006 Input: gcd(14218,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:51:53 2006 Input: Mod(7^67^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(14219, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:51:41 2006 Input: gcd(20814,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:51:26 2006 Input: Mod(7^61^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(20815, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:50:36 2006 Input: gcd(7896,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:50:21 2006 Input: Mod(7^59^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7897, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:50:03 2006 Input: gcd(4507,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:49:58 2006 Input: gcd(4507,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:49:47 2006 Input: Mod(7^57^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4508, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:49:31 2006 Input: gcd(15268,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:49:17 2006 Input: Mod(7^53^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(15269, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:49:03 2006 Input: gcd(25953,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:48:48 2006 Input: Mod(7^51^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(25954, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:48:34 2006 Input: gcd(24838,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:48:17 2006 Input: Mod(7^49^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(24839, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:48:00 2006 Input: Mod(7^47^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:47:26 2006 Input: gcd(14589,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:47:11 2006 Input: Mod(7^43^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(14590, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:46:23 2006 Input: gcd(7,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:46:07 2006 Input: Mod(7^47^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:36:54 2006 Input: gcd(2902,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:36:39 2006 Input: Mod(7^41^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2903, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:36:09 2006 Input: gcd(11976,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:35:52 2006 Input: Mod(7^39^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(11977, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:35:24 2006 Input: gcd(20409,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:35:10 2006 Input: Mod(7^37^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(20410, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:34:19 2006 Input: gcd(16591,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:33:59 2006 Input: Mod(7^31^3,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(16592, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:33:52 2006 Input: gcd(10288,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:33:39 2006 Input: Mod(7^31^2,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(10289, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.003s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:32:49 2006 Input: gcd(23111,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:32:38 2006 Input: Mod(7^29^3,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(23112, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:32:09 2006 Input: gcd(7132,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:31:58 2006 Input: Mod(7^27^3,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7133, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:31:28 2006 Input: gcd(6733,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:31:18 2006 Input: gcd(10686,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:31:05 2006 Input: Mod(7^23^3,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(10687, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:30:35 2006 Input: gcd(6734,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:30:22 2006 Input: Mod(7^19^3,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(6734, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:29:46 2006 Input: gcd(23337,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:29:33 2006 Input: Mod(7^17^3,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(23338, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:28:55 2006 Input: gcd(8498,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:28:42 2006 Input: Mod(7^13^3,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(8499, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:28:11 2006 Input: gcd(21041,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:27:48 2006 Input: Mod(7^11^4,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(21042, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.010s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:27:18 2006 Input: gcd(12816,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:27:01 2006 Input: Mod(7^7^5,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(12817, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:26:28 2006 Input: gcd(1802,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:26:12 2006 Input: Mod(7^5^6,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1803, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:25:04 2006 Input: gcd(7132,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:24:51 2006 Input: Mod(7^3^9,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7133, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:23:11 2006 Input: gcd(11215,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:22:27 2006 Input: gcd(11216,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:21:07 2006 Input: Mod(7^2^14,26869) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(11216, 26869) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:20:37 2006 Input: Mod(2^2^13,13193) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(6245, 13193) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:19:18 2006 Input: 7^(2^14) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1219797091776349447313473055831235474377936823257311387753723019918194420395888579205451162415611042102662944949317360997623422538145567718255770573118320126972399903225365088242591061126699071340873874241955652597181633145773305235005370498323081571644429986303392737452294058762723290130003880663079618041053101542828735586283173330958432602715083454308183017212454064056065186670585855629540245679808797690118070822743995933328648034797458889941682412555081055741216923311142277860100840169819462760683063609322561121087685902761627601802468525013410730106513300874916079450849672671621903004932859131226927792618161047285824013960647030765171499581239914330176371402278512375164608213123452133942070629387393069382546148647943654315189253913746259834597800395652483705200743963092161951718907493027049092000534403779757662713974317293571604507643293587311315367420205013341422379480679699933046857532309048621182635881110687145711230697205172177943983661103336917803336228779992432225598871419191087500454625332580044227986811275405309382985082757824373268697035659412897485333556249333048807575647374214967958130396367540263637768841283658372746021772006435420483529523904547534289963731811566122742001832273430449618578093478016983392454309364588179037403937607403582780288053159802302016489542273793263914514549149225242257649928769671235790362357823114328628647696799962162770957485441771339319976112039149029972916674043128833622512506295111781252821329555084168003532198846958667366672101987189018525389899529853820876664614419962314611759568835740684421301948167314060903131038753753448593233267809704656511005418067703071958495521405709591074743282132220142191076257489832593651537955224576359693749169683409755269601548224598142940876328988183469986273439637113014212370430467616795563956514404369463599652928655897226929192816163843315613688249088428968004946142218545930294967467042655096691716131382153563541778566940874480813017009978444501638320115779476466690107160253798970535773817784680735575385254458981414317346624804696418098673412397680996046636908120321078428467602541557837490671111033996404562174909729406759052374516262995928002794612026757955774612275344254195651807131969396855433058252245822359453039291797740573520089227447222953893564744499777994441398919136687720020219884986134832716469843684793914724716730745476546924605127234831664973823814607538158622698666224712055538291711094559183056802445208271226092783230424367276995819403172838703017699186255683558689089620574869121720805576993437401454201978695543656705290185305246806601910399238144527623995417717456451727020916717359777367802895595162278172140242610040911356250800258296854726114648616216348227588511736466149957638689629106919779602375798488388595019864494400278004231487192491037841182092473894887168477235466869698264238551266236277327492393481627438289075256836685448316174591250541210551538424185029702679189642708094483968443947509820139572930548777680408360554968559823771889922388954664163592386958588740727313105128786188414823437381824079421355139836375932098092431529646068327984319708387152113139174675601716769765334118504915992229123286720652059925243662474621217695617873[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.014s sys 0m0.010s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:18:39 2006 Input: (7^2)^14 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 459986536544739960976801 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:18:21 2006 Input: 7^2^14 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1219797091776349447313473055831235474377936823257311387753723019918194420395888579205451162415611042102662944949317360997623422538145567718255770573118320126972399903225365088242591061126699071340873874241955652597181633145773305235005370498323081571644429986303392737452294058762723290130003880663079618041053101542828735586283173330958432602715083454308183017212454064056065186670585855629540245679808797690118070822743995933328648034797458889941682412555081055741216923311142277860100840169819462760683063609322561121087685902761627601802468525013410730106513300874916079450849672671621903004932859131226927792618161047285824013960647030765171499581239914330176371402278512375164608213123452133942070629387393069382546148647943654315189253913746259834597800395652483705200743963092161951718907493027049092000534403779757662713974317293571604507643293587311315367420205013341422379480679699933046857532309048621182635881110687145711230697205172177943983661103336917803336228779992432225598871419191087500454625332580044227986811275405309382985082757824373268697035659412897485333556249333048807575647374214967958130396367540263637768841283658372746021772006435420483529523904547534289963731811566122742001832273430449618578093478016983392454309364588179037403937607403582780288053159802302016489542273793263914514549149225242257649928769671235790362357823114328628647696799962162770957485441771339319976112039149029972916674043128833622512506295111781252821329555084168003532198846958667366672101987189018525389899529853820876664614419962314611759568835740684421301948167314060903131038753753448593233267809704656511005418067703071958495521405709591074743282132220142191076257489832593651537955224576359693749169683409755269601548224598142940876328988183469986273439637113014212370430467616795563956514404369463599652928655897226929192816163843315613688249088428968004946142218545930294967467042655096691716131382153563541778566940874480813017009978444501638320115779476466690107160253798970535773817784680735575385254458981414317346624804696418098673412397680996046636908120321078428467602541557837490671111033996404562174909729406759052374516262995928002794612026757955774612275344254195651807131969396855433058252245822359453039291797740573520089227447222953893564744499777994441398919136687720020219884986134832716469843684793914724716730745476546924605127234831664973823814607538158622698666224712055538291711094559183056802445208271226092783230424367276995819403172838703017699186255683558689089620574869121720805576993437401454201978695543656705290185305246806601910399238144527623995417717456451727020916717359777367802895595162278172140242610040911356250800258296854726114648616216348227588511736466149957638689629106919779602375798488388595019864494400278004231487192491037841182092473894887168477235466869698264238551266236277327492393481627438289075256836685448316174591250541210551538424185029702679189642708094483968443947509820139572930548777680408360554968559823771889922388954664163592386958588740727313105128786188414823437381824079421355139836375932098092431529646068327984319708387152113139174675601716769765334118504915992229123286720652059925243662474621217695617873[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.020s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:12:15 2006 Input: gcd(21,7) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.117.126 (209.184.117.126) Time: Thu Jul 6 14:12:06 2006 Input: gcd(26869,7) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.010s sys 0m0.002s '82.56.5' ************** PARI ***************** Host 82.56.59.205 (82.56.59.205) Time: Thu Jul 6 13:58:20 2006 Input: sage: maxima("ilt( -1/s ,s,t)") Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: :maxima("ilt( -1/s ,s,t)"). *** unexpected character: sage:maxima("ilt( -1/s ^-------------------- Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '66.249.' ************** PARI ***************** Host 66.249.65.147 (66.249.65.147) Time: Thu Jul 6 12:36:51 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '66.249.' ************** PARI ***************** Host 66.249.65.147 (66.249.65.147) Time: Thu Jul 6 12:36:46 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.055s user 0m0.010s sys 0m0.006s '66.249.' ************** PARI ***************** Host 66.249.65.147 (66.249.65.147) Time: Thu Jul 6 11:40:10 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.049s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Thu Jul 6 11:02:34 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.082s user 0m0.006s sys 0m0.006s '72.58.7' ************** PARI ***************** Host 72.58.77.11 (72.58.77.11) Time: Thu Jul 6 10:17:08 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.86 (68.142.251.86) Time: Thu Jul 6 09:43:27 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.278s user 0m0.007s sys 0m0.009s '58.69.7' ************** PARI ***************** Host 58.69.75.168 (58.69.75.168) Time: Thu Jul 6 01:53:58 2006 Input: 0.00000016(0.00024) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.00024000000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (0.00024). Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.13 (68.142.251.13) Time: Wed Jul 5 22:38:58 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.119s user 0m0.007s sys 0m0.010s '72.30.1' ************** PARI ***************** Host 72.30.129.123 (72.30.129.123) Time: Wed Jul 5 21:18:36 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.031s user 0m0.008s sys 0m0.005s '137.151' ************** PARI ***************** Host 137.151.174.48 (137.151.174.48) Time: Wed Jul 5 18:18:17 2006 Input: 327/425 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 327/425 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.132.102 (72.30.132.102) Time: Wed Jul 5 15:07:00 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 14:15:01 2006 Input: (-2*t+4)^2 + (2*h-4*h*t)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (16*h^2 + 4)*t^2 + (-16*h^2 - 16)*t + (4*h^2 + 16) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 14:14:40 2006 Input: (-2*t+4)^2 + (2*h-4*h)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4*t^2 - 16*t + (4*h^2 + 16) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 14:10:33 2006 Input: (-2*t+4)^2 + (2*h-4*h)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4*t^2 - 16*t + (4*h^2 + 16) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.103.19 (72.30.103.19) Time: Wed Jul 5 14:06:46 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.060s user 0m0.005s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:55:42 2006 Input: (-h*(-1/4) + h - (1/2*h)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3/4*h ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:55:23 2006 Input: (h/2*(-1/4) + h - (1/2*h)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3/8*h ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:54:28 2006 Input: -2*(1- t)^2 + t^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -t^2 + 4*t - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:50:39 2006 Input: (h/2*(-1/4) + h - (-1/2*h)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 11/8*h ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:48:09 2006 Input: 9/8*(-1/2*h)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 9/32*h^2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:47:41 2006 Input: (-1*h*(-1/4) + h - (-1/2*h)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7/4*h ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:46:42 2006 Input: (h/2*(-1/4) + h - (-1/2*h)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 11/8*h ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '169.226' ************** PARI ***************** Host 169.226.18.76 (169.226.18.76) Time: Wed Jul 5 13:30:20 2006 Input: 10/80 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1/8 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.011s sys 0m0.001s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:26:32 2006 Input: (h/2*x + h -y) * (-1*h*x +h -y) + c * (y)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1/2*h^2*x^2 + (-1/2*h^2 + 1/2*y*h)*x + (h^2 - 2*y*h + (c + 1)*y^2) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:18:15 2006 Input: (h/2*x + h) * (-1*h*x +h) + c * (y)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1/2*h^2*x^2 - 1/2*h^2*x + (h^2 + y^2*c) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:01:38 2006 Input: y = t*( -1*(1/4*t^2 + 1/2*t + 1/4)/(-1/4*t^2 + 1/2*t - 1/4) - 1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -4*t^2/(-t^2 + 2*t - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 13:01:18 2006 Input: y = t*(( -1*(1/4*t^2 + 1/2*t + 1/4)/(-1/4*t^2 + 1/2*t - 1/4) -1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...)/(-1/4*t^2+1/2*t-1/4)-1) ^ Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:58:45 2006 Input: y = t*(x-1) (x * y + (-1/4)*( -1 * x - y + 1)^2)/(x-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = t*x - t ? %2 = (-1/4*t^2 + 1/2*t - 1/4)*x + (1/4*t^2 + 1/2*t + 1/4) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:57:12 2006 Input: y = t*(x-1) x * y + (-1/4)*( -1 * x - y + 1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = t*x - t ? %2 = (-1/4*t^2 + 1/2*t - 1/4)*x^2 + (1/2*t^2 + 1/2)*x + (-1/4*t^2 - 1/2*t - 1/4) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:42:40 2006 Input: x * y + (-1/4)*( -1 * x - y + 1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = -1/4*x^2 + (1/2*y + 1/2)*x + (-1/4*y^2 + 1/2*y - 1/4) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:37:33 2006 Input: t* ( (-1/4*t^2 - 1/2*t - 1/4)/(1/4*t^2 + 3/2*t + 1/4) -1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (-2*t^3 - 8*t^2 - 2*t)/(t^2 + 6*t + 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:34:33 2006 Input: y = t*(x-1) (x * y + (1/4)*( -1 * x - y + 1)^2)/(x-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = t*x - t ? %2 = (1/4*t^2 + 3/2*t + 1/4)*x + (-1/4*t^2 - 1/2*t - 1/4) ? Goodbye! Errors/timing (if any): Timing: real 0m0.087s user 0m0.007s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:33:20 2006 Input: y = t*(x-1) x * y + (1/4)*( -1 * x - y + 1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = t*x - t ? %2 = (1/4*t^2 + 3/2*t + 1/4)*x^2 + (-1/2*t^2 - 2*t - 1/2)*x + (1/4*t^2 + 1/2*t + 1/4) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:31:44 2006 Input: x * y + (1/4)*( -1 * x - y + 1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1/4*x^2 + (3/2*y - 1/2)*x + (1/4*y^2 - 1/2*y + 1/4) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:31:21 2006 Input: x * y + (c)*( -1 * x - y + 1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = c*x^2 + ((2*c + 1)*y - 2*c)*x + (c*y^2 - 2*c*y + c) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:31:02 2006 Input: x * y + (1/2)*( -1 * x - y + 1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1/2*x^2 + (2*y - 1)*x + (1/2*y^2 - y + 1/2) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:30:01 2006 Input: (2*c +1)^2 - 4*(c*c) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4*c + 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:27:36 2006 Input: x * y + c*( -1 * x - y + 1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = c*x^2 + ((2*c + 1)*y - 2*c)*x + (c*y^2 - 2*c*y + c) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:23:54 2006 Input: x = 1 y = 0 x * y + c*( -1 * x - y + 1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 0 ? ? %3 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:22:58 2006 Input: x * y + c*( -1 * x - y + 1)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = c*x^2 + ((2*c + 1)*y - 2*c)*x + (c*y^2 - 2*c*y + c) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:17:59 2006 Input: m = [ 1, 0, 0; -2, 2, 0; 1, -2, 1] v = [ a^2; -2*a; 1] m^(-1)* v Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [-2 2 0] [1 -2 1] ? ? %2 = [a^2] [-2*a] [1] ? ? %3 = [a^2] [a^2 - a] [a^2 - 2*a + 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:16:21 2006 Input: m = [ 1, 0, 0; -2, 2, 0; 1, -2, 1] v = [ -a^2; -2*a; 1] m^(-1)* v Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [-2 2 0] [1 -2 1] ? ? %2 = [-a^2] [-2*a] [1] ? ? %3 = [-a^2] [-a^2 - a] [-a^2 - 2*a + 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:14:20 2006 Input: m = [ 1, 0, 0; -2, 2, 0; 1, -2, 1] v = [ -1*a; 1; 0] m^(-1)* v Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [-2 2 0] [1 -2 1] ? ? %2 = [-a] [1] [0] ? ? %3 = [-a] [-a + 1/2] [-a + 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:11:12 2006 Input: m = [ 1, 0, 0; -2, 2, 0; 1, -2, 1] v = [t-a; 0; 0] m^(-1)* v Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [-2 2 0] [1 -2 1] ? ? %2 = [t - a] [0] [0] ? ? %3 = [t - a] [t - a] [t - a] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:07:36 2006 Input: m = [ 1, 0, 0; -2, 2, 0; 1, -2, 1] m^(-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [-2 2 0] [1 -2 1] ? ? %2 = [1 0 0] [1 1/2 0] [1 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 12:07:05 2006 Input: m = [ 1, 0, 0; -2, 2, 0; 1, -2, 1;] m^(-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 1/m ? Goodbye! Errors/timing (if any): *** unexpected character: m=[1,0,0;-2,2,0;1,-2,1;] ^- Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '66.158.' ************** PARI ***************** Host 66.158.49.19 (66.158.49.19) Time: Wed Jul 5 11:47:28 2006 Input: y=x x=y^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x ? ? %2 = x^2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '66.158.' ************** PARI ***************** Host 66.158.49.19 (66.158.49.19) Time: Wed Jul 5 11:47:04 2006 Input: y=? x=y^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = y^2 ? Goodbye! Errors/timing (if any): *** unexpected character: y=? ^- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '66.158.' ************** PARI ***************** Host 66.158.49.19 (66.158.49.19) Time: Wed Jul 5 11:46:55 2006 Input: y=? x^.5=y^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: y=? ^- *** unexpected character: x^.5=y^2 ^---- Timing: real 0m0.014s user 0m0.004s sys 0m0.007s '66.158.' ************** PARI ***************** Host 66.158.49.19 (66.158.49.19) Time: Wed Jul 5 11:46:22 2006 Input: y=4 x^.5=y^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? ? Goodbye! Errors/timing (if any): *** unexpected character: x^.5=y^2 ^---- Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '66.158.' ************** PARI ***************** Host 66.158.49.19 (66.158.49.19) Time: Wed Jul 5 11:46:04 2006 Input: y=4 x^5=y^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? ? Goodbye! Errors/timing (if any): *** unexpected character: x^5=y^2 ^---- Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '66.158.' ************** PARI ***************** Host 66.158.49.19 (66.158.49.19) Time: Wed Jul 5 11:45:00 2006 Input: y=4 x=y^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? %2 = 16 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:43:54 2006 Input: (t*x - t* a + a^2 - x^2 )/(x- a) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -x + (t - a) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:43:22 2006 Input: (t*x - t* a + a^2 - x^2 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -x^2 + t*x + (-a*t + a^2) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:37:04 2006 Input: (x^2 + 4*(t*x - t)^2 - 1)/(x-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (4*t^2 + 1)*x + (-4*t^2 + 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:36:29 2006 Input: (x^2 + 4*(t*x - t)^2 - 1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (4*t^2 + 1)*x^2 - 8*t^2*x + (4*t^2 - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:27:57 2006 Input: (x^2 + 4*(t*x- 2*t)^2 - 4)/(x-2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (4*t^2 + 1)*x + (-8*t^2 + 2) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:26:56 2006 Input: x^2 + 4*(t*x- 2*t)^2 - 4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (4*t^2 + 1)*x^2 - 16*t^2*x + (16*t^2 - 4) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:15:15 2006 Input: y = -1 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1 ? ? ? %2 = x^2 - 15/4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.009s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:13:57 2006 Input: y = 1 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? ? %2 = x^2 - 2*x + 1/4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:12:26 2006 Input: y = 0 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0 ? ? ? %2 = x^2 - x - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:12:17 2006 Input: x = 0 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0 ? ? ? %2 = 1/4*y^2 + 2*y - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:11:26 2006 Input: x = 1 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? ? %2 = 1/4*y^2 + y - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:11:09 2006 Input: x = 0 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0 ? ? ? %2 = 1/4*y^2 + 2*y - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:11:01 2006 Input: x = 1 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? ? %2 = 1/4*y^2 + y - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:10:53 2006 Input: x = 0 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0 ? ? ? %2 = 1/4*y^2 + 2*y - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:10:00 2006 Input: x = 1 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? ? ? %2 = 1/4*y^2 + y - 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:09:24 2006 Input: x = 0 y = 0 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0 ? %2 = 0 ? ? ? %3 = -2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:08:45 2006 Input: x = 1 y = 3 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 3 ? ? ? %3 = 13/4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:08:36 2006 Input: x = 1 y = 2 f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 2 ? ? ? %3 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:07:55 2006 Input: x = 1 y = 1 (x-y+1)*(2-x) f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 1 ? %3 = 1 ? %4 = -3/4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:07:44 2006 Input: //x = 1 //y = 1 (x-y+1)*(2-x) f =(x-y+1)*(x-2) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = -x^2 + (y + 1)*x + (-2*y + 2) ? %2 = x^2 + (-y - 1)*x + (1/4*y^2 + 2*y - 2) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=1 ^----- Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:07:16 2006 Input: //x = 1 //y = 1 (x-y+1)*(2-x) f =(x-y+1)*(2-x) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = -x^2 + (y + 1)*x + (-2*y + 2) ? %2 = -x^2 + (y + 1)*x + (1/4*y^2 - 2*y + 2) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=1 ^----- Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:06:32 2006 Input: //x = 1 //y = 1 f =(x-y+1)*(2-x) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = -x^2 + (y + 1)*x + (1/4*y^2 - 2*y + 2) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=1 ^----- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 11:06:18 2006 Input: x = 1 y = 1 f =(x-y+1)*(2-x) +(1/4)*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 1 ? ? %3 = 5/4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:59:15 2006 Input: x = 1 y = 1 f =(x-y+1)*(2-x) +c*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 1 ? ? %3 = c + 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:58:53 2006 Input: x = 1 y = 1 f =(x-y+1)*(x-2) +c*(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 1 ? ? %3 = c - 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:55:22 2006 Input: f =(x-y+1)*(x-2) +(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = x^2 + (-y - 1)*x + (y^2 + 2*y - 2) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:55:17 2006 Input: x = 1 y = 1 f =(x-y+1)*(x-2) +(y^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 1 ? ? %3 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:54:45 2006 Input: x = 1 y = 1 f =(x-y+1)*(x-2) + c* (y^2) poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 1 ? ? %3 = c - 1 ? %4 = 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:50:55 2006 Input: x = -1/8 y = 1 f =(x-y+1)*(x-2) poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1/8 ? %2 = 1 ? ? %3 = 17/64 ? ? Goodbye! Errors/timing (if any): *** poldisc: incorrect type in discsr. Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:50:03 2006 Input: x = -1/8 y = 1 f =(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1/8 ? %2 = 1 ? ? %3 = 49/32 ? ? ? Goodbye! Errors/timing (if any): *** poldisc: incorrect type in discsr. Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:49:13 2006 Input: f= 0 f =(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0 ? %2 = 10*x^2 + (-10*y + 17)*x + (9/4*y^2 - 7*y + 7) ? ? %3 = 10*y^2 - 60*y + 9 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.010s sys 0m0.001s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:48:00 2006 Input: f =(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 y = 1 poldisc(f(0)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 10*x^2 + (-10*y + 17)*x + (9/4*y^2 - 7*y + 7) ? ? %2 = 1 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: poldisc(f(0)) ^---- Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:47:48 2006 Input: f =(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 y = 1 poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 10*x^2 + (-10*y + 17)*x + (9/4*y^2 - 7*y + 7) ? ? %2 = 1 ? %3 = 10*y^2 - 60*y + 9 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:46:26 2006 Input: f =(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 10*x^2 + (-10*y + 17)*x + (9/4*y^2 - 7*y + 7) ? ? ? %2 = 10*y^2 - 60*y + 9 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:44:00 2006 Input: x = -1/4 y = 1 f =(x-y+1)*(x-2) + (c)*(2*x - y + 2)^2 //poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1/4 ? %2 = 1 ? ? %3 = 1/4*c + 9/16 ? ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //poldisc(f) ^------------ Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:41:16 2006 Input: x = -1/8 y = 1 f =(x-y+1)*(x-2) + (c)*(2*x - y + 2)^2 c //poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1/8 ? %2 = 1 ? ? %3 = 9/16*c + 17/64 ? ? %4 = c ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: //poldisc(f) ^------------ Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.129.138 (72.30.129.138) Time: Wed Jul 5 10:40:39 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:39:24 2006 Input: f =(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 10*x^2 + (-10*y + 17)*x + (9/4*y^2 - 7*y + 7) ? ? ? %2 = 10*y^2 - 60*y + 9 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:39:12 2006 Input: f (x, y)=(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Goodbye! Errors/timing (if any): *** poldisc: incorrect type in discsr. Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:38:21 2006 Input: f (x, y)=(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 = 0 poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 1 ? Goodbye! Errors/timing (if any): *** unexpected character: ...)*(x-2)+(9/4)*(2*x-y+2)^2=0 ^-- Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:38:09 2006 Input: f =(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 = 0 poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 1 ? Goodbye! Errors/timing (if any): *** unexpected character: ...)*(x-2)+(9/4)*(2*x-y+2)^2=0 ^-- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:37:05 2006 Input: f =(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 poldisc(f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 10*x^2 + (-10*y + 17)*x + (9/4*y^2 - 7*y + 7) ? ? %2 = 10*y^2 - 60*y + 9 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:36:40 2006 Input: f =(x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 10*x^2 + (-10*y + 17)*x + (9/4*y^2 - 7*y + 7) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:31:03 2006 Input: (x-y+1)*(x-2) + (9/4)*(2*x - y + 2)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = 10*x^2 + (-10*y + 17)*x + (9/4*y^2 - 7*y + 7) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:30:24 2006 Input: x = -1/4 y = 1 (x-y+1)*(x-2) + c*(2*x - y + 2)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1/4 ? %2 = 1 ? ? %3 = 1/4*c + 9/16 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:29:29 2006 Input: x = -1/2 y = 1 (x-y+1)*(x-2) + c*(2*x - y + 2)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1/2 ? %2 = 1 ? ? %3 = 5/4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:29:19 2006 Input: x = -1/2 y = 1 (x-y+1)*(x-2) + c(2*x - y + 2)^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -1/2 ? %2 = 1 ? ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: (x-y+1)*(x-2)+ *** c(2*x-y+2)^2 ^------------ Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:22:36 2006 Input: c = 99/75 (-3*x-y-3)*(2*x -y - 6) + c*(y)*( -x - 6*y + 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 33/25 ? ? %2 = -6*x^2 + (-8/25*y + 12)*x + (-173/25*y^2 + 753/25*y + 18) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:21:35 2006 Input: x = 1 y = 5 (-3*x-y-3)*(2*x -y - 6) + c*(y)*( -x - 6*y + 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 5 ? ? %3 = -75*c + 99 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:20:44 2006 Input: x = 1 y = 5 (-3*x-y-3)*(2*x -y - 6) + c*(y)*( x - 6*y + 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 5 ? ? %3 = -65*c + 99 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:18:29 2006 Input: x = 1 y = 5 (3*x+y+3)*(2*x -y - 6) + c*(y)*( x - 6*y + 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 5 ? ? %3 = -65*c - 99 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:15:04 2006 Input: x = 1 y = 5 (3*x+y+3)*(-2*x +y - 6) + c*(y)*( x + 6*y - 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 5 ? ? %3 = 75*c - 33 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:14:46 2006 Input: (3*x+y+3)*(-2*x +y - 6) + (-11/25)*(y)*( x + 6*y - 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = -6*x^2 + (14/25*y - 24)*x + (-41/25*y^2 + 101/25*y - 18) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:14:29 2006 Input: (3*x+y+3)*(-2*x +y - 6) + (11/25)*(y)*( x + 6*y - 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = -6*x^2 + (36/25*y - 24)*x + (91/25*y^2 - 251/25*y - 18) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:09:01 2006 Input: //x = 1 //y = 5 (3*x+y+3)*(-2*x +y - 6) + (11/25)*(y)*( x + 6*y - 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = -6*x^2 + (36/25*y - 24)*x + (91/25*y^2 - 251/25*y - 18) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=5 ^----- Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:07:59 2006 Input: x = 1 y = 5 (3*x+y+3)*(-2*x +y - 6) + c*(y)*( x + 6*y - 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 5 ? ? %3 = 75*c - 33 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:07:08 2006 Input: (3*x+y+3)*(-2*x +y - 6) + (7/8)*(y)*( x + 6*y - 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = -6*x^2 + (15/8*y - 24)*x + (25/4*y^2 - 17*y - 18) ? Goodbye! Errors/timing (if any): Timing: real 0m0.034s user 0m0.005s sys 0m0.007s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:06:34 2006 Input: x = 2 y = 5 (3*x+y+3)*(-2*x +y - 6) + c*(y)*( x + 6*y - 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2 ? %2 = 5 ? ? %3 = 80*c - 70 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.005s sys 0m0.008s '206.15.' ************** PARI ***************** Host 206.15.72.193 (206.15.72.193) Time: Wed Jul 5 10:06:01 2006 Input: (3*x+y+3)*(-2*x +y - 6) + c*(y)*( x + 6*y - 16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -6*x^2 + ((c + 1)*y - 24)*x + ((6*c + 1)*y^2 + (-16*c - 3)*y - 18) ? Goodbye! Errors/timing (if any): Timing: real 0m0.064s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.44 (209.184.114.44) Time: Wed Jul 5 08:46:32 2006 Input: Mod(2^121,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(3642, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.44 (209.184.114.44) Time: Wed Jul 5 08:46:17 2006 Input: Mod((2^(107*32))*32^1545,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(3642, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.066s user 0m0.006s sys 0m0.007s '72.146.' ************** PARI ***************** Host 72.146.229.75 (72.146.229.75) Time: Wed Jul 5 07:49:43 2006 Input: 2* -2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.204s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.44 (209.184.114.44) Time: Wed Jul 5 06:55:58 2006 Input: Mod(2^121,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(3642, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.107s user 0m0.006s sys 0m0.005s '4.155.5' ************** PARI ***************** Host 4.155.51.57 (4.155.51.57) Time: Wed Jul 5 06:41:28 2006 Input: 271.28+144.46= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 271.28+144.46= ^- Timing: real 0m0.334s user 0m0.006s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Wed Jul 5 02:54:31 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.037s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.88 (68.142.249.88) Time: Wed Jul 5 02:31:06 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.123s user 0m0.006s sys 0m0.011s '62.171.' ************** PARI ***************** Host 62.171.194.4 (62.171.194.4) Time: Wed Jul 5 02:02:40 2006 Input: (8*4)*6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 192 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Wed Jul 5 00:40:32 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.031s user 0m0.026s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Tue Jul 4 23:49:17 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.024s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:29:34 2006 Input: //x = 1 //y = 5 ( 3*x + y + 3 )*(y) + (11/9)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = -22/9*x^2 + (-94/9*y + 286/9)*x + (25/3*y^2 - 545/9*y + 352/3) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=5 ^----- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:29:00 2006 Input: x = 1 y = 5 ( 3*x + y + 3 )*(y) + (c)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 5 ? ? %3 = -45*c + 55 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:28:54 2006 Input: x = 1 y = 4 ( 3*x + y + 3 )*(y) + (c)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 4 ? ? %3 = -36*c + 40 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:27:57 2006 Input: //x = 1 //y = -1 ( 3*x + y + 3 )*(y) + (11/9)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = -22/9*x^2 + (-94/9*y + 286/9)*x + (25/3*y^2 - 545/9*y + 352/3) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=-1 ^------ Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:23:25 2006 Input: //x = 1 //y = -1 ( 3*x + y + 3 )*(y) + (5/189)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = -10/189*x^2 + (512/189*y + 130/189)*x + (73/63*y^2 + 307/189*y + 160/63) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=-1 ^------ Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:23:21 2006 Input: x = 1 y = -1 ( 3*x + y + 3 )*(y) + (5/189)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = -1 ? ? %3 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:23:03 2006 Input: x = 1 y = -1 ( 3*x + y + 3 )*(y) + (c)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = -1 ? ? %3 = 189*c - 5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:21:55 2006 Input: //x = 1 //y = 3 ( 3*x + y + 3 )*(y) + (27/15)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = -18/5*x^2 + (-84/5*y + 234/5)*x + (59/5*y^2 - 453/5*y + 864/5) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=3 ^----- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:21:47 2006 Input: x = 1 y = 3 ( 3*x + y + 3 )*(y) + (27/15)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 3 ? ? %3 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:21:31 2006 Input: x = 1 y = 3 ( 3*x + y + 3 )*(y) + (c)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 3 ? ? %3 = -15*c + 27 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:20:43 2006 Input: //x = 1 //y = 20 ( 3*x + y + 3 )*(y) + (-520/1260)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 52/63*x^2 + (475/63*y - 676/63)*x + (-31/21*y^2 + 1541/63*y - 832/21) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=20 ^------ Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:20:17 2006 Input: x = 1 y = 20 ( 3*x + y + 3 )*(y) + (c)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 20 ? ? %3 = 1260*c + 520 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:19:25 2006 Input: //x = 1 //y = 10 ( 3*x + y + 3 )*(y) + (-160/90)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 32/9*x^2 + (203/9*y - 416/9)*x + (-29/3*y^2 + 859/9*y - 512/3) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=10 ^------ Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:19:09 2006 Input: x = 1 y = 10 ( 3*x + y + 3 )*(y) + (c)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 10 ? ? %3 = 90*c + 160 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:17:06 2006 Input: //x = -3 //y = 1 ( 3*x + y + 3 )*(y) + (-5/13)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 10/13*x^2 + (94/13*y - 10)*x + (-17/13*y^2 + 23*y - 480/13) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=-3 ^------ *** unexpected character: //y=1 ^----- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:16:45 2006 Input: x = -3 y = 1 ( 3*x + y + 3 )*(y) + (c)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -3 ? %2 = 1 ? ? %3 = -13*c - 5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:13:58 2006 Input: //x = 1 //y = 4 ( 3*x + y + 3 )*(y) + (40/36)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = -20/9*x^2 + (-83/9*y + 260/9)*x + (23/3*y^2 - 493/9*y + 320/3) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=4 ^----- Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:13:29 2006 Input: ;x = 1 ;y = 4 ( 3*x + y + 3 )*(y) + (c)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 4 ? ? %3 = -36*c + 40 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:13:14 2006 Input: //x = 1 //y = 4 ( 3*x + y + 3 )*(y) + (c)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = -2*c*x^2 + ((-11*c + 3)*y + 26*c)*x + ((6*c + 1)*y^2 + (-52*c + 3)*y + 96*c) ? Goodbye! Errors/timing (if any): *** unexpected character: //x=1 ^----- *** unexpected character: //y=4 ^----- Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:12:55 2006 Input: x = 1 y = 4 ( 3*x + y + 3 )*(y) + (c)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 4 ? ? %3 = -36*c + 40 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.003s sys 0m0.008s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:11:49 2006 Input: ( 3*x + y + 3 )*(y) + (11/9)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -22/9*x^2 + (-94/9*y + 286/9)*x + (25/3*y^2 - 545/9*y + 352/3) ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.007s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:07:56 2006 Input: ( 3*x + y + 3 )*(y) + (11)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = -22*x^2 + (-118*y + 286)*x + (67*y^2 - 569*y + 1056) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:07:29 2006 Input: x = 1 y = 5 ( 3*x + y + 3 )*(y) + (11)*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 5 ? ? %3 = -440 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.250.190 (68.142.250.190) Time: Tue Jul 4 22:06:38 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:06:29 2006 Input: x = 1 y = 5 ( 3*x + y + 3 )*(y) + c*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 5 ? ? %3 = -45*c + 55 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:05:40 2006 Input: ( 3*x + y + 3 )*(y) + c*(-2* x + y - 6 ) * (x + 6 * y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -2*c*x^2 + ((-11*c + 3)*y + 26*c)*x + ((6*c + 1)*y^2 + (-52*c + 3)*y + 96*c) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:05:20 2006 Input: (3*x + y + 3)*(y) + c*(-2* x + y - 6 ) * (x + 6 y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...+3)*(y)+c*(-2*x+y-6)*(x+6y-16) ^----- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 22:05:13 2006 Input: (3x + y + 3)*(y) + c*(-2* x + y - 6 ) * (x + 6 y - 16 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: (3x+y+3)*(y)+c*(-2*x+y ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '24.247.' ************** PARI ***************** Host 24.247.252.228 (24.247.252.228) Time: Tue Jul 4 20:26:15 2006 Input: 6+5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 11 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 20:01:45 2006 Input: (-2*x+ y - 2) * ( x + y - 2) + (2/9)*(3* x+ 2* y + 3) * ( -3 * x + y + 6 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = -4*x^2 + (-5/3*y + 4)*x + (13/9*y^2 - 2/3*y + 8) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 20:01:38 2006 Input: c = 2/9 (-2*x+ y - 2) * ( x + y - 2) + (2/9)*(3* x+ 2* y + 3) * ( -3 * x + y + 6 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2/9 ? %2 = -4*x^2 + (-5/3*y + 4)*x + (13/9*y^2 - 2/3*y + 8) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 19:59:59 2006 Input: c = 2/9 (-2*x+ y - 2) * ( x+y-2) + c*(3* x+ 2* y + 3) * ( -3 * x + y + 6 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2/9 ? %2 = -4*x^2 + (-5/3*y + 4)*x + (13/9*y^2 - 2/3*y + 8) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 19:58:26 2006 Input: x = 0 y = 0 (-2*x+ y - 2) * ( x+y-2) + c*(3* x+ 2* y + 3) * ( -3 * x + y + 6 ) c Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0 ? %2 = 0 ? %3 = 18*c + 4 ? ? %4 = c ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 19:58:16 2006 Input: x = 0 y = 0 0 = (-2*x+ y - 2) * ( x+y-2) + c*(3* x+ 2* y + 3) * ( -3 * x + y + 6 ) c Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0 ? %2 = 0 ? ? ? %3 = c ? Goodbye! Errors/timing (if any): *** unexpected character: 0=(-2*x+y-2)*(x+y-2)+ ^-------------------- Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 19:57:49 2006 Input: x = 0 y = 0 (-2*x+ y - 2) * ( x+y-2) + c*(3* x+ 2* y + 3) * ( -3 * x + y + 6 ) = 0 c Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0 ? %2 = 0 ? ? ? %3 = c ? Goodbye! Errors/timing (if any): *** unexpected character: ...+c*(3*x+2*y+3)*(-3*x+y+6)=0 ^-- Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '71.231.' ************** PARI ***************** Host 71.231.40.180 (71.231.40.180) Time: Tue Jul 4 19:57:00 2006 Input: (-2*x+ y - 2) * ( x+y-2) + c*(3* x+ 2* y + 3) * ( -3 * x + y + 6 ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = (-9*c - 2)*x^2 + ((-3*c - 1)*y + (9*c + 2))*x + ((2*c + 1)*y^2 + (15*c - 4)*y + (18*c + 4)) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '75.0.23' ************** PARI ***************** Host 75.0.236.210 (75.0.236.210) Time: Tue Jul 4 18:11:48 2006 Input: 64*2.54 135/2.2 61.4*30 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 162.56000000000000000000000000000000000 ? %2 = 61.363636363636363636363636363636363636 ? %3 = 1842.0000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '75.0.23' ************** PARI ***************** Host 75.0.236.210 (75.0.236.210) Time: Tue Jul 4 18:09:39 2006 Input: 64*2.54 135/2.2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 162.56000000000000000000000000000000000 ? %2 = 61.363636363636363636363636363636363636 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '75.0.23' ************** PARI ***************** Host 75.0.236.210 (75.0.236.210) Time: Tue Jul 4 18:08:30 2006 Input: 2-2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.007s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.250.194 (68.142.250.194) Time: Tue Jul 4 16:35:53 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.022s sys 0m0.007s '67.163.' ************** PARI ***************** Host 67.163.103.71 (67.163.103.71) Time: Tue Jul 4 16:18:00 2006 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Tue Jul 4 15:39:57 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Tue Jul 4 11:46:13 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.065s user 0m0.022s sys 0m0.008s '87.210.' ************** PARI ***************** Host 87.210.86.120 (87.210.86.120) Time: Tue Jul 4 09:29:07 2006 Input: zz=(-1+sqrt(-3))/2; subst(((12.000000000000000000000000000000000000 + 7.052966104933725048 E-38*I)*L^9 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830861*I)*L^7 + (18.000000000000000000000000000000000000 + 109.11920087683926949222911951486995912*I)*L^6 + (-1.7296040355507741987 E-36 + 280.59223082615812155144630732395132344*I)*L^5 + (243.00000000000000000000000000000000000 - 140.29611541307906077572315366197566172*I)*L^4 + (103.50000000000000000000000000000000000 - 101.32497224277932167135561097809353347*I)*L^3 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830862*I)*L^2 + (-9.403954806578300064 E-38 + 3.761581922631320025 E-37*I)*L + (-12.000000000000000000000000000000000000 + 0.E-37*I))/(L^9 + (3/2 - 2.5980762113533159402911695122588085504*I)*L^6 + (-1.5000000000000000000000000000000000000 - 2.5980762113533159402911695122588085504*I)*L^3 + (-1.0000000000000000000000000000000000000 - 2.938735877055718770 E-39*I)), L, (-zz*y+1)/(y-zz)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = ((-474.00000000000000000000000000000000000 + 841.77669247847436465433892197185397033*I)*y^18 + (2700.0000000000000000000000000000000000 + 10849.566258611447366655923883192784506*I)*y^17 + (51246.000000000000000000000000000000000 + 34138.721417182571455425967391080744352*I)*y^16 + (213282.00000000000000000000000000000000 - 29462.184236746602762901862269014888962*I)*y^15 + (352984.50000000000000000000000000000000 - 405619.45234511374454607825776238196731*I)*y^14 + (-4927.5000000000000000000000000000000015 - 1019695.5495081607935614185013408494387*I)*y^13 + (-1025887.5000000000000000000000000000000 - 1115985.4500533373889404898258041854012*I)*y^12 + (-1787278.5000000000000000000000000000000 - 102018.65859121065702741335323786663533*I)*y^11 + (-1223329.5000000000000000000000000000000 + 1159243.4189723700993463377981832945636*I)*y^10 + (77155.500000000000000000000000000000009 + 1266242.5896607450630312893233761613349*I)*y^9 + (652671.00000000000000000000000000000002 + 417193.88186669276706007541793949495943*I)*y^8 + (360396.00000000000000000000000000000003 - 168822.99221373846980012019490657737960*I)*y^7 + (15732.000000000000000000000000000000027 - 178877.54715167580248904702091901896871*I)*y^6 + (-58954.499999999999999999999999999999990 - 39680.417975999194356067031960728783002*I)*y^5 + (-19980.000000000000000000000000000000000 + 12299.292784546597661338396471033199671*I)*y^4 + (1750.4999999999999999999999999999999986 + 6102.8810204689391437439571842959412830*I)*y^3 + (1349.9999999999999999999999999999999995 - 46.765371804359686925241051220658554060*I)*y^2 + (67.499999999999999999999999999999999919 - 116.91342951089921731310262805164638474*I)*y + (11.999999999999999999999999999999999996 + 4.607937855223367031 E-36*I))/((1.0000000000000000000000000000000000000 + 8.816207631167156310 E-39*I)*y^18 + (22.500000000000000000000000000000000000 - 7.7942286340599478208735085367764256511*I)*y^17 + (180.00000000000000000000000000000000000 - 171.47302994931885205921718780908136432*I)*y^16 + (439.50000000000000000000000000000000001 - 1473.1092118373301381450931134507444481*I)*y^15 + (-1921.5000000000000000000000000000000000 - 6040.5271913964595611769691160017298796*I)*y^14 + (-15223.500000000000000000000000000000000 - 10389.706769201910445224386879522975393*I)*y^13 + (-38702.999999999999999999999999999999999 + 4629.7718086316090055988640708451968366*I)*y^12 + (-38790.000000000000000000000000000000000 + 47248.613979671403690135208749938692297*I)*y^11 + (8873.9999999999999999999999999999999999 + 71332.780458916642456634350128577847559*I)*y^10 + (53318.500000000000000000000000000000000 + 34723.288564737067541991480531338976276*I)*y^9 + (39465.000000000000000000000000000000000 - 15775.518755337334389447981278435485518*I)*y^8 + (2047.4999999999999999999999999999999999 - 21784.869032197554159341456360290109695*I)*y^7 + (-8692.5000000000000000000000000000000000 - 3577.5509430335160497809404183803793743*I)*y^6 + (-2007.0000000000000000000000000000000001 + 3024.1607100152597544989213122692531526*I)*y^5 + (845.99999999999999999999999999999999996 + 779.42286340599478208735085367764256514*I)*y^4 + (196.49999999999999999999999999999999999 - 210.44417311961859116[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.082s user 0m0.007s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Tue Jul 4 08:54:31 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.249s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Tue Jul 4 08:34:34 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.047s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Tue Jul 4 08:18:47 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.049s user 0m0.006s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Tue Jul 4 07:39:10 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '65.54.1' ************** PARI ***************** Host 65.54.188.53 (65.54.188.53) Time: Tue Jul 4 07:38:19 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.089s user 0m0.006s sys 0m0.006s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Tue Jul 4 06:27:57 2006 Input: zz=(-1+sqrt(-3))/2; subst(((12.000000000000000000000000000000000000 + 7.052966104933725048 E-38*I)*L^9 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830861*I)*L^7 + (18.000000000000000000000000000000000000 + 109.11920087683926949222911951486995912*I)*L^6 + (-1.7296040355507741987 E-36 + 280.59223082615812155144630732395132344*I)*L^5 + (243.00000000000000000000000000000000000 - 140.29611541307906077572315366197566172*I)*L^4 + (103.50000000000000000000000000000000000 - 101.32497224277932167135561097809353347*I)*L^3 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830862*I)*L^2 + (-9.403954806578300064 E-38 + 3.761581922631320025 E-37*I)*L + (-12.000000000000000000000000000000000000 + 0.E-37*I))/(L^9 + (3/2 - 2.5980762113533159402911695122588085504*I)*L^6 + (-1.5000000000000000000000000000000000000 - 2.5980762113533159402911695122588085504*I)*L^3 + (-1.0000000000000000000000000000000000000 - 2.938735877055718770 E-39*I)),L, (-zz*y+1)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = ((-12.000000000000000000000000000000000000 - 2.350988701644575016 E-38*I)*y^9 + (-54.000000000000000000000000000000000000 - 93.530743608719373850482102441317107814*I)*y^8 + (94.500000000000000000000000000000000000 - 303.97491672833796501406683293428060040*I)*y^7 + (175.50000000000000000000000000000000000 - 381.91720306893744322280191830204485690*I)*y^6 + (-6.770847460736376046 E-36 - 1075.6035515002727992805441780751467399*I)*y^5 + (728.99999999999999999999999999999999999 - 2151.2071030005455985610883561502934797*I)*y^4 + (1809.0000000000000000000000000000000000 - 1870.6148721743874770096420488263421563*I)*y^3 + (1620.0000000000000000000000000000000000 - 701.48057706539530387861576830987830859*I)*y^2 + (688.49999999999999999999999999999999998 - 70.148057706539530387861576830987830863*I)*y + (121.50000000000000000000000000000000000 + 7.7942286340599478208735085367764256460*I))/((-1.0000000000000000000000000000000000000 + 0.E-38*I)*y^9 + (-4.4999999999999999999999999999999999999 - 7.7942286340599478208735085367764256512*I)*y^8 + (18.000000000000000000000000000000000000 - 31.176914536239791283494034147105702605*I)*y^7 + (85.500000000000000000000000000000000000 - 2.5980762113533159402911695122588085502*I)*y^6 + (80.999999999999999999999999999999999999 + 109.11920087683926949222911951486995912*I)*y^5 + (-40.500000000000000000000000000000000001 + 148.09034404713900859659666219875208737*I)*y^4 + (-112.50000000000000000000000000000000000 + 54.559600438419634746114559757434979558*I)*y^3 + (-67.499999999999999999999999999999999999 - 23.382685902179843462620525610329276954*I)*y^2 + (-13.500000000000000000000000000000000000 - 23.382685902179843462620525610329276954*I)*y + (0.E-38 - 5.1961524227066318805823390245176171008*I)) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.250.122 (68.142.250.122) Time: Tue Jul 4 06:20:06 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.009s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Tue Jul 4 06:09:18 2006 Input: zz=(-1+sqrt(-3))/2; subst(((12.000000000000000000000000000000000000 + 7.052966104933725048 E-38*I)*L^9 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830861*I)*L^7 + (18.000000000000000000000000000000000000 + 109.11920087683926949222911951486995912*I)*L^6 + (-1.7296040355507741987 E-36 + 280.59223082615812155144630732395132344*I)*L^5 + (243.00000000000000000000000000000000000 - 140.29611541307906077572315366197566172*I)*L^4 + (103.50000000000000000000000000000000000 - 101.32497224277932167135561097809353347*I)*L^3 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830862*I)*L^2 + (-9.403954806578300064 E-38 + 3.761581922631320025 E-37*I)*L + (-12.000000000000000000000000000000000000 + 0.E-37*I))/(L^9 + (3/2 - 2.5980762113533159402911695122588085504*I)*L^6 + (-1.5000000000000000000000000000000000000 - 2.5980762113533159402911695122588085504*I)*L^3 + (-1.0000000000000000000000000000000000000 - 2.938735877055718770 E-39*I)),L, (-zz*y+1)/(y-zz)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = ((-474.00000000000000000000000000000000000 + 841.77669247847436465433892197185397033*I)*y^18 + (2700.0000000000000000000000000000000000 + 10849.566258611447366655923883192784506*I)*y^17 + (51246.000000000000000000000000000000000 + 34138.721417182571455425967391080744352*I)*y^16 + (213282.00000000000000000000000000000000 - 29462.184236746602762901862269014888962*I)*y^15 + (352984.50000000000000000000000000000000 - 405619.45234511374454607825776238196731*I)*y^14 + (-4927.5000000000000000000000000000000015 - 1019695.5495081607935614185013408494387*I)*y^13 + (-1025887.5000000000000000000000000000000 - 1115985.4500533373889404898258041854012*I)*y^12 + (-1787278.5000000000000000000000000000000 - 102018.65859121065702741335323786663533*I)*y^11 + (-1223329.5000000000000000000000000000000 + 1159243.4189723700993463377981832945636*I)*y^10 + (77155.500000000000000000000000000000009 + 1266242.5896607450630312893233761613349*I)*y^9 + (652671.00000000000000000000000000000002 + 417193.88186669276706007541793949495943*I)*y^8 + (360396.00000000000000000000000000000003 - 168822.99221373846980012019490657737960*I)*y^7 + (15732.000000000000000000000000000000027 - 178877.54715167580248904702091901896871*I)*y^6 + (-58954.499999999999999999999999999999990 - 39680.417975999194356067031960728783002*I)*y^5 + (-19980.000000000000000000000000000000000 + 12299.292784546597661338396471033199671*I)*y^4 + (1750.4999999999999999999999999999999986 + 6102.8810204689391437439571842959412830*I)*y^3 + (1349.9999999999999999999999999999999995 - 46.765371804359686925241051220658554060*I)*y^2 + (67.499999999999999999999999999999999919 - 116.91342951089921731310262805164638474*I)*y + (11.999999999999999999999999999999999996 + 4.607937855223367031 E-36*I))/((1.0000000000000000000000000000000000000 + 8.816207631167156310 E-39*I)*y^18 + (22.500000000000000000000000000000000000 - 7.7942286340599478208735085367764256511*I)*y^17 + (180.00000000000000000000000000000000000 - 171.47302994931885205921718780908136432*I)*y^16 + (439.50000000000000000000000000000000001 - 1473.1092118373301381450931134507444481*I)*y^15 + (-1921.5000000000000000000000000000000000 - 6040.5271913964595611769691160017298796*I)*y^14 + (-15223.500000000000000000000000000000000 - 10389.706769201910445224386879522975393*I)*y^13 + (-38702.999999999999999999999999999999999 + 4629.7718086316090055988640708451968366*I)*y^12 + (-38790.000000000000000000000000000000000 + 47248.613979671403690135208749938692297*I)*y^11 + (8873.9999999999999999999999999999999999 + 71332.780458916642456634350128577847559*I)*y^10 + (53318.500000000000000000000000000000000 + 34723.288564737067541991480531338976276*I)*y^9 + (39465.000000000000000000000000000000000 - 15775.518755337334389447981278435485518*I)*y^8 + (2047.4999999999999999999999999999999999 - 21784.869032197554159341456360290109695*I)*y^7 + (-8692.5000000000000000000000000000000000 - 3577.5509430335160497809404183803793743*I)*y^6 + (-2007.0000000000000000000000000000000001 + 3024.1607100152597544989213122692531526*I)*y^5 + (845.99999999999999999999999999999999996 + 779.42286340599478208735085367764256514*I)*y^4 + (196.49999999999999999999999999999999999 - 210.44417311961859116[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.006s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Tue Jul 4 06:02:36 2006 Input: zz=(-1+sqrt(-3))/2; subst(((12.000000000000000000000000000000000000 + 7.052966104933725048 E-38*I)*L^9 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830861*I)*L^7 + (18.000000000000000000000000000000000000 + 109.11920087683926949222911951486995912*I)*L^6 + (-1.7296040355507741987 E-36 + 280.59223082615812155144630732395132344*I)*L^5 + (243.00000000000000000000000000000000000 - 140.29611541307906077572315366197566172*I)*L^4 + (103.50000000000000000000000000000000000 - 101.32497224277932167135561097809353347*I)*L^3 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830862*I)*L^2 + (-9.403954806578300064 E-38 + 3.761581922631320025 E-37*I)*L + (-12.000000000000000000000000000000000000 + 0.E-37*I))/(L^9 + (3/2 - 2.5980762113533159402911695122588085504*I)*L^6 + (-1.5000000000000000000000000000000000000 - 2.5980762113533159402911695122588085504*I)*L^3 + (-1.0000000000000000000000000000000000000 - 2.938735877055718770 E-39*I)),L, (-zz*y+1)/y-zz) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %2 = ((-29160.000000000000000000000000000000000 + 26313.315868586383843268964820157212998*I)*y^9 + (-114048.00000000000000000000000000000000 - 48823.048163751513149951657474367530279*I)*y^8 + (-3361.5000000000000000000000000000000004 - 178246.21463231694671555626672754007822*I)*y^7 + (139495.50000000000000000000000000000000 - 64699.891891331626861070994363781109330*I)*y^6 + (66014.999999999999999999999999999999999 + 58597.010870862687717327037179485168046*I)*y^5 + (-10854.000000000000000000000000000000000 + 33484.006211921535838472592673991524597*I)*y^4 + (-9746.9999999999999999999999999999999999 + 1091.1920087683926949222911951486995911*I)*y^3 + (-985.49999999999999999999999999999999999 - 1566.6399554460495119955752158920615559*I)*y^2 + (108.00000000000000000000000000000000000 - 187.06148721743874770096420488263421563*I)*y + (12.000000000000000000000000000000000000 + 4.701977403289150032 E-38*I))/((-405.00000000000000000000000000000000000 - 145.49226783578569265630549268649327882*I)*y^9 + (-593.99999999999999999999999999999999999 - 1964.1456157831068508601241512676592641*I)*y^8 + (2646.0000000000000000000000000000000000 - 3367.1067699138974586173556878874158813*I)*y^7 + (5134.5000000000000000000000000000000000 + 413.09411760517723450629595244915055952*I)*y^6 + (1836.0000000000000000000000000000000000 + 3491.8144280588566237513318244758386917*I)*y^5 + (-1026.0000000000000000000000000000000000 + 1714.7302994931885205921718780908136433*I)*y^4 + (-670.49999999999999999999999999999999999 - 2.5980762113533159402911695122588085527*I)*y^3 + (-71.999999999999999999999999999999999999 - 124.70765814495916513397613658842281042*I)*y^2 + (9 - 15.588457268119895641747017073552851302*I)*y + 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.097s user 0m0.006s sys 0m0.006s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Tue Jul 4 06:02:08 2006 Input: zz=(-1+sqrt(-3))/2; subst(((12.000000000000000000000000000000000000 + 7.052966104933725048 E-38*I)*L^9 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830861*I)*L^7 + (18.000000000000000000000000000000000000 + 109.11920087683926949222911951486995912*I)*L^6 + (-1.7296040355507741987 E-36 + 280.59223082615812155144630732395132344*I)*L^5 + (243.00000000000000000000000000000000000 - 140.29611541307906077572315366197566172*I)*L^4 + (103.50000000000000000000000000000000000 - 101.32497224277932167135561097809353347*I)*L^3 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830862*I)*L^2 + (-9.403954806578300064 E-38 + 3.761581922631320025 E-37*I)*L + (-12.000000000000000000000000000000000000 + 0.E-37*I))/(L^9 + (3/2 - 2.5980762113533159402911695122588085504*I)*L^6 + (-1.5000000000000000000000000000000000000 - 2.5980762113533159402911695122588085504*I)*L^3 + (-1.0000000000000000000000000000000000000 - 2.938735877055718770 E-39*I),L, (-zz*y+1)/y-zz) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...938735877055718770E-39*I) *** ,L,(-zz*y+1)/y-zz) ^------------------ Timing: real 0m0.013s user 0m0.006s sys 0m0.008s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Tue Jul 4 06:00:09 2006 Input: zz=(-1+sqrt(-3))/2; subst((12.000000000000000000000000000000000000 + 7.052966104933725048 E-38*I)*L^9 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830861*I)*L^7 + (18.000000000000000000000000000000000000 + 109.11920087683926949222911951486995912*I)*L^6 + (-1.7296040355507741987 E-36 + 280.59223082615812155144630732395132344*I)*L^5 + (243.00000000000000000000000000000000000 - 140.29611541307906077572315366197566172*I)*L^4 + (103.50000000000000000000000000000000000 - 101.32497224277932167135561097809353347*I)*L^3 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830862*I)*L^2 + (-9.403954806578300064 E-38 + 3.761581922631320025 E-37*I)*L + (-12.000000000000000000000000000000000000 + 0.E-37*I))/(L^9 + (3/2 - 2.5980762113533159402911695122588085504*I)*L^6 + (-1.5000000000000000000000000000000000000 - 2.5980762113533159402911695122588085504*I)*L^3 + (-1.0000000000000000000000000000000000000 - 2.938735877055718770 E-39*I),L, (-zz*y+1)/y-zz) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...000000000000000+0.E-37*I) *** )/(L^9+(3/2-2.598076 ^-------------------- Timing: real 0m0.049s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Tue Jul 4 00:39:42 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '69.194.' ************** PARI ***************** Host 69.194.230.105 (69.194.230.105) Time: Tue Jul 4 00:35:12 2006 Input: 0+0.1(1-1(0)-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (1-1(0)-1). *** expected character: ')' instead of: 0+0.1(1-1(0)-1) ^------ Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Mon Jul 3 23:50:38 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '68.142.' ************** PARI ***************** Host 68.142.249.160 (68.142.249.160) Time: Mon Jul 3 20:20:12 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.064s user 0m0.007s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.102.206 (72.30.102.206) Time: Mon Jul 3 15:52:10 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.127s user 0m0.008s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 15:04:14 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); print(a); print(b); print(c); print(d); print("D=",(d-a)^2+4*b*c); a=lift(a); d=lift(d); c=lift(c); t=-bezout(2*c,M); x=lift(Mod((a-d)*t[1],M)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Mod(l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^3, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(l, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? D=0 ? ? ? ? ? ? %10 = l ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 15:04:04 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); print(a); print(b); print(c); print(d); print("D=",(d-a)^2+4*b*c); a=lift(a); d=lift(d); c=lift(c); t=-bezout(2*c,M) x=lift(Mod((a-d)*t[1],M)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Mod(l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^3, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(l, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? D=0 ? ? ? ? ? %9 = [1/2*l^4 - 1/2*l^3 - 2*l^2 + 3/2*l + 3/2, -1, 1] ? %10 = l ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 15:03:11 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); print(a); print(b); print(c); print(d); print("D=",(d-a)^2+4*b*c); a=lift(a); d=lift(d); c=lift(c); t=bezout(2*c,M) /*x=lift(Mod((a-d)*t[1],M))*/ Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Mod(l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^3, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(l, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? D=0 ? ? ? ? ? %9 = [-1/2*l^4 + 1/2*l^3 + 2*l^2 - 3/2*l - 3/2, 1, -1] ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 15:01:05 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); print(a); print(b); print(c); print(d); print("D=",(d-a)^2+4*b*c); a=lift(a); d=lift(d); c=lift(c); t=bezout(2*c,M); x=lift(Mod((a-d)*t[1],M)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Mod(l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^3, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(l, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? D=0 ? ? ? ? ? ? %10 = -l ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 15:00:43 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); print(a); print(b); print(c); print(d); print("D=",(d-a)^2+4*b*c); a=lift(a); d=lift(d); c=lift(c); t=bezout(2*c,M); x=lift(Mod((a-d)*t[1],M) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Mod(l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^3, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(l, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? D=0 ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: x=lift(Mod((a-d)*t[1],M) ^ Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 15:00:06 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); print(a); print(b); print(c); print(d); print("D=",(d-a)^2+4*b*c); a=lift(a); d=lift(d); c=lift(c); t=bezout(2*c,M); x=(a-d)*t[1] Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Mod(l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^3, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(l, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? D=0 ? ? ? ? ? ? %10 = -l^6 + l^5 + 4*l^4 - 3*l^3 - 3*l^2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:59:45 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); print(a); print(b); print(c); print(d); print("D=",(d-a)^2+4*b*c); a=lift(a); d=lift(d); c=lift(c); t=bezout(2*c,M); x=(a-d)*t[1]; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Mod(l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^3, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(l, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? D=0 ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:58:50 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); print(a); print(b); print(c); print(d); print("D=",(d-a)^2+4*b*c); a=lift(a); d=lift(d); c=lift(c); t=bezout(2*c,M) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Mod(l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^3, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(l, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? D=0 ? ? ? ? ? %9 = [-1/2*l^4 + 1/2*l^3 + 2*l^2 - 3/2*l - 3/2, 1, -1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:54:39 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); print(a); print(b); print(c); print(d); (d-a)^2+4*b*c Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Mod(l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^3, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(l, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Mod(-l^2 + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? %6 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:54:21 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); Print(a); Print(b); Print(c); Print(d); (d-a)^2+4*b*c Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? ? ? ? ? %6 = 0 ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: Print(a); ^- *** expected character: '=' instead of: Print(b); ^- *** expected character: '=' instead of: Print(c); ^- *** expected character: '=' instead of: Print(d); ^- Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:53:32 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); (d-a)^2+4*b*c Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? %6 = 0 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:53:02 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l),M); b=Mod((-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1),M); c=Mod((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1),M); d=Mod(((-l^7 + 6*l^5 - 10*l^3 + 4*l),M); (d-a)^2+4*b*c Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? %5 = Mod(-3*l^4 + (-2*d + 2)*l^2 + (d^2 - 2*d + 1), l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(((-l^7+6*l^5-10*l^3+4*l),M); ^---- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:50:35 2006 Input: 2*l-1/(l-1/(l-1/(l-1/(l-1/(l-1/(l-1/(l-1/(l-1/x)))))))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((2*l^9 - 15*l^7 + 36*l^5 - 30*l^3 + 6*l)*x + (-2*l^8 + 13*l^6 - 25*l^4 + 14*l^2 - 1))/((l^8 - 7*l^6 + 15*l^4 - 10*l^2 + 1)*x + (-l^7 + 6*l^5 - 10*l^3 + 4*l)) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:38:52 2006 Input: M=l^5-l^4-4*l^3+3*l^2+3*l-1; a=Mod((2*l^9 - 2*l^8 - 13*l^7 + 10*l^6 + 26*l^5 - 12*l^4 - 18*l^3 + 2*l^2 + 4*l),M); b=Mod((-2*l^8 + 2*l^7 + 11*l^6 - 8*l^5 - 17*l^4 + 6*l^3 + 8*l^2 - 1),M); c=Mod((l^8 - l^7 - 6*l^6 + 5*l^5 + 10*l^4 - 6*l^3 - 4*l^2 + l),M); d=Mod((-l^7 + l^6 + 5*l^5 - 4*l^4 - 6*l^3 + 3*l^2 + l),M); (d-a)^2+4*b*c Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? %6 = Mod(13*l^4 - 23*l^3 - 2*l^2 + 14*l - 3, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:38:30 2006 Input: M=x^5-x^4-4*x^3+3*x^2+3*x-1; a=Mod((2*l^9 - 2*l^8 - 13*l^7 + 10*l^6 + 26*l^5 - 12*l^4 - 18*l^3 + 2*l^2 + 4*l),M); b=Mod((-2*l^8 + 2*l^7 + 11*l^6 - 8*l^5 - 17*l^4 + 6*l^3 + 8*l^2 - 1),M); c=Mod((l^8 - l^7 - 6*l^6 + 5*l^5 + 10*l^4 - 6*l^3 - 4*l^2 + l),M); d=Mod((-l^7 + l^6 + 5*l^5 - 4*l^4 - 6*l^3 + 3*l^2 + l),M); (d-a)^2+4*b*c Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? %6 = Mod(4*l^18 - 8*l^17 - 52*l^16 + 100*l^15 + 276*l^14 - 496*l^13 - 779*l^12 + 1246*l^11 + 1281*l^10 - 1680*l^9 - 1262*l^8 + 1188*l^7 + 726*l^6 - 400*l^5 - 215*l^4 + 50*l^3 + 25*l^2 - 4*l, x^5 - x^4 - 4*x^3 + 3*x^2 + 3*x - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:34:39 2006 Input: Mod(-8*l^8 + 12*l^7 + 53*l^6 - 64*l^5 - 104*l^4 + 88*l^3 + 64*l^2 - 32*l + 4,l^5-l^4-4*l^3+3*l^2+3*l-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(9*l^4 - 3*l^3 - 10*l^2 - 10*l + 5, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:33:33 2006 Input: (5*l^3-4*l^2-8*l+2)^2-4*(-l^4+l^3+2*l^2-1)*(-2*l^4+l^3+4*l^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -8*l^8 + 12*l^7 + 53*l^6 - 64*l^5 - 104*l^4 + 88*l^3 + 64*l^2 - 32*l + 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:26:23 2006 Input: Mod(-8*l^8 + 12*l^7 + 53*l^6 - 4*l^5 + 4*l^4 + 20*l^3 + 32*l^2,l^5-l^4-4*l^3+3*l^2+3*l-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(177*l^4 + 169*l^3 - 222*l^2 - 158*l + 61, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:26:07 2006 Input: Mod(-8*l^8 + 12*l^7 + 53*l^6 - 4*l^5 + 4*l^4 + 20*l^3 + 32*l^2,l^5-l^4-4*x^3+3*x^2+3*x-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(-8*l^8 + 12*l^7 + 53*l^6 - 4*l^5 + 4*l^4 + 20*l^3 + 32*l^2, -4*x^3 + 3*x^2 + 3*x + (l^5 - l^4 - 1)) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:25:20 2006 Input: (5*l^3+2*l^2+4*l)^2-4*(-l^4+l^3+2*l^2-1)*(-2*l^4+l^3+4*l^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -8*l^8 + 12*l^7 + 53*l^6 - 4*l^5 + 4*l^4 + 20*l^3 + 32*l^2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:24:51 2006 Input: (5*l^3+2*l^2+4*l)^2-4*(-l^4+l^3+2*l^2-1)(-2*l^4+l^3+4*l^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -2*l^4 + l^3 + 4*l^2 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (-2*l^4+l^3+4*l^2). Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:16:42 2006 Input: Mod(((-l^7 + l^6 + 5*l^5 - 4*l^4 - 6*l^3 + 3*l^2 + l)),l^5-l^4-4*l^3+3*l^2+3*l-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(l^3 - l^2 - 2*l + 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:15:42 2006 Input: Mod((l^8 - l^7 - 6*l^6 + 5*l^5 + 10*l^4 - 6*l^3 - 4*l^2 + l),l^5-l^4-4*l^3+3*l^2+3*l-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(-l^4 + l^3 + 2*l^2 - l, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:14:42 2006 Input: Mod(-2*l^8 + 2*l^7 + 11*l^6 - 8*l^5 - 17*l^4 + 6*l^3 + 8*l^2 - 1,l^5-l^4-4*l^3+3*l^2+3*l-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2*l^4 - l^3 - 4*l^2, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:14:31 2006 Input: Mod(-2*l^8 + 2*l^7 + 11*l^6 - 8*l^5 - 17*l^4 + 6*l^3 + 8*l^2 - 1),l^5-l^4-4*l^3+3*l^2+3*l-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...*l^5-17*l^4+6*l^3+8*l^2-1 *** ),l^5-l^4-4*l^3+3*l^ ^-------------------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:13:01 2006 Input: Mod((2*l^9 - 2*l^8 - 13*l^7 + 10*l^6 + 26*l^5 - 12*l^4 - 18*l^3 + 2*l^2 + 4*l),l^5-l^4-4*l^3+3*l^2+3*l-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(-4*l^3 + 3*l^2 + 6*l - 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:12:46 2006 Input: mod((2*l^9 - 2*l^8 - 13*l^7 + 10*l^6 + 26*l^5 - 12*l^4 - 18*l^3 + 2*l^2 + 4*l),l^5-l^4-4*l^3+3*l^2+3*l-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** obsolete function: mod((2*l^9-2*l^8-13* ^-------------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.021s user 0m0.007s sys 0m0.005s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:12:40 2006 Input: Mod((2*l^9 - 2*l^8 - 13*l^7 + 10*l^6 + 26*l^5 - 12*l^4 - 18*l^3 + 2*l^2 + 4*l),l^5-l^4-4*l^3+3*l^2+3*l-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(-4*l^3 + 3*l^2 + 6*l - 1, l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:12:18 2006 Input: Mod((2*l^9 - 2*l^8 - 13*l^7 + 10*l^6 + 26*l^5 - 12*l^4 - 18*l^3 + 2*l^2 + 4*l),x^5-x^4-4*x^3+3*x^2+3*x-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2*l^9 - 2*l^8 - 13*l^7 + 10*l^6 + 26*l^5 - 12*l^4 - 18*l^3 + 2*l^2 + 4*l, x^5 - x^4 - 4*x^3 + 3*x^2 + 3*x - 1) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:09:11 2006 Input: ?bezout Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? bezout(x,y): gives a 3-dimensional row vector [u,v,d] such that d=gcd(x,y) and u*x+v*y=d. ? Goodbye! Errors/timing (if any): Timing: real 0m0.037s user 0m0.006s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:09:00 2006 Input: ??bezout Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): sh: /home/was/sage/sage-0.7.5-2005-09-29/source/../local/bin/gphelp: No such file or directory Timing: real 0m0.016s user 0m0.008s sys 0m0.009s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:07:31 2006 Input: bezout(((l^8 - l^7 - 6*l^6 + 5*l^5 + 10*l^4 - 6*l^3 - 4*l^2 + l)*x + (-l^7 + l^6 + 5*l^5 - 4*l^4 - 6*l^3 + 3*l^2 + l)),l^5-l^4-4*l^3+3*l^2+3*l-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1/(l^5 - l^4 - 4*l^3 + 3*l^2 + 3*l - 1), 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:06:40 2006 Input: bezout(((l^8 - l^7 - 6*l^6 + 5*l^5 + 10*l^4 - 6*l^3 - 4*l^2 + l)*x + (-l^7 + l^6 + 5*l^5 - 4*l^4 - 6*l^3 + 3*l^2 + l)),x^5-x^4-4*x^3+3*x^2+3*x-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [((-l^28 + 4*l^27 + 18*l^26 - 88*l^25 - 125*l^24 + 852*l^23 + 342*l^22 - 4776*l^21 + 486*l^20 + 17160*l^19 - 6828*l^18 - 41328*l^17 + 24379*l^16 + 67796*l^15 - 48930*l^14 - 75468*l^13 + 61542*l^12 + 55764*l^11 - 49324*l^10 - 26120*l^9 + 24642*l^8 + 7012*l^7 - 7276*l^6 - 744*l^5 + 1140*l^4 - 72*l^3 - 72*l^2 + 16*l - 1)/(-l^36 + 8*l^35 + 8*l^34 - 211*l^33 + 220*l^32 + 2441*l^31 - 4757*l^30 - 16094*l^29 + 43909*l^28 + 64915*l^27 - 246506*l^26 - 152423*l^25 + 933964*l^24 + 121171*l^23 - 2497127*l^22 + 462062*l^21 + 4801858*l^20 - 1946543*l^19 - 6664218*l^18 + 3797946*l^17 + 6616186*l^16 - 4635152*l^15 - 4599462*l^14 + 3736404*l^13 + 2158051*l^12 - 1982792*l^11 - 643692*l^10 + 668689*l^9 + 109981*l^8 - 133922*l^7 - 8445*l^6 + 14113*l^5 - 12*l^4 - 591*l^3 + 22*l^2 + l))*x^4 + ((l^28 - 5*l^27 - 14*l^26 + 105*l^25 + 41*l^24 - 961*l^23 + 430*l^22 + 5024*l^21 - 4566*l^20 - 16506*l^19 + 20532*l^18 + 35255*l^17 - 54903*l^16 - 48689*l^15 + 94597*l^14 + 41180*l^13 - 107045*l^12 - 17610*l^11 + 78658*l^10 - 290*l^9 - 36217*l^8 + 3930*l^7 + 9778*l^6 - 1760*l^5 - 1342*l^4 + 340*l^3 + 60*l^2 - 25*l + 2)/(-l^36 + 8*l^35 + 8*l^34 - 211*l^33 + 220*l^32 + 2441*l^31 - 4757*l^30 - 16094*l^29 + 43909*l^28 + 64915*l^27 - 246506*l^26 - 152423*l^25 + 933964*l^24 + 121171*l^23 - 2497127*l^22 + 462062*l^21 + 4801858*l^20 - 1946543*l^19 - 6664218*l^18 + 3797946*l^17 + 6616186*l^16 - 4635152*l^15 - 4599462*l^14 + 3736404*l^13 + 2158051*l^12 - 1982792*l^11 - 643692*l^10 + 668689*l^9 + 109981*l^8 - 133922*l^7 - 8445*l^6 + 14113*l^5 - 12*l^4 - 591*l^3 + 22*l^2 + l))*x^3 + ((4*l^28 - 15*l^27 - 77*l^26 + 339*l^25 + 600*l^24 - 3379*l^23 - 2234*l^22 + 19552*l^21 + 2304*l^20 - 72750*l^19 + 14363*l^18 + 182189*l^17 - 72264*l^16 - 312419*l^15 + 164691*l^14 + 366118*l^13 - 224009*l^12 - 287638*l^11 + 190692*l^10 + 145528*l^9 - 100329*l^8 - 43778*l^7 + 31030*l^6 + 6332*l^5 - 5094*l^4 - 52*l^3 + 347*l^2 - 53*l + 2)/(-l^36 + 8*l^35 + 8*l^34 - 211*l^33 + 220*l^32 + 2441*l^31 - 4757*l^30 - 16094*l^29 + 43909*l^28 + 64915*l^27 - 246506*l^26 - 152423*l^25 + 933964*l^24 + 121171*l^23 - 2497127*l^22 + 462062*l^21 + 4801858*l^20 - 1946543*l^19 - 6664218*l^18 + 3797946*l^17 + 6616186*l^16 - 4635152*l^15 - 4599462*l^14 + 3736404*l^13 + 2158051*l^12 - 1982792*l^11 - 643692*l^10 + 668689*l^9 + 109981*l^8 - 133922*l^7 - 8445*l^6 + 14113*l^5 - 12*l^4 - 591*l^3 + 22*l^2 + l))*x^2 + ((-3*l^28 + 16*l^27 + 39*l^26 - 337*l^25 - 51*l^24 + 3087*l^23 - 2044*l^22 - 16096*l^21 + 18234*l^20 + 52421*l^19 - 78955*l^18 - 109695*l^17 + 208901*l^16 + 144619*l^15 - 359804*l^14 - 108270*l^13 + 409051*l^12 + 25720*l^11 - 302737*l^10 + 25568*l^9 + 140435*l^8 - 24210*l^7 - 38116*l^6 + 8516*l^5 + 5266*l^4 - 1389*l^3 - 248*l^2 + 87*l - 5)/(-l^36 + 8*l^35 + 8*l^34 - 211*l^33 + 220*l^32 + 2441*l^31 - 4757*l^30 - 16094*l^29 + 43909*l^28 + 64915*l^27 - 246506*l^26 - 152423*l^25 + 933964*l^24 + 121171*l^23 - 2497127*l^22 + 462062*l^21 + 4801858*l^20 - 1946543*l^19 - 6664218*l^18 + 3797946*l^17 + 6616186*l^16 - 4635152*l^15 - 4599462*l^14 + 3736404*l^13 + 2158051*l^12 - 1982792*l^11 - 643692*l^10 + 668689*l^9 + 109981*l^8 - 133922*l^7 - 8445*l^6 + 14113*l^5 - 12*l^4 - 591*l^3 + 22*l^2 + l))*x + ((-3*l^28 + 9*l^27 + 70*l[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.011s sys 0m0.004s '134.173' ************** PARI ***************** Host 134.173.171.51 (134.173.171.51) Time: Mon Jul 3 14:02:46 2006 Input: 2*l-1/(l-l/(l-1/(l-1/(l-1/(l-1/(l-1/(l-1/(l-1/x)))))))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((2*l^9 - 2*l^8 - 13*l^7 + 10*l^6 + 26*l^5 - 12*l^4 - 18*l^3 + 2*l^2 + 4*l)*x + (-2*l^8 + 2*l^7 + 11*l^6 - 8*l^5 - 17*l^4 + 6*l^3 + 8*l^2 - 1))/((l^8 - l^7 - 6*l^6 + 5*l^5 + 10*l^4 - 6*l^3 - 4*l^2 + l)*x + (-l^7 + l^6 + 5*l^5 - 4*l^4 - 6*l^3 + 3*l^2 + l)) ? Goodbye! Errors/timing (if any): Timing: real 0m0.104s user 0m0.008s sys 0m0.006s '67.34.2' ************** PARI ***************** Host 67.34.228.106 (67.34.228.106) Time: Mon Jul 3 13:38:11 2006 Input: 1+7% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '129.186' ************** PARI ***************** Host 129.186.52.128 (129.186.52.128) Time: Mon Jul 3 13:00:32 2006 Input: ellinit(e=[0,0,0,a,b]) elladd(e,[x,y],[x,y]) elladd(e,[x,y],%2) Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '129.186' ************** PARI ***************** Host 129.186.52.128 (129.186.52.128) Time: Mon Jul 3 12:59:22 2006 Input: ellinit(e=[0,0,0,a,b]) elladd(e,[x,y],[x,y]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 0, 0, a, b, 0, 2*a, 4*b, -a^2, -48*a, -864*b, -64*a^3 - 432*b^2, -6912*a^3/(-4*a^3 - 27*b^2), 0, 0, 0, 0, 0, 0] ? %2 = [9/(4*y^2)*x^4 + 3/(2*y^2)*a*x^2 - 2*x + 1/(4*y^2)*a^2, -27/(8*y^3)*x^6 - 27/(8*y^3)*a*x^4 + 9/(2*y)*x^3 - 9/(8*y^3)*a^2*x^2 + 3/(2*y)*a*x + (-1/(8*y^3)*a^3 - y)] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.011s sys 0m0.002s '129.186' ************** PARI ***************** Host 129.186.52.128 (129.186.52.128) Time: Mon Jul 3 12:59:15 2006 Input: ellinit(e=[0,0,0,a,b]) elladd([x,y],[x,y]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 0, 0, a, b, 0, 2*a, 4*b, -a^2, -48*a, -864*b, -64*a^3 - 432*b^2, -6912*a^3/(-4*a^3 - 27*b^2), 0, 0, 0, 0, 0, 0] ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: elladd([x,y],[x,y]) ^- Timing: real 0m0.013s user 0m0.006s sys 0m0.005s '129.186' ************** PARI ***************** Host 129.186.52.128 (129.186.52.128) Time: Mon Jul 3 12:59:00 2006 Input: ellinit(e=[0,0,0,a,b]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 0, 0, a, b, 0, 2*a, 4*b, -a^2, -48*a, -864*b, -64*a^3 - 432*b^2, -6912*a^3/(-4*a^3 - 27*b^2), 0, 0, 0, 0, 0, 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '129.186' ************** PARI ***************** Host 129.186.52.128 (129.186.52.128) Time: Mon Jul 3 12:58:52 2006 Input: ellinit(e=[0,0,0,a,b]); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '129.186' ************** PARI ***************** Host 129.186.52.128 (129.186.52.128) Time: Mon Jul 3 12:58:44 2006 Input: ? 5 ellinit(e=[0,0,0,a,b]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? %1 = [0, 0, 0, a, b, 0, 2*a, 4*b, -a^2, -48*a, -864*b, -64*a^3 - 432*b^2, -6912*a^3/(-4*a^3 - 27*b^2), 0, 0, 0, 0, 0, 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.077s user 0m0.006s sys 0m0.005s '129.186' ************** PARI ***************** Host 129.186.52.128 (129.186.52.128) Time: Mon Jul 3 12:58:26 2006 Input: ? 5 ellint(e=[0,0,0,a,b]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: ellint(e=[0,0,0,a,b]) ^ Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '129.186' ************** PARI ***************** Host 129.186.52.128 (129.186.52.128) Time: Mon Jul 3 12:58:19 2006 Input: ? ellint(e=[0,0,0,a,b]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Help topics: for a list of relevant subtopics, type ?n for n in 0: user-defined identifiers (variable, alias, function) 1: Standard monadic or dyadic OPERATORS 2: CONVERSIONS and similar elementary functions 3: TRANSCENDENTAL functions 4: NUMBER THEORETICAL functions 5: Functions related to ELLIPTIC CURVES 6: Functions related to general NUMBER FIELDS 7: POLYNOMIALS and power series 8: Vectors, matrices, LINEAR ALGEBRA and sets 9: SUMS, products, integrals and similar functions 10: GRAPHIC functions 11: PROGRAMMING under GP 12: The PARI community Also: ? functionname (short on-line help) ?\ (keyboard shortcuts) ?. (member functions) ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: ellint(e=[0,0,0,a,b]) ^ Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '129.186' ************** PARI ***************** Host 129.186.52.128 (129.186.52.128) Time: Mon Jul 3 12:57:53 2006 Input: ellint(e=[0,0,0,a,b]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: ellint(e=[0,0,0,a,b]) ^ Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '129.186' ************** PARI ***************** Host 129.186.52.128 (129.186.52.128) Time: Mon Jul 3 12:57:49 2006 Input: ellint(e=[0,0,0,a,b]); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: ellint(e=[0,0,0,a,b]); ^- Timing: real 0m0.016s user 0m0.004s sys 0m0.009s '142.177' ************** PARI ***************** Host 142.177.190.211 (142.177.190.211) Time: Mon Jul 3 10:52:28 2006 Input: $681. x 29.90% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '66.21.1' ************** PARI ***************** Host 66.21.142.211 (66.21.142.211) Time: Mon Jul 3 08:54:48 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '165.234' ************** PARI ***************** Host 165.234.216.246 (165.234.216.246) Time: Mon Jul 3 08:43:23 2006 Input: The graph of the function f(x)= 3x^2-4/X^2-16 has a horizontal asymptote at y= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x^2-4/X^2-16hasahorizontalasymptoteaty=. *** unexpected character: ...sahorizontalasymptoteaty= ^ Timing: real 0m0.044s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:38:52 2006 Input: Mod(-8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:38:35 2006 Input: Mod(8^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:27:48 2006 Input: Mod(1^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:27:42 2006 Input: Mod(2^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:27:36 2006 Input: Mod(3^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(0, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:27:31 2006 Input: Mod(4^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:27:26 2006 Input: Mod(4^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:27:21 2006 Input: Mod(5^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:27:16 2006 Input: Mod(6^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(0, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:27:10 2006 Input: Mod(7^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:26:55 2006 Input: Mod(8^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:26:12 2006 Input: Mod(3^4,5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 5) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:26:06 2006 Input: Mod(2^4,5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 5) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:23:28 2006 Input: Mod(8^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:23:18 2006 Input: Mod(7^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:23:12 2006 Input: Mod(6^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(0, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:23:04 2006 Input: Mod(5^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:22:58 2006 Input: Mod(4^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(7, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:22:51 2006 Input: Mod(3^8,9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(0, 9) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:02:53 2006 Input: Mod((2^(107*32))*32^1545,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(3642, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:01:42 2006 Input: Mod((2^(107*32))*32^3397,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1679, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.221 (209.184.114.221) Time: Mon Jul 3 08:01:05 2006 Input: Mod(2^2029,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1679, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.010s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Mon Jul 3 07:55:14 2006 Input: Mod(2^121,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(3642, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Mon Jul 3 07:54:56 2006 Input: Mod((2^3424)*32^3397,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1679, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Mon Jul 3 07:53:38 2006 Input: Mod(2^121,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(3642, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Mon Jul 3 07:51:02 2006 Input: Mod(2^982,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2737, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Mon Jul 3 07:50:48 2006 Input: Mod((2^982,3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: Mod((2^982,3677) ^------ Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Mon Jul 3 07:50:22 2006 Input: Mod((2^(107*32))*(32^3397),3677) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1679, 3677) ? Goodbye! Errors/timing (if any): Timing: real 0m0.295s user 0m0.006s sys 0m0.009s '129.78.' ************** PARI ***************** Host 129.78.208.4 (129.78.208.4) Time: Mon Jul 3 02:42:34 2006 Input: (1+x)^7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.085s user 0m0.005s sys 0m0.007s '65.40.1' ************** PARI ***************** Host 65.40.109.31 (65.40.109.31) Time: Mon Jul 3 00:15:49 2006 Input: factor (11048546173416288693839243179043636404907551253850222324764735773426960799386155367351499591084286517) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 6250 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.130s user 0m20.863s sys 0m0.137s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Sun Jul 2 23:28:59 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.026s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sun Jul 2 21:33:32 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.86 (68.142.251.86) Time: Sun Jul 2 18:05:22 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.004s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Sun Jul 2 17:16:32 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Sun Jul 2 17:02:00 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.045s user 0m0.005s sys 0m0.006s '63.207.' ************** PARI ***************** Host 63.207.56.74 (63.207.56.74) Time: Sun Jul 2 15:37:06 2006 Input: (21*13)+26+120+100+(26*24)+70+(13*10.5)+(3*26) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1427.5000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Sun Jul 2 12:22:39 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.026s sys 0m0.003s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 11:22:39 2006 Input: matid(3) matinverseimage(mathilbert(5),matid(5)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [0 1 0] [0 0 1] ? %2 = [25 -300 1050 -1400 630] [-300 4800 -18900 26880 -12600] [1050 -18900 79380 -117600 56700] [-1400 26880 -117600 179200 -88200] [630 -12600 56700 -88200 44100] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 11:21:54 2006 Input: matid(3) mathilbert(5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [0 1 0] [0 0 1] ? %2 = [1 1/2 1/3 1/4 1/5] [1/2 1/3 1/4 1/5 1/6] [1/3 1/4 1/5 1/6 1/7] [1/4 1/5 1/6 1/7 1/8] [1/5 1/6 1/7 1/8 1/9] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 11:20:53 2006 Input: matid(3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 0 0] [0 1 0] [0 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:49:23 2006 Input: a=mathilbert(3) b=matinverseimage(a,[1,0,0;0,1,0;0,0,1]) a*b Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? %2 = [9 -36 30] [-36 192 -180] [30 -180 180] ? %3 = [1 0 0] [0 1 0] [0 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:49:00 2006 Input: a=mathilbert(3) matinverseimage(a,[1,0,0;0,1,0;0,0,1]) a*b Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? %2 = [9 -36 30] [-36 192 -180] [30 -180 180] ? %3 = [b 1/2*b 1/3*b] [1/2*b 1/3*b 1/4*b] [1/3*b 1/4*b 1/5*b] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:48:34 2006 Input: a=mathilbert(3) b=matinverseimage(mathilbert(3),[1,0,0;0,1,0;0,0,1]) a*b Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? %2 = [9 -36 30] [-36 192 -180] [30 -180 180] ? %3 = [1 0 0] [0 1 0] [0 0 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:48:14 2006 Input: a=mathilbert(3) a=matinverseimage(mathilbert(3),[1,0,0;0,1,0;0,0,1]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? %2 = [9 -36 30] [-36 192 -180] [30 -180 180] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:47:43 2006 Input: a=matinverseimage(mathilbert(3),[1,0,0;0,1,0;0,0,1]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [9 -36 30] [-36 192 -180] [30 -180 180] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:46:31 2006 Input: matinverseimage(mathilbert(3),[1,0,0;0,1,0;0,0,1]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [9 -36 30] [-36 192 -180] [30 -180 180] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:45:44 2006 Input: matinverseimage(mathilbert(3),[1;0;0]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [9] [-36] [30] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:45:33 2006 Input: matinverseimage(mathilbert(3),[1,0,0]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** matinverseimage: incorrect type in inverseimage. Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:44:55 2006 Input: matinverseimage(mathilbert(3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...nverseimage(mathilbert(3)) ^- Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:44:36 2006 Input: matinverse(mathilbert(3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: matinverse( *** mathilbert(3)) ^-------------- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:44:21 2006 Input: mathilbert(3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:44:06 2006 Input: mathibert(3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: mathibert(3) ^------------ Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '83.192.' ************** PARI ***************** Host 83.192.123.142 (83.192.123.142) Time: Sun Jul 2 10:43:54 2006 Input: hibert(3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: hibert(3) ^--------- Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '83.198.' ************** PARI ***************** Host 83.198.121.239 (83.198.121.239) Time: Sun Jul 2 10:03:01 2006 Input: a=mathilbert(3) matinvert(a) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: matinvert(a) ^ Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '83.198.' ************** PARI ***************** Host 83.198.121.239 (83.198.121.239) Time: Sun Jul 2 10:02:37 2006 Input: a=mathilbert(3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '83.198.' ************** PARI ***************** Host 83.198.121.239 (83.198.121.239) Time: Sun Jul 2 10:02:20 2006 Input: mathilbert(3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? Goodbye! Errors/timing (if any): Timing: real 0m0.038s user 0m0.007s sys 0m0.006s '83.198.' ************** PARI ***************** Host 83.198.121.239 (83.198.121.239) Time: Sun Jul 2 09:57:06 2006 Input: 2+3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.131.227 (72.30.131.227) Time: Sun Jul 2 09:53:31 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.007s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:42:53 2006 Input: zz=(-1+sqrt(-3))/2;subst(zz^(-1)*(y^3+9*y-6),y,3*L*sqrt(-3)*(-L^2-zz^(-1))/(L^3-zz)+sqrt(-3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((12.000000000000000000000000000000000000 + 7.052966104933725048 E-38*I)*L^9 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830861*I)*L^7 + (18.000000000000000000000000000000000000 + 109.11920087683926949222911951486995912*I)*L^6 + (-1.7296040355507741987 E-36 + 280.59223082615812155144630732395132344*I)*L^5 + (243.00000000000000000000000000000000000 - 140.29611541307906077572315366197566172*I)*L^4 + (103.50000000000000000000000000000000000 - 101.32497224277932167135561097809353347*I)*L^3 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830862*I)*L^2 + (-9.403954806578300064 E-38 + 3.761581922631320025 E-37*I)*L + (-12.000000000000000000000000000000000000 + 0.E-37*I))/(L^9 + (3/2 - 2.5980762113533159402911695122588085504*I)*L^6 + (-1.5000000000000000000000000000000000000 - 2.5980762113533159402911695122588085504*I)*L^3 + (-1.0000000000000000000000000000000000000 - 2.938735877055718770 E-39*I)) ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:41:44 2006 Input: zz=(-1+sqrt(-3))/2;subst(zz^(-1)*(y^3+9*y-6),y,3*l*sqrt(-3)*(-ll^2-zz^(-1))/(l^3-zz)+sqrt(-3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 12721 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.010s user 0m20.960s sys 0m0.044s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:30:47 2006 Input: 2.5980762113533159402911695122588085504^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6.7499999999999999999999999999999999999 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:28:36 2006 Input: zz=(-1+sqrt(-3))/2;subst(zz^(-1)*(y^3+9*y-6),y,3*l*sqrt(-3)*(-l^2-zz^(-1))/(l^3-zz)+sqrt(-3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((12.000000000000000000000000000000000000 + 7.052966104933725048 E-38*I)*l^9 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830861*I)*l^7 + (18.000000000000000000000000000000000000 + 109.11920087683926949222911951486995912*I)*l^6 + (-1.7296040355507741987 E-36 + 280.59223082615812155144630732395132344*I)*l^5 + (243.00000000000000000000000000000000000 - 140.29611541307906077572315366197566172*I)*l^4 + (103.50000000000000000000000000000000000 - 101.32497224277932167135561097809353347*I)*l^3 + (-121.50000000000000000000000000000000000 - 70.148057706539530387861576830987830862*I)*l^2 + (-9.403954806578300064 E-38 + 3.761581922631320025 E-37*I)*l + (-12.000000000000000000000000000000000000 + 0.E-37*I))/(l^9 + (3/2 - 2.5980762113533159402911695122588085504*I)*l^6 + (-1.5000000000000000000000000000000000000 - 2.5980762113533159402911695122588085504*I)*l^3 + (-1.0000000000000000000000000000000000000 - 2.938735877055718770 E-39*I)) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.028s user 0m0.009s sys 0m0.003s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:28:28 2006 Input: zz=(-1+sqrt(-3))/2;subst(zz^(-1)*(y^3+9*y-6),y,3*l*sqrt(-3)*(-ll^2-zz^(-1))/(l^3-zz)+sqrt(-3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 12687 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.015s user 0m20.965s sys 0m0.039s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:27:50 2006 Input: zz=(-1+sqrt(-3))/2;subst(zz^(-1)*(y^3+9*y-6),y,3*l*sqrt(-3)*(-ll^2-zz^(-1))/(l^3-zz)+sqrt(-3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 12681 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.019s user 0m20.947s sys 0m0.057s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:26:18 2006 Input: zz=(-1+sqrt(-3))/2;subst(zz^(-1)*(y^3+9*y-6),y,3*l*sqrt(-3)*(-ll^2-zz^(-1))/(l^3-zz)+sqrt(-3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 12676 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.032s user 0m20.907s sys 0m0.096s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:25:45 2006 Input: zz=(-1+sqrt(-3))/2;subst(zz^(-1)*(y^3+9*y-6),y,3*l*sqrt(-3)*(-ll^2-zz^(-1))/(l^3-zz)+sqrt(-3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 12668 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.023s user 0m20.953s sys 0m0.049s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:25:41 2006 Input: zz=(-1+sqrt(-3))/2;subst(zz^(-1)*(y^3+9*y-6),y,3*l*sqrt(-3)*(-ll^2-zz^(-1))/(l^3-zz)+sqrt(-3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 12664 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.081s user 0m20.957s sys 0m0.046s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:24:17 2006 Input: ?subst Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? subst(x,y,z): in expression x, replace the variable y by the expression z. ? Goodbye! Errors/timing (if any): Timing: real 0m0.033s user 0m0.004s sys 0m0.007s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:23:34 2006 Input: zz=(-1+sqrt(-3))/2;subst(zz^(-1)*(y^3+9*y-6,y,3*l*sqrt(-3)*(-ll^2-zz^(-1))/(l^3-zz)+sqrt(-3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...;subst(zz^(-1)*(y^3+9*y-6 *** ,y,3*l*sqrt(-3)*(-ll ^-------------------- Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '82.172.' ************** PARI ***************** Host 82.172.110.95 (82.172.110.95) Time: Sun Jul 2 09:19:17 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Sun Jul 2 07:58:22 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Sun Jul 2 06:42:30 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Sun Jul 2 06:14:48 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.006s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Sun Jul 2 01:17:24 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.022s sys 0m0.007s '71.111.' ************** PARI ***************** Host 71.111.189.223 (71.111.189.223) Time: Sun Jul 2 00:44:31 2006 Input: [1.80]3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: 3. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Sun Jul 2 00:34:28 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sat Jul 1 23:35:01 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Sat Jul 1 23:32:40 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.129.123 (72.30.129.123) Time: Sat Jul 1 20:27:57 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.009s '203.147' ************** PARI ***************** Host 203.147.0.44 (203.147.0.44) Time: Sat Jul 1 19:30:38 2006 Input: 1+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.007s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.132.102 (72.30.132.102) Time: Sat Jul 1 15:52:29 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.88 (68.142.249.88) Time: Sat Jul 1 15:05:25 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.108s user 0m0.006s sys 0m0.013s '72.30.9' ************** PARI ***************** Host 72.30.98.35 (72.30.98.35) Time: Sat Jul 1 12:44:26 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.026s sys 0m0.005s '69.215.' ************** PARI ***************** Host 69.215.146.199 (69.215.146.199) Time: Sat Jul 1 11:40:01 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '69.215.' ************** PARI ***************** Host 69.215.146.199 (69.215.146.199) Time: Sat Jul 1 11:37:14 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '69.215.' ************** PARI ***************** Host 69.215.146.199 (69.215.146.199) Time: Sat Jul 1 11:35:35 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '69.215.' ************** PARI ***************** Host 69.215.146.199 (69.215.146.199) Time: Sat Jul 1 11:34:53 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '69.215.' ************** PARI ***************** Host 69.215.146.199 (69.215.146.199) Time: Sat Jul 1 11:34:47 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '216.173' ************** PARI ***************** Host 216.173.171.190 (216.173.171.190) Time: Sat Jul 1 10:35:43 2006 Input: 3(X-4)-4(X-3)=X+3-(X-2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: (X-4)-4(X-3)=X+3-(X-2). *** unexpected character: 3(X-4)-4(X-3)=X+3-(X-2) ^---------- Timing: real 0m0.027s user 0m0.006s sys 0m0.006s '71.137.' ************** PARI ***************** Host 71.137.108.1 (71.137.108.1) Time: Sat Jul 1 10:11:30 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sat Jul 1 02:47:27 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '72.30.1' ************** PARI ***************** Host 72.30.103.19 (72.30.103.19) Time: Sat Jul 1 00:11:04 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '200.121' ************** PARI ***************** Host 200.121.195.108 (200.121.195.108) Time: Fri Jun 30 21:53:35 2006 Input: print gap('SymmetricGroup(7)') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printgap('SymmetricGroup(7)') ^----- Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '200.121' ************** PARI ***************** Host 200.121.195.108 (200.121.195.108) Time: Fri Jun 30 21:52:45 2006 Input: tex2html_wrap_inline$Q(α#alpha;)$ Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: $Q(α#alpha;)$. *** unexpected character: tex2html_wrap_inline$Q(α#alpha;)$ ^------------------ Timing: real 0m0.011s user 0m0.009s sys 0m0.002s '69.231.' ************** PARI ***************** Host 69.231.225.218 (69.231.225.218) Time: Fri Jun 30 19:19:27 2006 Input: 30.38*360 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 10936.800000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.160 (68.142.249.160) Time: Fri Jun 30 19:14:15 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.47 (68.142.249.47) Time: Fri Jun 30 18:21:11 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.251.86 (68.142.251.86) Time: Fri Jun 30 18:08:09 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.031s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jun 30 14:16:41 2006 Input: a=13 p=37 q=79 n=p*q r=Mod(a^(n-1), n) Mod(r^(q-p),n) Mod(r^(n-1),n) Mod(a^((q-p)*(q-p)),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 13 ? %2 = 37 ? %3 = 79 ? %4 = 2923 ? %5 = Mod(2786, 2923) ? %6 = Mod(334, 2923) ? %7 = Mod(1444, 2923) ? %8 = Mod(1444, 2923) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jun 30 14:15:52 2006 Input: a=13 p=37 q=79 n=p*q r=Mod(a^(n-1), n) Mod(r^(q-p),n) Mod(r^(n-1),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 13 ? %2 = 37 ? %3 = 79 ? %4 = 2923 ? %5 = Mod(2786, 2923) ? %6 = Mod(334, 2923) ? %7 = Mod(1444, 2923) ? Goodbye! Errors/timing (if any): Timing: real 0m0.051s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jun 30 14:05:59 2006 Input: a=13 p=37 q=79 n=p*q r=Mod(a^(n-1), n) Mod(a^((q+p)*(q-p)),p) Mod(a^((n+1)*(n-1)),p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 13 ? %2 = 37 ? %3 = 79 ? %4 = 2923 ? %5 = Mod(2786, 2923) ? %6 = Mod(10, 37) ? %7 = Mod(10, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m1.827s user 0m1.782s sys 0m0.045s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jun 30 14:05:40 2006 Input: a=13 p=37 q=79 n=p*q r=Mod(a^(n-1), n) Mod(a^((q+p)*(q-p)),n) Mod(a^((n+1)*(n-1)),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 13 ? %2 = 37 ? %3 = 79 ? %4 = 2923 ? %5 = Mod(2786, 2923) ? %6 = Mod(1601, 2923) ? %7 = Mod(380, 2923) ? Goodbye! Errors/timing (if any): Timing: real 0m1.822s user 0m1.777s sys 0m0.045s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jun 30 14:05:31 2006 Input: a=13 p=37 q=73 n=p*q r=Mod(a^(n-1), n) Mod(a^((q+p)*(q-p)),n) Mod(a^((n+1)*(n-1)),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 13 ? %2 = 37 ? %3 = 73 ? %4 = 2701 ? %5 = Mod(2554, 2701) ? %6 = Mod(1, 2701) ? %7 = Mod(1, 2701) ? Goodbye! Errors/timing (if any): Timing: real 0m1.426s user 0m1.391s sys 0m0.035s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jun 30 14:05:21 2006 Input: a=7 p=37 q=73 n=p*q r=Mod(a^(n-1), n) Mod(a^((q+p)*(q-p)),n) Mod(a^((n+1)*(n-1)),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7 ? %2 = 37 ? %3 = 73 ? %4 = 2701 ? %5 = Mod(2554, 2701) ? %6 = Mod(1, 2701) ? %7 = Mod(1, 2701) ? Goodbye! Errors/timing (if any): Timing: real 0m1.004s user 0m0.975s sys 0m0.030s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Fri Jun 30 14:04:47 2006 Input: a=41 p=241 q=547 n=p*q r=Mod(a^(n-1), n) Mod(a^((q+p)*(q-p)),n) Mod(a^((n+1)*(n-1)),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 241 ? %3 = 547 ? %4 = 131827 ? %5 = Mod(52513, 131827) ? %6 = Mod(31180, 131827) ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 2056 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.118s user 0m20.582s sys 0m0.445s '68.44.2' ************** PARI ***************** Host 68.44.204.154 (68.44.204.154) Time: Fri Jun 30 13:59:49 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.050s user 0m0.007s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Fri Jun 30 12:52:11 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.066s user 0m0.027s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Fri Jun 30 12:01:57 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.061s user 0m0.004s sys 0m0.009s '66.174.' ************** PARI ***************** Host 66.174.79.240 (66.174.79.240) Time: Fri Jun 30 11:41:09 2006 Input: sin(pi) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = pi - 1/6*pi^3 + 1/120*pi^5 - 1/5040*pi^7 + 1/362880*pi^9 - 1/39916800*pi^11 + 1/6227020800*pi^13 - 1/1307674368000*pi^15 + O(pi^17) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.065s user 0m0.007s sys 0m0.005s '72.184.' ************** PARI ***************** Host 72.184.21.131 (72.184.21.131) Time: Fri Jun 30 10:34:09 2006 Input: 85-10%= Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Fri Jun 30 10:01:33 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.078s user 0m0.006s sys 0m0.006s '72.137.' ************** PARI ***************** Host 72.137.117.160 (72.137.117.160) Time: Fri Jun 30 09:22:20 2006 Input: loan of 18000 compounded at 8%semiannually for 4years Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Fri Jun 30 07:07:28 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.085s user 0m0.007s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Fri Jun 30 05:17:34 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.022s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Fri Jun 30 04:01:26 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.038s user 0m0.023s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Fri Jun 30 00:05:00 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '72.30.9' ************** PARI ***************** Host 72.30.99.77 (72.30.99.77) Time: Thu Jun 29 23:31:32 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.073s user 0m0.013s sys 0m0.001s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Thu Jun 29 22:37:33 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.005s sys 0m0.010s '64.124.' ************** PARI ***************** Host 64.124.10.163 (64.124.10.163) Time: Thu Jun 29 20:17:47 2006 Input: 500*.2316 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 115.80000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.194.' ************** PARI ***************** Host 71.194.152.231 (71.194.152.231) Time: Thu Jun 29 20:03:03 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '129.72.' ************** PARI ***************** Host 129.72.144.21 (129.72.144.21) Time: Thu Jun 29 19:41:58 2006 Input: S2(n, k) = if(k<1|k>n, 0, if(n==1, 1, k*S2(n-1, k)+S2(n-1, k-1))); printp(matrix(19, 19, n, k, S2(n, k))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? [1 0 0 0 0 0 0 0 0 0 0 0 0 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 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 7 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 15 25 10 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 31 90 65 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 63 301 350 140 21 1 0 0 0 0 0 0 0 0 0 0 0 0] [1 127 966 1701 1050 266 28 1 0 0 0 0 0 0 0 0 0 0 0] [1 255 3025 7770 6951 2646 462 36 1 0 0 0 0 0 0 0 0 0 0] [1 511 9330 34105 42525 22827 5880 750 45 1 0 0 0 0 0 0 0 0 0] [1 1023 28501 145750 246730 179487 63987 11880 1155 55 1 0 0 0 0 0 0 0 0] [1 2047 86526 611501 1379400 1323652 627396 159027 22275 1705 66 1 0 0 0 0 0 0 0] [1 4095 261625 2532530 7508501 9321312 5715424 1899612 359502 39325 2431 78 1 0 0 0 0 0 0] [1 8191 788970 10391745 40075035 63436373 49329280 20912320 5135130 752752 66066 3367 91 1 0 0 0 0 0] [1 16383 2375101 42355950 210766920 420693273 408741333 216627840 67128490 12662650 1479478 106470 4550 105 1 0 0 0 0] [1 32767 7141686 171798901 1096190550 2734926558 3281882604 2141764053 820784250 193754990 28936908 2757118 165620 6020 120 1 0 0 0] [1 65535 21457825 694337290 5652751651 17505749898 25708104786 20415995028 9528822303 2758334150 512060978 62022324 4910178 249900 7820 136 1 0 0] [1 131071 64439010 2798806985 28958095545 110687251039 197462483400 189036065010 106175395755 37112163803 8391004908 1256328866 125854638 8408778 367200 9996 153 1 0] [1 262143 193448101 11259666950 147589284710 693081601779 1492924634839 1709751003480 1144614626805 477297033785 129413217791 23466951300 2892439160 243577530 13916778 527136 12597 171 1] ? Goodbye! Errors/timing (if any): Timing: real 0m11.029s user 0m11.010s sys 0m0.004s '129.72.' ************** PARI ***************** Host 129.72.144.21 (129.72.144.21) Time: Thu Jun 29 19:41:48 2006 Input: S2(n, k) = if(k<1|k>n, 0, if(n==1, 1, k*S2(n-1, k)+S2(n-1, k-1))); printp(matrix(19, 19, n, k, S2(n, k))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? [1 0 0 0 0 0 0 0 0 0 0 0 0 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 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 7 6 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 15 25 10 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 31 90 65 15 1 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 63 301 350 140 21 1 0 0 0 0 0 0 0 0 0 0 0 0] [1 127 966 1701 1050 266 28 1 0 0 0 0 0 0 0 0 0 0 0] [1 255 3025 7770 6951 2646 462 36 1 0 0 0 0 0 0 0 0 0 0] [1 511 9330 34105 42525 22827 5880 750 45 1 0 0 0 0 0 0 0 0 0] [1 1023 28501 145750 246730 179487 63987 11880 1155 55 1 0 0 0 0 0 0 0 0] [1 2047 86526 611501 1379400 1323652 627396 159027 22275 1705 66 1 0 0 0 0 0 0 0] [1 4095 261625 2532530 7508501 9321312 5715424 1899612 359502 39325 2431 78 1 0 0 0 0 0 0] [1 8191 788970 10391745 40075035 63436373 49329280 20912320 5135130 752752 66066 3367 91 1 0 0 0 0 0] [1 16383 2375101 42355950 210766920 420693273 408741333 216627840 67128490 12662650 1479478 106470 4550 105 1 0 0 0 0] [1 32767 7141686 171798901 1096190550 2734926558 3281882604 2141764053 820784250 193754990 28936908 2757118 165620 6020 120 1 0 0 0] [1 65535 21457825 694337290 5652751651 17505749898 25708104786 20415995028 9528822303 2758334150 512060978 62022324 4910178 249900 7820 136 1 0 0] [1 131071 64439010 2798806985 28958095545 110687251039 197462483400 189036065010 106175395755 37112163803 8391004908 1256328866 125854638 8408778 367200 9996 153 1 0] [1 262143 193448101 11259666950 147589284710 693081601779 1492924634839 1709751003480 1144614626805 477297033785 129413217791 23466951300 2892439160 243577530 13916778 527136 12597 171 1] ? Goodbye! Errors/timing (if any): Timing: real 0m10.906s user 0m10.888s sys 0m0.006s '129.72.' ************** PARI ***************** Host 129.72.144.21 (129.72.144.21) Time: Thu Jun 29 19:41:21 2006 Input: S2(n, k) = if(k<1|k>n, 0, if(n==1, 1, k*S2(n-1, k)+S2(n-1, k-1))); printp(matrix(9, 9, n, k, S2(n, k))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? [1 0 0 0 0 0 0 0 0] [1 1 0 0 0 0 0 0 0] [1 3 1 0 0 0 0 0 0] [1 7 6 1 0 0 0 0 0] [1 15 25 10 1 0 0 0 0] [1 31 90 65 15 1 0 0 0] [1 63 301 350 140 21 1 0 0] [1 127 966 1701 1050 266 28 1 0] [1 255 3025 7770 6951 2646 462 36 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.043s user 0m0.020s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 19:40:40 2006 Input: a=71 p=37 q=173 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) gcd(n,r^(q-p)-l) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 37 ? %3 = 173 ? %4 = 6401 ? %5 = Mod(1329, 6401) ? %6 = Mod(6250, 6401) ? %7 = Mod(2957, 6401) ? %8 = Mod(4255, 6401) ? %9 = Mod(0, 37) ? %10 = Mod(37, 6401) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 19:40:30 2006 Input: a=71 p=37 q=173 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(n-1)-l,n) Mod(r^(n-1)-l,p) gcd(n,r^(q-p)-l) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 37 ? %3 = 173 ? %4 = 6401 ? %5 = Mod(1329, 6401) ? %6 = Mod(6250, 6401) ? %7 = Mod(2957, 6401) ? %8 = Mod(0, 6401) ? %9 = Mod(0, 37) ? %10 = Mod(37, 6401) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '129.72.' ************** PARI ***************** Host 129.72.144.21 (129.72.144.21) Time: Thu Jun 29 19:40:12 2006 Input: T(n, k)=if(n<1, 0, n!*polcoeff(polcoeff((1+x+x*O(x^n))^y, n), k)) x^3 + x^2 + 2*x + 1 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = x^3 + x^2 + 2*x + 1 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '129.72.' ************** PARI ***************** Host 129.72.144.21 (129.72.144.21) Time: Thu Jun 29 19:39:09 2006 Input: T(n, k)=if(n<1, 0, n!*polcoeff(polcoeff((1+x+x*O(x^n))^y, n), k)) T(4,3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = -6 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.008s '129.72.' ************** PARI ***************** Host 129.72.144.21 (129.72.144.21) Time: Thu Jun 29 19:39:01 2006 Input: T(n, k)=if(n<1, 0, n!*polcoeff(polcoeff((1+x+x*O(x^n))^y, n), k)) T(4,2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 11 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '129.72.' ************** PARI ***************** Host 129.72.144.21 (129.72.144.21) Time: Thu Jun 29 19:38:47 2006 Input: T(n, k)=if(n<1, 0, n!*polcoeff(polcoeff((1+x+x*O(x^n))^y, n), k)) T(10,5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = -269325 ? Goodbye! Errors/timing (if any): Timing: real 0m0.057s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 19:10:28 2006 Input: a=71 p=37 q=173 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) gcd(n,r^(q-p)-l) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 37 ? %3 = 173 ? %4 = 6401 ? %5 = Mod(1329, 6401) ? %6 = Mod(6250, 6401) ? %7 = Mod(2957, 6401) ? %8 = Mod(4255, 6401) ? %9 = Mod(0, 37) ? %10 = Mod(37, 6401) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 19:10:14 2006 Input: a=71 p=37 q=173 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(n-1)-l,n) Mod(r^(n-1)-l,p) gcd(n,r^(n-1)-l) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 37 ? %3 = 173 ? %4 = 6401 ? %5 = Mod(1329, 6401) ? %6 = Mod(6250, 6401) ? %7 = Mod(2957, 6401) ? %8 = Mod(0, 6401) ? %9 = Mod(0, 37) ? %10 = 6401 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 19:10:03 2006 Input: a=71 p=37 q=173 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(n-1)-l,p) gcd(n,r^(n-1)-l) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 37 ? %3 = 173 ? %4 = 6401 ? %5 = Mod(1329, 6401) ? %6 = Mod(6250, 6401) ? %7 = Mod(2957, 6401) ? %8 = Mod(4255, 6401) ? %9 = Mod(0, 37) ? %10 = 6401 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:46:39 2006 Input: a=71 p=37 q=173 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) gcd(n,r^(q-p)-l) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 37 ? %3 = 173 ? %4 = 6401 ? %5 = Mod(1329, 6401) ? %6 = Mod(6250, 6401) ? %7 = Mod(2957, 6401) ? %8 = Mod(4255, 6401) ? %9 = Mod(0, 37) ? %10 = Mod(37, 6401) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:46:08 2006 Input: a=71 p=37 q=173 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 37 ? %3 = 173 ? %4 = 6401 ? %5 = Mod(1329, 6401) ? %6 = Mod(6250, 6401) ? %7 = Mod(2957, 6401) ? %8 = Mod(4255, 6401) ? %9 = Mod(0, 37) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:45:45 2006 Input: a=71 p=37 q=171 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 37 ? %3 = 171 ? %4 = 6327 ? %5 = Mod(5932, 6327) ? %6 = Mod(5932, 6327) ? %7 = Mod(1810, 6327) ? %8 = Mod(0, 6327) ? %9 = Mod(0, 37) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:45:39 2006 Input: a=71 p=37 q=171 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 37 ? %3 = 171 ? %4 = 6327 ? %5 = Mod(5932, 6327) ? %6 = Mod(5932, 6327) ? %7 = Mod(1810, 6327) ? %8 = Mod(0, 6327) ? %9 = Mod(0, 37) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:45:30 2006 Input: a=71 p=37 q=89 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 37 ? %3 = 89 ? %4 = 3293 ? %5 = Mod(1402, 3293) ? %6 = Mod(3030, 3293) ? %7 = Mod(1043, 3293) ? %8 = Mod(1036, 3293) ? %9 = Mod(0, 37) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:45:25 2006 Input: a=71 p=23 q=89 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 71 ? %2 = 23 ? %3 = 89 ? %4 = 2047 ? %5 = Mod(622, 2047) ? %6 = Mod(622, 2047) ? %7 = Mod(1, 2047) ? %8 = Mod(0, 2047) ? %9 = Mod(0, 23) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:45:13 2006 Input: a=17 p=23 q=89 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 17 ? %2 = 23 ? %3 = 89 ? %4 = 2047 ? %5 = Mod(622, 2047) ? %6 = Mod(622, 2047) ? %7 = Mod(1, 2047) ? %8 = Mod(0, 2047) ? %9 = Mod(0, 23) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:45:09 2006 Input: a=17 p=41 q=89 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 17 ? %2 = 41 ? %3 = 89 ? %4 = 3649 ? %5 = Mod(2353, 3649) ? %6 = Mod(16, 3649) ? %7 = Mod(242, 3649) ? %8 = Mod(2460, 3649) ? %9 = Mod(0, 41) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:44:51 2006 Input: a=17 p=41 q=2047 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 17 ? %2 = 41 ? %3 = 2047 ? %4 = 83927 ? %5 = Mod(68847, 83927) ? %6 = Mod(27396, 83927) ? %7 = Mod(29879, 83927) ? %8 = Mod(49897, 83927) ? %9 = Mod(0, 41) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.828s user 0m0.788s sys 0m0.035s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:44:38 2006 Input: a=17 p=23 q=89 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 17 ? %2 = 23 ? %3 = 89 ? %4 = 2047 ? %5 = Mod(622, 2047) ? %6 = Mod(622, 2047) ? %7 = Mod(1, 2047) ? %8 = Mod(0, 2047) ? %9 = Mod(0, 23) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:44:30 2006 Input: a=17 p=23 q=127 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 17 ? %2 = 23 ? %3 = 127 ? %4 = 2921 ? %5 = Mod(1428, 2921) ? %6 = Mod(1819, 2921) ? %7 = Mod(2355, 2921) ? %8 = Mod(2806, 2921) ? %9 = Mod(0, 23) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.010s sys 0m0.002s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:44:20 2006 Input: a=17 p=23 q=89 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 17 ? %2 = 23 ? %3 = 89 ? %4 = 2047 ? %5 = Mod(622, 2047) ? %6 = Mod(622, 2047) ? %7 = Mod(1, 2047) ? %8 = Mod(0, 2047) ? %9 = Mod(0, 23) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:44:14 2006 Input: a=8 p=23 q=89 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 8 ? %2 = 23 ? %3 = 89 ? %4 = 2047 ? %5 = Mod(1, 2047) ? %6 = Mod(1, 2047) ? %7 = Mod(1, 2047) ? %8 = Mod(0, 2047) ? %9 = Mod(0, 23) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:43:50 2006 Input: a=89 p=211 q=479 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 89 ? %2 = 211 ? %3 = 479 ? %4 = 101069 ? %5 = Mod(86661, 101069) ? %6 = Mod(57543, 101069) ? %7 = Mod(54774, 101069) ? %8 = Mod(4009, 101069) ? %9 = Mod(0, 211) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.045s user 0m0.038s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:43:41 2006 Input: a=37 p=211 q=479 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 211 ? %3 = 479 ? %4 = 101069 ? %5 = Mod(78328, 101069) ? %6 = Mod(60604, 101069) ? %7 = Mod(6600, 101069) ? %8 = Mod(99381, 101069) ? %9 = Mod(0, 211) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.036s user 0m0.033s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:43:36 2006 Input: a=41 p=211 q=479 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 211 ? %3 = 479 ? %4 = 101069 ? %5 = Mod(91626, 101069) ? %6 = Mod(11024, 101069) ? %7 = Mod(27057, 101069) ? %8 = Mod(65832, 101069) ? %9 = Mod(0, 211) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.037s user 0m0.031s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:43:31 2006 Input: a=47 p=211 q=479 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 47 ? %2 = 211 ? %3 = 479 ? %4 = 101069 ? %5 = Mod(96486, 101069) ? %6 = Mod(76441, 101069) ? %7 = Mod(87238, 101069) ? %8 = Mod(89042, 101069) ? %9 = Mod(0, 211) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.039s user 0m0.034s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:42:49 2006 Input: a=23 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 23 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(43945, 69973) ? %6 = Mod(9042, 69973) ? %7 = Mod(48727, 69973) ? %8 = Mod(41249, 69973) ? %9 = Mod(0, 167) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.021s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:42:44 2006 Input: a=89 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 89 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(23943, 69973) ? %6 = Mod(62019, 69973) ? %7 = Mod(68823, 69973) ? %8 = Mod(16700, 69973) ? %9 = Mod(0, 167) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.035s user 0m0.027s sys 0m0.007s '72.30.9' ************** PARI ***************** Host 72.30.98.26 (72.30.98.26) Time: Thu Jun 29 18:42:42 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:42:39 2006 Input: a=11 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 11 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(63455, 69973) ? %6 = Mod(11518, 69973) ? %7 = Mod(14571, 69973) ? %8 = Mod(23714, 69973) ? %9 = Mod(0, 167) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.013s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:42:32 2006 Input: a=41 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(47478, 69973) ? %6 = Mod(56162, 69973) ? %7 = Mod(23297, 69973) ? %8 = Mod(38577, 69973) ? %9 = Mod(0, 167) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.023s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:42:23 2006 Input: a=41 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(47478, 69973) ? %6 = Mod(56162, 69973) ? %7 = Mod(23297, 69973) ? %8 = Mod(0, 167) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.028s user 0m0.024s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:42:07 2006 Input: a=41 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p)-l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(47478, 69973) ? %6 = Mod(56162, 69973) ? %7 = Mod(23297, 69973) ? %8 = Mod(38577, 69973) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.028s user 0m0.021s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:40:19 2006 Input: a=41 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p),n)-l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(47478, 69973) ? %6 = Mod(56162, 69973) ? %7 = Mod(23297, 69973) ? %8 = Mod(38577, 69973) ? Goodbye! Errors/timing (if any): *** Warning: unused characters: ,n). Timing: real 0m0.028s user 0m0.023s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:40:04 2006 Input: a=41 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p),n)-l.n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(47478, 69973) ? %6 = Mod(56162, 69973) ? %7 = Mod(23297, 69973) ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: ). *** unknown member function: Mod(r^(q-p),n)-l.n) ^-- Timing: real 0m0.028s user 0m0.024s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:39:36 2006 Input: a=41 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(Mod(r^(q-p),n)-l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(47478, 69973) ? %6 = Mod(56162, 69973) ? %7 = Mod(23297, 69973) ? %8 = Mod(38577, 69973) ? Goodbye! Errors/timing (if any): Timing: real 0m0.028s user 0m0.024s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:39:11 2006 Input: a=41 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Mod(r^(q-p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(47478, 69973) ? %6 = Mod(56162, 69973) ? %7 = Mod(23297, 69973) ? %8 = Mod(61874, 69973) ? Goodbye! Errors/timing (if any): Timing: real 0m0.028s user 0m0.023s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:38:50 2006 Input: a=41 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(47478, 69973) ? %6 = Mod(56162, 69973) ? %7 = Mod(23297, 69973) ? Goodbye! Errors/timing (if any): Timing: real 0m0.028s user 0m0.022s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:38:17 2006 Input: a=41 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) l=(a^((q-p)*(q-p)),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(47478, 69973) ? %6 = Mod(56162, 69973) ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: l=(a^((q-p)*(q-p)),n) ^--- Timing: real 0m0.021s user 0m0.017s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:37:23 2006 Input: a=41 p=167 q=419 n=p*q que=Mod(a^(q-p),n) r=Mod(a^(n-1),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(47478, 69973) ? %6 = Mod(56162, 69973) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.014s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Thu Jun 29 18:35:55 2006 Input: a=41 p=167 q=419 n=p*q r=Mod(a^(n-1),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 167 ? %3 = 419 ? %4 = 69973 ? %5 = Mod(56162, 69973) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.015s sys 0m0.005s '170.20.' ************** PARI ***************** Host 170.20.11.116 (170.20.11.116) Time: Thu Jun 29 17:34:02 2006 Input: 22/3 * 13/4 * 71/2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 10153/12 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '204.128' ************** PARI ***************** Host 204.128.192.8 (204.128.192.8) Time: Thu Jun 29 17:02:35 2006 Input: log (4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1.3862943611198906188344642429163531362 ? Goodbye! Errors/timing (if any): Timing: real 0m0.059s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Thu Jun 29 16:44:58 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '68.178.' ************** PARI ***************** Host 68.178.99.194 (68.178.99.194) Time: Thu Jun 29 15:33:42 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.039s user 0m0.005s sys 0m0.007s '68.178.' ************** PARI ***************** Host 68.178.99.194 (68.178.99.194) Time: Thu Jun 29 15:33:28 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '18.245.' ************** PARI ***************** Host 18.245.6.168 (18.245.6.168) Time: Thu Jun 29 15:26:38 2006 Input: exp(-2.4)/(12.5 - 12.5*exp(-2.4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.0079815017676940306699967972627239266250 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '18.245.' ************** PARI ***************** Host 18.245.6.168 (18.245.6.168) Time: Thu Jun 29 15:25:41 2006 Input: 50000*exp(-2.4)/(12.5 - 12.5*exp(-2.4)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 399.07508838470153349983986313619633125 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '18.245.' ************** PARI ***************** Host 18.245.6.168 (18.245.6.168) Time: Thu Jun 29 15:24:19 2006 Input: exp(2.4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 11.023176380641601652237939769667802009 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '18.245.' ************** PARI ***************** Host 18.245.6.168 (18.245.6.168) Time: Thu Jun 29 15:24:13 2006 Input: exp(x) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + 1/3628800*x^10 + 1/39916800*x^11 + 1/479001600*x^12 + 1/6227020800*x^13 + 1/87178291200*x^14 + 1/1307674368000*x^15 + 1/20922789888000*x^16 + O(x^17) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '18.245.' ************** PARI ***************** Host 18.245.6.168 (18.245.6.168) Time: Thu Jun 29 15:24:09 2006 Input: exp(x); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.035s user 0m0.007s sys 0m0.004s '18.245.' ************** PARI ***************** Host 18.245.6.168 (18.245.6.168) Time: Thu Jun 29 15:22:13 2006 Input: exp(2.4); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.006s '18.245.' ************** PARI ***************** Host 18.245.6.168 (18.245.6.168) Time: Thu Jun 29 15:22:05 2006 Input: exp^(2.4); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: exp^(2.4); ^------- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '18.245.' ************** PARI ***************** Host 18.245.6.168 (18.245.6.168) Time: Thu Jun 29 15:21:55 2006 Input: e^(2.4); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** gpow: need integer exponent if series valuation != 0. Timing: real 0m0.033s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Thu Jun 29 13:48:39 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.064s user 0m0.005s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Thu Jun 29 13:27:27 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '192.88.' ************** PARI ***************** Host 192.88.212.44 (192.88.212.44) Time: Thu Jun 29 13:15:24 2006 Input: .75^2/4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.14062500000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.104s user 0m0.004s sys 0m0.008s '209.120' ************** PARI ***************** Host 209.120.230.194 (209.120.230.194) Time: Thu Jun 29 12:34:40 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '210.173' ************** PARI ***************** Host 210.173.62.3 (210.173.62.3) Time: Thu Jun 29 11:32:52 2006 Input: print maxima('tan(x)').integrate('x') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printmaxima('tan *** (x)').integrate('x') ^-------------------- Timing: real 0m0.011s user 0m0.003s sys 0m0.010s '210.173' ************** PARI ***************** Host 210.173.62.3 (210.173.62.3) Time: Thu Jun 29 11:32:21 2006 Input: print maxima(solve(x^2,x)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: printmaxima(solve(x^2,x)); ^------- Timing: real 0m0.011s user 0m0.008s sys 0m0.005s '210.173' ************** PARI ***************** Host 210.173.62.3 (210.173.62.3) Time: Thu Jun 29 11:31:52 2006 Input: maxima(solve(x^2,x)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: maxima(solve(x^2,x)); ^------- Timing: real 0m0.092s user 0m0.003s sys 0m0.009s '64.234.' ************** PARI ***************** Host 64.234.18.142 (64.234.18.142) Time: Thu Jun 29 11:23:13 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Thu Jun 29 10:44:44 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.047s user 0m0.008s sys 0m0.007s '63.241.' ************** PARI ***************** Host 63.241.61.7 (63.241.61.7) Time: Thu Jun 29 08:18:31 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.099s user 0m0.005s sys 0m0.006s '63.241.' ************** PARI ***************** Host 63.241.61.7 (63.241.61.7) Time: Thu Jun 29 07:45:11 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.109s user 0m0.010s sys 0m0.003s '134.102' ************** PARI ***************** Host 134.102.116.85 (134.102.116.85) Time: Thu Jun 29 04:02:45 2006 Input: factor(100) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 2] [5 2] ? Goodbye! Errors/timing (if any): Timing: real 0m0.056s user 0m0.008s sys 0m0.003s '69.180.' ************** PARI ***************** Host 69.180.139.103 (69.180.139.103) Time: Wed Jun 28 20:00:33 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '65.26.1' ************** PARI ***************** Host 65.26.119.144 (65.26.119.144) Time: Wed Jun 28 19:29:39 2006 Input: s(t) = 256-16t2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = t2 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: t2. Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '65.26.1' ************** PARI ***************** Host 65.26.119.144 (65.26.119.144) Time: Wed Jun 28 19:25:40 2006 Input: x+6= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: x+6= ^- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '24.14.1' ************** PARI ***************** Host 24.14.130.21 (24.14.130.21) Time: Wed Jun 28 18:52:14 2006 Input: 4x1/2+8-5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1/2*x1 + 3 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x1/2+8-5. Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.110.15 (72.30.110.15) Time: Wed Jun 28 17:16:52 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:38:19 2006 Input: a=41 p=73 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) que=Mod(a^(q-p),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(r^(n-1),p) Mod(que^(n-1),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 73 ? %3 = 347 ? %4 = 25331 ? %5 = Mod(1829, 25331) ? %6 = Mod(9498, 25331) ? %7 = Mod(14969, 25331) ? %8 = Mod(14710, 25331) ? %9 = Mod(24711, 25331) ? %10 = Mod(10001, 25331) ? %11 = Mod(0, 73) ? %12 = Mod(37, 73) ? %13 = Mod(37, 73) ? %14 = Mod(37, 73) ? %15 = Mod(37, 73) ? %16 = Mod(8, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.010s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:38:02 2006 Input: a=41 p=73 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) que=Mod(a^(q-p),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Mod(r^(q-p)-l,p) Mod(que^(q-p),p) Mod(r^(n-1),p) Mod(que^(n-1),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 73 ? %3 = 347 ? %4 = 25331 ? %5 = Mod(1829, 25331) ? %6 = Mod(9498, 25331) ? %7 = Mod(14969, 25331) ? %8 = Mod(14710, 25331) ? %9 = Mod(24711, 25331) ? %10 = Mod(10001, 25331) ? %11 = Mod(0, 73) ? %12 = Mod(29, 73) ? %13 = Mod(37, 73) ? %14 = Mod(37, 73) ? %15 = Mod(37, 73) ? %16 = Mod(8, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:36:03 2006 Input: a=41 p=73 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) que=Mod(a^(q-p),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(r^(n-1),p) Mod(que^(n-1),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 73 ? %3 = 347 ? %4 = 25331 ? %5 = Mod(1829, 25331) ? %6 = Mod(9498, 25331) ? %7 = Mod(14969, 25331) ? %8 = Mod(14710, 25331) ? %9 = Mod(24711, 25331) ? %10 = Mod(10001, 25331) ? %11 = Mod(0, 73) ? %12 = Mod(37, 73) ? %13 = Mod(37, 73) ? %14 = Mod(37, 73) ? %15 = Mod(37, 73) ? %16 = Mod(8, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.013s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:35:10 2006 Input: a=41 p=73 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) que=Mod(a^(q-p),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Mod(r^(q-p),p) Mod(l,p) Mod(que^(q-p),p) Mod(r^(q-p),p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 73 ? %3 = 347 ? %4 = 25331 ? %5 = Mod(1829, 25331) ? %6 = Mod(9498, 25331) ? %7 = Mod(14969, 25331) ? %8 = Mod(14710, 25331) ? %9 = Mod(24711, 25331) ? %10 = Mod(10001, 25331) ? %11 = Mod(0, 73) ? %12 = Mod(37, 73) ? %13 = Mod(8, 73) ? %14 = Mod(37, 73) ? %15 = Mod(37, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Wed Jun 28 16:26:56 2006 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:24:04 2006 Input: a=41 p=73 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) que=Mod(a^(q-p),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Mod(r^(q-p),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 73 ? %3 = 347 ? %4 = 25331 ? %5 = Mod(1829, 25331) ? %6 = Mod(9498, 25331) ? %7 = Mod(14969, 25331) ? %8 = Mod(14710, 25331) ? %9 = Mod(24711, 25331) ? %10 = Mod(10001, 25331) ? %11 = Mod(0, 73) ? %12 = Mod(37, 73) ? %13 = Mod(8, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.011s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:23:27 2006 Input: a=41 p=73 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) que=Mod(a^(q-p),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-l,n) Mod(ok2-l,p) Mod(r^(q-p),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 73 ? %3 = 347 ? %4 = 25331 ? %5 = Mod(1829, 25331) ? %6 = Mod(9498, 25331) ? %7 = Mod(14969, 25331) ? %8 = Mod(14710, 25331) ? %9 = Mod(24711, 25331) ? %10 = Mod(15213, 25331) ? %11 = Mod(29, 73) ? %12 = Mod(37, 73) ? %13 = Mod(8, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.012s sys 0m0.004s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Wed Jun 28 16:22:42 2006 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Wed Jun 28 16:22:34 2006 Input: 2+2=4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 2+2=4 ^-- Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '169.231' ************** PARI ***************** Host 169.231.35.225 (169.231.35.225) Time: Wed Jun 28 16:22:23 2006 Input: 2+2=4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 2+2=4 ^-- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:22:05 2006 Input: a=41 p=73 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) que=Mod(a^(q-p),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Mod(r^(q-p),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 73 ? %3 = 347 ? %4 = 25331 ? %5 = Mod(1829, 25331) ? %6 = Mod(9498, 25331) ? %7 = Mod(14969, 25331) ? %8 = Mod(14710, 25331) ? %9 = Mod(24711, 25331) ? %10 = Mod(10001, 25331) ? %11 = Mod(0, 73) ? %12 = Mod(37, 73) ? %13 = Mod(8, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.010s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:20:48 2006 Input: a=41 p=73 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Mod(r^(q-p),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 73 ? %3 = 347 ? %4 = 25331 ? %5 = Mod(1829, 25331) ? %6 = Mod(9498, 25331) ? %7 = Mod(14710, 25331) ? %8 = Mod(24711, 25331) ? %9 = Mod(10001, 25331) ? %10 = Mod(0, 73) ? %11 = Mod(37, 73) ? %12 = Mod(8, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:20:31 2006 Input: a=41 p=127 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Mod(r^(q-p),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 127 ? %3 = 347 ? %4 = 44069 ? %5 = Mod(552, 44069) ? %6 = Mod(2463, 44069) ? %7 = Mod(10958, 44069) ? %8 = Mod(8164, 44069) ? %9 = Mod(41275, 44069) ? %10 = Mod(0, 127) ? %11 = Mod(36, 127) ? %12 = Mod(50, 127) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.017s sys 0m0.004s '72.30.9' ************** PARI ***************** Host 72.30.98.145 (72.30.98.145) Time: Wed Jun 28 16:20:26 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:19:36 2006 Input: a=41 p=127 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Mod(ok2-l,n) Mod(ok2-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 127 ? %3 = 347 ? %4 = 44069 ? %5 = Mod(552, 44069) ? %6 = Mod(2463, 44069) ? %7 = Mod(10958, 44069) ? %8 = Mod(8164, 44069) ? %9 = Mod(41275, 44069) ? %10 = Mod(0, 127) ? %11 = Mod(5701, 44069) ? %12 = Mod(113, 127) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.014s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:18:48 2006 Input: a=41 p=127 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Mod(ok-l,n) Mod(ok-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 127 ? %3 = 347 ? %4 = 44069 ? %5 = Mod(552, 44069) ? %6 = Mod(2463, 44069) ? %7 = Mod(10958, 44069) ? %8 = Mod(8164, 44069) ? %9 = Mod(41275, 44069) ? %10 = Mod(0, 127) ? %11 = Mod(8495, 44069) ? %12 = Mod(113, 127) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.016s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:17:45 2006 Input: a=41 p=127 q=347 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 127 ? %3 = 347 ? %4 = 44069 ? %5 = Mod(552, 44069) ? %6 = Mod(2463, 44069) ? %7 = Mod(10958, 44069) ? %8 = Mod(8164, 44069) ? %9 = Mod(41275, 44069) ? %10 = Mod(0, 127) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.016s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:17:21 2006 Input: a=41 p=127 q=241 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 127 ? %3 = 241 ? %4 = 30607 ? %5 = Mod(25, 30607) ? %6 = Mod(11418, 30607) ? %7 = Mod(11240, 30607) ? %8 = Mod(18352, 30607) ? %9 = Mod(7112, 30607) ? %10 = Mod(0, 127) ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:16:39 2006 Input: a=41 p=89 q=241 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 89 ? %3 = 241 ? %4 = 21449 ? %5 = Mod(573, 21449) ? %6 = Mod(19457, 21449) ? %7 = Mod(5507, 21449) ? %8 = Mod(9245, 21449) ? %9 = Mod(3738, 21449) ? %10 = Mod(0, 89) ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:16:21 2006 Input: a=41 p=71 q=241 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 71 ? %3 = 241 ? %4 = 17111 ? %5 = Mod(9704, 17111) ? %6 = Mod(5641, 17111) ? %7 = Mod(5783, 17111) ? %8 = Mod(5783, 17111) ? %9 = Mod(0, 17111) ? %10 = Mod(0, 71) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:16:14 2006 Input: a=41 p=71 q=241 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 71 ? %3 = 241 ? %4 = 17111 ? %5 = Mod(9704, 17111) ? %6 = Mod(5641, 17111) ? %7 = Mod(5783, 17111) ? %8 = Mod(5783, 17111) ? %9 = Mod(0, 17111) ? %10 = Mod(0, 71) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:15:51 2006 Input: a=41 p=71 q=241 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) ok2-ok Mod(ok2-ok,n) Mod(ok2-ok,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 71 ? %3 = 241 ? %4 = 17111 ? %5 = Mod(9704, 17111) ? %6 = Mod(5641, 17111) ? %7 = Mod(5783, 17111) ? %8 = Mod(5783, 17111) ? %9 = Mod(0, 17111) ? %10 = Mod(0, 17111) ? %11 = Mod(0, 71) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:15:29 2006 Input: a=41 p=71 q=241 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 71 ? %3 = 241 ? %4 = 17111 ? %5 = Mod(9704, 17111) ? %6 = Mod(5641, 17111) ? %7 = Mod(5783, 17111) ? %8 = Mod(5783, 17111) ? %9 = Mod(0, 17111) ? %10 = Mod(0, 71) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Wed Jun 28 16:14:49 2006 Input: a=41 p=73 q=241 n=p*q r=Mod(a^(n-1),n) l=Mod(a^(n+1),n) ok=Mod(r^(n-1),n) ok2=Mod(r^(q-p),n) Mod(ok2-ok,n) Mod(ok2-ok,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 73 ? %3 = 241 ? %4 = 17593 ? %5 = Mod(11907, 17593) ? %6 = Mod(12426, 17593) ? %7 = Mod(1169, 17593) ? %8 = Mod(3943, 17593) ? %9 = Mod(2774, 17593) ? %10 = Mod(0, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.079s user 0m0.009s sys 0m0.006s '128.218' ************** PARI ***************** Host 128.218.157.135 (128.218.157.135) Time: Wed Jun 28 15:55:15 2006 Input: 1/8 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1/8 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.155 (68.142.251.155) Time: Wed Jun 28 14:23:38 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.010s sys 0m0.002s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Wed Jun 28 13:22:43 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.051s user 0m0.005s sys 0m0.007s '88.109.' ************** PARI ***************** Host 88.109.119.136 (88.109.119.136) Time: Wed Jun 28 13:11:31 2006 Input: two hundred and seventy eight divided by 22 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = twohundredandseventyeightdividedby22 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '66.188.' ************** PARI ***************** Host 66.188.52.4 (66.188.52.4) Time: Wed Jun 28 12:25:18 2006 Input: 1+1 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '158.109' ************** PARI ***************** Host 158.109.54.195 (158.109.54.195) Time: Wed Jun 28 11:25:03 2006 Input: P:=PolynomialRing(GF(9)); h= (x^8-1)/x^4+2*x^3+2*x+2; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: P:=PolynomialRing(GF( ^-------------------- Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '158.109' ************** PARI ***************** Host 158.109.54.195 (158.109.54.195) Time: Wed Jun 28 11:23:29 2006 Input: GF(3^2); h= (x^8-1)/x^4+2*x^3+2*x+2; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: GF(3^2); ^-------- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '158.109' ************** PARI ***************** Host 158.109.54.195 (158.109.54.195) Time: Wed Jun 28 11:23:18 2006 Input: GF(9); h= (x^8-1)/x^4+2*x^3+2*x+2; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: GF(9); ^------ Timing: real 0m0.335s user 0m0.009s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Wed Jun 28 10:48:20 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.033s user 0m0.024s sys 0m0.007s '24.53.2' ************** PARI ***************** Host 24.53.219.241 (24.53.219.241) Time: Wed Jun 28 10:40:57 2006 Input: 102600000*.06 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6156000.0000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.063s user 0m0.008s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.131.199 (72.30.131.199) Time: Wed Jun 28 10:35:28 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Wed Jun 28 10:24:29 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.066s user 0m0.008s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Wed Jun 28 07:36:39 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.030s user 0m0.024s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.86 (68.142.251.86) Time: Wed Jun 28 06:46:14 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.078s user 0m0.006s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Wed Jun 28 04:28:29 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.035s user 0m0.008s sys 0m0.003s '68.142.' ************** PARI ***************** Host 68.142.249.88 (68.142.249.88) Time: Tue Jun 27 23:55:31 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Tue Jun 27 23:18:23 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.026s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Tue Jun 27 22:22:45 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.006s '70.106.' ************** PARI ***************** Host 70.106.113.26 (70.106.113.26) Time: Tue Jun 27 21:17:16 2006 Input: 2+3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 21:12:48 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^((q-p)*(q-p)),n) Mod(que^((n-1)*(n-1)),n) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Mod(que-r,p) Mod(que-r,n) Mod(a^n-a*r,p) Mod(a^n-a*r,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = Mod(0, 47) ? %22 = Mod(0, 4559) ? %23 = Mod(3255, 4559) ? ? %24 = Mod(2312, 4559) ? %25 = Mod(103, 4559) ? ? %26 = Mod(3149, 4559) ? %27 = Mod(0, 47) ? %28 = Mod(3255, 4559) ? %29 = Mod(3255, 4559) ? ? %30 = Mod(0, 47) ? %31 = Mod(4136, 4559) ? ? %32 = Mod(0, 47) ? %33 = Mod(0, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:50:30 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^((q-p)*(q-p)),n) Mod(que^((n-1)*(n-1)),n) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Mod(que-r,p) Mod(que-r,n) Mod(r^(n-1),n) Mod(l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = Mod(0, 47) ? %22 = Mod(0, 4559) ? %23 = Mod(3255, 4559) ? ? %24 = Mod(2312, 4559) ? %25 = Mod(103, 4559) ? ? %26 = Mod(3149, 4559) ? %27 = Mod(0, 47) ? %28 = Mod(3255, 4559) ? %29 = Mod(3255, 4559) ? ? %30 = Mod(0, 47) ? %31 = Mod(4136, 4559) ? %32 = Mod(3255, 4559) ? %33 = Mod(3255, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:48:03 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^((q-p)*(q-p)),n) Mod(que^((n-1)*(n-1)),n) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Mod(que-r,p) Mod(que-r,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = Mod(0, 47) ? %22 = Mod(0, 4559) ? %23 = Mod(3255, 4559) ? ? %24 = Mod(2312, 4559) ? %25 = Mod(103, 4559) ? ? %26 = Mod(3149, 4559) ? %27 = Mod(0, 47) ? %28 = Mod(3255, 4559) ? %29 = Mod(3255, 4559) ? ? %30 = Mod(0, 47) ? %31 = Mod(4136, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:46:30 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^((q-p)*(q-p)),n) Mod(que^((n-1)*(n-1)),n) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Mod(r^(n-1), n) Mod(l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = Mod(0, 47) ? %22 = Mod(0, 4559) ? %23 = Mod(3255, 4559) ? ? %24 = Mod(2312, 4559) ? %25 = Mod(103, 4559) ? ? %26 = Mod(3149, 4559) ? %27 = Mod(0, 47) ? %28 = Mod(3255, 4559) ? %29 = Mod(3255, 4559) ? ? %30 = Mod(3255, 4559) ? %31 = Mod(3255, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.004s sys 0m0.010s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:31:33 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^((q-p)*(q-p)),n) Mod(que^((n-1)*(n-1)),n) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = Mod(0, 47) ? %22 = Mod(0, 4559) ? %23 = Mod(3255, 4559) ? ? %24 = Mod(2312, 4559) ? %25 = Mod(103, 4559) ? ? %26 = Mod(3149, 4559) ? %27 = Mod(0, 47) ? %28 = Mod(3255, 4559) ? %29 = Mod(3255, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:29:58 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^((q-p)*(q-p)),n) Mod(que^((n-1)*(n-1)),n) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? %26 = Mod(3255, 4559) ? ? %27 = Mod(2312, 4559) ? %28 = Mod(103, 4559) ? ? %29 = Mod(3149, 4559) ? %30 = Mod(0, 47) ? %31 = Mod(3255, 4559) ? %32 = Mod(3255, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:28:50 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^((q-p)*(q-p)),p) Mod(que^((n-1)*(n-1)),p) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? %26 = Mod(3255, 4559) ? ? %27 = Mod(9, 47) ? %28 = Mod(9, 47) ? ? %29 = Mod(3149, 4559) ? %30 = Mod(0, 47) ? %31 = Mod(3255, 4559) ? %32 = Mod(3255, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:27:55 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^((q-p)*(q-p)),n) Mod(que^((n-1)*(n-1)),n) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? %26 = Mod(3255, 4559) ? ? %27 = Mod(2312, 4559) ? %28 = Mod(103, 4559) ? ? %29 = Mod(3149, 4559) ? %30 = Mod(0, 47) ? %31 = Mod(3255, 4559) ? %32 = Mod(3255, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:25:30 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^((q-p)*(q-p)),n) Mod(que^((n-1)*(n-1)),n) Mod(r^(n-1),n) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? %26 = Mod(3255, 4559) ? ? %27 = Mod(2312, 4559) ? %28 = Mod(103, 4559) ? ? %29 = Mod(3255, 4559) ? %30 = Mod(3149, 4559) ? %31 = Mod(0, 47) ? %32 = Mod(3255, 4559) ? %33 = Mod(3255, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:24:54 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^((q-p)*(q-p),n) Mod(que^((n-10*(n-1)),n) Mod(r^(n-1),n) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? %26 = Mod(3255, 4559) ? ? ? ? ? %27 = Mod(3255, 4559) ? %28 = Mod(3149, 4559) ? %29 = Mod(0, 47) ? %30 = Mod(3255, 4559) ? %31 = Mod(3255, 4559) ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: Mod(r^((q-p)*(q-p),n) ^--- *** expected character: ')' instead of: Mod(que^((n-10*(n-1)),n) ^--- Timing: real 0m0.014s user 0m0.005s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:21:36 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^(q-p),n) Mod(que^(n-1),n) Mod(r^(n-1),n) Mod(3255-106, n) Mod(3255-106, p) Mod(r^(n-1),n) Mod(que^(q-p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? %26 = Mod(3255, 4559) ? %27 = Mod(106, 4559) ? %28 = Mod(106, 4559) ? %29 = Mod(3255, 4559) ? %30 = Mod(3149, 4559) ? %31 = Mod(0, 47) ? ? ? %32 = Mod(3255, 4559) ? %33 = Mod(3255, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:19:52 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^(q-p),n) Mod(que^(n-1),n) Mod(r^(n-1),n) Mod(3255-106, n) Mod(3255-106, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? %26 = Mod(3255, 4559) ? %27 = Mod(106, 4559) ? %28 = Mod(106, 4559) ? %29 = Mod(3255, 4559) ? %30 = Mod(3149, 4559) ? %31 = Mod(0, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:19:11 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^(q-p),n) Mod(3255-106, n) Mod(3255-106, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? %26 = Mod(3255, 4559) ? %27 = Mod(106, 4559) ? %28 = Mod(3149, 4559) ? %29 = Mod(0, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:18:25 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^(q-p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? %26 = Mod(3255, 4559) ? %27 = Mod(106, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.010s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:17:58 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Mod(que^(q-p),n) Mod(r^(q-p),p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? %26 = Mod(3255, 4559) ? %27 = Mod(12, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:15:29 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Mod(r^(n-1)-l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? %25 = Mod(0, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.009s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:15:02 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Mod(r^(n-1)-l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? %24 = Mod(0, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:13:31 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 r^(q+p) 779^(97+47) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? %22 = Mod(3202, 4559) ? %23 = 240654454497686322525192340392590186076470582616337361064770167537273566158778544974633866383300569671280723503998829924754517688736844527585746722291193941659510025242580888371857623350111598899480916008685617894750884976360105767527152866004131676875857152123408759182726172420589742762081234495189628561114886628428281155904528784098780242216611700487126440473861754694936597537743098216631065656226836130702246081 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:12:57 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 r*r*l 779*779*3255 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? %20 = Mod(3202, 4559) ? %21 = 1975267455 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:10:52 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) hm=Mod(r^(n+1)-l*r^2,100000) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 100000) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:10:02 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) hm=r^(n+1)-l*r^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:09:46 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) r^(n+1)-l*r^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:06:38 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) oka=Mod(l*r,p) okb=Mod(r^n, n) Mod(okb-oka, n) Mod(okb-oka, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(42, 47) ? %20 = Mod(841, 4559) ? %21 = Mod(0, 4559) ? %22 = Mod(0, 47) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:05:50 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) ok=Mod(l*r,p) ok2=Mod(r^n, n) Mod(ok2-ok, n) Mod(ok2-ok, p) Mod(841-42, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(42, 47) ? %20 = Mod(841, 4559) ? %21 = Mod(0, 4559) ? %22 = Mod(0, 47) ? %23 = Mod(799, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:05:42 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) ok=Mod(l*r,p) ok2=Mod(r^n, n) Mod(ok2-ok, n) Mod(ok2-ok, p) Mod(841-42, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(42, 47) ? %20 = Mod(841, 4559) ? %21 = Mod(0, 4559) ? %22 = Mod(0, 47) ? %23 = Mod(0, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:05:27 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) ok=Mod(l*r,p) ok2=Mod(r^n, n) Mod(ok2-ok, n) Mod(ok2-ok, p) 841-42 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(42, 47) ? %20 = Mod(841, 4559) ? %21 = Mod(0, 4559) ? %22 = Mod(0, 47) ? %23 = 799 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:02:32 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) ok=Mod(l*r,p) ok2=Mod(r^n, n) Mod(ok2-ok, n) Mod(ok2-ok, p) ok2-ok Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(42, 47) ? %20 = Mod(841, 4559) ? %21 = Mod(0, 4559) ? %22 = Mod(0, 47) ? %23 = Mod(0, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:02:16 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) ok=Mod(l*r,p) ok2=Mod(r^n, n) Mod(ok2-ok, n) Mod(ok2-ok, p) ok2-ok Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(42, 47) ? %20 = Mod(841, 4559) ? %21 = Mod(0, 4559) ? %22 = Mod(0, 47) ? ? %23 = Mod(0, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:02:02 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) ok=Mod(l*r,p) ok2=Mod(r^n, n) Mod(ok2-ok, n) Mod(ok2-ok, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(42, 47) ? %20 = Mod(841, 4559) ? %21 = Mod(0, 4559) ? %22 = Mod(0, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:01:13 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) ok=Mod(l*r,p) ok2=Mod(r^n, n) Mod(ok2-ok, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(42, 47) ? %20 = Mod(841, 4559) ? %21 = Mod(0, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:01:05 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) ok=Mod(l*r,p) ok2=Mod(r^n, n) Mod(ok2-ok, p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(42, 47) ? %20 = Mod(841, 4559) ? %21 = Mod(0, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 20:00:10 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) Mod(l*r,p) Mod(r^n, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(42, 47) ? %20 = Mod(841, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:59:55 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) Mod(l*r,n) Mod(r^n, n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(841, 4559) ? %20 = Mod(841, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:59:12 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) Mod(l*r,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(841, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:58:30 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) l*r Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(841, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:58:18 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) Mod(r^n,n) - l*r Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 4559) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:58:06 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) Mod(r^n,p) - l*r Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? %19 = Mod(0, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.010s sys 0m0.002s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:55:42 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(que,p) Mod(r,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(27, 47) ? %18 = Mod(27, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:55:01 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:54:50 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(12^(n-1),p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(9, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:54:39 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(12^(q-p),p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? %17 = Mod(9, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:54:05 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Mod(r^(q-p),p) Mod(que^(q-p),p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? %15 = Mod(12, 47) ? %16 = Mod(12, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:53:34 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Mod(que^(n-1),p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? %14 = Mod(12, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:52:42 2006 Input: a=41 p=47 q=97 n=p*q e=q+p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 144 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.009s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 19:52:30 2006 Input: a=41 p=47 q=97 n=p*q e=q*p h=q-p r=Mod(a^(n-1),n) l=Mod(a^((q-p)*(q-p)),n) que=Mod(a^(q-p),n) Mod(r^(n-1),n) Mod(l,n) Mod(r^(n-1),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 47 ? %3 = 97 ? %4 = 4559 ? %5 = 4559 ? %6 = 50 ? %7 = Mod(779, 4559) ? %8 = Mod(3255, 4559) ? %9 = Mod(356, 4559) ? %10 = Mod(3255, 4559) ? %11 = Mod(3255, 4559) ? %12 = Mod(12, 47) ? %13 = Mod(12, 47) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '69.203.' ************** PARI ***************** Host 69.203.67.70 (69.203.67.70) Time: Tue Jun 27 19:12:31 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.132.102 (72.30.132.102) Time: Tue Jun 27 17:42:10 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '216.227' ************** PARI ***************** Host 216.227.72.136 (216.227.72.136) Time: Tue Jun 27 16:16:35 2006 Input: 9200/48 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 575/3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '68.157.' ************** PARI ***************** Host 68.157.38.8 (68.157.38.8) Time: Tue Jun 27 16:12:22 2006 Input: 6.40×35 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6.4035000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 15:50:33 2006 Input: p=97 q=839 n=p*q a=29 l=Mod(a^((q-p)*(q-p)), n) que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(l,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) gcd(l,r) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 29 ? %5 = Mod(38175, 81383) ? %6 = Mod(33205, 81383) ? %7 = Mod(20110, 81383) ? %8 = Mod(54, 97) ? %9 = Mod(54, 97) ? %10 = Mod(54, 97) ? %11 = Mod(54, 97) ? %12 = Mod(31, 97) ? %13 = Mod(31, 97) ? %14 = Mod(54, 97) ? %15 = Mod(20377, 81383) ? %16 = Mod(7, 97) ? %17 = Mod(1, 81383) ? Goodbye! Errors/timing (if any): Timing: real 0m0.118s user 0m0.107s sys 0m0.013s '24.99.9' ************** PARI ***************** Host 24.99.96.65 (24.99.96.65) Time: Tue Jun 27 15:41:52 2006 Input: (2x + 1)(x - 2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: (2x+1)(x-2) ^--------- Timing: real 0m0.011s user 0m0.012s sys 0m0.001s '24.99.9' ************** PARI ***************** Host 24.99.96.65 (24.99.96.65) Time: Tue Jun 27 15:40:21 2006 Input: 3x - 4(x-3) = 2(3x + 4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x-4(x-3)=2(3x+4). *** unexpected character: 3x-4(x-3)=2(3x+4) ^-------- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.160 (68.142.249.160) Time: Tue Jun 27 15:15:53 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:47:31 2006 Input: p=97 q=839 n=p*q a=101 l=Mod(a^((q-p)*(q-p)), n) que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(l,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) gcd(l,r) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 101 ? %5 = Mod(25088, 81383) ? %6 = Mod(7172, 81383) ? %7 = Mod(35787, 81383) ? %8 = Mod(62, 97) ? %9 = Mod(62, 97) ? %10 = Mod(62, 97) ? %11 = Mod(62, 97) ? %12 = Mod(91, 97) ? %13 = Mod(91, 97) ? %14 = Mod(62, 97) ? %15 = Mod(55408, 81383) ? %16 = Mod(21, 97) ? %17 = Mod(1, 81383) ? Goodbye! Errors/timing (if any): Timing: real 0m0.164s user 0m0.153s sys 0m0.011s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:46:02 2006 Input: p=97 q=839 n=p*q a=101 l=Mod(a^((q-p)*(q-p)), n) que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(l,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 101 ? %5 = Mod(25088, 81383) ? %6 = Mod(7172, 81383) ? %7 = Mod(35787, 81383) ? %8 = Mod(62, 97) ? %9 = Mod(62, 97) ? %10 = Mod(62, 97) ? %11 = Mod(62, 97) ? %12 = Mod(91, 97) ? %13 = Mod(91, 97) ? %14 = Mod(62, 97) ? %15 = Mod(55408, 81383) ? %16 = Mod(21, 97) ? Goodbye! Errors/timing (if any): Timing: real 0m0.162s user 0m0.155s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:45:44 2006 Input: p=97 q=839 n=p*q a=101 l=(a^((q-p)*(q-p)), n) que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(l,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 101 ? ? %5 = Mod(7172, 81383) ? %6 = Mod(35787, 81383) ? %7 = Mod(62, 97) ? %8 = Mod(62, 97) ? %9 = Mod(62, 97) ? %10 = Mod(62, 97) ? %11 = Mod(91, 97) ? %12 = Mod(91, 97) ? ? %13 = Mod(55408, 81383) ? %14 = Mod(21, 97) ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: l=(a^((q-p)*(q-p)),n) ^--- *** Mod: incorrect type in Rg_to_Fl. Timing: real 0m0.028s user 0m0.020s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:45:20 2006 Input: p=97 q=839 n=p*q a=101 l=(a^((q-p)^2), n) que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(l,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 101 ? ? %5 = Mod(7172, 81383) ? %6 = Mod(35787, 81383) ? %7 = Mod(62, 97) ? %8 = Mod(62, 97) ? %9 = Mod(62, 97) ? %10 = Mod(62, 97) ? %11 = Mod(91, 97) ? %12 = Mod(91, 97) ? ? %13 = Mod(55408, 81383) ? %14 = Mod(21, 97) ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: l=(a^((q-p)^2),n) ^--- *** Mod: incorrect type in Rg_to_Fl. Timing: real 0m0.028s user 0m0.022s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:44:34 2006 Input: p=97 q=839 n=p*q a=101 l=(a^((n-1)^2), n) que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(l,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 101 ? ? %5 = Mod(7172, 81383) ? %6 = Mod(35787, 81383) ? %7 = Mod(62, 97) ? %8 = Mod(62, 97) ? %9 = Mod(62, 97) ? %10 = Mod(62, 97) ? %11 = Mod(91, 97) ? %12 = Mod(91, 97) ? ? %13 = Mod(55408, 81383) ? %14 = Mod(21, 97) ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: l=(a^((n-1)^2),n) ^--- *** Mod: incorrect type in Rg_to_Fl. Timing: real 0m0.028s user 0m0.022s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:44:18 2006 Input: p=97 q=839 n=p*q a=101 l=(a^((n-1)^2), n) que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 101 ? ? %5 = Mod(7172, 81383) ? %6 = Mod(35787, 81383) ? %7 = Mod(62, 97) ? %8 = Mod(62, 97) ? %9 = Mod(62, 97) ? %10 = Mod(62, 97) ? %11 = Mod(91, 97) ? %12 = Mod(91, 97) ? %13 = Mod(55408, 81383) ? %14 = Mod(21, 97) ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: l=(a^((n-1)^2),n) ^--- Timing: real 0m0.028s user 0m0.023s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:44:06 2006 Input: p=97 q=839 n=p*q a=101 l=(a^((q-p)^2), n) que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 101 ? ? %5 = Mod(7172, 81383) ? %6 = Mod(35787, 81383) ? %7 = Mod(62, 97) ? %8 = Mod(62, 97) ? %9 = Mod(62, 97) ? %10 = Mod(62, 97) ? %11 = Mod(91, 97) ? %12 = Mod(91, 97) ? %13 = Mod(55408, 81383) ? %14 = Mod(21, 97) ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: l=(a^((q-p)^2),n) ^--- Timing: real 0m0.028s user 0m0.023s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:44:00 2006 Input: p=97 q=839 n=p*q a=101 l=(a^((q-p)^2), n) que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 101 ? ? %5 = Mod(7172, 81383) ? %6 = Mod(35787, 81383) ? %7 = Mod(62, 97) ? %8 = Mod(62, 97) ? %9 = Mod(62, 97) ? %10 = Mod(62, 97) ? %11 = Mod(91, 97) ? %12 = Mod(91, 97) ? %13 = Mod(55408, 81383) ? %14 = Mod(21, 97) ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: l=(a^((q-p)^2),n) ^--- Timing: real 0m0.028s user 0m0.023s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:43:47 2006 Input: p=97 q=839 n=p*q a=101 l:=(a^((q-p)^2), n) que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 101 ? ? %5 = Mod(7172, 81383) ? %6 = Mod(35787, 81383) ? %7 = Mod(62, 97) ? %8 = Mod(62, 97) ? %9 = Mod(62, 97) ? %10 = Mod(62, 97) ? %11 = Mod(91, 97) ? %12 = Mod(91, 97) ? %13 = Mod(55408, 81383) ? %14 = Mod(21, 97) ? Goodbye! Errors/timing (if any): *** Warning: unused characters: :=(a^((q-p)^2),n). *** unexpected character: l:=(a^((q-p)^2),n) ^----------------- Timing: real 0m0.037s user 0m0.020s sys 0m0.011s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:21:54 2006 Input: p=97 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 97 ? %2 = 839 ? %3 = 81383 ? %4 = 101 ? %5 = Mod(7172, 81383) ? %6 = Mod(35787, 81383) ? %7 = Mod(62, 97) ? %8 = Mod(62, 97) ? %9 = Mod(62, 97) ? %10 = Mod(62, 97) ? %11 = Mod(91, 97) ? %12 = Mod(91, 97) ? %13 = Mod(55408, 81383) ? %14 = Mod(21, 97) ? Goodbye! Errors/timing (if any): Timing: real 0m0.028s user 0m0.023s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:21:48 2006 Input: p=87 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 87 ? %2 = 839 ? %3 = 72993 ? %4 = 101 ? %5 = Mod(70225, 72993) ? %6 = Mod(35599, 72993) ? %7 = Mod(7, 87) ? %8 = Mod(7, 87) ? %9 = Mod(7, 87) ? %10 = Mod(7, 87) ? %11 = Mod(16, 87) ? %12 = Mod(16, 87) ? %13 = Mod(29313, 72993) ? %14 = Mod(81, 87) ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.017s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:21:40 2006 Input: p=37 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 839 ? %3 = 31043 ? %4 = 101 ? %5 = Mod(21803, 31043) ? %6 = Mod(2822, 31043) ? %7 = Mod(10, 37) ? %8 = Mod(10, 37) ? %9 = Mod(10, 37) ? %10 = Mod(10, 37) ? %11 = Mod(10, 37) ? %12 = Mod(10, 37) ? %13 = Mod(10915, 31043) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.010s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:21:31 2006 Input: p=59 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 59 ? %2 = 839 ? %3 = 49501 ? %4 = 101 ? %5 = Mod(3057, 49501) ? %6 = Mod(17807, 49501) ? %7 = Mod(25, 59) ? %8 = Mod(25, 59) ? %9 = Mod(25, 59) ? %10 = Mod(25, 59) ? %11 = Mod(48, 59) ? %12 = Mod(48, 59) ? %13 = Mod(1520, 49501) ? %14 = Mod(45, 59) ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:21:15 2006 Input: p=41 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 41 ? %2 = 839 ? %3 = 34399 ? %4 = 101 ? %5 = Mod(14970, 34399) ? %6 = Mod(23867, 34399) ? %7 = Mod(23, 41) ? %8 = Mod(23, 41) ? %9 = Mod(23, 41) ? %10 = Mod(23, 41) ? %11 = Mod(5, 41) ? %12 = Mod(5, 41) ? %13 = Mod(20602, 34399) ? %14 = Mod(20, 41) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.011s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:20:58 2006 Input: p=31 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 31 ? %2 = 839 ? %3 = 26009 ? %4 = 101 ? %5 = Mod(2465, 26009) ? %6 = Mod(9471, 26009) ? %7 = Mod(4, 31) ? %8 = Mod(4, 31) ? %9 = Mod(4, 31) ? %10 = Mod(4, 31) ? %11 = Mod(16, 31) ? %12 = Mod(16, 31) ? %13 = Mod(6176, 26009) ? %14 = Mod(7, 31) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.009s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:20:51 2006 Input: p=11 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 11 ? %2 = 839 ? %3 = 9229 ? %4 = 101 ? %5 = Mod(5811, 9229) ? %6 = Mod(8187, 9229) ? %7 = Mod(5, 11) ? %8 = Mod(5, 11) ? %9 = Mod(5, 11) ? %10 = Mod(5, 11) ? %11 = Mod(3, 11) ? %12 = Mod(3, 11) ? %13 = Mod(8489, 9229) ? %14 = Mod(8, 11) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:20:45 2006 Input: p=7 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7 ? %2 = 839 ? %3 = 5873 ? %4 = 101 ? %5 = Mod(4050, 5873) ? %6 = Mod(81, 5873) ? %7 = Mod(4, 7) ? %8 = Mod(4, 7) ? %9 = Mod(4, 7) ? %10 = Mod(4, 7) ? %11 = Mod(4, 7) ? %12 = Mod(4, 7) ? %13 = Mod(2758, 5873) ? %14 = Mod(0, 7) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:20:38 2006 Input: p=17 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 17 ? %2 = 839 ? %3 = 14263 ? %4 = 101 ? %5 = Mod(4795, 14263) ? %6 = Mod(10405, 14263) ? %7 = Mod(1, 17) ? %8 = Mod(1, 17) ? %9 = Mod(1, 17) ? %10 = Mod(1, 17) ? %11 = Mod(1, 17) ? %12 = Mod(1, 17) ? %13 = Mod(13804, 14263) ? %14 = Mod(0, 17) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:20:31 2006 Input: p=37 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 839 ? %3 = 31043 ? %4 = 101 ? %5 = Mod(21803, 31043) ? %6 = Mod(2822, 31043) ? %7 = Mod(10, 37) ? %8 = Mod(10, 37) ? %9 = Mod(10, 37) ? %10 = Mod(10, 37) ? %11 = Mod(10, 37) ? %12 = Mod(10, 37) ? %13 = Mod(10915, 31043) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.009s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:20:17 2006 Input: p=79 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 79 ? %2 = 839 ? %3 = 66281 ? %4 = 101 ? %5 = Mod(5108, 66281) ? %6 = Mod(28492, 66281) ? %7 = Mod(65, 79) ? %8 = Mod(65, 79) ? %9 = Mod(65, 79) ? %10 = Mod(65, 79) ? %11 = Mod(52, 79) ? %12 = Mod(52, 79) ? %13 = Mod(27433, 66281) ? %14 = Mod(20, 79) ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.019s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:20:04 2006 Input: p=37 q=839 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 839 ? %3 = 31043 ? %4 = 101 ? %5 = Mod(21803, 31043) ? %6 = Mod(2822, 31043) ? %7 = Mod(10, 37) ? %8 = Mod(10, 37) ? %9 = Mod(10, 37) ? %10 = Mod(10, 37) ? %11 = Mod(10, 37) ? %12 = Mod(10, 37) ? %13 = Mod(10915, 31043) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:19:46 2006 Input: p=37 q=89 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 89 ? %3 = 3293 ? %4 = 101 ? %5 = Mod(1601, 3293) ? %6 = Mod(1601, 3293) ? %7 = Mod(10, 37) ? %8 = Mod(10, 37) ? %9 = Mod(10, 37) ? %10 = Mod(10, 37) ? %11 = Mod(10, 37) ? %12 = Mod(10, 37) ? %13 = Mod(888, 3293) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.003s sys 0m0.009s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:09:07 2006 Input: p=83 q=347 n=p*q a=43 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod((r^(n-2)-1),p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) hmm=Mod(r^(n-1),n) Mod(hmm-l,n) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(l,p) Mod(r^n-l*r,p) Mod(r^n-l*r,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 43 ? %5 = Mod(19792, 28801) ? %6 = Mod(10330, 28801) ? %7 = Mod(75, 83) ? %8 = Mod(75, 83) ? %9 = Mod(75, 83) ? %10 = Mod(75, 83) ? %11 = Mod(5802, 28801) ? %12 = Mod(11197, 28801) ? %13 = Mod(11197, 28801) ? %14 = Mod(5802, 28801) ? %15 = Mod(38, 83) ? %16 = Mod(38, 83) ? %17 = Mod(23763, 28801) ? %18 = Mod(25, 83) ? %19 = Mod(11197, 28801) ? %20 = Mod(0, 28801) ? ? %21 = Mod(11197, 28801) ? %22 = Mod(0, 28801) ? %23 = Mod(75, 83) ? %24 = Mod(75, 83) ? %25 = Mod(75, 83) ? ? %26 = Mod(0, 83) ? %27 = Mod(0, 28801) ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.018s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:08:39 2006 Input: p=83 q=347 n=p*q a=43 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod((r^(n-2)-1),p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) hmm=Mod(r^(n-1),n) Mod(hmm-l,n) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(l,p) Mod(r^n-l*r,p) Mod(r^(n-1)-l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 43 ? %5 = Mod(19792, 28801) ? %6 = Mod(10330, 28801) ? %7 = Mod(75, 83) ? %8 = Mod(75, 83) ? %9 = Mod(75, 83) ? %10 = Mod(75, 83) ? %11 = Mod(5802, 28801) ? %12 = Mod(11197, 28801) ? %13 = Mod(11197, 28801) ? %14 = Mod(5802, 28801) ? %15 = Mod(38, 83) ? %16 = Mod(38, 83) ? %17 = Mod(23763, 28801) ? %18 = Mod(25, 83) ? %19 = Mod(11197, 28801) ? %20 = Mod(0, 28801) ? ? %21 = Mod(11197, 28801) ? %22 = Mod(0, 28801) ? %23 = Mod(75, 83) ? %24 = Mod(75, 83) ? %25 = Mod(75, 83) ? ? %26 = Mod(0, 83) ? %27 = Mod(0, 28801) ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.018s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 14:00:57 2006 Input: p=83 q=347 n=p*q a=43 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod((r^(n-2)-1),p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) hmm=Mod(r^(n-1),n) Mod(hmm-l,n) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(l,p) Mod(r^n-l*r,p) Mod(r^n-l*r,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 43 ? %5 = Mod(19792, 28801) ? %6 = Mod(10330, 28801) ? %7 = Mod(75, 83) ? %8 = Mod(75, 83) ? %9 = Mod(75, 83) ? %10 = Mod(75, 83) ? %11 = Mod(5802, 28801) ? %12 = Mod(11197, 28801) ? %13 = Mod(11197, 28801) ? %14 = Mod(5802, 28801) ? %15 = Mod(38, 83) ? %16 = Mod(38, 83) ? %17 = Mod(23763, 28801) ? %18 = Mod(25, 83) ? %19 = Mod(11197, 28801) ? %20 = Mod(0, 28801) ? ? %21 = Mod(11197, 28801) ? %22 = Mod(0, 28801) ? %23 = Mod(75, 83) ? %24 = Mod(75, 83) ? %25 = Mod(75, 83) ? ? %26 = Mod(0, 83) ? %27 = Mod(0, 28801) ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.016s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:59:32 2006 Input: p=83 q=347 n=p*q a=43 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod((r^(n-2)-1),p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) hmm=Mod(r^(n-1),n) Mod(hmm-l,n) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 43 ? %5 = Mod(19792, 28801) ? %6 = Mod(10330, 28801) ? %7 = Mod(75, 83) ? %8 = Mod(75, 83) ? %9 = Mod(75, 83) ? %10 = Mod(75, 83) ? %11 = Mod(5802, 28801) ? %12 = Mod(11197, 28801) ? %13 = Mod(11197, 28801) ? %14 = Mod(5802, 28801) ? %15 = Mod(38, 83) ? %16 = Mod(38, 83) ? %17 = Mod(23763, 28801) ? %18 = Mod(25, 83) ? %19 = Mod(11197, 28801) ? %20 = Mod(0, 28801) ? ? %21 = Mod(11197, 28801) ? %22 = Mod(0, 28801) ? %23 = Mod(75, 83) ? %24 = Mod(75, 83) ? %25 = Mod(75, 83) ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.017s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:59:15 2006 Input: p=83 q=347 n=p*q a=43 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod((r^(n-2)-1),p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) hmm=Mod(r^(n-1),n) Mod(hmm-l,p) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 43 ? %5 = Mod(19792, 28801) ? %6 = Mod(10330, 28801) ? %7 = Mod(75, 83) ? %8 = Mod(75, 83) ? %9 = Mod(75, 83) ? %10 = Mod(75, 83) ? %11 = Mod(5802, 28801) ? %12 = Mod(11197, 28801) ? %13 = Mod(11197, 28801) ? %14 = Mod(5802, 28801) ? %15 = Mod(38, 83) ? %16 = Mod(38, 83) ? %17 = Mod(23763, 28801) ? %18 = Mod(25, 83) ? %19 = Mod(11197, 28801) ? %20 = Mod(0, 28801) ? ? %21 = Mod(11197, 28801) ? %22 = Mod(0, 83) ? %23 = Mod(75, 83) ? %24 = Mod(75, 83) ? %25 = Mod(75, 83) ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.020s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:57:49 2006 Input: p=83 q=347 n=p*q a=43 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod((r^(n-2)-1),p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) Mod(r^(q-p),p) Mod(que^(q-p),p) Mod(l,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 43 ? %5 = Mod(19792, 28801) ? %6 = Mod(10330, 28801) ? %7 = Mod(75, 83) ? %8 = Mod(75, 83) ? %9 = Mod(75, 83) ? %10 = Mod(75, 83) ? %11 = Mod(5802, 28801) ? %12 = Mod(11197, 28801) ? %13 = Mod(11197, 28801) ? %14 = Mod(5802, 28801) ? %15 = Mod(38, 83) ? %16 = Mod(38, 83) ? %17 = Mod(23763, 28801) ? %18 = Mod(25, 83) ? %19 = Mod(11197, 28801) ? %20 = Mod(0, 28801) ? ? %21 = Mod(75, 83) ? %22 = Mod(75, 83) ? %23 = Mod(75, 83) ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.018s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:57:15 2006 Input: p=83 q=347 n=p*q a=43 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod((r^(n-2)-1),p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) r^(q-p) mod p que^(q-p) mod p l mod p Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 43 ? %5 = Mod(19792, 28801) ? %6 = Mod(10330, 28801) ? %7 = Mod(75, 83) ? %8 = Mod(75, 83) ? %9 = Mod(75, 83) ? %10 = Mod(75, 83) ? %11 = Mod(5802, 28801) ? %12 = Mod(11197, 28801) ? %13 = Mod(11197, 28801) ? %14 = Mod(5802, 28801) ? %15 = Mod(38, 83) ? %16 = Mod(38, 83) ? %17 = Mod(23763, 28801) ? %18 = Mod(25, 83) ? %19 = Mod(11197, 28801) ? %20 = Mod(0, 28801) ? ? %21 = modp ? %22 = modp ? %23 = lmodp ? Goodbye! Errors/timing (if any): *** Warning: unused characters: modp. *** Warning: unused characters: modp. Timing: real 0m0.024s user 0m0.019s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:55:47 2006 Input: p=83 q=347 n=p*q a=43 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod((r^(n-2)-1),p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 43 ? %5 = Mod(19792, 28801) ? %6 = Mod(10330, 28801) ? %7 = Mod(75, 83) ? %8 = Mod(75, 83) ? %9 = Mod(75, 83) ? %10 = Mod(75, 83) ? %11 = Mod(5802, 28801) ? %12 = Mod(11197, 28801) ? %13 = Mod(11197, 28801) ? %14 = Mod(5802, 28801) ? %15 = Mod(38, 83) ? %16 = Mod(38, 83) ? %17 = Mod(23763, 28801) ? %18 = Mod(25, 83) ? %19 = Mod(11197, 28801) ? %20 = Mod(0, 28801) ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.020s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:55:34 2006 Input: p=83 q=347 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod((r^(n-2)-1),p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 41 ? %5 = Mod(10992, 28801) ? %6 = Mod(5016, 28801) ? %7 = Mod(16, 83) ? %8 = Mod(16, 83) ? %9 = Mod(16, 83) ? %10 = Mod(16, 83) ? %11 = Mod(7984, 28801) ? %12 = Mod(7403, 28801) ? %13 = Mod(7403, 28801) ? %14 = Mod(7984, 28801) ? %15 = Mod(36, 83) ? %16 = Mod(36, 83) ? %17 = Mod(2969, 28801) ? %18 = Mod(64, 83) ? %19 = Mod(7403, 28801) ? %20 = Mod(0, 28801) ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.019s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:44:08 2006 Input: p=83 q=347 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 41 ? %5 = Mod(10992, 28801) ? %6 = Mod(5016, 28801) ? %7 = Mod(16, 83) ? %8 = Mod(16, 83) ? %9 = Mod(16, 83) ? %10 = Mod(16, 83) ? %11 = Mod(7984, 28801) ? %12 = Mod(7403, 28801) ? %13 = Mod(7403, 28801) ? %14 = Mod(7984, 28801) ? %15 = Mod(36, 83) ? %16 = Mod(36, 83) ? %17 = Mod(2969, 28801) ? %18 = Mod(64, 83) ? %19 = Mod(7403, 28801) ? %20 = Mod(0, 28801) ? Goodbye! Errors/timing (if any): Timing: real 0m0.024s user 0m0.017s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:43:44 2006 Input: p=83 q=347 n=p*q a=839 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) l=Mod(a^((q-p)*(q-p)), n) Mod(r^(n+1)-(r^2)*l,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 839 ? %5 = Mod(15839, 28801) ? %6 = Mod(11025, 28801) ? %7 = Mod(21, 83) ? %8 = Mod(21, 83) ? %9 = Mod(21, 83) ? %10 = Mod(21, 83) ? %11 = Mod(5748, 28801) ? %12 = Mod(15376, 28801) ? %13 = Mod(15376, 28801) ? %14 = Mod(5748, 28801) ? %15 = Mod(69, 83) ? %16 = Mod(69, 83) ? %17 = Mod(20374, 28801) ? %18 = Mod(39, 83) ? %19 = Mod(15376, 28801) ? %20 = Mod(0, 28801) ? Goodbye! Errors/timing (if any): Timing: real 0m0.040s user 0m0.035s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:38:32 2006 Input: p=83 q=347 n=p*q a=839 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 839 ? %5 = Mod(15839, 28801) ? %6 = Mod(11025, 28801) ? %7 = Mod(21, 83) ? %8 = Mod(21, 83) ? %9 = Mod(21, 83) ? %10 = Mod(21, 83) ? %11 = Mod(5748, 28801) ? %12 = Mod(15376, 28801) ? %13 = Mod(15376, 28801) ? %14 = Mod(5748, 28801) ? %15 = Mod(69, 83) ? %16 = Mod(69, 83) ? %17 = Mod(20374, 28801) ? %18 = Mod(39, 83) ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.011s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:34:29 2006 Input: p=83 q=347 n=p*q a=88 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 83 ? %2 = 347 ? %3 = 28801 ? %4 = 88 ? %5 = Mod(131, 28801) ? %6 = Mod(18640, 28801) ? %7 = Mod(17, 83) ? %8 = Mod(17, 83) ? %9 = Mod(17, 83) ? %10 = Mod(17, 83) ? %11 = Mod(17613, 28801) ? %12 = Mod(9811, 28801) ? %13 = Mod(9811, 28801) ? %14 = Mod(17613, 28801) ? %15 = Mod(48, 83) ? %16 = Mod(48, 83) ? %17 = Mod(16608, 28801) ? %18 = Mod(8, 83) ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.010s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:33:50 2006 Input: p=101 q=347 n=p*q a=88 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 101 ? %2 = 347 ? %3 = 35047 ? %4 = 88 ? %5 = Mod(15834, 35047) ? %6 = Mod(26944, 35047) ? %7 = Mod(37, 101) ? %8 = Mod(37, 101) ? %9 = Mod(37, 101) ? %10 = Mod(37, 101) ? %11 = Mod(20035, 35047) ? %12 = Mod(9430, 35047) ? %13 = Mod(9430, 35047) ? %14 = Mod(20035, 35047) ? %15 = Mod(78, 101) ? %16 = Mod(78, 101) ? %17 = Mod(4336, 35047) ? %18 = Mod(94, 101) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.011s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:33:29 2006 Input: p=101 q=347 n=p*q a=7 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 101 ? %2 = 347 ? %3 = 35047 ? %4 = 7 ? %5 = Mod(25474, 35047) ? %6 = Mod(27595, 35047) ? %7 = Mod(71, 101) ? %8 = Mod(71, 101) ? %9 = Mod(71, 101) ? %10 = Mod(71, 101) ? %11 = Mod(25220, 35047) ? %12 = Mod(8353, 35047) ? %13 = Mod(8353, 35047) ? %14 = Mod(25220, 35047) ? %15 = Mod(22, 101) ? %16 = Mod(22, 101) ? %17 = Mod(34457, 35047) ? %18 = Mod(16, 101) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:32:54 2006 Input: p=101 q=347 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 101 ? %2 = 347 ? %3 = 35047 ? %4 = 41 ? %5 = Mod(13843, 35047) ? %6 = Mod(22630, 35047) ? %7 = Mod(95, 101) ? %8 = Mod(95, 101) ? %9 = Mod(95, 101) ? %10 = Mod(95, 101) ? %11 = Mod(8579, 35047) ? %12 = Mod(5852, 35047) ? %13 = Mod(5852, 35047) ? %14 = Mod(8579, 35047) ? %15 = Mod(6, 101) ? %16 = Mod(6, 101) ? %17 = Mod(32621, 35047) ? %18 = Mod(99, 101) ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.010s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:32:16 2006 Input: p=89 q=347 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 89 ? %2 = 347 ? %3 = 30883 ? %4 = 101 ? %5 = Mod(8777, 30883) ? %6 = Mod(28090, 30883) ? %7 = Mod(88, 89) ? %8 = Mod(88, 89) ? %9 = Mod(88, 89) ? %10 = Mod(88, 89) ? %11 = Mod(21359, 30883) ? %12 = Mod(7831, 30883) ? %13 = Mod(7831, 30883) ? %14 = Mod(21359, 30883) ? %15 = Mod(55, 89) ? %16 = Mod(55, 89) ? %17 = Mod(6907, 30883) ? %18 = Mod(54, 89) ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.010s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:31:22 2006 Input: p=89 q=127 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 89 ? %2 = 127 ? %3 = 11303 ? %4 = 101 ? %5 = Mod(10625, 11303) ? %6 = Mod(2348, 11303) ? %7 = Mod(88, 89) ? %8 = Mod(88, 89) ? %9 = Mod(88, 89) ? %10 = Mod(88, 89) ? %11 = Mod(5606, 11303) ? %12 = Mod(5962, 11303) ? %13 = Mod(5962, 11303) ? %14 = Mod(5606, 11303) ? %15 = Mod(34, 89) ? %16 = Mod(34, 89) ? %17 = Mod(300, 11303) ? %18 = Mod(33, 89) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:30:23 2006 Input: p=37 q=127 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 101 ? %5 = Mod(3812, 4699) ? %6 = Mod(445, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(3812, 4699) ? %12 = Mod(445, 4699) ? %13 = Mod(445, 4699) ? %14 = Mod(3812, 4699) ? %15 = Mod(1, 37) ? %16 = Mod(1, 37) ? %17 = Mod(0, 4699) ? %18 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:24:07 2006 Input: p=37 q=89 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) notok=Mod(que^(n-1), n) notok2=Mod(r^(n-1), n) notok3=Mod(que^(q-p), n) notok4=Mod(r^(q-p), n) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 89 ? %3 = 3293 ? %4 = 101 ? %5 = Mod(1601, 3293) ? %6 = Mod(1601, 3293) ? %7 = Mod(10, 37) ? %8 = Mod(10, 37) ? %9 = Mod(10, 37) ? %10 = Mod(10, 37) ? ? %11 = Mod(713, 3293) ? %12 = Mod(713, 3293) ? %13 = Mod(713, 3293) ? %14 = Mod(713, 3293) ? ? %15 = Mod(10, 37) ? %16 = Mod(10, 37) ? %17 = Mod(888, 3293) ? %18 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.131.227 (72.30.131.227) Time: Tue Jun 27 13:07:36 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:07:28 2006 Input: p=37 q=413 n=p*q a=43 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 413 ? %3 = 15281 ? %4 = 43 ? %5 = Mod(5181, 15281) ? %6 = Mod(9584, 15281) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(1, 37) ? %12 = Mod(1, 37) ? %13 = Mod(6475, 15281) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:07:18 2006 Input: p=37 q=413 n=p*q a=33 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 413 ? %3 = 15281 ? %4 = 33 ? %5 = Mod(3152, 15281) ? %6 = Mod(8073, 15281) ? %7 = Mod(34, 37) ? %8 = Mod(34, 37) ? %9 = Mod(34, 37) ? %10 = Mod(34, 37) ? %11 = Mod(7, 37) ? %12 = Mod(7, 37) ? %13 = Mod(469, 15281) ? %14 = Mod(25, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:07:02 2006 Input: p=37 q=127 n=p*q a=33 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 33 ? %5 = Mod(778, 4699) ? %6 = Mod(3183, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(1, 37) ? %12 = Mod(1, 37) ? %13 = Mod(0, 4699) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:06:48 2006 Input: p=37 q=127 n=p*q a=(10^5-1)/9 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 11111 ? %5 = Mod(778, 4699) ? %6 = Mod(3183, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(1, 37) ? %12 = Mod(1, 37) ? %13 = Mod(0, 4699) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:06:23 2006 Input: p=37 q=127 n=p*q a=413 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 413 ? %5 = Mod(258, 4699) ? %6 = Mod(3588, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(36, 37) ? %12 = Mod(36, 37) ? %13 = Mod(2921, 4699) ? %14 = Mod(35, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:06:08 2006 Input: p=37 q=127 n=p*q a=43 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 43 ? %5 = Mod(1405, 4699) ? %6 = Mod(3699, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(36, 37) ? %12 = Mod(36, 37) ? %13 = Mod(2921, 4699) ? %14 = Mod(35, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:05:53 2006 Input: p=37 q=127 n=p*q a=23 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 23 ? %5 = Mod(3366, 4699) ? %6 = Mod(2034, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(36, 37) ? %12 = Mod(36, 37) ? %13 = Mod(2921, 4699) ? %14 = Mod(35, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:05:40 2006 Input: p=37 q=127 n=p*q a=89 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 89 ? %5 = Mod(3366, 4699) ? %6 = Mod(2034, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(36, 37) ? %12 = Mod(36, 37) ? %13 = Mod(2921, 4699) ? %14 = Mod(35, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 13:05:09 2006 Input: p=37 q=127 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 101 ? %5 = Mod(3812, 4699) ? %6 = Mod(445, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(1, 37) ? %12 = Mod(1, 37) ? %13 = Mod(0, 4699) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:52:33 2006 Input: p=37 q=89 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 89 ? %3 = 3293 ? %4 = 101 ? %5 = Mod(1601, 3293) ? %6 = Mod(1601, 3293) ? %7 = Mod(10, 37) ? %8 = Mod(10, 37) ? %9 = Mod(10, 37) ? %10 = Mod(10, 37) ? %11 = Mod(10, 37) ? %12 = Mod(10, 37) ? %13 = Mod(888, 3293) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:52:15 2006 Input: p=37 q=127 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 101 ? %5 = Mod(3812, 4699) ? %6 = Mod(445, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(1, 37) ? %12 = Mod(1, 37) ? %13 = Mod(0, 4699) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:52:05 2006 Input: p=37 q=83 n=p*q a=101 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 83 ? %3 = 3071 ? %4 = 101 ? %5 = Mod(10, 3071) ? %6 = Mod(1934, 3071) ? %7 = Mod(10, 37) ? %8 = Mod(10, 37) ? %9 = Mod(10, 37) ? %10 = Mod(10, 37) ? %11 = Mod(10, 37) ? %12 = Mod(10, 37) ? %13 = Mod(1924, 3071) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:51:35 2006 Input: p=37 q=83 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 83 ? %3 = 3071 ? %4 = 41 ? %5 = Mod(70, 3071) ? %6 = Mod(2956, 3071) ? %7 = Mod(33, 37) ? %8 = Mod(33, 37) ? %9 = Mod(33, 37) ? %10 = Mod(33, 37) ? %11 = Mod(33, 37) ? %12 = Mod(33, 37) ? %13 = Mod(2516, 3071) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:51:21 2006 Input: p=37 q=127 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 41 ? %5 = Mod(2036, 4699) ? %6 = Mod(667, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(1, 37) ? %12 = Mod(1, 37) ? %13 = Mod(0, 4699) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:51:03 2006 Input: p=37 q=127 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 41 ? %5 = Mod(2036, 4699) ? %6 = Mod(667, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(1, 37) ? %12 = Mod(1, 37) ? %13 = Mod(0, 4699) ? %14 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:50:36 2006 Input: p=37 q=127 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 41 ? %5 = Mod(2036, 4699) ? %6 = Mod(667, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(1, 37) ? %12 = Mod(1, 37) ? %13 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:50:18 2006 Input: p=37 q=83 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 83 ? %3 = 3071 ? %4 = 41 ? %5 = Mod(70, 3071) ? %6 = Mod(2956, 3071) ? %7 = Mod(33, 37) ? %8 = Mod(33, 37) ? %9 = Mod(33, 37) ? %10 = Mod(33, 37) ? %11 = Mod(33, 37) ? %12 = Mod(33, 37) ? %13 = Mod(0, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:50:00 2006 Input: p=37 q=83 n=p*q a=8 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 83 ? %3 = 3071 ? %4 = 8 ? %5 = Mod(2009, 3071) ? %6 = Mod(1787, 3071) ? %7 = Mod(26, 37) ? %8 = Mod(26, 37) ? %9 = Mod(26, 37) ? %10 = Mod(26, 37) ? %11 = Mod(11, 37) ? %12 = Mod(11, 37) ? %13 = Mod(35, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:47:54 2006 Input: p=37 q=127 n=p*q a=8 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 37 ? %2 = 127 ? %3 = 4699 ? %4 = 8 ? %5 = Mod(3699, 4699) ? %6 = Mod(1405, 4699) ? %7 = Mod(1, 37) ? %8 = Mod(1, 37) ? %9 = Mod(1, 37) ? %10 = Mod(1, 37) ? %11 = Mod(36, 37) ? %12 = Mod(36, 37) ? %13 = Mod(35, 37) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:47:26 2006 Input: p=23 q=89 n=p*q a=8 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 23 ? %2 = 89 ? %3 = 2047 ? %4 = 8 ? %5 = Mod(1, 2047) ? %6 = Mod(1, 2047) ? %7 = Mod(1, 23) ? %8 = Mod(1, 23) ? %9 = Mod(1, 23) ? %10 = Mod(1, 23) ? %11 = Mod(1, 23) ? %12 = Mod(1, 23) ? %13 = Mod(0, 23) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:47:01 2006 Input: p=73 q=101 n=p*q a=8 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 8 ? %5 = Mod(738, 7373) ? %6 = Mod(1906, 7373) ? %7 = Mod(8, 73) ? %8 = Mod(8, 73) ? %9 = Mod(8, 73) ? %10 = Mod(8, 73) ? %11 = Mod(8, 73) ? %12 = Mod(8, 73) ? %13 = Mod(0, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:46:46 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? %9 = Mod(32, 73) ? %10 = Mod(32, 73) ? %11 = Mod(32, 73) ? %12 = Mod(32, 73) ? %13 = Mod(0, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:46:31 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? %9 = Mod(32, 73) ? %10 = Mod(32, 73) ? %11 = Mod(32, 73) ? %12 = Mod(32, 73) ? %13 = Mod(1752, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:46:18 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? %9 = Mod(32, 73) ? %10 = Mod(32, 73) ? %11 = Mod(32, 73) ? %12 = Mod(32, 73) ? %13 = Mod(0, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.035s user 0m0.005s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:45:42 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) mod(r^(n-2)-1,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? %9 = Mod(32, 73) ? %10 = Mod(32, 73) ? %11 = Mod(32, 73) ? %12 = Mod(32, 73) ? ? ? Goodbye! Errors/timing (if any): *** obsolete function: mod(r^(n-2)-1,p) ^---------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:43:14 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Mod(que,q) Mod(r,q) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? %9 = Mod(32, 73) ? %10 = Mod(32, 73) ? %11 = Mod(32, 73) ? %12 = Mod(32, 73) ? %13 = Mod(87, 101) ? %14 = Mod(36, 101) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:42:57 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) Mod(r,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? %9 = Mod(32, 73) ? %10 = Mod(32, 73) ? %11 = Mod(32, 73) ? %12 = Mod(32, 73) ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:42:32 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) Mod(que,p) M(r,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? %9 = Mod(32, 73) ? %10 = Mod(32, 73) ? %11 = Mod(32, 73) ? ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: M(r,p) ^ Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:42:05 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) ok3=Mod(que^(q-p), p) ok4=Mod(r^(q-p), p) que mod p r mod p Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? %9 = Mod(32, 73) ? %10 = Mod(32, 73) ? %11 = quemodp ? %12 = rmodp ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:40:59 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(q+p+99), p) ok2=Mod(r^(q+p+99), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(64, 73) ? %8 = Mod(64, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:40:39 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(q*p+99), p) ok2=Mod(r^(q*p+99), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(2, 73) ? %8 = Mod(2, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:40:29 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(q*p+9), p) ok2=Mod(r^(q*p+9), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(2, 73) ? %8 = Mod(2, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:40:17 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(q), p) ok2=Mod(r^(q), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(2, 73) ? %8 = Mod(2, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:40:05 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(q+p), p) ok2=Mod(r^(q+p), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(64, 73) ? %8 = Mod(64, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:39:54 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(q-p), p) ok2=Mod(r^(q-p), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:39:14 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.004s sys 0m0.008s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:38:51 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), n) ok2=Mod(r^(n-1), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(1711, 7373) ? %8 = Mod(2003, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:38:41 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(n-1), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), n) ok2=Mod(r^(n-1), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5288, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(2003, 7373) ? %8 = Mod(2003, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:38:08 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), n) ok2=Mod(r^(n-1), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(1711, 7373) ? %8 = Mod(2003, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:37:51 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) ok=Mod(que^(n-1), p) ok2=Mod(r^(n-1), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? %7 = Mod(32, 73) ? %8 = Mod(32, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 12:36:48 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) r=Mod(a^(n-1), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(5288, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '206.8.1' ************** PARI ***************** Host 206.8.10.132 (206.8.10.132) Time: Tue Jun 27 12:02:44 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '64.12.1' ************** PARI ***************** Host 64.12.116.196 (64.12.116.196) Time: Tue Jun 27 11:49:02 2006 Input: 598%/26% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '64.12.1' ************** PARI ***************** Host 64.12.116.196 (64.12.116.196) Time: Tue Jun 27 11:49:02 2006 Input: 598%/26% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '64.12.1' ************** PARI ***************** Host 64.12.116.196 (64.12.116.196) Time: Tue Jun 27 11:48:14 2006 Input: 598% / 26% Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:25:37 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) Mod(que^(n-1), p) Mod(que^(q-p),n) Mod(2003-32,p) Mod(n-1-2003.n) 2+3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(32, 73) ? %7 = Mod(2003, 7373) ? %8 = Mod(0, 73) ? ? %9 = 5 ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: Mod(n-1-2003.n) ^- Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:25:31 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) Mod(que^(n-1), p) Mod(que^(q-p),n) Mod(2003-32,p) Mod(n-1-2003.n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(32, 73) ? %7 = Mod(2003, 7373) ? %8 = Mod(0, 73) ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: Mod(n-1-2003.n) ^- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:25:16 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) Mod(que^(n-1), p) Mod(que^(q-p),n) Mod(2003-32,p) Mod(n-1-2003.p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(32, 73) ? %7 = Mod(2003, 7373) ? %8 = Mod(0, 73) ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: Mod(n-1-2003.p) ^- Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:20:34 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) Mod(que^(n-1), p) Mod(que^(q-p),n) Mod(2003-32,p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(32, 73) ? %7 = Mod(2003, 7373) ? %8 = Mod(0, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:20:15 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) Mod(que^(n-1), p) Mod(que^(q-p),n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(32, 73) ? %7 = Mod(2003, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:20:00 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) Mod(que^(n-1), p) Mod(que^(q-p) mod n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(32, 73) ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: Mod(que^(q-p)modn) ^----- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:19:01 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) Mod(que^(n-1), p) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(32, 73) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:18:20 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) que^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(4236, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:17:58 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) que^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? %6 = Mod(4236, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:17:43 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.002s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:17:21 2006 Input: p=73 q=101 n=p*q a=41 Mod(a^(q-p), n, 1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Tue Jun 27 11:16:56 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:16:47 2006 Input: p=73 q=101 n=p*q a=41 mod(a^(q-p), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? ? Goodbye! Errors/timing (if any): *** obsolete function: mod(a^(q-p),n) ^-------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:16:29 2006 Input: p=73 q=101 n=p*q a=41 Mod(a^(q-p), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:16:21 2006 Input: p=73 q=101; n=p*q a=41 Mod(a^(q-p), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:16:16 2006 Input: p=73 q=101 n=p*q a=41 Mod(a^(q-p), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:15:52 2006 Input: p=73 q=101 n=p*q a=41 Mod(a^(q-p), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:15:34 2006 Input: p=73 q=101 n=p*q a=41 que=Mod(a^(q-p), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? %5 = Mod(5945, 7373) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:15:19 2006 Input: p=73 q=101 n=p*q a=41 que=mod(a^(q-p), n) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? ? Goodbye! Errors/timing (if any): *** obsolete function: que=mod(a^(q-p),n) ^-------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:15:15 2006 Input: p=73 q=101 n=p*q a=41 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? %4 = 41 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:14:23 2006 Input: p=73 q=101 n=p*q Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 73 ? %2 = 101 ? %3 = 7373 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:11:29 2006 Input: 73*101 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7373 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:11:16 2006 Input: 73*101; Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:10:48 2006 Input: p=73; q=101; factor(p); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:10:37 2006 Input: p=73; q=101; ifactor(p); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: '=' instead of: ifactor(p); ^- Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '71.39.1' ************** PARI ***************** Host 71.39.185.145 (71.39.185.145) Time: Tue Jun 27 11:10:23 2006 Input: p=73; q=101; nextprime(p); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '58.9.20' ************** PARI ***************** Host 58.9.200.15 (58.9.200.15) Time: Tue Jun 27 10:41:31 2006 Input: polgalois(2*X^5 - 10*X + 5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [120, -1, 1, "S5"] ? Goodbye! Errors/timing (if any): Timing: real 0m0.185s user 0m0.010s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Tue Jun 27 09:04:26 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.071s user 0m0.004s sys 0m0.007s '72.30.9' ************** PARI ***************** Host 72.30.98.35 (72.30.98.35) Time: Tue Jun 27 08:33:22 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.110s user 0m0.027s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:10:03 2006 Input: Mod(47669^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(60, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.017s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:10:01 2006 Input: Mod(47669^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(60, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.017s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:09:41 2006 Input: Mod(70491^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(813, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.023s user 0m0.020s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:09:23 2006 Input: Mod(153750^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(70, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.023s user 0m0.018s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:09:01 2006 Input: Mod(34112^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(419, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.015s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:08:39 2006 Input: Mod(39468^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(132, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.016s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:08:15 2006 Input: Mod(130441^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(400, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.023s user 0m0.017s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:07:56 2006 Input: Mod(68641^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(2, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.019s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:05:45 2006 Input: Mod(17029^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(718, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.014s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:05:28 2006 Input: Mod(2828^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(41, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.012s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:05:10 2006 Input: Mod(111777^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(421, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.023s user 0m0.017s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:04:57 2006 Input: Mod(20908^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(130, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.017s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:04:46 2006 Input: Mod(20908^26851,167328) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(124480, 167328) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.016s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:04:34 2006 Input: Mod(9547*26851,167328) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 167328) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:04:13 2006 Input: Mod(9547*26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(53434, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:04:03 2006 Input: Mod(9547*26851),168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: Mod(9547*26851),168503) ^--------- Timing: real 0m0.024s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 08:02:52 2006 Input: Mod(2828^(26851),168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(41, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.015s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 07:58:30 2006 Input: Mod(2828^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(41, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.013s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 07:58:09 2006 Input: Mod(111777^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(421, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.019s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 07:57:13 2006 Input: Mod(20908^26851,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(130, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.016s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 07:55:11 2006 Input: Mod(20908^26851,167328) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(124480, 167328) ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.015s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 07:54:04 2006 Input: Mod(9547*26851,167328) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 167328) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 07:46:16 2006 Input: Mod(9547*8185,167328) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(19, 167328) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 07:23:14 2006 Input: Mod(9547*8185,167328) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(19, 167328) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 07:10:19 2006 Input: Mod(613^29,1943) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4, 1943) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:49:46 2006 Input: Mod(47669^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(18869, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.072s user 0m0.065s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:49:23 2006 Input: Mod(70491^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(88596, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.073s user 0m0.064s sys 0m0.010s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:48:59 2006 Input: Mod(153750^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(30189, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.079s user 0m0.073s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:48:31 2006 Input: Mod(34112^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(65528, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.069s user 0m0.063s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:48:06 2006 Input: Mod(39468^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(131111, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.070s user 0m0.066s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:47:39 2006 Input: Mod(130441^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(152759, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.079s user 0m0.072s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:47:11 2006 Input: Mod(68641^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(153371, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.073s user 0m0.067s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:46:42 2006 Input: Mod(17029^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(77418, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.063s user 0m0.057s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:46:12 2006 Input: Mod(2828^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(142969, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.049s user 0m0.039s sys 0m0.011s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:45:47 2006 Input: Mod(111777^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(122627, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.077s user 0m0.073s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:45:21 2006 Input: Mod(20908^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(112797, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.065s user 0m0.057s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:44:08 2006 Input: Mod(9547*108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:43:33 2006 Input: Mod(-59780,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(108723, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:43:07 2006 Input: Mod(9547*(108732),168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(85924, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:42:56 2006 Input: Mod(9547*(-59780),168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.025s user 0m0.004s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:39:07 2006 Input: Mod(14560^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(140312, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.071s user 0m0.055s sys 0m0.010s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:38:43 2006 Input: Mod(0^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(0, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.009s sys 0m0.003s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:38:19 2006 Input: Mod(14238^108723,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(133858, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.114s user 0m0.054s sys 0m0.009s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:37:44 2006 Input: Mod(-59780,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(108723, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.007s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:37:08 2006 Input: Mod(0^(-59780),168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** division by zero Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:36:28 2006 Input: Mod(14560^(-59780),168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(132378, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.044s user 0m0.038s sys 0m0.007s '209.184' ************** PARI ***************** Host 209.184.114.249 (209.184.114.249) Time: Tue Jun 27 06:36:16 2006 Input: Mod(2684^(-59780),168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(67228, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.035s user 0m0.027s sys 0m0.008s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Tue Jun 27 06:35:47 2006 Input: Mod(2684^-59780,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(67228, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.035s user 0m0.030s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Tue Jun 27 06:35:14 2006 Input: Mod(2444^-59780,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(65643, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.034s user 0m0.028s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Tue Jun 27 06:34:39 2006 Input: Mod(4454^-59780,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(111551, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.043s user 0m0.032s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Tue Jun 27 06:33:52 2006 Input: Mod(7052^-59780,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(105739, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.039s user 0m0.034s sys 0m0.006s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Tue Jun 27 06:30:04 2006 Input: Mod(14238^-59780,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(48806, 168503) ? Goodbye! Errors/timing (if any): Timing: real 0m0.168s user 0m0.037s sys 0m0.005s '209.184' ************** PARI ***************** Host 209.184.114.254 (209.184.114.254) Time: Tue Jun 27 06:29:24 2006 Input: mod(14238^-59780,168503) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** obsolete function: mod(14238^-59780,168 ^-------------------- For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.238s user 0m0.006s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.103.19 (72.30.103.19) Time: Mon Jun 26 23:55:45 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '68.94.8' ************** PARI ***************** Host 68.94.8.219 (68.94.8.219) Time: Mon Jun 26 21:23:17 2006 Input: 73 x 0.30 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x0.30. *** unknown member function: 73x0.30 ^-- Timing: real 0m0.011s user 0m0.004s sys 0m0.008s '68.94.8' ************** PARI ***************** Host 68.94.8.219 (68.94.8.219) Time: Mon Jun 26 21:22:55 2006 Input: 73x.30 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x.30. *** unknown member function: 73x.30 ^-- Timing: real 0m0.012s user 0m0.003s sys 0m0.008s '69.33.4' ************** PARI ***************** Host 69.33.46.42 (69.33.46.42) Time: Mon Jun 26 20:49:35 2006 Input: 1+1 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Mon Jun 26 18:59:39 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.055s user 0m0.006s sys 0m0.005s '72.30.1' ************** PARI ***************** Host 72.30.129.123 (72.30.129.123) Time: Mon Jun 26 17:41:24 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.067s user 0m0.007s sys 0m0.005s '128.95.' ************** PARI ***************** Host 128.95.47.126 (128.95.47.126) Time: Mon Jun 26 15:35:23 2006 Input: 43^1111 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 607371135656277995430959818511201636681707479727941209445905883231820636840558511354047297318718074891273086617200732800897890093037499003751675687169247524072173404905910448447148012327094326827236228005960966586043325728551834943285549655091750185769064731627446668896540224696092021480632659800898423272479596246530128263292114431168832042305702148622334038262806421255196377718607371119654581916237013207740426101287501016951207659783041329245156016425609672628895988326676037033470463550889052442799569431906794588187455689655724348621000710267990226326211271703341937599514427702701190346918319753921211324515390178487969937706864932926664524618920126595663549998007842906199589222024273868318000148891355408206867544356584630650943293546232397453941892869398517495239027256533618670473911274041760301229940190280837952714759404247997516636574759702107858872546403354208574315299708763429367879959700514796717294282777338269947490130310216264612055479520834570746220814343739628189802287100011296910644457726829736113182856090509189192350494107282161381362512422983677632818012766035123558067803877355492614675703662579489946247476674437224333467094121459408012163608668479082723653843508802538040763832519043290639911993819113403043939331368173421946130088694720198157930902191428606203547412198879405619599955663408551311923475139042718161423691964241360828320634260840969477212045565582410710906920677158216123350582037623055833995554507180970072684153211137605186501893256491015775080379019082033321543589038618755764105317717935704546073147717367846400398662872828924156712573321903698361460741446749804585506684805890263114268397786067823068832563310261543032857093540499424732083455805088432219773532282073251849618053237422835605660939210566441372388732546073374602823419761210935747547879858475412707 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '128.95.' ************** PARI ***************** Host 128.95.47.143 (128.95.47.143) Time: Mon Jun 26 15:34:15 2006 Input: 728347! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 8733 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m23.074s user 0m20.826s sys 0m0.193s '128.95.' ************** PARI ***************** Host 128.95.47.128 (128.95.47.128) Time: Mon Jun 26 15:34:10 2006 Input: 10256122! Output: ** WARNING: Computation used more memory than allowed. ** GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** the PARI stack overflows ! current stack size: 256000000 (244.141 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.562s user 0m0.249s sys 0m0.251s '128.95.' ************** PARI ***************** Host 128.95.47.128 (128.95.47.128) Time: Mon Jun 26 15:34:03 2006 Input: 10256122! Output: ** WARNING: Computation used more memory than allowed. ** GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** the PARI stack overflows ! current stack size: 256000000 (244.141 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m1.160s user 0m0.261s sys 0m0.295s '128.95.' ************** PARI ***************** Host 128.95.47.120 (128.95.47.120) Time: Mon Jun 26 15:34:01 2006 Input: factorial(610) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 8.3826160990316653882862988443391267190 E1435 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '128.95.' ************** PARI ***************** Host 128.95.47.130 (128.95.47.130) Time: Mon Jun 26 15:33:55 2006 Input: factorial(1000) 10000000! Output: ** WARNING: Computation used more memory than allowed. ** GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4.0238726007709377354370243392300398572 E2567 ? ? Goodbye! Errors/timing (if any): *** the PARI stack overflows ! current stack size: 256000000 (244.141 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m1.035s user 0m0.258s sys 0m0.275s '128.95.' ************** PARI ***************** Host 128.95.47.128 (128.95.47.128) Time: Mon Jun 26 15:33:53 2006 Input: 56324! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4287055176745019563347565954372986987618347600119888015975251386596924098052349801444893957584517183236030367939426807053237780240337089086931345553489049191176805412580601816951890373045868170697995189364794184512457036234852063981631537003559456708883608115041949070567292531719333345050103649030215412026296927009255142143809696340921531448984395094264276051624042775831197027915180789561881361632054777517448034704630616248009342498518298932994522894028544253781355145091049148519465668399403935911562992098442257698239991765861775407913569763310607598736907518976235957947224751670605369826609314199364976090066684483342943032530906382727446774653965729248045481242854263663834551921459243651685957215450949130253647651507126380506637990102355457946680585416183306933574103704855274465580324733361244071725865568693177134884458442372686697906389133880901651236583705956386171112874106229367560631123206039997062811415699455860160658688677144891469668963274817623710084354190542827300032556897164925151283345693389886719868609741805390227529803672643083054438589452743295573506087741898641932087703886698287945177384688577318880085527437945176884482573742341206236162252083877856091972475572139014528508422866295204244473498136208524521297592904425617713190666001947667193379392211211709604053262786290377405965397132504683383809299746014777477591980957781710417127233513201070893253571369792278159854208674788189990747449711033601572524769091027519016406939727172932650824328918059554580649651236480245576831103578531114242163111301062760313646798322042644293134657334955545958333103044581613197263262238936088508524619308640514211950862603743424631007353585450359815251227710314084471596143399401330615229152363929808597894291589945631925927666646943464593314732343316336448824045312663370199911299224779960892726209250215523375119004789499117226544559935843386021939437123639442631200941329596272906537134442880321148227015870046610703059482767957262978797837968365112095645356263721493760010844697929674136678709081927079809706924560903157990359265880570665350330477261850346270127146797503608119279725822593252562810296855271033964787368789944359544412411696101521343024968973049079980147853207715844944912584998523832284874262935369481359220990263928354818082669979396468526731143598155233733011649966295455308837930856074239382740092693935738471340313194957922907286624504043247579746410024189732445155662444917034296670409772294594173771216576516404658676739608788678916462462628699996145216457389284730725745260523957595719451266754151991282944793991603446676822286518372769995933995516541633408434219436729635125712904872985098988253957799967908530829923682401870929950881047842378804467254538491878380142670305938346397878469071877528887150400739038909115928648004483206102340041419778932511132875096154400311466074557078713888607220223536566168994427804959885313144517414756058984080986054422228216282634798429023478082234587397612004135842526124748995035791049891054976716255919346110861228929812418207872293720520562019589446453983446551982864978394559354636908088319904340977767006256284645368289978312019903102859291194784592723830064679247863242399427806088959815092078[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m3.146s user 0m2.734s sys 0m0.135s '128.95.' ************** PARI ***************** Host 128.95.47.145 (128.95.47.145) Time: Mon Jun 26 15:33:50 2006 Input: log(n,10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: log(n,10) ^---- Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '128.95.' ************** PARI ***************** Host 128.95.47.139 (128.95.47.139) Time: Mon Jun 26 15:33:44 2006 Input: 1000! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '128.95.' ************** PARI ***************** Host 128.95.47.128 (128.95.47.128) Time: Mon Jun 26 15:33:40 2006 Input: 43! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 60415263063373835637355132068513997507264512000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '128.95.' ************** PARI ***************** Host 128.95.47.129 (128.95.47.129) Time: Mon Jun 26 15:33:38 2006 Input: 10000! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2846259680917054518906413212119868890148051401702799230794179994274411340003764443772990786757784775815884062142317528830042339940153518739052421161382716174819824199827592418289259787898124253120594659962598670656016157203603239792632873671705574197596209947972034615369811989709261127750048419884541047554464244213657330307670362882580354896746111709736957860367019107151273058728104115864056128116538532596842582599558468814643042558983664931705925171720427659740744613340005419405246230343686915405940406622782824837151203832217864462718382292389963899282722187970245938769380309462733229257055545969002787528224254434802112755901916942542902891690721909708369053987374745248337289952180236328274121704026808676921045155584056717255537201585213282903427998981844931361064038148930449962159999935967089298019033699848440466541923625842494716317896119204123310826865107135451684554093603300960721034694437798234943078062606942230268188522759205702923084312618849760656074258627944882715595683153344053442544664841689458042570946167361318760523498228632645292152942347987060334429073715868849917893258069148316885425195600617237263632397442078692464295601230628872012265295296409150830133663098273380635397290150658182257429547589439976511386554120812578868370423920876448476156900126488927159070630640966162803878404448519164379080718611237062213341541506599184387596102392671327654698616365770662643863802984805195276953619525924093090861447190739076858575593478698172073437209310482547562856777769408156407496227525499338411280928963751699021987049240561753178634693979802461973707904186832993101655415074230839317687836692369484902599960772968429397742753626311982541668153189176323483919082100014717893218422780513518173492190114624687576983537344145601312261522139117875968836736408720793700299203827919803870237207803914031236899760815284030605111670948472222487038919999344207139583698306396223207911562404425080891991431983712044559834404755675948921210149815245454359428541439084356441998422485547853216362403009844285533182925315420655123707970581639346029624769701038874220644153662673371542870078912274934068433644288984710084064160009362393526124803797529334392876439831639031277645072247926785170082666959838952615075900734921519759265919270887320259406638211880198885474826604834225645770574397312225970067193606176351357952982179429079770532728326750148802444352868164502616566283754651900617187344226043891929850607151539003110668472736013581670643786175675743918437647965813610059963868955233464878174614324357322486432679848198145843270303589550842053478849336458248259203328808902578238823326577020524897093704721021424841334246526820680673231421448385407418213962184687010835958294696523563276487047571835161687923506836627174371191572336114307012112076760869785155972184648598591864364171685089962551682091079357023111851817477501080462258552131476489749066075287708289766751495100968232968973200062239288805665803614031128546592908407803397490066495320587316494809388381619865885082738246803489786475711667989042356801830350413387573197263089790943571068779730163391808786847494363353389337358690640584841782806519627582643442925805842221294764940294862267076183298[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m0.104s user 0m0.067s sys 0m0.036s '128.95.' ************** PARI ***************** Host 128.95.47.144 (128.95.47.144) Time: Mon Jun 26 15:33:34 2006 Input: 1000! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '128.95.' ************** PARI ***************** Host 128.95.47.139 (128.95.47.139) Time: Mon Jun 26 15:33:30 2006 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.004s sys 0m0.006s '128.95.' ************** PARI ***************** Host 128.95.47.136 (128.95.47.136) Time: Mon Jun 26 15:33:26 2006 Input: factorial(1000) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4.0238726007709377354370243392300398572 E2567 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.006s sys 0m0.008s '128.95.' ************** PARI ***************** Host 128.95.47.144 (128.95.47.144) Time: Mon Jun 26 15:33:24 2006 Input: factorial(1000) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4.0238726007709377354370243392300398572 E2567 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.95.' ************** PARI ***************** Host 128.95.47.128 (128.95.47.128) Time: Mon Jun 26 15:33:12 2006 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.95.' ************** PARI ***************** Host 128.95.47.139 (128.95.47.139) Time: Mon Jun 26 15:33:10 2006 Input: factorial(1000) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4.0238726007709377354370243392300398572 E2567 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.95.' ************** PARI ***************** Host 128.95.47.140 (128.95.47.140) Time: Mon Jun 26 15:33:06 2006 Input: 3+3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 6 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.004s '128.95.' ************** PARI ***************** Host 128.95.47.123 (128.95.47.123) Time: Mon Jun 26 15:33:04 2006 Input: factorial(1001) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4.0278964733717086731724613635692698970 E2570 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.007s sys 0m0.005s '128.95.' ************** PARI ***************** Host 128.95.47.141 (128.95.47.141) Time: Mon Jun 26 15:33:04 2006 Input: 56+25 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 81 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '128.95.' ************** PARI ***************** Host 128.95.47.139 (128.95.47.139) Time: Mon Jun 26 15:32:53 2006 Input: factorial(1000) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4.0238726007709377354370243392300398572 E2567 ? Goodbye! Errors/timing (if any): Timing: real 0m0.069s user 0m0.004s sys 0m0.010s '128.95.' ************** PARI ***************** Host 128.95.47.131 (128.95.47.131) Time: Mon Jun 26 15:32:31 2006 Input: 2+22 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 24 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.007s sys 0m0.004s '128.95.' ************** PARI ***************** Host 128.95.47.128 (128.95.47.128) Time: Mon Jun 26 15:32:26 2006 Input: 34*34 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1156 ? Goodbye! Errors/timing (if any): Timing: real 0m0.031s user 0m0.004s sys 0m0.008s '72.30.1' ************** PARI ***************** Host 72.30.102.206 (72.30.102.206) Time: Mon Jun 26 13:51:14 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.033s user 0m0.006s sys 0m0.005s '134.53.' ************** PARI ***************** Host 134.53.25.50 (134.53.25.50) Time: Mon Jun 26 12:44:26 2006 Input: lim(f,100000000, sqrt(2*6.6742e-11*5.9742e24*f)/(6.3783e6+f)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: lim(f,100000000,sqrt ^-------------------- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.25.50 (134.53.25.50) Time: Mon Jun 26 12:44:16 2006 Input: lim(f,100000000, sqrt(2*6.6742e-11*5.9742e24*f)/(6.3783e6+f) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...5.9742e24*f)/(6.3783e6+f) ^ Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '134.53.' ************** PARI ***************** Host 134.53.25.50 (134.53.25.50) Time: Mon Jun 26 12:42:01 2006 Input: 9+8 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 17 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '151.198' ************** PARI ***************** Host 151.198.23.169 (151.198.23.169) Time: Mon Jun 26 12:23:34 2006 Input: 9+9= Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 9+9= ^- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Mon Jun 26 11:43:52 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.029s user 0m0.024s sys 0m0.006s '71.129.' ************** PARI ***************** Host 71.129.174.198 (71.129.174.198) Time: Mon Jun 26 10:26:17 2006 Input: x^3+x^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = x^4 + x^3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.043s user 0m0.008s sys 0m0.003s '166.82.' ************** PARI ***************** Host 166.82.28.133 (166.82.28.133) Time: Mon Jun 26 09:34:50 2006 Input: 181 11/16" divided by 7 3/4" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = " divided by 7 3/4" ? Goodbye! Errors/timing (if any): *** Warning: unused characters: " divided by 7 3/4". Timing: real 0m0.055s user 0m0.005s sys 0m0.006s '70.186.' ************** PARI ***************** Host 70.186.69.229 (70.186.69.229) Time: Mon Jun 26 08:45:12 2006 Input: 2 + 2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.032s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Mon Jun 26 07:50:44 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.290s user 0m0.007s sys 0m0.012s '72.30.9' ************** PARI ***************** Host 72.30.99.77 (72.30.99.77) Time: Mon Jun 26 05:20:15 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.117s user 0m0.007s sys 0m0.008s '4.249.1' ************** PARI ***************** Host 4.249.180.57 (4.249.180.57) Time: Mon Jun 26 02:29:54 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '4.249.1' ************** PARI ***************** Host 4.249.180.57 (4.249.180.57) Time: Mon Jun 26 02:29:03 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.019s user 0m0.006s sys 0m0.012s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Mon Jun 26 01:44:47 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.058s user 0m0.023s sys 0m0.007s '72.30.9' ************** PARI ***************** Host 72.30.98.26 (72.30.98.26) Time: Sun Jun 25 22:16:10 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.232s user 0m0.004s sys 0m0.009s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sun Jun 25 18:48:25 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.007s '216.197' ************** PARI ***************** Host 216.197.162.52 (216.197.162.52) Time: Sun Jun 25 17:58:32 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Sun Jun 25 17:16:28 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.090s user 0m0.027s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Sun Jun 25 12:54:36 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '63.241.' ************** PARI ***************** Host 63.241.61.7 (63.241.61.7) Time: Sun Jun 25 12:07:19 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.251.91 (68.142.251.91) Time: Sun Jun 25 11:24:27 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.005s sys 0m0.008s '68.142.' ************** PARI ***************** Host 68.142.249.131 (68.142.249.131) Time: Sun Jun 25 11:05:54 2006 Input: vector(20,x,floor((x+1)*sqrt(2))-floor(x*sqrt(2))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.172s user 0m0.007s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.250.88 (68.142.250.88) Time: Sun Jun 25 08:55:42 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.004s '82.127.' ************** PARI ***************** Host 82.127.62.167 (82.127.62.167) Time: Sun Jun 25 07:16:01 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Sun Jun 25 07:06:36 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.200s user 0m0.011s sys 0m0.002s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Sun Jun 25 04:37:59 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.115s user 0m0.005s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.251.86 (68.142.251.86) Time: Sun Jun 25 02:20:22 2006 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.064s user 0m0.007s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.110.15 (72.30.110.15) Time: Sun Jun 25 00:21:19 2006 Input: for(x=1,50,print1("d(",x,")=",numdiv(x),", ")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? d(1)=1, d(2)=2, d(3)=2, d(4)=3, d(5)=2, d(6)=4, d(7)=2, d(8)=4, d(9)=3, d(10)=4, d(11)=2, d(12)=6, d(13)=2, d(14)=4, d(15)=4, d(16)=5, d(17)=2, d(18)=6, d(19)=2, d(20)=6, d(21)=4, d(22)=4, d(23)=2, d(24)=8, d(25)=3, d(26)=4, d(27)=4, d(28)=6, d(29)=2, d(30)=8, d(31)=2, d(32)=6, d(33)=4, d(34)=4, d(35)=4, d(36)=9, d(37)=2, d(38)=4, d(39)=4, d(40)=8, d(41)=2, d(42)=8, d(43)=2, d(44)=6, d(45)=6, d(46)=4, d(47)=2, d(48)=10, d(49)=3, d(50)=6, ? Goodbye! Errors/timing (if any): Timing: real 0m0.047s user 0m0.007s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sun Jun 25 00:10:18 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '72.30.1' ************** PARI ***************** Host 72.30.132.102 (72.30.132.102) Time: Sat Jun 24 21:36:04 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.057s user 0m0.006s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.249.160 (68.142.249.160) Time: Sat Jun 24 21:16:38 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.359s user 0m0.009s sys 0m0.009s '65.4.17' ************** PARI ***************** Host 65.4.175.159 (65.4.175.159) Time: Sat Jun 24 19:48:12 2006 Input: plot(sin(x),x=0..10) Output: WARNING: PARI command contains unsafe command 'plot', so it will not be executed. '72.30.9' ************** PARI ***************** Host 72.30.98.145 (72.30.98.145) Time: Sat Jun 24 15:59:05 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '69.169.' ************** PARI ***************** Host 69.169.32.30 (69.169.32.30) Time: Sat Jun 24 10:40:17 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.149s user 0m0.008s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.249.35 (68.142.249.35) Time: Sat Jun 24 08:46:35 2006 Input: collatzlength(x0)= { local(x,i); x=x0; i=0; while(x-1, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2);i=i++ ); i } collatzlength(299) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 75 ? Goodbye! Errors/timing (if any): Timing: real 0m0.031s user 0m0.007s sys 0m0.005s '70.160.' ************** PARI ***************** Host 70.160.50.169 (70.160.50.169) Time: Sat Jun 24 07:58:44 2006 Input: 11+27+1976 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2014 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '72.30.1' ************** PARI ***************** Host 72.30.107.8 (72.30.107.8) Time: Sat Jun 24 06:45:21 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.096s user 0m0.022s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.250.147 (68.142.250.147) Time: Sat Jun 24 05:19:27 2006 Input: for(n=1,20, print1(n,": ",valuation(n!,2),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 0, 2: 1, 3: 1, 4: 3, 5: 3, 6: 4, 7: 4, 8: 7, 9: 7, 10: 8, 11: 8, 12: 10, 13: 10, 14: 11, 15: 11, 16: 15, 17: 15, 18: 16, 19: 16, 20: 18, ? Goodbye! Errors/timing (if any): Timing: real 0m0.209s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Sat Jun 24 02:03:35 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '68.212.' ************** PARI ***************** Host 68.212.128.18 (68.212.128.18) Time: Fri Jun 23 22:32:56 2006 Input: print kash('NumberField(X^3 + 15*X^2 - 15*X + 15)') Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: printkash('NumberField *** (X^3+15*X^2-15*X+15) ^-------------------- Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.203.' ************** PARI ***************** Host 68.203.184.75 (68.203.184.75) Time: Fri Jun 23 22:05:53 2006 Input: 15000 x .12 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** Warning: unused characters: x.12. *** unknown member function: 15000x.12 ^-- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.88 (68.142.249.88) Time: Fri Jun 23 19:51:51 2006 Input: factor(x^6-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [x - 1 1] [x + 1 1] [x^2 - x + 1 1] [x^2 + x + 1 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.300s user 0m0.010s sys 0m0.007s '192.91.' ************** PARI ***************** Host 192.91.75.29 (192.91.75.29) Time: Fri Jun 23 14:56:24 2006 Input: 5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.124s user 0m0.006s sys 0m0.007s '192.91.' ************** PARI ***************** Host 192.91.75.29 (192.91.75.29) Time: Fri Jun 23 14:56:15 2006 Input: g Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = g ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '199.1.4' ************** PARI ***************** Host 199.1.45.1 (199.1.45.1) Time: Fri Jun 23 14:24:15 2006 Input: 7 4/9 * 10 2/3 = Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 74/9*102/3= ^- Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '68.142.' ************** PARI ***************** Host 68.142.251.155 (68.142.251.155) Time: Fri Jun 23 13:34:23 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '89.138.' ************** PARI ***************** Host 89.138.17.205 (89.138.17.205) Time: Fri Jun 23 10:08:31 2006 Input: 6.195/(49^(1/3)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1.6929440967535643545612184030006528503 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.007s '89.138.' ************** PARI ***************** Host 89.138.17.205 (89.138.17.205) Time: Fri Jun 23 10:06:11 2006 Input: 49^(1/3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3.6593057100229715172380733101194082635 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '89.138.' ************** PARI ***************** Host 89.138.17.205 (89.138.17.205) Time: Fri Jun 23 10:05:57 2006 Input: 49^(1/2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7.0000000000000000000000000000000000000 ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.028s user 0m0.009s sys 0m0.004s '89.138.' ************** PARI ***************** Host 89.138.17.205 (89.138.17.205) Time: Fri Jun 23 10:04:27 2006 Input: 79-5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 74 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '89.138.' ************** PARI ***************** Host 89.138.17.205 (89.138.17.205) Time: Fri Jun 23 10:04:27 2006 Input: 79-5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 74 ? Goodbye! Errors/timing (if any): Timing: real 0m0.067s user 0m0.006s sys 0m0.009s '68.142.' ************** PARI ***************** Host 68.142.251.11 (68.142.251.11) Time: Fri Jun 23 09:36:09 2006 Input: for( k=1, 12, print(k,": ",Mod(2^k,13)) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: Mod(2, 13) 2: Mod(4, 13) 3: Mod(8, 13) 4: Mod(3, 13) 5: Mod(6, 13) 6: Mod(12, 13) 7: Mod(11, 13) 8: Mod(9, 13) 9: Mod(5, 13) 10: Mod(10, 13) 11: Mod(7, 13) 12: Mod(1, 13) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '192.88.' ************** PARI ***************** Host 192.88.212.43 (192.88.212.43) Time: Fri Jun 23 08:34:48 2006 Input: (40-4.5)/40 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.88750000000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '192.88.' ************** PARI ***************** Host 192.88.212.43 (192.88.212.43) Time: Fri Jun 23 08:34:25 2006 Input: 40-4.5/40 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 39.887500000000000000000000000000000000 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '192.88.' ************** PARI ***************** Host 192.88.212.43 (192.88.212.43) Time: Fri Jun 23 08:34:01 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '68.142.' ************** PARI ***************** Host 68.142.250.91 (68.142.250.91) Time: Fri Jun 23 08:25:07 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2+1)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 1,2 2,5 5,13 13,34 34,89 ? Goodbye! Errors/timing (if any): Timing: real 0m0.150s user 0m0.022s sys 0m0.008s '68.203.' ************** PARI ***************** Host 68.203.201.54 (68.203.201.54) Time: Fri Jun 23 08:12:41 2006 Input: Mod(20908^26851,167328) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(124480, 167328) ? Goodbye! Errors/timing (if any): Timing: real 0m0.022s user 0m0.014s sys 0m0.007s '68.203.' ************** PARI ***************** Host 68.203.201.54 (68.203.201.54) Time: Fri Jun 23 08:11:39 2006 Input: Mod(613^29,1943) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(4, 1943) ? Goodbye! Errors/timing (if any): Timing: real 0m0.064s user 0m0.006s sys 0m0.008s '68.203.' ************** PARI ***************** Host 68.203.201.54 (68.203.201.54) Time: Fri Jun 23 08:10:41 2006 Input: Mod(4^701,1943) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(613, 1943) ? Goodbye! Errors/timing (if any): Timing: real 0m0.120s user 0m0.005s sys 0m0.007s '68.203.' ************** PARI ***************** Host 68.203.201.54 (68.203.201.54) Time: Fri Jun 23 08:10:01 2006 Input: 4^701 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 110676118811032480585967768747499536519328782386750375691764613314578460148244875589891832499633445220917590128663997175471542181491914428820706520725810707735684295364921800575936715846232204786559273412930006301336929760897461033653044898196274589986935573971434775355744077467576224499518515771224752022253695535843069654039149722860977658691528074438271278969579919833157792589402462962726390088044914327843941073813504 ? Goodbye! Errors/timing (if any): Timing: real 0m0.278s user 0m0.008s sys 0m0.005s '68.203.' ************** PARI ***************** Host 68.203.201.54 (68.203.201.54) Time: Fri Jun 23 08:09:41 2006 Input: 4^701 mod 1943 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = mod1943 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: mod1943. Timing: real 0m0.198s user 0m0.006s sys 0m0.006s '68.203.' ************** PARI ***************** Host 68.203.201.54 (68.203.201.54) Time: Fri Jun 23 08:09:31 2006 Input: 4^701 % 1943 Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '68.142.' ************** PARI ***************** Host 68.142.249.100 (68.142.249.100) Time: Fri Jun 23 08:00:59 2006 Input: for(b=1,100, for(a=1,b, if( frac((a^2+b^2)/(a*b))==0 , print(a,",",b), ) ) ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1,1 2,2 3,3 4,4 5,5 6,6 7,7 8,8 9,9 10,10 11,11 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21 22,22 23,23 24,24 25,25 26,26 27,27 28,28 29,29 30,30 31,31 32,32 33,33 34,34 35,35 36,36 37,37 38,38 39,39 40,40 41,41 42,42 43,43 44,44 45,45 46,46 47,47 48,48 49,49 50,50 51,51 52,52 53,53 54,54 55,55 56,56 57,57 58,58 59,59 60,60 61,61 62,62 63,63 64,64 65,65 66,66 67,67 68,68 69,69 70,70 71,71 72,72 73,73 74,74 75,75 76,76 77,77 78,78 79,79 80,80 81,81 82,82 83,83 84,84 85,85 86,86 87,87 88,88 89,89 90,90 91,91 92,92 93,93 94,94 95,95 96,96 97,97 98,98 99,99 100,100 ? Goodbye! Errors/timing (if any): Timing: real 0m0.097s user 0m0.024s sys 0m0.006s '75.16.2' ************** PARI ***************** Host 75.16.208.116 (75.16.208.116) Time: Fri Jun 23 07:56:16 2006 Input: (8^200000)mod 6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = mod6 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: mod6. Timing: real 0m0.333s user 0m0.027s sys 0m0.004s '75.16.2' ************** PARI ***************** Host 75.16.208.116 (75.16.208.116) Time: Fri Jun 23 07:55:13 2006 Input: 2^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.074s user 0m0.003s sys 0m0.009s '75.16.2' ************** PARI ***************** Host 75.16.208.116 (75.16.208.116) Time: Fri Jun 23 07:54:49 2006 Input: 2^200000 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 9980051818471209560859346309213505420041765610346220829126570959195807493223281009034491688459450029180405619772465299384020878521785380969051464518340832825094027267918386963684448752958718980274020850798213311027763212137813883289959647384877546795977235831526317325470277184725609174807369684823136976033122822961904431694541699548022641336697007765593743832319325548503664493346008271533204539831188961149915750728642920964584169564037616464267721212484116246995691842836056561529719175223592360220756433047198880083551717213289166286863081641180682451486914299326008838137363126200453029877109708228005209626492112258394314792350469808094133043712979590428257819311364323501650280812543338930916804952118219992682428018534057429148399639327041310355439174730911496947880801432967813077337967459306647671383813376770826633081907115630857484880618494014576205602691031097968381924394787677369814771867723438007924115393795870238239862684426886672688910033774190792664850845372822677311588590203850112414194636871679023208090350243796597442926500392687595673820966556875664260163237198650381993575087088289667293910894985717082847945055187918854237747326151073045843681783199482155232827723292941974953771613798991794680841351256463580273523590587809269583545359645590369629555810167275884796524307703000476966333337069307369825430136719179779375398382363833961710064856757800305835510003557387145856455001420308996178223785489268695448888482970389741087389524524235123429442462978424281736544613729521800838109387461647216773817778257232976893801651244859615422364347148296721489221261238671489530421736460757661146978245212465038468725728214254678344736818804438902569719528362742262077040757620129120609980995190751944542710664939865715848786007032012946074368500988292045101961752160206062371583517522845146548116203002508312925059361165067457762440258215114003669526019524622823614429515722224882045796677167645684321251919589859880158824025971966762304747630209662670103080010004806517296162958286119894585268096017004163865187261515920841707092889035994723311246932781769156790937147608512849644758564703061690608545190838709421497386086225813848618631147488096290122298840787044860128881792387109786755775508888233569077356060545857983136408925830127066260769950742643412722428829082842888649978017303358166299492043154392980216297709860399436749828833838091353518999658970576390806819879926544787510471037806156868572592378555215293804478972801409794721660035726432677009731747662589319470975062278211633255949027895572830023548979778205170363098776926913014637089779726696014234938441079541428818269184544202525201859604993114285151571168658902741985969687824592669921006108880867481691387826475742418340629761033270584139486198563727002337160744399071756287527465885341612932876544199275354303909243346783264361466723303794402047879198613218700233495579277397865166979530359969811703628030637197246158869017455218470343821522005413181172860526230676243933663324471426547394339689941451125544688916187908873382891215203658853842817332781781806655798149365680582207748033932494215455190366825417159996063173922436905764162667771383522982865607976621325353126476992594560493838842[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m1.099s user 0m0.164s sys 0m0.114s '75.16.2' ************** PARI ***************** Host 75.16.208.116 (75.16.208.116) Time: Fri Jun 23 07:54:27 2006 Input: "Replace this by some code, then click [SAGE] or [PARI]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [SAGE] or [PARI]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.018s user 0m0.004s sys 0m0.009s '65.54.1' ************** PARI ***************** Host 65.54.188.55 (65.54.188.55) Time: Fri Jun 23 05:56:30 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '65.54.1' ************** PARI ***************** Host 65.54.188.56 (65.54.188.56) Time: Fri Jun 23 05:45:33 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.007s sys 0m0.009s '68.142.' ************** PARI ***************** Host 68.142.249.166 (68.142.249.166) Time: Fri Jun 23 03:55:07 2006 Input: for(n=1,7, print1(n,": ",sum(x=1,n,1/x),", ") ) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 1: 1, 2: 3/2, 3: 11/6, 4: 25/12, 5: 137/60, 6: 49/20, 7: 363/140, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '72.30.1' ************** PARI ***************** Host 72.30.129.106 (72.30.129.106) Time: Fri Jun 23 03:39:20 2006 Input: y=210; for(x=1,8,y=sumdiv(y,x,x)-y;print1(y,",")) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? 366,378,582,594,846,1026,1374,1386, ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '213.84.' ************** PARI ***************** Host 213.84.201.227 (213.84.201.227) Time: Fri Jun 23 03:32:51 2006 Input: cos(tan(1)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.013388202148675800721560718743178292188 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.004s '213.84.' ************** PARI ***************** Host 213.84.201.227 (213.84.201.227) Time: Fri Jun 23 03:32:35 2006 Input: cos(tan(-1)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.013388202148675800721560718743178292188 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '213.84.' ************** PARI ***************** Host 213.84.201.227 (213.84.201.227) Time: Fri Jun 23 03:32:25 2006 Input: cos(tan-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 0.013388202148675800721560718743178292188 ? Goodbye! Errors/timing (if any): Timing: real 0m0.107s user 0m0.008s sys 0m0.005s '213.84.' ************** PARI ***************** Host 213.84.201.227 (213.84.201.227) Time: Fri Jun 23 03:32:15 2006 Input: cos(tan^-1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: cos(tan^-1) ^---- Timing: real 0m0.107s user 0m0.008s sys 0m0.005s '213.84.' ************** PARI ***************** Host 213.84.201.227 (213.84.201.227) Time: Fri Jun 23 03:31:41 2006 Input: cos(tan^-1x) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: cos(tan^-1x) ^-- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '213.84.' ************** PARI ***************** Host 213.84.201.227 (213.84.201.227) Time: Fri Jun 23 03:31:15 2006 Input: cos(tan^-1(x)) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: cos(tan^-1(x)) ^---- Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '213.84.' ************** PARI ***************** Host 213.84.201.227 (213.84.201.227) Time: Fri Jun 23 03:30:53 2006 Input: y=10-x y=x-6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -x + 10 ? %2 = x - 6 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '213.84.' ************** PARI ***************** Host 213.84.201.227 (213.84.201.227) Time: Fri Jun 23 03:30:33 2006 Input: 10-x=y x-6=y Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -y + 10 ? ? Goodbye! Errors/timing (if any): *** unexpected character: x-6=y ^-- Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '213.84.' ************** PARI ***************** Host 213.84.201.227 (213.84.201.227) Time: Fri Jun 23 03:30:24 2006 Input: 10-x=y x-6=y5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -y + 10 ? ? Goodbye! Errors/timing (if any): *** unexpected character: x-6=y5 ^--- Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '213.84.' ************** PARI ***************** Host 213.84.201.227 (213.84.201.227) Time: Fri Jun 23 03:28:46 2006 Input: 10-x+y=0 x-6y=5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = -x + 10 ? %2 = 5 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: y=5. Timing: real 0m0.069s user 0m0.007s sys 0m0.005s '68.142.' ************** PARI ***************** Host 68.142.249.32 (68.142.249.32) Time: Thu Jun 22 22:03:41 2006 Input: factor(2^(2^5)+1) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [641 1] [6700417 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '68.203.' ************** PARI ***************** Host 68.203.201.54 (68.203.201.54) Time: Thu Jun 22 21:43:33 2006 Input: 20908^26851 mod 167328 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = mod167328 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: mod167328. Timing: real 0m0.021s user 0m0.016s sys 0m0.005s '68.203.' ************** PARI ***************** Host 68.203.201.54 (68.203.201.54) Time: Thu Jun 22 21:43:13 2006 Input: Mod (20908^26851, 167328) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(124480, 167328) ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.013s sys 0m0.008s '68.203.' ************** PARI ***************** Host 68.203.201.54 (68.203.201.54) Time: Thu Jun 22 21:42:09 2006 Input: 20908^26851 mod 167328 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = mod167328 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: mod167328. Timing: real 0m0.098s user 0m0.013s sys 0m0.007s '68.142.' ************** PARI ***************** Host 68.142.250.189 (68.142.250.189) Time: Thu Jun 22 20:58:47 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.007s '72.49.2' ************** PARI ***************** Host 72.49.204.176 (72.49.204.176) Time: Thu Jun 22 16:59:55 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '68.5.20' ************** PARI ***************** Host 68.5.208.73 (68.5.208.73) Time: Thu Jun 22 16:33:48 2006 Input: {ss(n)=sum(x=1,n,n/gcd(n,x))} ss(60) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 1617 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '64.106.' ************** PARI ***************** Host 64.106.20.22 (64.106.20.22) Time: Thu Jun 22 15:19:57 2006 Input: 3+2+5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 10 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:42:54 2006 Input: 4 /3 mud(r,s)= r - s * floor(r / s) a(n)=if( 0 > n, 0, if( 1 > n, 1 , sum(i=0, n/2, a(n-1-2*i)*a(i) ))) 777 a(0) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4/3 ? ? ? ? %2 = 777 ? %3 = 1 ? %4 = 1 ? %5 = 1 ? %6 = 2 ? %7 = 3 ? %8 = 5 ? %9 = 8 ? %10 = 14 ? %11 = 23 ? %12 = 39 ? %13 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.018s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:36:51 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 0 > n, 0, if( 1 > n, 1 , sum(i=0, n/2, a(n-1-2*i)*a(i) ))) 777 a(0) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 777 ? %2 = 1 ? %3 = 1 ? %4 = 1 ? %5 = 2 ? %6 = 3 ? %7 = 5 ? %8 = 8 ? %9 = 14 ? %10 = 23 ? %11 = 39 ? %12 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.120s user 0m0.015s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:36:38 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 0 > n, 0, if( 1 > n, 1 , sum(i=0, n/2, a(n-1-2*i)*a(i) ))) 777 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 777 ? %2 = 1 ? %3 = 1 ? %4 = 2 ? %5 = 3 ? %6 = 5 ? %7 = 8 ? %8 = 14 ? %9 = 23 ? %10 = 39 ? %11 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.021s user 0m0.020s sys 0m0.001s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:36:15 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 0 > n, 0, if( 1 > n, 1 , sum(i=0, (n-0)/2, a(n-1-2*i)*a(i) ))) 777 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 777 ? %2 = 1 ? %3 = 1 ? %4 = 2 ? %5 = 3 ? %6 = 5 ? %7 = 8 ? %8 = 14 ? %9 = 23 ? %10 = 39 ? %11 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.016s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:35:24 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 0 > n, 0, if( 1 > n, 1 , sum(i=0, (n-1)/2, a(n-1-2*i)*a(i) ))) 777 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 777 ? %2 = 1 ? %3 = 1 ? %4 = 2 ? %5 = 3 ? %6 = 5 ? %7 = 8 ? %8 = 14 ? %9 = 23 ? %10 = 39 ? %11 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.184s user 0m0.012s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:34:34 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 0 > n, 0, if( 1 > n, 1 , sum(i=0, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 1 ? %2 = 1 ? %3 = 2 ? %4 = 3 ? %5 = 5 ? %6 = 8 ? %7 = 14 ? %8 = 23 ? %9 = 39 ? %10 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.204s user 0m0.014s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:34:27 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 0 > n, 0, if( 1 > n, 1 , sum(i=0, (n-1)/2, a(n-1-2*i)*a(i) ))) a(17) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 2475 ? %2 = 1 ? %3 = 2 ? %4 = 3 ? %5 = 5 ? %6 = 8 ? %7 = 14 ? %8 = 23 ? %9 = 39 ? %10 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.253s user 0m0.072s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:34:20 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 0 > n, 0, if( 1 > n, 1 , sum(i=0, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 1 ? %2 = 1 ? %3 = 2 ? %4 = 3 ? %5 = 5 ? %6 = 8 ? %7 = 14 ? %8 = 23 ? %9 = 39 ? %10 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.013s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:33:15 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 1 ? %2 = 1 ? %3 = 2 ? %4 = 3 ? %5 = 5 ? %6 = 8 ? %7 = 14 ? %8 = 23 ? %9 = 39 ? %10 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.011s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:32:20 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 1 ? %2 = 1 ? %3 = 2 ? %4 = 3 ? %5 = 5 ? %6 = 8 ? %7 = 14 ? %8 = 23 ? %9 = 39 ? %10 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.044s user 0m0.011s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:32:14 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n, 2)*a((n-1)/2) + sum(i=1, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? %1 = 2 ? ? ? ? ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: ...,0,if(3>n,1,a(n-1)+mud(n, ^ *** Warning: unused characters: )*a((n-1)/2)+sum(i=1,(n-1)/2,a(n-1-2*i)*a(i)))). *** unknown function or error in formal parameters: a(1) ^---- *** unknown function or error in formal parameters: a(2) ^---- *** unknown function or error in formal parameters: a(3) ^---- *** unknown function or error in formal parameters: a(4) ^---- *** unknown function or error in formal parameters: a(5) ^---- *** unknown function or error in formal parameters: a(6) ^---- *** unknown function or error in formal parameters: a(7) ^---- *** unknown function or error in formal parameters: a(8) ^---- *** unknown function or error in formal parameters: a(9) ^---- *** unknown function or error in formal parameters: a(10) ^----- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:31:53 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: a(n)=if(1>n,0, ^ *** Warning: unused characters: ). *** if: incorrect type in comparison. *** unknown function or error in formal parameters: a(1) ^---- *** unknown function or error in formal parameters: a(2) ^---- *** unknown function or error in formal parameters: a(3) ^---- *** unknown function or error in formal parameters: a(4) ^---- *** unknown function or error in formal parameters: a(5) ^---- *** unknown function or error in formal parameters: a(6) ^---- *** unknown function or error in formal parameters: a(7) ^---- *** unknown function or error in formal parameters: a(8) ^---- *** unknown function or error in formal parameters: a(9) ^---- *** unknown function or error in formal parameters: a(10) ^----- Timing: real 0m0.126s user 0m0.008s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:31:39 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 1 ? %2 = 1 ? %3 = 2 ? %4 = 3 ? %5 = 5 ? %6 = 8 ? %7 = 14 ? %8 = 23 ? %9 = 39 ? %10 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.050s user 0m0.012s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:31:31 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: ...if(1>n,0,if(3>n,1,a(n-1)+ ^ *** Warning: unused characters: )). *** unknown function or error in formal parameters: mud(n,2)* *** a((n-1)/2)+sum(i=1,( ^-------------------- *** unknown function or error in formal parameters: a(1) ^---- *** unknown function or error in formal parameters: a(2) ^---- *** unknown function or error in formal parameters: a(3) ^---- *** unknown function or error in formal parameters: a(4) ^---- *** unknown function or error in formal parameters: a(5) ^---- *** unknown function or error in formal parameters: a(6) ^---- *** unknown function or error in formal parameters: a(7) ^---- *** unknown function or error in formal parameters: a(8) ^---- *** unknown function or error in formal parameters: a(9) ^---- *** unknown function or error in formal parameters: a(10) ^----- Timing: real 0m0.180s user 0m0.010s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:31:17 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 1 ? %2 = 1 ? %3 = 2 ? %4 = 3 ? %5 = 5 ? %6 = 8 ? %7 = 14 ? %8 = 23 ? %9 = 39 ? %10 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.017s user 0m0.012s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:30:49 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: ...n-1)+mud(n,2)*a((n-1)/2)+ ^ *** Warning: unused characters: )). *** sum: incorrect type in comparison. *** unknown function or error in formal parameters: a(1) ^---- *** unknown function or error in formal parameters: a(2) ^---- *** unknown function or error in formal parameters: a(3) ^---- *** unknown function or error in formal parameters: a(4) ^---- *** unknown function or error in formal parameters: a(5) ^---- *** unknown function or error in formal parameters: a(6) ^---- *** unknown function or error in formal parameters: a(7) ^---- *** unknown function or error in formal parameters: a(8) ^---- *** unknown function or error in formal parameters: a(9) ^---- *** unknown function or error in formal parameters: a(10) ^----- Timing: real 0m0.144s user 0m0.007s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:30:35 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1, (n-1)/2, a(n-1-2*i)*a(i) ))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...(n-1)+mud(n,2)*a((n-1)/2) ^ *** Warning: unused characters: )). *** sum: incorrect type in comparison. *** unknown function or error in formal parameters: a(1) ^---- *** unknown function or error in formal parameters: a(2) ^---- *** unknown function or error in formal parameters: a(3) ^---- *** unknown function or error in formal parameters: a(4) ^---- *** unknown function or error in formal parameters: a(5) ^---- *** unknown function or error in formal parameters: a(6) ^---- *** unknown function or error in formal parameters: a(7) ^---- *** unknown function or error in formal parameters: a(8) ^---- *** unknown function or error in formal parameters: a(9) ^---- *** unknown function or error in formal parameters: a(10) ^----- Timing: real 0m0.013s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:29:51 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( -1 > n * 0, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(0 n * 0, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,a(n-1-2*i)*a(i)))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 1 ? %2 = 1 ? %3 = 3 ? %4 = 4 ? %5 = 7 ? %6 = 11 ? %7 = 22 ? %8 = 35 ? %9 = 61 ? %10 = 103 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.009s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:28:53 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,a(n-1-2*i)*a(i)))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 1 ? %2 = 1 ? %3 = 2 ? %4 = 3 ? %5 = 5 ? %6 = 8 ? %7 = 14 ? %8 = 23 ? %9 = 39 ? %10 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.009s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:25:41 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 1 ? %2 = 1 ? %3 = 2 ? %4 = 3 ? %5 = 5 ? %6 = 8 ? %7 = 14 ? %8 = 23 ? %9 = 39 ? %10 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.013s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:25:19 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , $(n-1) + mud(n,2)*$((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*$(n-1-2*i)*$(i)))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: a(n)=if(1>n,0,if(3>n,1,$(n-1)+mud(n,2)*$((n ^-------------------- *** unknown function or error in formal parameters: a(1) ^---- *** unknown function or error in formal parameters: a(2) ^---- *** unknown function or error in formal parameters: a(3) ^---- *** unknown function or error in formal parameters: a(4) ^---- *** unknown function or error in formal parameters: a(5) ^---- *** unknown function or error in formal parameters: a(6) ^---- *** unknown function or error in formal parameters: a(7) ^---- *** unknown function or error in formal parameters: a(8) ^---- *** unknown function or error in formal parameters: a(9) ^---- *** unknown function or error in formal parameters: a(10) ^----- Timing: real 0m0.303s user 0m0.007s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:25:08 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , $$(n-1) + mud(n,2)*$$((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*$$(n-1-2*i)*$$(i)))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: a(n)=if(1>n,0,if(3>n,1,$$(n-1)+mud(n,2)*$$( ^-------------------- *** unknown function or error in formal parameters: a(1) ^---- *** unknown function or error in formal parameters: a(2) ^---- *** unknown function or error in formal parameters: a(3) ^---- *** unknown function or error in formal parameters: a(4) ^---- *** unknown function or error in formal parameters: a(5) ^---- *** unknown function or error in formal parameters: a(6) ^---- *** unknown function or error in formal parameters: a(7) ^---- *** unknown function or error in formal parameters: a(8) ^---- *** unknown function or error in formal parameters: a(9) ^---- *** unknown function or error in formal parameters: a(10) ^----- Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:24:01 2006 Input: mud(r,s)= r - s * floor(r / s) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %1 = 1 ? %2 = 1 ? %3 = 2 ? %4 = 3 ? %5 = 5 ? %6 = 8 ? %7 = 14 ? %8 = 23 ? %9 = 39 ? %10 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.012s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:23:43 2006 Input: mud(r,s)= r - s * floor(r / s) mud(5,13) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 5 ? ? ? %2 = 222 ? %3 = 1 ? %4 = 1 ? %5 = 2 ? %6 = 3 ? %7 = 5 ? %8 = 8 ? %9 = 14 ? %10 = 23 ? %11 = 39 ? %12 = 65 ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.010s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:23:26 2006 Input: mud(r,s)= r - s * floor(r / s) mud(5,13) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 5 ? ? ? %2 = 222 ? %3 = 1 ? %4 = 1 ? %5 = 2 ? %6 = 3 ? %7 = 5 ? %8 = 8 ? %9 = 14 ? %10 = 23 ? %11 = 39 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:22:24 2006 Input: mud(r,s)= r - s * (r / s) mud(5,13) (13/5) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 0 ? %2 = 13/5 ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 1 ? %7 = 2 ? %8 = 3 ? %9 = 5 ? %10 = 8 ? %11 = 13 ? %12 = 21 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.012s sys 0m0.002s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:22:20 2006 Input: mud(r,s)= r - s * (r / s) mud(5,13) (13/5)*5 a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 0 ? %2 = 13 ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 1 ? %7 = 2 ? %8 = 3 ? %9 = 5 ? %10 = 8 ? %11 = 13 ? %12 = 21 ? Goodbye! Errors/timing (if any): Timing: real 0m0.168s user 0m0.009s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:21:46 2006 Input: mud(r,s)= r - s * (r / s) mud(5,13) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 0 ? ? ? %2 = 222 ? %3 = 1 ? %4 = 1 ? %5 = 1 ? %6 = 2 ? %7 = 3 ? %8 = 5 ? %9 = 8 ? %10 = 13 ? %11 = 21 ? Goodbye! Errors/timing (if any): Timing: real 0m0.156s user 0m0.012s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:21:32 2006 Input: mud(r,s)= r - s*(r / s) mud(13,5) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 0 ? ? ? %2 = 222 ? %3 = 1 ? %4 = 1 ? %5 = 1 ? %6 = 2 ? %7 = 3 ? %8 = 5 ? %9 = 8 ? %10 = 13 ? %11 = 21 ? Goodbye! Errors/timing (if any): Timing: real 0m0.204s user 0m0.010s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:21:06 2006 Input: mud(r,s)= r - s*(r / s) mud(13,2) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 0 ? ? ? %2 = 222 ? %3 = 1 ? %4 = 1 ? %5 = 1 ? %6 = 2 ? %7 = 3 ? %8 = 5 ? %9 = 8 ? %10 = 13 ? %11 = 21 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.009s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:20:51 2006 Input: mud(r,s)= r - s (r / s) mud(13,2) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1/s*r ? %2 = 11 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 2 ? %7 = 5 ? %8 = 9 ? %9 = 16 ? %10 = 32 ? %11 = 60 ? %12 = 118 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:20:39 2006 Input: mud(r,s)= r - s (r / s) mud(5,2) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1/s*r ? %2 = 3 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 2 ? %7 = 5 ? %8 = 9 ? %9 = 16 ? %10 = 32 ? %11 = 60 ? %12 = 118 ? Goodbye! Errors/timing (if any): Timing: real 0m0.284s user 0m0.009s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:20:33 2006 Input: mud(r,s)= r - s (r / s) mud(5,2) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-0)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1/s*r ? %2 = 3 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 2 ? %7 = 5 ? %8 = 9 ? %9 = 16 ? %10 = 32 ? %11 = 60 ? %12 = 118 ? Goodbye! Errors/timing (if any): Timing: real 0m0.207s user 0m0.010s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:20:05 2006 Input: mud(r,s)= s (r / s) - r mud(5,2) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-0)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 2 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 49 ? %12 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.123s user 0m0.007s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:19:29 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-0)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 49 ? %12 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.138s user 0m0.010s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:19:16 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,(n-1)/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 49 ? %12 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.009s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:18:54 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 49 ? %12 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.133s user 0m0.010s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:18:43 2006 Input: mud(r,s)= s (r / s) - r; mud(7,3); a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 49 ? %12 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.293s user 0m0.010s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:18:36 2006 Input: mud(r,s)= s (r / s) - r; mud(7,3); sum(i=1,4/2,1) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %3 = 2 ? ? %4 = 222 ? %5 = 1 ? %6 = 1 ? %7 = 3 ? %8 = 6 ? %9 = 9 ? %10 = 15 ? %11 = 28 ? %12 = 49 ? %13 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:18:32 2006 Input: mud(r,s)= s (r / s) - r; mud(7,3); sum(i=1,3/2,1) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %3 = 1 ? ? %4 = 222 ? %5 = 1 ? %6 = 1 ? %7 = 3 ? %8 = 6 ? %9 = 9 ? %10 = 15 ? %11 = 28 ? %12 = 49 ? %13 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.216s user 0m0.010s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:18:27 2006 Input: mud(r,s)= s (r / s) - r; mud(7,3); sum(i=1,2,1) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %3 = 2 ? ? %4 = 222 ? %5 = 1 ? %6 = 1 ? %7 = 3 ? %8 = 6 ? %9 = 9 ? %10 = 15 ? %11 = 28 ? %12 = 49 ? %13 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.316s user 0m0.008s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:18:21 2006 Input: mud(r,s)= s (r / s) - r; mud(7,3); sum(i=1,1,1) a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %3 = 1 ? ? %4 = 222 ? %5 = 1 ? %6 = 1 ? %7 = 3 ? %8 = 6 ? %9 = 9 ? %10 = 15 ? %11 = 28 ? %12 = 49 ? %13 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:18:05 2006 Input: mud(r,s)= s (r / s) - r; mud(7,3); a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 49 ? %12 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.020s user 0m0.009s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:17:50 2006 Input: mud(r,s)= s (r / s) - r; mud(7,3); a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>17)*a(n-1-2*i)*a(i)))); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 5 ? %8 = 7 ? %9 = 9 ? %10 = 15 ? %11 = 21 ? %12 = 31 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.011s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:17:08 2006 Input: mud(r,s)= s (r / s) - r; mud(7,3); a(n)=if( 1 > n, 0, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i)))); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 49 ? %12 = 85 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.011s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:14:15 2006 Input: mud(r,s)= s (r / s) - r; mud(7,3); a(n)=if( 0 < n, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i))), 0); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 51 ? %12 = 87 ? Goodbye! Errors/timing (if any): Timing: real 0m0.142s user 0m0.009s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:14:09 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 0 < n, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i))), 0); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 51 ? %12 = 87 ? Goodbye! Errors/timing (if any): Timing: real 0m0.052s user 0m0.010s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:14:03 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 0 < n, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i))), 0); 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 51 ? %12 = 87 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.007s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:13:55 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 0 < n, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i))), 0) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 51 ? %12 = 87 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.008s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:11:02 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 0 < n, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>0)*a(n-1-2*i)*a(i))), 0) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 6 ? %8 = 9 ? %9 = 15 ? %10 = 28 ? %11 = 51 ? %12 = 87 ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.005s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:10:28 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 0 < n, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(n-1-2*i>i)*a(n-1-2*i)*a(i))), 0) 222 a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? %3 = 222 ? %4 = 1 ? %5 = 1 ? %6 = 3 ? %7 = 5 ? %8 = 8 ? %9 = 13 ? %10 = 24 ? %11 = 41 ? %12 = 69 ? Goodbye! Errors/timing (if any): Timing: real 0m0.086s user 0m0.012s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 14:09:44 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 0 < n, if( 3 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n/2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n-1,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n-1,2)*a((n-1)/2) + sum(i=1,n-1,(0 n, if( 2 > n, 1 , a(n-1) + mud(n-1,2)*a((n-1)/2) + sum(i=1,n-1,(0 n, if( 2 > n, 1 , a(n-1) + mud(n-1,2)*a((n-1)/2) + sum(i=1,n-1,(0 n, 1 , a(n-1) + mud(n-1,2)*a((n-1)/2) + sum(i=1,n-1,(0 n, 1 , a(n-1) + mud(n-1,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n-1,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n-1,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-2,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,(0 n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,(04) a(n)=if( 2 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,()*a(i)*a(n-2*i))) a(4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? %3 = 0 ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: ...*a((n-1)/2)+sum(i=1,n-1,()*a(i)*a(n-2*i))) ^----------------- *** unknown function or error in formal parameters: a(4) ^---- Timing: real 0m0.245s user 0m0.010s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:59:14 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) (3>2) a(n)=if( 2 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,()*a(i)*a(n-2*i))) a(4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? %3 = 1 ? ? ? Goodbye! Errors/timing (if any): *** unexpected character: ...*a((n-1)/2)+sum(i=1,n-1,()*a(i)*a(n-2*i))) ^----------------- *** unknown function or error in formal parameters: a(4) ^---- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:58:57 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 2 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,a(i)*a(n-2*i))) a(4) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? %3 = 32 ? Goodbye! Errors/timing (if any): Timing: real 0m0.257s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:58:49 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 2 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,a(i)*a(n-2*i))) a(5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? %3 = 98 ? Goodbye! Errors/timing (if any): Timing: real 0m0.227s user 0m0.006s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:58:22 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) a(n)=if( 2 > n, 1 , a(n-1) + mud(n,2)*a((n-1)/2) + sum(i=1,n-1,a(i)*a(n-2*i)) a(5) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? ? ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...um(i=1,n-1,a(i)*a(n-2*i)) ^ *** unknown function or error in formal parameters: a(5) ^---- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:56:33 2006 Input: mud(r,s)= s (r / s) - r mud(7,3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((-s + 1)/s)*r ? %2 = 3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.246s user 0m0.008s sys 0m0.004s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:55:51 2006 Input: ?mud Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? mud: unknown identifier ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.004s sys 0m0.009s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:55:36 2006 Input: Mod(7,3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = Mod(1, 3) ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:55:13 2006 Input: ?mod Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? mod: obsolete function For full compatibility with GP 1.39.15, type "default(compatible,3)", or set "compatible = 3" in your GPRC file. New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. ? Goodbye! Errors/timing (if any): Timing: real 0m0.332s user 0m0.004s sys 0m0.008s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:55:01 2006 Input: sum(i=1,10,i) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 55 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:54:39 2006 Input: 2*5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 10 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '128.197' ************** PARI ***************** Host 128.197.54.222 (128.197.54.222) Time: Thu Jun 22 13:53:57 2006 Input: 1+7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 8 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.009s '128.197' **************onal flag is 1, omit them altogether. x can also be a string, in this case the coefficients of the curve with matching name are looked in the elldata database if available. ? Goodbye! Errors/timing (if any): *** ellj: bad argument for modular function. Timing: real 0m0.012s user 0m0.008s sys 0m0.005s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:33:52 2005 Input: ellinit([0,a,0,b,0]) ellj([0,a,0,b,0]) ?5 ?ellj Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellj(x): elliptic j invariant of x. ? Goodbye! Errors/timing (if any): *** ellj: bad argument for modular function. Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:33:44 2005 Input: ellinit([0,a,0,b,0]); ellj([0,a,0,b,0]); ?5 ?ellj Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellj(x): elliptic j invariant of x. ? Goodbye! Errors/timing (if any): *** ellj: bad argument for modular function. Timing: real 0m0.011s user 0m0.007s sys 0m0.005s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:33:34 2005 Input: ellinit([0,a,0,b,0]) ellj([0,a,0,b,0]) ?5 ?ellj Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellj(x): elliptic j invariant of x. ? Goodbye! Errors/timing (if any): *** ellj: bad argument for modular function. Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:33:19 2005 Input: ellinit([0,a,0,b,0]) ellj(ellinit[0,a,0,b,0]) ?5 ?ellj Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellj(x): elliptic j invariant of x. ? Goodbye! Errors/timing (if any): *** expected character: ']' instead of: ellj(ellinit[0,a,0,b,0]) ^-------- Timing: real 0m0.022s user 0m0.007s sys 0m0.008s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:33:08 2005 Input: ellinit([0,a,0,b,0]) ellj([0,a,0,b,0]) ?5 ?ellj Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellj(x): elliptic j invariant of x. ? Goodbye! Errors/timing (if any): *** ellj: bad argument for modular function. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:32:57 2005 Input: ellinit([0,a,0,b,0]) ellj([0,a,0,b,0]) ?5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Goodbye! Errors/timing (if any): *** ellj: bad argument for modular function. Timing: real 0m0.012s user 0m0.004s sys 0m0.008s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:32:46 2005 Input: ellinit([0,a,0,b,0]) ellj([0,a,0,b,0]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? ? Goodbye! Errors/timing (if any): *** ellj: bad argument for modular function. Timing: real 0m0.011s user 0m0.003s sys 0m0.009s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:32:19 2005 Input: ?ellinit ellinit([0,a,0,b,0]) ellj([0,a,0,b,0]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6] defining the curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6, gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. x can also be a string, in this case the coefficients of the curve with matching name are looked in the elldata database if available. ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? ? Goodbye! Errors/timing (if any): *** ellj: bad argument for modular function. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:31:48 2005 Input: ?ellinit ellinit([0,a,0,b,0]) ?ellj Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6] defining the curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6, gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. x can also be a string, in this case the coefficients of the curve with matching name are looked in the elldata database if available. ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? ellj(x): elliptic j invariant of x. ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:31:36 2005 Input: ?ellinit ellinit([0,a,0,b,0]) ?5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6] defining the curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6, gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. x can also be a string, in this case the coefficients of the curve with matching name are looked in the elldata database if available. ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:31:20 2005 Input: ?ellinit ellinit([0,a,0,b,0]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6] defining the curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6, gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. x can also be a string, in this case the coefficients of the curve with matching name are looked in the elldata database if available. ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:31:00 2005 Input: ?5 ?ellinit ellinit([0,a,0,b,0]) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6] defining the curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6, gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. x can also be a string, in this case the coefficients of the curve with matching name are looked in the elldata database if available. ? %1 = [0, a, 0, b, 0, 4*a, 2*b, 0, -b^2, 16*a^2 - 48*b, -64*a^3 + 288*b*a, 16*b^2*a^2 - 64*b^3, (256*a^6 - 2304*b*a^4 + 6912*b^2*a^2 - 6912*b^3)/(b^2*a^2 - 4*b^3), 0, 0, 0, 0, 0, 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.104s user 0m0.007s sys 0m0.005s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:30:08 2005 Input: ?5 ?ellinit Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? ellinit(x,{flag=0}): x being the vector [a1,a2,a3,a4,a6] defining the curve Y^2 + a1.XY + a3.Y = X^3 + a2.X^2 + a4.X + a6, gives the vector: [a1,a2,a3,a4,a6,b2,b4,b6,b8,c4,c6,delta,j,[e1,e2,e3],w1,w2,eta1,eta2,area]. If the curve is defined over a p-adic field, the last six components are replaced by root,u^2,u,q,w,0. If optional flag is 1, omit them altogether. x can also be a string, in this case the coefficients of the curve with matching name are looked in the elldata database if available. ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '60.44.3' ************** PARI ***************** Host 60.44.34.252 (60.44.34.252) Time: Thu Nov 3 10:29:59 2005 Input: ?5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellidentify ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsearch ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Goodbye! Errors/timing (if any): Timing: real 0m0.332s user 0m0.008s sys 0m0.005s '62.152.' ************** PARI ***************** Host 62.152.82.115 (62.152.82.115) Time: Wed Nov 2 18:34:05 2005 Input: fibonacci(1000000) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1953282128707757731632014947596256332443542996591873396953405194571625257887015694766641987634150146128879524335220236084625510912019560233744015438115196636156919962125642894303370113827800638002767411527927466669865578379318822832061271497583230334854893489572599230722912901928209264331627521730861460017912582042699659936020959339202005184862028402447343139811367418720203868480175318538621112878108240617741383293554561687606454065125954718029126547942894036981659206361019359291352135410376799082940320155702716115395031975973247782162957631629653356694777663285062345245593460647575025935813443457816767646258788590113727299073729478511448089572456191503507025589529116868550008802013233458747217794781447546792016090170642585629359747546532757575740077432034913428785189795354304734560307765078938767286539166799232817449361991523768149557632085371047859706188438731530582395627560879063107819004975169594709736713891745704555202135123350794403360712030504144685221041565037321067932275625864751191461141736034968121738023422478608029202109319249649040983239706683247054441763512526732455275419501683845206023007394959854279298297831204382115757645787692495583351402522152720662441809003259380753628491796680952971185071913798336788737704599136393339558142120369902616179721132509184002305532760710431647819097430043464779336328760146999612802392582947155731668894333945542929287187748774789204296166356536610796023919702109728472966709427334586344798048633944635211654971507261342768205479320931750798880101304160279825063541823440345587422367012826663569346112946131231283890600365473276602456931515185001832848315064548002997893598516123707404615822935444070174833951457586954749175026454212636426222472060048855462589961190475892101224280542898621594646662478564373572217775549876087685912030118551635668902010344639983977326638889036507841618070915452529927597352139574154777291460087943143391560604458251078235116627189263792331301464388059787946844487906057678629746098962742666356968247429338674020743655942605794479071193052258931590719386545525880429139747140181849169733838138446154843063123649290835584278078456131936457559117221369463381803116003078962116686528959537784364644023825163624497181973854441495631317140028503389282227413460301809422483721632185471727045281382407842563874736524914111808078386650633994537623920670051339187333107136069698189628284763245423299306272870457991293245741167533902274499963096566680922262516468582544557851349824144127261240158157538180984666671450069888391785518008943701890257219924852087429155602619177522812466062899678716652967848726848490504132849729771268801163997837643428020245225155010224035416988518537501584673881194047619720619603126534496759917893244478170702904446589571950228809157793897642423751814020998999581612314779022957811001686701867386198617971381398546662819695485537407073562286161655394280764184080921204793281668300598450478792940635631809747975515203509468276591874161090763750690276529436756153980326138890194485941004529227541880945735620795421899662963441346396955980991375010053760259440113617219176881147264713549808756023398475901193275473892575308479804907335837236726817033732665046629357765[+++] ? Goodbye! Errors/timing (if any): Timing: real 0m2.151s user 0m2.001s sys 0m0.149s '62.152.' ************** PARI ***************** Host 62.152.82.115 (62.152.82.115) Time: Wed Nov 2 18:33:35 2005 Input: fibonacci(10000000) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 4843 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.073s user 0m20.823s sys 0m0.192s '62.152.' ************** PARI ***************** Host 62.152.82.115 (62.152.82.115) Time: Wed Nov 2 18:32:12 2005 Input: fibonacci(30) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 832040 ? Goodbye! Errors/timing (if any): Timing: real 0m0.094s user 0m0.008s sys 0m0.003s '64.95.1' ************** PARI ***************** Host 64.95.191.16 (64.95.191.16) Time: Wed Nov 2 15:01:18 2005 Input: 5 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 5 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '64.95.1' ************** PARI ***************** Host 64.95.191.16 (64.95.191.16) Time: Wed Nov 2 15:01:10 2005 Input: 3 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '64.95.1' ************** PARI ***************** Host 64.95.191.16 (64.95.191.16) Time: Wed Nov 2 15:00:53 2005 Input: 3^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 9 ? Goodbye! Errors/timing (if any): Timing: real 0m0.062s user 0m0.007s sys 0m0.005s '64.95.1' ************** PARI ***************** Host 64.95.191.16 (64.95.191.16) Time: Wed Nov 2 15:00:43 2005 Input: 3**2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** unexpected character: 3**2 ^-- Timing: real 0m0.012s user 0m0.005s sys 0m0.008s '67.127.' ************** PARI ***************** Host 67.127.56.4 (67.127.56.4) Time: Wed Nov 2 01:15:24 2005 Input: collatz(x0,n)= { local(x,i,ans); x=x0; ans=[x]; for(i=1,n, x=if(Mod(x,2)==Mod(0,2), x/2, (3*x+1)/2); ans =concat(ans,x) ); ans } collatz(19,16) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = [19, 29, 44, 22, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.071s user 0m0.005s sys 0m0.006s '219.88.' ************** PARI ***************** Host 219.88.20.125 (219.88.20.125) Time: Tue Nov 1 21:45:58 2005 Input: 6^2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 36 ? Goodbye! Errors/timing (if any): Timing: real 0m0.055s user 0m0.006s sys 0m0.005s '80.139.' ************** PARI ***************** Host 80.139.137.195 (80.139.137.195) Time: Tue Nov 1 19:50:14 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '152.6.1' ************** PARI ***************** Host 152.6.18.163 (152.6.18.163) Time: Tue Nov 1 16:26:23 2005 Input: ? Mod(3,726377359)^363188679 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.123 (165.95.7.123) Time: Tue Nov 1 16:16:41 2005 Input: 123456789999*1234567654321 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 152415759639065721935679 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.123 (165.95.7.123) Time: Tue Nov 1 16:15:11 2005 Input: 123456789999*1234567654321 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 152415759639065721935679 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '165.95.' ************** PARI ***************** Host 165.95.7.123 (165.95.7.123) Time: Tue Nov 1 16:14:34 2005 Input: 12345678/78 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2057613/13 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '165.95.' ************** PARI ***************** Host 165.95.7.123 (165.95.7.123) Time: Tue Nov 1 16:14:06 2005 Input: 12345678 mod 78 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = mod78 ? Goodbye! Errors/timing (if any): *** Warning: unused characters: mod78. Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '165.95.' ************** PARI ***************** Host 165.95.7.123 (165.95.7.123) Time: Tue Nov 1 16:13:24 2005 Input: 12345678*12345678 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 152415765279684 ? Goodbye! Errors/timing (if any): Timing: real 0m0.343s user 0m0.004s sys 0m0.006s '87.68.2' ************** PARI ***************** Host 87.68.2.21 (87.68.2.21) Time: Mon Oct 31 17:08:35 2005 Input: 123 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 123 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '81.170.' ************** PARI ***************** Host 81.170.166.87 (81.170.166.87) Time: Mon Oct 31 15:14:18 2005 Input: 3+4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 7 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '84.159.' ************** PARI ***************** Host 84.159.131.39 (84.159.131.39) Time: Mon Oct 31 12:55:02 2005 Input: vector(77,i,lift(Mod(i^2,77))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 4, 9, 16, 25, 36, 49, 64, 4, 23, 44, 67, 15, 42, 71, 25, 58, 16, 53, 15, 56, 22, 67, 37, 9, 60, 36, 14, 71, 53, 37, 23, 11, 1, 70, 64, 60, 58, 58, 60, 64, 70, 1, 11, 23, 37, 53, 71, 14, 36, 60, 9, 37, 67, 22, 56, 15, 53, 16, 58, 25, 71, 42, 15, 67, 44, 23, 4, 64, 49, 36, 25, 16, 9, 4, 1, 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.003s sys 0m0.009s '84.159.' ************** PARI ***************** Host 84.159.131.39 (84.159.131.39) Time: Mon Oct 31 12:54:13 2005 Input: vector(143,i,lift(Mod(i^2,143))) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 1, 26, 53, 82, 113, 3, 38, 75, 114, 12, 55, 100, 4, 53, 104, 14, 69, 126, 42, 103, 23, 88, 12, 81, 9, 82, 14, 91, 27, 108, 48, 133, 77, 23, 114, 64, 16, 113, 69, 27, 130, 92, 56, 22, 133, 103, 75, 49, 25, 3, 126, 108, 92, 78, 66, 56, 48, 42, 38, 36, 36, 38, 42, 48, 56, 66, 78, 92, 108, 126, 3, 25, 49, 75, 103, 133, 22, 56, 92, 130, 27, 69, 113, 16, 64, 114, 23, 77, 133, 48, 108, 27, 91, 14, 82, 9, 81, 12, 88, 23, 103, 42, 126, 69, 14, 104, 53, 4, 100, 55, 12, 114, 75, 38, 3, 113, 82, 53, 26, 1, 121, 100, 81, 64, 49, 36, 25, 16, 9, 4, 1, 0] ? Goodbye! Errors/timing (if any): Timing: real 0m0.049s user 0m0.008s sys 0m0.004s '84.159.' ************** PARI ***************** Host 84.159.131.39 (84.159.131.39) Time: Mon Oct 31 12:53:38 2005 Input: vector(300,i,i) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %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, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300] ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '194.212' ************** PARI ***************** Host 194.212.28.14 (194.212.28.14) Time: Mon Oct 31 08:14:10 2005 Input: (x ^ x)' Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** gpow: need integer exponent if series valuation != 0. Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '194.212' ************** PARI ***************** Host 194.212.28.14 (194.212.28.14) Time: Mon Oct 31 08:13:59 2005 Input: (x ^ 3)' Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3*x^2 ? Goodbye! Errors/timing (if any): Timing: real 0m0.014s user 0m0.006s sys 0m0.007s '194.212' ************** PARI ***************** Host 194.212.28.14 (194.212.28.14) Time: Mon Oct 31 08:13:45 2005 Input: (x ^ x)' Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** gpow: need integer exponent if series valuation != 0. Timing: real 0m0.014s user 0m0.008s sys 0m0.004s '194.212' ************** PARI ***************** Host 194.212.28.14 (194.212.28.14) Time: Mon Oct 31 08:13:03 2005 Input: 11! Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 39916800 ? Goodbye! Errors/timing (if any): Timing: real 0m0.373s user 0m0.005s sys 0m0.010s '200.125' ************** PARI ***************** Host 200.125.53.247 (200.125.53.247) Time: Sun Oct 30 19:26:28 2005 Input: p=3*x^5-4*x^4+32*x-15*x^2-1234 q=167*x^2-166 bezout(p,q) u+v Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3*x^5 - 4*x^4 - 15*x^2 + 32*x - 1234 ? %2 = 167*x^2 - 166 ? %3 = [-1135391672677/50932240912538776*x - 20342098410005/25466120456269388, 20396257593/50932240912538776*x^4 + 351829412483/25466120456269388*x^3 - 477098827903/25466120456269388*x^2 + 597464011103/50932240912538776*x - 2192596495923/25466120456269388, 1] ? %4 = u + v ? ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '200.125' ************** PARI ***************** Host 200.125.53.247 (200.125.53.247) Time: Sun Oct 30 19:25:46 2005 Input: p=3*x^5-4*x^4+32*x-15*x^2-1234 q=167*x^2-166 bezout(p,q) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 3*x^5 - 4*x^4 - 15*x^2 + 32*x - 1234 ? %2 = 167*x^2 - 166 ? %3 = [-1135391672677/50932240912538776*x - 20342098410005/25466120456269388, 20396257593/50932240912538776*x^4 + 351829412483/25466120456269388*x^3 - 477098827903/25466120456269388*x^2 + 597464011103/50932240912538776*x - 2192596495923/25466120456269388, 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.005s '200.125' ************** PARI ***************** Host 200.125.53.247 (200.125.53.247) Time: Sun Oct 30 19:25:04 2005 Input: p=3*x^5-4*x^4+32*x-15*x2-1234 q=167*x^2-166 bezout(p,q) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? %1 = 3*x^5 - 4*x^4 + 32*x + (-15*x2 - 1234) ? %2 = 167*x^2 - 166 ? %3 = [-4541566690708/(29225696761575*x2^2 + 4824002233222500*x2 + 198904970921503804)*x + ((-1948379784105*x2 - 160800074440750)/(29225696761575*x2^2 + 4824002233222500*x2 + 198904970921503804)), 81585030372/(29225696761575*x2^2 + 4824002233222500*x2 + 198904970921503804)*x^4 + ((35000834445*x2 + 2779844051254)/(29225696761575*x2^2 + 4824002233222500*x2 + 198904970921503804))*x^3 + ((-46667779260*x2 - 3770402291744)/(29225696761575*x2^2 + 4824002233222500*x2 + 198904970921503804))*x^2 + ((34791248610*x2 + 2763198278492)/(29225696761575*x2^2 + 4824002233222500*x2 + 198904970921503804))*x + ((-46388331480*x2 - 2877584708544)/(29225696761575*x2^2 + 4824002233222500*x2 + 198904970921503804)), 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.057s user 0m0.007s sys 0m0.007s '200.125' ************** PARI ***************** Host 200.125.53.247 (200.125.53.247) Time: Sun Oct 30 19:24:20 2005 Input: bezout(p,q) p=3*x^5-4*x^4+32*x-15*x2-1234 q=167*x^2-166 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [0, 1/q, 1] ? %2 = 3*x^5 - 4*x^4 + 32*x + (-15*x2 - 1234) ? %3 = 167*x^2 - 166 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.007s '200.187' ************** PARI ***************** Host 200.187.66.234 (200.187.66.234) Time: Sun Oct 30 18:23:13 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.003s sys 0m0.008s '129.234' ************** PARI ***************** Host 129.234.4.1 (129.234.4.1) Time: Sun Oct 30 15:42:40 2005 Input: factor(268) 268/67 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 2] [67 1] ? ? %2 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.048s user 0m0.005s sys 0m0.006s '129.234' ************** PARI ***************** Host 129.234.4.1 (129.234.4.1) Time: Sun Oct 30 15:42:16 2005 Input: factor(268) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 2] [67 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '129.234' ************** PARI ***************** Host 129.234.4.1 (129.234.4.1) Time: Sun Oct 30 15:41:17 2005 Input: factor(456) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [2 3] [3 1] [19 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.046s user 0m0.007s sys 0m0.004s '129.234' ************** PARI ***************** Host 129.234.4.1 (129.234.4.1) Time: Sun Oct 30 15:41:04 2005 Input: 3*6 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 18 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '70.190.' ************** PARI ***************** Host 70.190.207.146 (70.190.207.146) Time: Sun Oct 30 15:32:55 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [PARI] or [MAGMA]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '70.190.' ************** PARI ***************** Host 70.190.207.146 (70.190.207.146) Time: Sun Oct 30 15:32:47 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [PARI] or [MAGMA]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '70.190.' ************** PARI ***************** Host 70.190.207.146 (70.190.207.146) Time: Sun Oct 30 15:32:43 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [PARI] or [MAGMA]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.007s sys 0m0.004s '83.177.' ************** PARI ***************** Host 83.177.200.111 (83.177.200.111) Time: Sun Oct 30 14:29:14 2005 Input: 2*2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.273s user 0m0.004s sys 0m0.007s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:33:22 2005 Input: vector(200,n,n^3+(n+1)^3+(n+2)^3-(n+3)^3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-28, -26, 0, 62, 172, 342, 584, 910, 1332, 1862, 2512, 3294, 4220, 5302, 6552, 7982, 9604, 11430, 13472, 15742, 18252, 21014, 24040, 27342, 30932, 34822, 39024, 43550, 48412, 53622, 59192, 65134, 71460, 78182, 85312, 92862, 100844, 109270, 118152, 127502, 137332, 147654, 158480, 169822, 181692, 194102, 207064, 220590, 234692, 249382, 264672, 280574, 297100, 314262, 332072, 350542, 369684, 389510, 410032, 431262, 453212, 475894, 499320, 523502, 548452, 574182, 600704, 628030, 656172, 685142, 714952, 745614, 777140, 809542, 842832, 877022, 912124, 948150, 985112, 1023022, 1061892, 1101734, 1142560, 1184382, 1227212, 1271062, 1315944, 1361870, 1408852, 1456902, 1506032, 1556254, 1607580, 1660022, 1713592, 1768302, 1824164, 1881190, 1939392, 1998782, 2059372, 2121174, 2184200, 2248462, 2313972, 2380742, 2448784, 2518110, 2588732, 2660662, 2733912, 2808494, 2884420, 2961702, 3040352, 3120382, 3201804, 3284630, 3368872, 3454542, 3541652, 3630214, 3720240, 3811742, 3904732, 3999222, 4095224, 4192750, 4291812, 4392422, 4494592, 4598334, 4703660, 4810582, 4919112, 5029262, 5141044, 5254470, 5369552, 5486302, 5604732, 5724854, 5846680, 5970222, 6095492, 6222502, 6351264, 6481790, 6614092, 6748182, 6884072, 7021774, 7161300, 7302662, 7445872, 7590942, 7737884, 7886710, 8037432, 8190062, 8344612, 8501094, 8659520, 8819902, 8982252, 9146582, 9312904, 9481230, 9651572, 9823942, 9998352, 10174814, 10353340, 10533942, 10716632, 10901422, 11088324, 11277350, 11468512, 11661822, 11857292, 12054934, 12254760, 12456782, 12661012, 12867462, 13076144, 13287070, 13500252, 13715702, 13933432, 14153454, 14375780, 14600422, 14827392, 15056702, 15288364, 15522390, 15758792, 15997582] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:32:57 2005 Input: vector(200,n,n^3+(n+1)^3-(n+2)^3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-18, -29, -34, -27, -2, 47, 126, 241, 398, 603, 862, 1181, 1566, 2023, 2558, 3177, 3886, 4691, 5598, 6613, 7742, 8991, 10366, 11873, 13518, 15307, 17246, 19341, 21598, 24023, 26622, 29401, 32366, 35523, 38878, 42437, 46206, 50191, 54398, 58833, 63502, 68411, 73566, 78973, 84638, 90567, 96766, 103241, 109998, 117043, 124382, 132021, 139966, 148223, 156798, 165697, 174926, 184491, 194398, 204653, 215262, 226231, 237566, 249273, 261358, 273827, 286686, 299941, 313598, 327663, 342142, 357041, 372366, 388123, 404318, 420957, 438046, 455591, 473598, 492073, 511022, 530451, 550366, 570773, 591678, 613087, 635006, 657441, 680398, 703883, 727902, 752461, 777566, 803223, 829438, 856217, 883566, 911491, 939998, 969093, 998782, 1029071, 1059966, 1091473, 1123598, 1156347, 1189726, 1223741, 1258398, 1293703, 1329662, 1366281, 1403566, 1441523, 1480158, 1519477, 1559486, 1600191, 1641598, 1683713, 1726542, 1770091, 1814366, 1859373, 1905118, 1951607, 1998846, 2046841, 2095598, 2145123, 2195422, 2246501, 2298366, 2351023, 2404478, 2458737, 2513806, 2569691, 2626398, 2683933, 2742302, 2801511, 2861566, 2922473, 2984238, 3046867, 3110366, 3174741, 3239998, 3306143, 3373182, 3441121, 3509966, 3579723, 3650398, 3721997, 3794526, 3867991, 3942398, 4017753, 4094062, 4171331, 4249566, 4328773, 4408958, 4490127, 4572286, 4655441, 4739598, 4824763, 4910942, 4998141, 5086366, 5175623, 5265918, 5357257, 5449646, 5543091, 5637598, 5733173, 5829822, 5927551, 6026366, 6126273, 6227278, 6329387, 6432606, 6536941, 6642398, 6748983, 6856702, 6965561, 7075566, 7186723, 7299038, 7412517, 7527166, 7642991, 7759998, 7878193] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:32:38 2005 Input: vector(200,n,n^3+(n+1)^3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [9, 35, 91, 189, 341, 559, 855, 1241, 1729, 2331, 3059, 3925, 4941, 6119, 7471, 9009, 10745, 12691, 14859, 17261, 19909, 22815, 25991, 29449, 33201, 37259, 41635, 46341, 51389, 56791, 62559, 68705, 75241, 82179, 89531, 97309, 105525, 114191, 123319, 132921, 143009, 153595, 164691, 176309, 188461, 201159, 214415, 228241, 242649, 257651, 273259, 289485, 306341, 323839, 341991, 360809, 380305, 400491, 421379, 442981, 465309, 488375, 512191, 536769, 562121, 588259, 615195, 642941, 671509, 700911, 731159, 762265, 794241, 827099, 860851, 895509, 931085, 967591, 1005039, 1043441, 1082809, 1123155, 1164491, 1206829, 1250181, 1294559, 1339975, 1386441, 1433969, 1482571, 1532259, 1583045, 1634941, 1687959, 1742111, 1797409, 1853865, 1911491, 1970299, 2030301, 2091509, 2153935, 2217591, 2282489, 2348641, 2416059, 2484755, 2554741, 2626029, 2698631, 2772559, 2847825, 2924441, 3002419, 3081771, 3162509, 3244645, 3328191, 3413159, 3499561, 3587409, 3676715, 3767491, 3859749, 3953501, 4048759, 4145535, 4243841, 4343689, 4445091, 4548059, 4652605, 4758741, 4866479, 4975831, 5086809, 5199425, 5313691, 5429619, 5547221, 5666509, 5787495, 5910191, 6034609, 6160761, 6288659, 6418315, 6549741, 6682949, 6817951, 6954759, 7093385, 7233841, 7376139, 7520291, 7666309, 7814205, 7963991, 8115679, 8269281, 8424809, 8582275, 8741691, 8903069, 9066421, 9231759, 9399095, 9568441, 9739809, 9913211, 10088659, 10266165, 10445741, 10627399, 10811151, 10997009, 11184985, 11375091, 11567339, 11761741, 11958309, 12157055, 12357991, 12561129, 12766481, 12974059, 13183875, 13395941, 13610269, 13826871, 14045759, 14266945, 14490441, 14716259, 14944411, 15174909, 15407765, 15642991, 15880599, 16120601] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:31:25 2005 Input: vector(200,n,3*(n^3)-(n+1)^3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [-5, -3, 17, 67, 159, 305, 517, 807, 1187, 1669, 2265, 2987, 3847, 4857, 6029, 7375, 8907, 10637, 12577, 14739, 17135, 19777, 22677, 25847, 29299, 33045, 37097, 41467, 46167, 51209, 56605, 62367, 68507, 75037, 81969, 89315, 97087, 105297, 113957, 123079, 132675, 142757, 153337, 164427, 176039, 188185, 200877, 214127, 227947, 242349, 257345, 272947, 289167, 306017, 323509, 341655, 360467, 379957, 400137, 421019, 442615, 464937, 487997, 511807, 536379, 561725, 587857, 614787, 642527, 671089, 700485, 730727, 761827, 793797, 826649, 860395, 895047, 930617, 967117, 1004559, 1042955, 1082317, 1122657, 1163987, 1206319, 1249665, 1294037, 1339447, 1385907, 1433429, 1482025, 1531707, 1582487, 1634377, 1687389, 1741535, 1796827, 1853277, 1910897, 1969699, 2029695, 2090897, 2153317, 2216967, 2281859, 2348005, 2415417, 2484107, 2554087, 2625369, 2697965, 2771887, 2847147, 2923757, 3001729, 3081075, 3161807, 3243937, 3327477, 3412439, 3498835, 3586677, 3675977, 3766747, 3858999, 3952745, 4047997, 4144767, 4243067, 4342909, 4444305, 4547267, 4651807, 4757937, 4865669, 4975015, 5085987, 5198597, 5312857, 5428779, 5546375, 5665657, 5786637, 5909327, 6033739, 6159885, 6287777, 6417427, 6548847, 6682049, 6817045, 6953847, 7092467, 7232917, 7375209, 7519355, 7665367, 7813257, 7963037, 8114719, 8268315, 8423837, 8581297, 8740707, 8902079, 9065425, 9230757, 9398087, 9567427, 9738789, 9912185, 10087627, 10265127, 10444697, 10626349, 10810095, 10995947, 11183917, 11374017, 11566259, 11760655, 11957217, 12155957, 12356887, 12560019, 12765365, 12972937, 13182747, 13394807, 13609129, 13825725, 14044607, 14265787, 14489277, 14715089, 14943235, 15173727, 15406577, 15641797, 15879399] ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:31:07 2005 Input: vector(200,n,3n^3-(n+1)^3) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: vector(200,n,3n^3-(n+1)^3) ^------------ Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:30:40 2005 Input: vector(200,i,i^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 5041, 5184, 5329, 5476, 5625, 5776, 5929, 6084, 6241, 6400, 6561, 6724, 6889, 7056, 7225, 7396, 7569, 7744, 7921, 8100, 8281, 8464, 8649, 8836, 9025, 9216, 9409, 9604, 9801, 10000, 10201, 10404, 10609, 10816, 11025, 11236, 11449, 11664, 11881, 12100, 12321, 12544, 12769, 12996, 13225, 13456, 13689, 13924, 14161, 14400, 14641, 14884, 15129, 15376, 15625, 15876, 16129, 16384, 16641, 16900, 17161, 17424, 17689, 17956, 18225, 18496, 18769, 19044, 19321, 19600, 19881, 20164, 20449, 20736, 21025, 21316, 21609, 21904, 22201, 22500, 22801, 23104, 23409, 23716, 24025, 24336, 24649, 24964, 25281, 25600, 25921, 26244, 26569, 26896, 27225, 27556, 27889, 28224, 28561, 28900, 29241, 29584, 29929, 30276, 30625, 30976, 31329, 31684, 32041, 32400, 32761, 33124, 33489, 33856, 34225, 34596, 34969, 35344, 35721, 36100, 36481, 36864, 37249, 37636, 38025, 38416, 38809, 39204, 39601, 40000] ? Goodbye! Errors/timing (if any): Timing: real 0m0.032s user 0m0.006s sys 0m0.008s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:30:29 2005 Input: vector(i,300,i^2) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** variable name expected: vector(i,300,i^2) ^-------- Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:04:39 2005 Input: 2^4+3^4+4^4 5^4 5^4+3^4+4^4 6^4 5^4+6^4+4^4 7^4 5^4+6^4+7^4 8^4 8^4+6^4+7^4 9^4 8^4+9^4+7^4 10^4 8^4+9^4+10^4 11^4 11^4+9^4+10^4 12^4 11^4+12^4+10^4 13^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 353 ? %2 = 625 ? %3 = 962 ? %4 = 1296 ? %5 = 2177 ? %6 = 2401 ? %7 = 4322 ? %8 = 4096 ? %9 = 7793 ? %10 = 6561 ? %11 = 13058 ? %12 = 10000 ? %13 = 20657 ? %14 = 14641 ? %15 = 31202 ? %16 = 20736 ? %17 = 45377 ? %18 = 28561 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:03:15 2005 Input: 2^4+3^4+4^4 5^4 2^4+3^4+4^4 6^4 6^4+3^4+4^4 7^4 6^4+7^4+4^4 8^4 6^4+7^4+8^4 9^4 6^4+7^4+8^4 10^4 10^4+7^4+8^4 11^4 10^4+11^4+8^4 12^4 10^4+11^4+12^4 13^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 353 ? %2 = 625 ? %3 = 353 ? %4 = 1296 ? %5 = 1633 ? %6 = 2401 ? %7 = 3953 ? %8 = 4096 ? %9 = 7793 ? %10 = 6561 ? %11 = 7793 ? %12 = 10000 ? %13 = 16497 ? %14 = 14641 ? %15 = 28737 ? %16 = 20736 ? %17 = 45377 ? %18 = 28561 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:57:17 2005 Input: 1^4+2^4+3^4+4^4 5^4 5^4+2^4+3^4+4^4 6^4 5^4+6^4+3^4+4^4 7^4 5^4+6^4+7^4+4^4 8^4 5^4+6^4+7^4+8^4 9^4 9^4+6^4+7^4+8^4 10^4 9^4+10^4+7^4+8^4 11^4 9^4+10^4+11^4+8^4 12^4 9^4+10^4+11^4+12^4 13^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 354 ? %2 = 625 ? %3 = 978 ? %4 = 1296 ? %5 = 2258 ? %6 = 2401 ? %7 = 4578 ? %8 = 4096 ? %9 = 8418 ? %10 = 6561 ? %11 = 14354 ? %12 = 10000 ? %13 = 23058 ? %14 = 14641 ? %15 = 35298 ? %16 = 20736 ? %17 = 51938 ? %18 = 28561 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:56:42 2005 Input: 1^4+2^4+3^4+4^4 5^4+2^4+3^4+4^4 5^4+6^4+3^4+4^4 5^4+6^4+7^4+4^4 5^4+6^4+7^4+8^4 9^4+6^4+7^4+8^4 9^4+10^4+7^4+8^4 9^4+10^4+11^4+8^4 9^4+10^4+11^4+12^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 354 ? %2 = 978 ? %3 = 2258 ? %4 = 4578 ? %5 = 8418 ? %6 = 14354 ? %7 = 23058 ? %8 = 35298 ? %9 = 51938 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:55:06 2005 Input: 7^4 7^4-6^4 7^4-6^4-5^4 7^4-6^4-5^4-4^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 2401 ? %2 = 1105 ? %3 = 480 ? %4 = 224 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:54:42 2005 Input: 1^4 2^4 3^4 4^4 5^4 6^4 7^4-6^4-5^4-4^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 16 ? %3 = 81 ? %4 = 256 ? %5 = 625 ? %6 = 1296 ? %7 = 224 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '141.70.' ************** PARI ***************** Host 141.70.97.51 (141.70.97.51) Time: Sun Oct 30 01:54:14 2005 Input: 1^4 2^4 3^4 4^4 5^4 6^4 7^4 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1 ? %2 = 16 ? %3 = 81 ? %4 = 256 ? %5 = 625 ? %6 = 1296 ? %7 = 2401 ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.006s sys 0m0.006s '213.103' ************** PARI ***************** Host 213.103.18.222 (213.103.18.222) Time: Sat Oct 29 14:07:47 2005 Input: solve(-2*a*m^3+2*m*b+b^2=0,m); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors/timing (if any): *** variable name expected: solve(-2*a*m^3+2*m*b+b^2=0 ^-------------------- Timing: real 0m0.012s user 0m0.008s sys 0m0.003s '217.185' ************** PARI ***************** Host 217.185.17.206 (217.185.17.206) Time: Sat Oct 29 13:34:50 2005 Input: 2*7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 14 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '217.185' ************** PARI ***************** Host 217.185.17.206 (217.185.17.206) Time: Sat Oct 29 13:34:29 2005 Input: 2*7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 14 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.004s sys 0m0.007s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Sat Oct 29 09:11:35 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*35); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*37; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 350M up to 370M (350000041 to 370000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m13.542s user 0m13.377s sys 0m0.154s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Sat Oct 29 09:11:08 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*32); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*35; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 320M up to 350M (320000071 to 350000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m20.350s user 0m20.211s sys 0m0.135s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Sat Oct 29 09:10:30 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*29); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*32; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 290M up to 320M (290000011 to 320000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m19.811s user 0m19.646s sys 0m0.154s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Sat Oct 29 09:09:47 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*27); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*29; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 270M up to 290M (270000001 to 290000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m13.600s user 0m13.111s sys 0m0.151s '212.45.' ************** PARI ***************** Host 212.45.53.119 (212.45.53.119) Time: Sat Oct 29 06:25:44 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [PARI] or [MAGMA]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.007s sys 0m0.007s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Fri Oct 28 22:45:55 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*25); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*27; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 249M up to 270M (249999991 to 270000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m13.669s user 0m13.528s sys 0m0.120s '209.151' ************** PARI ***************** Host 209.151.52.198 (209.151.52.198) Time: Fri Oct 28 21:06:22 2005 Input: Input: n=5141; e=101; print(Mod(4353^e,n)); print(Mod(4916^e,n)); print(Mod(4782^e,n)); print(Mod(633^e,n)); print(Mod(1384^e,n)); print(Mod(2663^e,n)); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? Mod(32934826725095613297650367798536868278895726509807460817487277759608811433657897325109598015465667113576815760295342157465690865883671580571528373562341163501552908290801059281241273195327277414596282222128658903974817681588637051855988463568443681092665825337478901665957512343307497983072651012591357660195148107759135363848596164134752674435781263755053835816580353, n) ? Mod(7125236691720019811972621763757285069508293281694286340603158156513148749597061823801628476292236304188416051780109645533186469892188389040103366762990567355781654172817516987152634115478053815800143105122142424522036003706882921423667630782732874795090510621283646115860176213427718505021728661583383593898687921848871698463440540699396918012398760676311420985419199676416, n) ? Mod(437085852688935926694040156215609890911153230942624564810073376193707327179510331362170829093282966225203535045807844221900309866673869039881496347671760656806779423046479302330694718330798094491072052897662043385376137318526408318616055958301609767214314864249344491772097304218389779085701677517721416297543040565356151451241947041198269874789297371197230455950285996032, n) ? Mod(8745299991617073504836095625203774081174229749065853213407147050914961525069574313829081262867196617660568375733435339731852548818981687228627094610316730976123046653454858532533107501060884183812983645740156396548428890988691554166109447280454854883699359095762335046652476123804633, n) ? Mod(179781542459592171893652465847128382821294900171717231185271681248183507255397556076265151828051141633484795642957285554462514186713950543252964012034026042732568813568239741506041582277679103018794040820178920492312539241809532155904591164112337912071722255691038879212409208810328280759680198100655542179651475472384, n) ? Mod(9172501898836976140140930134444777245626056567762624714900667729737173186238812820584989028781006273752379606216950742943789775732099628060173218685167722843536154236709061616560577788535256254037012939923231832860489335831558048868402176396830633612207844155210617597389999791566828285129622260714607739581528769457719450655242845690189464214663, n) ? Goodbye! Errors/timing (if any): *** Warning: unused characters: :n=5141;. *** unexpected character: Input:n=5141; ^-------- Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Fri Oct 28 19:19:10 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*25); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*25; print(floor(10^40*(1/6+1/28+1/496+1/8128+1/33550336+1/8589869056+1/137438691328+1/2305843008139952128+1/2658455991569831744654692615953842176+1/191561942608236107294793378084303638130997321548169216))); print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? 2045201428389264301781344290984555766773 ? Checking from 249M up to 250M (249999991 to 250000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Fri Oct 28 19:18:47 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*25); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*25; print(floor(10^20*(1/6+1/28+1/496+1/8128+1/33550336+1/8589869056+1/137438691328+1/2305843008139952128+1/2658455991569831744654692615953842176+1/191561942608236107294793378084303638130997321548169216))); print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? 20452014283892643017 ? Checking from 249M up to 250M (249999991 to 250000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Fri Oct 28 19:18:20 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*25); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*25; print(floor(10^20*(1/6+1/28+1/496+1/8128+1/33550336+1/8589869056+1/137438691328+1/2305843008139952128,2658455991569831744654692615953842176+1/191561942608236107294793378084303638130997321548169216))); print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Checking from 249M up to 250M (249999991 to 250000000)... ? ? done. ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...328+1/2305843008139952128 *** ,2658455991569831744 ^-------------------- Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Fri Oct 28 19:14:16 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*25); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*25; print(1/6+1/28+1/496+1/8128+1/33550336+1/8589869056+1/137438691328+1/2305843008139952128,2658455991569831744654692615953842176+1/191561942608236107294793378084303638130997321548169216); print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? 21946393419448395156572193153954532619/107306757734531203075108441921098350592509258994083621521346255538182294220404351890102946580078414343002346514721217253805654017/191561942608236107294793378084303638130997321548169216 ? Checking from 249M up to 250M (249999991 to 250000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Fri Oct 28 17:53:22 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*23); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*25; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 229M up to 250M (229999981 to 250000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m13.089s user 0m12.965s sys 0m0.122s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Fri Oct 28 17:52:41 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*20.5); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*23; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 204M up to 230M (204999991 to 230000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m17.093s user 0m16.968s sys 0m0.123s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Fri Oct 28 17:52:07 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*18); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*20.5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 180M up to 205M (180000001 to 205000000.00000000000000000000000000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m17.211s user 0m16.967s sys 0m0.119s '203.117' ************** PARI ***************** Host 203.117.33.23 (203.117.33.23) Time: Fri Oct 28 08:12:19 2005 Input: 2^100-7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1267650600228229401496703205369 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '203.117' ************** PARI ***************** Host 203.117.33.23 (203.117.33.23) Time: Fri Oct 28 08:11:49 2005 Input: 2^100-7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1267650600228229401496703205369 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '203.117' ************** PARI ***************** Host 203.117.33.23 (203.117.33.23) Time: Fri Oct 28 08:11:38 2005 Input: 2^100-7 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 1267650600228229401496703205369 ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '203.117' ************** PARI ***************** Host 203.117.33.23 (203.117.33.23) Time: Fri Oct 28 08:11:01 2005 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = "Replace this by some code, then click [PARI] or [MAGMA]!" ? Goodbye! Errors/timing (if any): Timing: real 0m0.101s user 0m0.008s sys 0m0.004s '129.177' ************** PARI ***************** Host 129.177.61.81 (129.177.61.81) Time: Fri Oct 28 07:15:15 2005 Input: R=olynomialRing(QQ,"x") g=(x^5+10*x+2)*R.cyclotomic_polynomial(7)*x^5 factor(g) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? %1 = [g 1] ? Goodbye! Errors/timing (if any): *** unknown function or error in formal parameters: R=olynomialRing(QQ,"x" ^-------------------- *** Warning: unused characters: (7)*x^5. *** unknown member function: g=(x^5+10*x+2)*R.cyclotomic_polynomia ^-------------------- Timing: real 0m0.096s user 0m0.006s sys 0m0.006s '137.222' ************** PARI ***************** Host 137.222.80.175 (137.222.80.175) Time: Fri Oct 28 07:09:52 2005 Input: factor(101010101010101) Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = [17 1] [73 1] [101 1] [137 1] [5882353 1] ? Goodbye! Errors/timing (if any): Timing: real 0m0.287s user 0m0.007s sys 0m0.008s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:39:04 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*15.5); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*18; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 155M up to 180M (155000011 to 180000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m16.005s user 0m15.843s sys 0m0.153s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:38:32 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*13); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*15.5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 129M up to 155M (129999991 to 155000000.00000000000000000000000000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m16.789s user 0m16.653s sys 0m0.133s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:38:03 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*11); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*13; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 110M up to 130M (110000011 to 130000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m13.414s user 0m13.275s sys 0m0.136s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:37:29 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*8); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*11; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 80M up to 110M (80000011 to 110000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m20.688s user 0m20.537s sys 0m0.145s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:36:28 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*1); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 9M up to 20M (9999991 to 20000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m6.706s user 0m6.623s sys 0m0.082s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:35:09 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^7*1); mn=mn-lift(Mod(mn,30))+1; mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(gcd(i,77)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 9M up to 20M (9999991 to 20000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m8.944s user 0m8.851s sys 0m0.092s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:34:23 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^6*1); mn=mn-lift(Mod(mn,30))+1; mx = 10^6*5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(gcd(i,77)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 0M up to 5M (999991 to 5000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m3.617s user 0m3.585s sys 0m0.032s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:34:00 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^6*1); mn=mn-lift(Mod(mn,30))+1; mx = 10^6*5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(gcd(i,1)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 0M up to 5M (999991 to 5000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m3.753s user 0m3.720s sys 0m0.032s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:32:56 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^6*1); mn=mn-lift(Mod(mn,30))+1; mx = 10^6*5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(gcd(i,7)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 0M up to 5M (999991 to 5000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m3.676s user 0m3.632s sys 0m0.044s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:32:31 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^6*1); mn=mn-lift(Mod(mn,30))+1; mx = 10^6*5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(gcd(i,35)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 0M up to 5M (999991 to 5000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m3.726s user 0m3.692s sys 0m0.033s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:32:08 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^6*1); mn=mn-lift(Mod(mn,30))+1; mx = 10^6*5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[6,4,2,4,2,4,6,2],if(gcd(i,105)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 0M up to 5M (999991 to 5000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m3.793s user 0m3.762s sys 0m0.030s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:31:01 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^6*1); mn=mn-lift(Mod(mn,30))+1; mx = 10^6*5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[4,2,4,2,4,2,4,2,4,2],if(gcd(i,105)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 0M up to 5M (999991 to 5000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m4.466s user 0m4.418s sys 0m0.047s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:28:31 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^6*1); mn=mn-lift(Mod(mn,6))+1; mx = 10^6*5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[4,2],if(gcd(i,105)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 1M up to 5M (1000003 to 5000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m4.465s user 0m4.414s sys 0m0.050s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:28:13 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^6*1); mn=mn-lift(Mod(mn,6))+1; mx = 10^6*5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[4,2],if(gcd(i,35)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 1M up to 5M (1000003 to 5000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m4.421s user 0m4.368s sys 0m0.048s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:27:25 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^6*1); mn=mn-lift(Mod(mn,6))+1; mx = 10^6*5; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[4,2],if(gcd(i,5)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 1M up to 5M (1000003 to 5000000)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m4.489s user 0m4.446s sys 0m0.042s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:26:29 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=5*7*11*13; mn = nextprime(10^1*1); mn=mn-lift(Mod(mn,6))+1; mx = 10^2*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[4,2],if(gcd(i,5)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? ? Checking from 0M up to 0M (7 to 200)... ? Mod(0, 7) Mod(0, 11) Mod(0, 13) Mod(0, 77) Mod(0, 91) Mod(0, 143) ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:26:11 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; mn = nextprime(10^1*1); mn=mn-lift(Mod(mn,6))+1; mx = 10^2*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[4,2],if(gcd(i,5)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? ? ? Checking from 0M up to 0M (7 to 200)... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.004s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:24:25 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=5*7*11*13*17^2*19; print("-----", x); mn = nextprime(10^1*1); mn=mn-lift(Mod(mn,6))-1; mx = 10^2*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M (", mn , " to ", mx , ")..."); forstep(i=mn,mx,[2,4],if(gcd(i,5)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? -----27482455 ? ? ? ? Checking from 0M up to 0M (5 to 200)... ? Mod(0, 7) Mod(0, 11) Mod(0, 13) Mod(0, 17) Mod(0, 19) Mod(0, 77) Mod(0, 91) Mod(0, 119) Mod(0, 133) Mod(0, 143) Mod(0, 187) ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.007s sys 0m0.005s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:21:29 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print(lift(Mod(7,3))); print("-----", x); mn = nextprime(10^7*1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(gcd(i,5)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? 1 ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 20M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m11.196s user 0m11.077s sys 0m0.116s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:17:11 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(gcd(i,5)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 20M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m11.658s user 0m11.538s sys 0m0.116s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:16:46 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(gcd(i,5)==1,if(x%i==0,print(Mod(x,i))))); print("done."); Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:13:19 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(gcd(i,5)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 20M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m11.796s user 0m11.682s sys 0m0.113s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:12:48 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,2,if(gcd(i,105)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 20M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m15.617s user 0m15.480s sys 0m0.134s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:08:22 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(gcd(i,35)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 20M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m10.902s user 0m10.782s sys 0m0.119s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:07:50 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(gcd(i,5005)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 20M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m11.484s user 0m11.369s sys 0m0.115s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:07:18 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(gcd(i,385)==1,if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 20M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m11.391s user 0m11.262s sys 0m0.127s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:04:56 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(ispseudoprime(i),if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 20M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m14.037s user 0m13.912s sys 0m0.124s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:02:40 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(Mod(x,i)==0,print(Mod(x,i)))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 20M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m8.179s user 0m8.069s sys 0m0.108s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:01:54 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(isprime(i),if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 20M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m14.045s user 0m13.944s sys 0m0.099s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:01:22 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*3; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(isprime(i),if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 10M up to 30M... ? Errors/timing (if any): /var/www/cgi-bin/calc/gp: line 1: 26023 Killed ./gp-2.2.11 -s 256000000 -emacs Timing: real 0m21.072s user 0m20.801s sys 0m0.214s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:00:22 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^3; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(isprime(i),if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? Checking from 0M up to 0M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 23:00:06 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); print(factor(x,0)); mn = nextprime(10^1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^3; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(isprime(i),if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? Mat([278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531, 1]) ? ? ? ? Checking from 0M up to 0M... ? ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m0.023s user 0m0.017s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:59:58 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=94596550060757067; print("-----", x); print(factor(x,0)); mn = nextprime(10^1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^3; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(isprime(i),if(Mod(x,i)==0,print(Mod(x,i))))); print("done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? -----94596550060757067 ? [3, 2; 397, 1; 26475384847679, 1] ? ? ? ? Checking from 0M up to 0M... ? Mod(0, 397) ? done. ? Goodbye! Errors/timing (if any): Timing: real 0m0.016s user 0m0.012s sys 0m0.003s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:59:37 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=94596550060757067; print("-----", x); print(factor(x,0)); mn = nextprime(10^1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^3; print("Checking from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M..."); forstep(i=mn,mx,[2,4],if(isprime(i),if(Mod(x,i)==0,print(Mod(x,i))))); print("...done."); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? -----94596550060757067 ? [3, 2; 397, 1; 26475384847679, 1] ? ? ? ? Checking from 0M up to 0M... ? Mod(0, 397) ? ...done. ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.009s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:58:43 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=94596550060757067; print("-----", x); print(factor(x,0)); mn = nextprime(10^1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^3; forstep(i=mn,mx,[2,4],if(isprime(i),if(Mod(x,i)==0,print(Mod(x,i))))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? -----94596550060757067 ? [3, 2; 397, 1; 26475384847679, 1] ? ? ? ? Mod(0, 397) ? Checked from 0M up to 0M ? Goodbye! Errors/timing (if any): Timing: real 0m0.015s user 0m0.010s sys 0m0.005s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:58:17 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=94596550060757067; print("-----", x); mn = nextprime(10^1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^3; forstep(i=mn,mx,[2,4],if(isprime(i),if(Mod(x,i)==0,print(Mod(x,i))))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? -----94596550060757067 ? ? ? ? Mod(0, 397) ? Checked from 0M up to 0M ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:57:47 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=94596550060757067; print("-----", x); mn = nextprime(10^1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^3; forstep(i=mn,mx,[2,4],if(isprime(i),if(Mod(x,i)==0,print(Mod(x,i)))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? -----94596550060757067 ? ? ? ? ? Checked from 0M up to 0M ? Goodbye! Errors/timing (if any): *** expected character: ')' instead of: ...,i)==0,print(Mod(x,i)))); ^ Timing: real 0m0.013s user 0m0.008s sys 0m0.003s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:57:32 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=94596550060757067; print("-----", x); mn = nextprime(10^1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^3; forstep(i=mn,mx,[2,4],if(isprime(i),if( Mod(x,i)==0,print(Mod(x,i) ))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? -----94596550060757067 ? ? ? ? ? %5 = 0 ? ? Checked from 0M up to 0M ? Goodbye! Errors/timing (if any): *** unexpected character: ...x,[2,4],if(isprime(i),if( ^ *** Warning: unused characters: ,print(Mod(x,i). *** Warning: unused characters: )));. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:56:59 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=94596550060757067; print("-----", x); mn = nextprime(10^1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^3; forstep(i=mn,mx,[2,4],if(isprime(i),print1(i," "))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? -----94596550060757067 ? ? ? ? 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 ? Checked from 0M up to 0M ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.008s sys 0m0.005s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:56:30 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=94596550060757067; print("-----", x); mn = nextprime(10^1); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^3; forstep(i=mn,mx,[2,4],if(isprime(i),print1(i))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? -----94596550060757067 ? ? ? ? 111317192329313741434753596167717379838997101103107109113127131137139149151157163167173179181191193197199211223227229233239241251257263269271277281283293307311313317331337347349353359367373379383389397401409419421431433439443449457461463467479487491499503509521523541547557563569571577587593599601607613617619631641643647653659661673677683691701709719727733739743751757761769773787797809811821823827829839853857859863877881883887907911919929937941947953967971977983991997 ? Checked from 0M up to 0M ? Goodbye! Errors/timing (if any): Timing: real 0m0.013s user 0m0.007s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:56:01 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; x=94596550060757067; print("-----", x); mn = nextprime(10^1*6); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^1*8; forstep(i=mn,mx,[2,4],if(isprime(i),print1(i))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? ? -----94596550060757067 ? ? ? ? 596167717379 ? Checked from 0M up to 0M ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.005s sys 0m0.007s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:55:35 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^1*6); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^1*8; forstep(i=mn,mx,[2,4],if(isprime(i),print1(i))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? 596167717379 ? Checked from 0M up to 0M ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:53:56 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^1*6); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^1*8; forstep(i=mn,mx,[2,4],if( isprime(i), print(i) )); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? ? i ? ? Checked from 0M up to 0M ? Goodbye! Errors/timing (if any): *** unexpected character: forstep(i=mn,mx,[2,4],if( ^ *** Warning: unused characters: ,. *** isprime: not an integer argument in an arithmetic function *** Warning: unused characters: ));. Timing: real 0m0.012s user 0m0.008s sys 0m0.004s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:52:52 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*6); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*8; forstep(i=mn,mx,[2,4],if( isprime(i), if( Mod(x,i)==0,print(Mod(x,i) ) )); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? ? ? %4 = 0 ? ? ? Checked from 60M up to 80M ? Goodbye! Errors/timing (if any): *** unexpected character: forstep(i=mn,mx,[2,4],if( ^ *** Warning: unused characters: ,. *** isprime: not an integer argument in an arithmetic function *** unexpected character: if( ^ *** Warning: unused characters: ,print(Mod(x,i). *** Warning: unused characters: ). *** Warning: unused characters: ));. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:51:49 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*6); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*8; forstep(i=mn,mx,[2,4],if( isprime(i),if( Mod(x,i)==0,print(Mod(x,i) ) )); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? ? %4 = 0 ? ? ? Checked from 60M up to 80M ? Goodbye! Errors/timing (if any): *** unexpected character: forstep(i=mn,mx,[2,4],if( ^ *** Warning: unused characters: ,if(. *** isprime: not an integer argument in an arithmetic function *** Warning: unused characters: ,print(Mod(x,i). *** Warning: unused characters: ). *** Warning: unused characters: ));. Timing: real 0m0.013s user 0m0.009s sys 0m0.004s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:49:38 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*6); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*8; forstep(i=mn,mx,[2,4],if( if(isprime(i),Mod(x,i)==0,print(Mod(x,i)) )); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? ? ? Checked from 60M up to 80M ? Goodbye! Errors/timing (if any): *** unexpected character: forstep(i=mn,mx,[2,4],if( ^ *** expected character: ')' instead of: ...d(x,i)==0,print(Mod(x,i)) ^ *** Warning: unused characters: ));. Timing: real 0m0.012s user 0m0.009s sys 0m0.003s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:48:36 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*6); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*8; forstep(i=mn,mx,[2,4],if(if(isprime(i),Mod(x,i)==0,print(Mod(x,i))))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? Checked from 60M up to 80M ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...(x,i)==0,print(Mod(x,i))))); ^--- Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:48:05 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*6); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*8; forstep(i=mn,mx,[2,4],if(if(ispseudoprime(i), Mod(x,i)==0,print(Mod(x,i)) ))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? %4 = 0 ? ? Checked from 60M up to 80M ? Goodbye! Errors/timing (if any): *** expected character: ',' instead of: ...],if(if(ispseudoprime(i), ^ *** Warning: unused characters: ,print(Mod(x,i)). *** Warning: unused characters: )));. Timing: real 0m0.012s user 0m0.006s sys 0m0.006s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:46:46 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*6); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*8; forstep(i=mn,mx,[2,4],if(Mod(x,i)==0,print(Mod(x,i)))); print("Checked from ", floor(mn / 10^6) , "M up to ", floor(mx / 10^6), "M"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? Checked from 60M up to 80M ? Goodbye! Errors/timing (if any): Timing: real 0m16.663s user 0m16.535s sys 0m0.126s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:45:27 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*4); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*6; forstep(i=mn,mx,[2,4],if(Mod(x,i)==0,print(Mod(x,i)))); print("Checked from ", mn, " up to ", mx / 10^6, " million"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? Checked from 40000001 up to 60 million ? Goodbye! Errors/timing (if any): Timing: real 0m17.047s user 0m16.925s sys 0m0.119s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:43:02 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7*2); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*4; forstep(i=mn,mx,[2,4],if(Mod(x,i)==0,print(Mod(x,i)))); print("Checked from ", mn, " up to ", mx / 10^6, " million"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? Checked from 20000003 up to 40 million ? Goodbye! Errors/timing (if any): Timing: real 0m17.386s user 0m17.226s sys 0m0.146s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:40:50 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(10^7); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7*2; forstep(i=mn,mx,[2,4],if(Mod(x,i)==0,print(Mod(x,i)))); print("Checked from ", mn, " up to ", mx / 10^6, " million"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? Checked from 10000019 up to 20 million ? Goodbye! Errors/timing (if any): Timing: real 0m8.161s user 0m8.046s sys 0m0.110s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:40:23 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(18); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^6; forstep(i=mn,mx,[2,4],if(Mod(x,i)==0,print(Mod(x,i)))); print("Checked from ", mn, " up to ", mx / 10^6, " million"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? Checked from 17 up to 1 million ? Goodbye! Errors/timing (if any): Timing: real 0m0.831s user 0m0.817s sys 0m0.014s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:40:12 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(16); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^6; forstep(i=mn,mx,[2,4],if(Mod(x,i)==0,print(Mod(x,i)))); print("Checked from ", mn, " up to ", mx / 10^6, " million"); Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? ? -----278490841076279407188741439481565179355926725853710201632331620642982062389901741890579963524423782637435949041666525000702723914662388812510545494307250950777886431051612811386531 ? ? ? ? ? Checked from 17 up to 1 million ? Goodbye! Errors/timing (if any): Timing: real 0m0.877s user 0m0.862s sys 0m0.014s '134.53.' ************** PARI ***************** Host 134.53.24.2 (134.53.24.2) Time: Thu Oct 27 22:39:46 2005 Input: x = 2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471*52662739*23003*30693651606209*37*1741*1313797957*887*71*7127*109*23*97*159227*643679794963466223081509857 *103*1079990819*9539*3143065813*29*3847*89*19*577*223*139703*457*9649*61*4357+ 1; print("-----", x); mn = nextprime(2.3); if (Mod(mn,6)==1,mn = mn - 2); mx = 10^7; forstep(i=mn,mx,[2,4],if(Mod(x,i)==0,print(Mod(x,i)))); print("Checked from ", mn, " up to ", mx / 10^6, " million"); Output: