version 1.1, 2001/10/02 11:17:13 |
version 1.2, 2002/09/11 07:27:12 |
Line 17 x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 5466035 |
|
Line 17 x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 5466035 |
|
? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8)); |
? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8)); |
? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8)); |
? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8)); |
? nf=nfinit(nfpol) |
? nf=nfinit(nfpol) |
[x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920 |
[x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -1.08911514572050482502495 |
69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929 |
27946671612684, -2.4285174907194186068992069565359418364, 0.7194669112891317 |
269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119 |
8943997506477288225733, -2.5558200350691694950646071159426779971; 1, -0.1383 |
211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I, |
8372073406036365047976417441696637 - 0.4918163765776864349975328551474152510 |
3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331 |
7*I, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940822 |
539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319 |
19556466857*I, -0.072312766896812300380582649294307897121 + 2.19808037538462 |
06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196 |
76641195195160383234877*I, -0.98796319352507039803950539735452837194 + 1.570 |
23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 + |
1452385894131769052374806001981108*I; 1, 1.682941293594312776162956161507997 |
1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610 |
6005 + 2.0500351226010726172974286983598602163*I, -0.75045317576910401286427 |
81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887 |
186094108607489 + 1.3101462685358123283560773619310445915*I, -0.787420688747 |
04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982 |
75359433940488309213323154 + 2.1336633893126618034168454610457936017*I, 1.26 |
34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I] |
58732110596551455718089553258673705 - 2.716479010374315056657802803578983483 |
, [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262 |
4*I], [1, -1.0891151457205048250249527946671612684, -2.428517490719418606899 |
77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515 |
2069565359418364, 0.71946691128913178943997506477288225733, -2.5558200350691 |
382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8 |
694950646071159426779971; 1.4142135623730950488016887242096980785, -0.195704 |
976972027301414394898806541072047941, 6.408909349142616853840753758109052071 |
13467375904264179382543977540673, 2.7785222450164664309920925654093065576, - |
2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441 |
0.10226569567819614506098907018896260035, -1.3971909474085893198147151262541 |
22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929 |
540506; 0, -0.69553338995335755797766403996841143190, 1.14510982744395651299 |
269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875 |
26149974389115722, 3.1085550780550843138423672171643499921, 2.22052069130868 |
724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 - |
72788181483285734827868; 1.4142135623730950488016887242096980785, 2.38003840 |
1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400 |
20787979181834702019470475018, -1.0613010590986270398182318786558994412, -1. |
435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104 |
1135810173202366904448352912286604470, 1.79021506332534372536778891648110361 |
7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231 |
60; 0, 2.8991874737236275652408825679737171586, 1.85282662165584876344468105 |
7837223883352537186677084*I], [5, 0.E-77, 10.0000000000000000000000000000000 |
12816401036, 3.0174557027049114270734649132936867272, -3.8416814583731999185 |
00000, -5.0000000000000000000000000000000000000, 7.0000000000000000000000000 |
306312841432940661], 0, [5, 2, 0, -1, -2; 2, -2, -5, -10, 20; 0, -5, 10, -10 |
000000000000; 0.E-77, 19.488486013650707197449403270536023970, 2.07268045322 |
, 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 0, 200, 110, 177; 0, 345 |
2666710 E-76, 19.488486013650707197449403270536023970, 4.1504592246706085588 |
, 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5175, 0 |
902013976045703227; 10.000000000000000000000000000000000000, 2.0726804532226 |
, -10350, -15525; 5175, 13800, -8625, -1725, 27600; 0, -8625, 37950, -17250, |
66710 E-76, 85.960217420851846480305133936577594605, -36.0342682914829798382 |
0; -10350, -1725, -17250, -24150, -15525; -15525, 27600, 0, -15525, -3450], |
67056239752434596, 53.576130452511107888183080361946556763; -5.0000000000000 |
[595125, [238050, -296700, 91425, 1725, 0]~]], [-2.428517490719418606899206 |
000000000000000000000000, 19.488486013650707197449403270536023970, -36.03426 |
9565359418364, 1.9647119211288133163138753392090569931 + 0.80971492418897895 |
8291482979838267056239752434596, 60.916248374441986300937507618575151517, -1 |
128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.31014 |
8.470101750219179344070032346246890434; 7.0000000000000000000000000000000000 |
62685358123283560773619310445915*I], [1, 1/15*x^4 - 2/3*x^2 + 1/3*x + 4/3, x |
000, 4.1504592246706085588902013976045703227, 53.576130452511107888183080361 |
, 2/15*x^4 - 1/3*x^2 + 2/3*x - 1/3, -1/15*x^4 + 1/3*x^3 + 1/3*x^2 - 4/3*x - |
946556763, -18.470101750219179344070032346246890434, 37.97015289284236734089 |
2/3], [1, 0, 3, 1, 10; 0, 0, -2, 1, -5; 0, 1, 0, 3, -5; 0, 0, 1, 1, 10; 0, 0 |
7384258599214282], [5, 0, 10, -5, 7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; - |
, 0, 3, 0], [1, 0, 0, 0, 0, 0, -1, -1, -2, 4, 0, -1, 3, -1, 1, 0, -2, -1, -3 |
5, 10, -55, 45, -39; 7, -5, 20, -39, 9], [345, 0, 340, 167, 150; 0, 345, 110 |
, -1, 0, 4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, -1, -1, 1, 0, -1, -2, -1, 1, 0, |
, 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [132825, -18975, - |
-1, -1, -1, 3, 0, 1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, -2 |
5175, 27600, 17250; -18975, 34500, 41400, 3450, -43125; -5175, 41400, -41400 |
, 0, 1, 0, -1, -1, 0, -1, -2, -1, -1; 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, |
, -15525, 51750; 27600, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -86 |
1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1; 0, 0, 0, 0, 1, 0, -1, -1, -1, 1, 0, -1 |
250], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.42851749071941860689 |
, 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1]] |
92069565359418364, 1.9647119211288133163138753392090569931 + 0.8097149241889 |
|
7895128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.3 |
|
101462685358123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3 |
|
, 1/15*x^4 + 1/3*x^2 + 1/3*x + 1/3], [1, 0, 0, 1, -5; 0, 1, 0, 0, -5; 0, 0, |
|
1, 1, -5; 0, 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0 |
|
, 1, -5, -5, -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0 |
|
, -2, 0, 0, 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0 |
|
, 1, 1, -2, 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1 |
|
, 0, 0, 0, 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0, 0, |
|
0, 1, 0, 0, 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]] |
|
? nf1=nfinit(nfpol,2) |
? nf1=nfinit(nfpol,2) |
[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145 |
[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145 |
7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59 |
7205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.71 |
741050929194782733001765987770358483, 0.158944197453903762065494816710718942 |
946691128913178943997506477288225733, 2.555820035069169495064607115942677997 |
89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753 |
1; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532 |
285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021 |
85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889 |
752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0 |
7895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.1 |
.13249517760521973840801462296650806543*I, -0.053650958656997725359297528357 |
980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283 |
602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312 |
7194 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162 |
7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035 |
9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769 |
26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I |
10401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.78 |
, -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013 |
742068874775359433940488309213323154 - 2.13366338931266180341684546104579360 |
48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544 |
17*I, -1.2658732110596551455718089553258673705 + 2.7164790103743150566578028 |
710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, - |
035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071 |
0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948 |
94186068992069565359418364, -0.71946691128913178943997506477288225733, 2.555 |
3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594 |
8200350691694950646071159426779971; 1.4142135623730950488016887242096980785, |
8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211 |
-0.19570413467375904264179382543977540674, -2.77852224501646643099209256540 |
60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2. |
93065576, 0.10226569567819614506098907018896260035, 1.3971909474085893198147 |
7407052124261919274965153538200060029 - 13.800355044576098954744153925969274 |
151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443 |
603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539 |
9565129926149974389115722, 3.1085550780550843138423672171643499922, 2.220520 |
303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732 |
6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2. |
72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15 |
3800384020787979181834702019470475018, 1.06130105909862703981823187865589944 |
894419745390376206549481671071894289, -0.10730191731399545071859505671520521 |
12, 1.1135810173202366904448352912286604470, -1.7902150633253437253677889164 |
623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468 |
811036160; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763 |
99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000 |
4446810512816401036, -3.0174557027049114270734649132936867272, 3.84168145837 |
0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17. |
31999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10, |
000000000000000000000000000000000000, -44.0000000000000000000000000000000000 |
-10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3 |
00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712 |
45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51 |
83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999 |
75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250 |
32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000 |
, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450], |
0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126 |
[595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527 |
2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8 |
946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864 |
42564718082452641322500190813370023; -17.00000000000000000000000000000000000 |
3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035 |
0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350 |
1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x |
1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018 |
- 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2], [ |
0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841 |
1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0, |
447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003 |
1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1 |
8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5, |
, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1 |
2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1 |
, -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1 |
01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215, |
, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2, |
311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, - |
1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1 |
296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700 |
, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]] |
, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897 |
|
00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725, |
|
0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504 |
|
7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359 |
|
43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1, |
|
x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1, |
|
0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0, |
|
0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0, |
|
0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14; |
|
0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2, |
|
-3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, - |
|
19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3 |
|
, 4, -4, 1, 2, 1, -4, -21]] |
|
? nfinit(nfpol,3) |
? nfinit(nfpol,3) |
[[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514 |
[[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514 |
57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5 |
57205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.7 |
9741050929194782733001765987770358483, 0.15894419745390376206549481671071894 |
1946691128913178943997506477288225733, 2.55582003506916949506460711594267799 |
289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975 |
71; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753 |
3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602 |
285514741525107*I, -1.9647119211288133163138753392090569931 + 0.809714924188 |
1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + |
97895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2. |
0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835 |
1980803753846276641195195160383234877*I, 0.987963193525070398039505397354528 |
7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431 |
37194 + 1.5701452385894131769052374806001981108*I; 1, 1.68294129359431277616 |
27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703 |
29561615079976005 + 2.0500351226010726172974286983598602163*I, 0.75045317576 |
526062130959637482576769100030014 + 6.9001775222880494773720769629846373016* |
910401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.7 |
I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301 |
8742068874775359433940488309213323154 - 2.1336633893126618034168454610457936 |
348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354 |
017*I, -1.2658732110596551455718089553258673705 + 2.716479010374315056657802 |
4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, |
8035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.4285174907 |
-0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294 |
194186068992069565359418364, -0.71946691128913178943997506477288225733, 2.55 |
83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459 |
58200350691694950646071159426779971; 1.4142135623730950488016887242096980785 |
48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821 |
, -0.19570413467375904264179382543977540674, -2.7785222450164664309920925654 |
160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2 |
093065576, 0.10226569567819614506098907018896260035, 1.397190947408589319814 |
.7407052124261919274965153538200060029 - 13.80035504457609895474415392596927 |
7151262541540506; 0, 0.69553338995335755797766403996841143190, 1.14510982744 |
4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753 |
39565129926149974389115722, 3.1085550780550843138423672171643499922, 2.22052 |
9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573 |
06913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2 |
272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1 |
.3800384020787979181834702019470475018, 1.0613010590986270398182318786558994 |
5894419745390376206549481671071894289, -0.1073019173139954507185950567152052 |
412, 1.1135810173202366904448352912286604470, -1.790215063325343725367788916 |
1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346 |
4811036160; 0, 2.8991874737236275652408825679737171587, -1.85282662165584876 |
899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000 |
34446810512816401036, -3.0174557027049114270734649132936867272, 3.8416814583 |
00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17 |
731999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10 |
.000000000000000000000000000000000000, -44.000000000000000000000000000000000 |
, -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, |
000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471 |
345, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5 |
283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499 |
175, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -1725 |
932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000 |
0, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450], |
00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912 |
[595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.089115145720504825024952 |
62388960975827806174040462368, 143.93295090847353519436673793501057176, -55. |
7946671612684, -0.13838372073406036365047976417441696637 + 0.491816376577686 |
842564718082452641322500190813370023; -17.0000000000000000000000000000000000 |
43499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.05003 |
00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935 |
51226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2* |
01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201 |
x - 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2], |
80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084 |
[1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0 |
1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400 |
, 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, - |
38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5, |
1, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, - |
2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, - |
1, -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, |
101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215 |
1, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2, |
, 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, |
1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, - |
-296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670 |
1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]], Mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2 |
0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89 |
*x + 1, x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)] |
700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725 |
|
, 0]~]], [-1.0891151457205048250249527946671612684, -0.138383720734060363650 |
|
47976417441696637 + 0.49181637657768643499753285514741525107*I, 1.6829412935 |
|
943127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1 |
|
, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1, |
|
0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0 |
|
, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0, |
|
0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14 |
|
; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2, |
|
-3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, |
|
-19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, |
|
3, 4, -4, 1, 2, 1, -4, -21]], Mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2*x + 1, x^ |
|
5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)] |
|
? nfinit(nfpol,4) |
? nfinit(nfpol,4) |
[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145 |
[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145 |
7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59 |
7205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.71 |
741050929194782733001765987770358483, 0.158944197453903762065494816710718942 |
946691128913178943997506477288225733, 2.555820035069169495064607115942677997 |
89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753 |
1; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532 |
285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021 |
85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889 |
752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0 |
7895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.1 |
.13249517760521973840801462296650806543*I, -0.053650958656997725359297528357 |
980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283 |
602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312 |
7194 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162 |
7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035 |
9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769 |
26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I |
10401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.78 |
, -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013 |
742068874775359433940488309213323154 - 2.13366338931266180341684546104579360 |
48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544 |
17*I, -1.2658732110596551455718089553258673705 + 2.7164790103743150566578028 |
710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, - |
035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071 |
0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948 |
94186068992069565359418364, -0.71946691128913178943997506477288225733, 2.555 |
3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594 |
8200350691694950646071159426779971; 1.4142135623730950488016887242096980785, |
8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211 |
-0.19570413467375904264179382543977540674, -2.77852224501646643099209256540 |
60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2. |
93065576, 0.10226569567819614506098907018896260035, 1.3971909474085893198147 |
7407052124261919274965153538200060029 - 13.800355044576098954744153925969274 |
151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443 |
603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539 |
9565129926149974389115722, 3.1085550780550843138423672171643499922, 2.220520 |
303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732 |
6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2. |
72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15 |
3800384020787979181834702019470475018, 1.06130105909862703981823187865589944 |
894419745390376206549481671071894289, -0.10730191731399545071859505671520521 |
12, 1.1135810173202366904448352912286604470, -1.7902150633253437253677889164 |
623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468 |
811036160; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763 |
99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000 |
4446810512816401036, -3.0174557027049114270734649132936867272, 3.84168145837 |
0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17. |
31999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10, |
000000000000000000000000000000000000, -44.0000000000000000000000000000000000 |
-10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3 |
00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712 |
45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51 |
83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999 |
75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250 |
32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000 |
, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450], |
0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126 |
[595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527 |
2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8 |
946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864 |
42564718082452641322500190813370023; -17.00000000000000000000000000000000000 |
3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035 |
0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350 |
1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x |
1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018 |
- 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2], [ |
0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841 |
1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0, |
447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003 |
1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1 |
8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5, |
, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1 |
2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1 |
, -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1 |
01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215, |
, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2, |
311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, - |
1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1 |
296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700 |
, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]] |
, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897 |
|
00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725, |
|
0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504 |
|
7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359 |
|
43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1, |
|
x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1, |
|
0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0, |
|
0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0, |
|
0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14; |
|
0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2, |
|
-3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, - |
|
19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3 |
|
, 4, -4, 1, 2, 1, -4, -21]] |
|
? nf3=nfinit(x^6+108); |
? nf3=nfinit(x^6+108); |
? nf4=nfinit(x^3-10*x+8) |
? nf4=nfinit(x^3-10*x+8) |
[x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -3.50466435358804770515010852590433205 |
[x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -0.36332823793268357037416860931988791 |
79, 6.1413361156553641347759399165844441383; 1, 0.86464088669540302583112842 |
960, -3.1413361156553641347759399165844441383; 1, -1.76155718183189058754537 |
266613688800, 0.37380193147270638662350044992137561317; 1, 2.640023466892644 |
11274124874988, 2.6261980685272936133764995500786243868; 1, 3.12488541976457 |
6793189801032381951699, 3.4848619528719294786005596334941802484], [1, 1, 1; |
41579195397367323754183, -0.48486195287192947860055963349418024846], [1, -0. |
-3.5046643535880477051501085259043320579, 0.86464088669540302583112842266613 |
36332823793268357037416860931988791960, -3.141336115655364134775939916584444 |
688800, 2.6400234668926446793189801032381951699; 6.1413361156553641347759399 |
1383; 1, -1.7615571818318905875453711274124874988, 2.62619806852729361337649 |
165844441383, 0.37380193147270638662350044992137561317, 3.484861952871929478 |
95500786243868; 1, 3.1248854197645741579195397367323754183, -0.4848619528719 |
6005596334941802484], [3, -3.454467422037777850 E-77, 10.0000000000000000000 |
2947860055963349418024846], 0, [3, 1, -1; 1, 13, -5; -1, -5, 17], [284, 76, |
00000000000000000; -3.454467422037777850 E-77, 20.00000000000000000000000000 |
46; 0, 2, 0; 0, 0, 1], [196, -12, 8; -12, 50, 14; 8, 14, 38], [568, [120, 21 |
0000000000, -12.000000000000000000000000000000000000; 10.0000000000000000000 |
0, 2]~]], [-3.5046643535880477051501085259043320579, 0.864640886695403025831 |
00000000000000000, -12.000000000000000000000000000000000000, 50.000000000000 |
12842266613688800, 2.6400234668926446793189801032381951699], [1, 1/2*x^2 + x |
000000000000000000000000], [3, 0, 10; 0, 20, -12; 10, -12, 50], [284, 168, 2 |
- 3, -1/2*x^2 + 3], [1, 0, 6; 0, 1, 0; 0, 1, -2], [1, 0, 0, 0, 4, -2, 0, -2 |
35; 0, 2, 0; 0, 0, 1], [856, -120, -200; -120, 50, 36; -200, 36, 60], [568, |
, 6; 0, 1, 0, 1, 2, 0, 0, 0, -2; 0, 0, 1, 0, 1, -1, 1, -1, -1]] |
[-216, 90, 8]~]], [-3.5046643535880477051501085259043320579, 0.8646408866954 |
|
0302583112842266613688800, 2.6400234668926446793189801032381951699], [1, x, |
|
1/2*x^2], [1, 0, 0; 0, 1, 0; 0, 0, 2], [1, 0, 0, 0, 0, -4, 0, -4, 0; 0, 1, 0 |
|
, 1, 0, 5, 0, 5, -2; 0, 0, 1, 0, 2, 0, 1, 0, 5]] |
|
? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7]; |
? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7]; |
? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2]) |
? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2]) |
[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060 |
[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060 |
61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468 |
61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468 |
08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672 |
08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065 |
2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1. |
2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701 |
2897619530652735025030086072395031017 + 0.E-57*I, -2.01097980249891575621226 |
48550268542821846861610071436900868, 0.E-57, 0.50057980363245587382620331339 |
34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590 |
071677436 + 3.1415926535897932384626433832795028842*I, 1.0888562540123011578 |
95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376 |
605958199158508674, 1.7241634548149836441438434283070556826 + 3.141592653589 |
98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I |
7932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.1 |
, -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983 |
415926535897932384626433832795028842*I, 2.1336294009747564707190997873636390 |
85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538 |
948 + 3.1415926535897932384626433832795028842*I, 0.0661783018827457321853684 |
79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653 |
92323164193433 + 3.1415926535897932384626433832795028842*I; -1.7903417566977 |
5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0 |
293763292119206302198760, -1.2897619530652735025030086072395031017, -0.70148 |
.E-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264 |
550268542821846861610071436900868, 0.E-57, -0.500579803632455873826203313390 |
33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795 |
71677436, -1.0888562540123011578605958199158508674, -1.724163454814983644143 |
864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424 |
8434283070556826, 0.34328764427702709438988786673341921876, -2.1336294009747 |
7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061 |
564707190997873636390948, -0.066178301882745732185368492323164193433], [[3, |
2 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.14159265358979323 |
[0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1, |
84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926 |
[2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [2 |
535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + |
, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [- |
3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342 |
2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [x |
4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389 |
^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058; |
88786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.14 |
1, 7.0663729752107779635959310246705326058], [1, -8.066372975210777963595931 |
15926535897932384626433832795028842*I, -24.478366048541841504313284087778334 |
0246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, 1 |
822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1 |
15], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.06637297521077 |
]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~ |
79635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - 1 |
, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1 |
], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.7 |
]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, |
124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + 7 |
1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, |
], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.79 |
8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310 |
03417566977293763292119206302198760]]], 0] |
246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729 |
|
752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2 |
|
, 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000 |
|
000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114; |
|
0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.066372975210777963595931024 |
|
6705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], |
|
[1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746 |
|
808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1), |
|
[[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846 |
|
26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071 |
|
795864769252867665590057684*I]]], 0] |
|
? setrand(1);bnfinit(x^2-x-100000,1) |
? setrand(1);bnfinit(x^2-x-100000,1) |
[Mat(5), Mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129. |
[Mat(5), Mat([3, 2, 1, 2, 0, 3, 0, 2, 2, 3, 1, 4, 3, 2, 2, 3, 3, 0]), [-129. |
82045011403975460991182396195022419 - 6.283185307179586476925286766559005768 |
82045011403975460991182396195022419 + 6.283185307179586476925286766559005768 |
4*I; 129.82045011403975460991182396195022419 - 12.56637061435917295385057353 |
4*I; 129.82045011403975460991182396195022419], [-41.811264589129943393339502 |
3118011536*I], [-41.811264589129943393339502258694361489 + 8.121413879410077 |
258694361489 + 6.2831853071795864769252867665590057684*I, 9.2399004147902289 |
514 E-115*I, 9.2399004147902289816376260438840931575 + 3.1415926535897932384 |
816376260438840931575 + 3.1415926535897932384626433832795028842*I, -11.87460 |
626433832795028842*I, -11.874609881075406725097315997431161032 + 9.424777960 |
9881075406725097315997431161032 + 3.1415926535897932384626433832795028842*I, |
7693797153879301498385086526*I, 389.46135034211926382973547188585067257 + 12 |
0.E-115, -51.051165003920172374977128302578454646 + 3.141592653589793238462 |
.566370614359172953850573533118011536*I, -440.512515346039436204712600188429 |
6433832795028842*I, -64.910225057019877304955911980975112095 + 3.14159265358 |
12722 + 0.E-113*I, -324.55112528509938652477955990487556047 + 6.283185307179 |
97932384626433832795028842*I, -29.936654708054536668242186261263200456 + 3.1 |
5864769252867665590057684*I, 229.70424552002497255158146166263724792 + 3.141 |
415926535897932384626433832795028842*I, -47.66831907156823399733291848270768 |
5926535897932384626433832795028842*I, -785.660451862534215720251179722755983 |
7878 + 6.2831853071795864769252867665590057684*I, 3.876293646477882506748482 |
25 + 6.2831853071795864769252867665590057684*I, -554.35531386699327377220656 |
4790355076166, -6.7377511782956880607802359510546381087 + 3.1415926535897932 |
215544062014 + 6.2831853071795864769252867665590057684*I, -47.66831907156823 |
384626433832795028842*I, -35.073513410834255332559266307639723380 + 3.141592 |
3997332918482707687879 + 9.4247779607693797153879301498385086526*I, 177.4887 |
6535897932384626433832795028842*I, 33.130781426597481571750300827582717074 + |
6918560798860724474244465791207 + 6.497131103528062011 E-114*I, -875.6123693 |
2.030353469852519378 E-115*I, 54.878404098312329644822020875673145627 + 4.0 |
7168080069763246690606885226 + 2.598852441411224804 E-113*I, 54.878404098312 |
60706939705038757 E-115*I, -14.980188104648613073630759189293219180 + 3.1415 |
329644822020875673145627 + 9.4247779607693797153879301498385086526*I, -404.4 |
926535897932384626433832795028842*I, -26.83107648448133031970874306940114230 |
4153844676787690336623107514389175 + 0.E-113*I, 232.809823743598178900114904 |
8 + 3.1415926535897932384626433832795028842*I, -19.7067490665160655124889078 |
85449930607 + 6.2831853071795864769252867665590057684*I, -668.80899963671483 |
34878146944 + 3.1415926535897932384626433832795028842*I, -22.104515522613877 |
856204802764462926790 + 9.4247779607693797153879301498385086526*I, 367.35683 |
880850594423816214544 + 3.1415926535897932384626433832795028842*I, -45.68755 |
481950538594888487746203445802 + 12.566370614359172953850573533118011536*I, |
8235607825900087984737729869105 + 6.2831853071795864769252867665590057684*I, |
-1214.0716092619656173892944003952818868 + 9.4247779607693797153879301498385 |
47.668319071568233997332918482707687879 + 8.121413879410077514 E-115*I; 41. |
086526*I, -125.94415646756187210316334148291471657 + 6.283185307179586476925 |
811264589129943393339502258694361489, -9.23990041479022898163762604388409315 |
2867665590057684*I; 41.811264589129943393339502258694361489 + 6.283185307179 |
75, 11.874609881075406725097315997431161032, 0.E-115, 51.0511650039201723749 |
5864769252867665590057684*I, -9.2399004147902289816376260438840931575 + 12.5 |
77128302578454646, 64.910225057019877304955911980975112095, 29.9366547080545 |
66370614359172953850573533118011536*I, 11.8746098810754067250973159974311610 |
36668242186261263200456, 47.668319071568233997332918482707687879, -3.8762936 |
32 + 8.121413879410077514 E-115*I, -389.46135034211926382973547188585067257 |
464778825067484824790355076166, 6.7377511782956880607802359510546381087, 35. |
+ 6.2831853071795864769252867665590057684*I, 440.512515346039436204712600188 |
073513410834255332559266307639723380, -33.1307814265974815717503008275827170 |
42912722 + 3.1415926535897932384626433832795028842*I, 324.551125285099386524 |
74, -54.878404098312329644822020875673145627, 14.980188104648613073630759189 |
77955990487556047 + 9.4247779607693797153879301498385086526*I, -229.70424552 |
293219180, 26.831076484481330319708743069401142309, 19.706749066516065512488 |
002497255158146166263724792 + 6.2831853071795864769252867665590057684*I, 785 |
907834878146944, 22.104515522613877880850594423816214544, 45.687558235607825 |
.66045186253421572025117972275598325 + 9.42477796076937971538793014983850865 |
900087984737729869105, -47.668319071568233997332918482707687878], [[2, [2, 1 |
26*I, 554.35531386699327377220656215544062014 + 3.14159265358979323846264338 |
]~, 1, 1, [1, 1]~], [5, [5, 1]~, 1, 1, [1, 1]~], [13, [-5, 1]~, 1, 1, [6, 1] |
32795028842*I, 47.668319071568233997332918482707687878 + 3.14159265358979323 |
~], [2, [3, 1]~, 1, 1, [0, 1]~], [5, [6, 1]~, 1, 1, [0, 1]~], [7, [4, 1]~, 2 |
84626433832795028842*I, -177.48876918560798860724474244465791207 + 6.2831853 |
, 1, [-3, 1]~], [13, [6, 1]~, 1, 1, [-5, 1]~], [23, [7, 1]~, 1, 1, [-6, 1]~] |
071795864769252867665590057684*I, 875.61236937168080069763246690606885226 + |
, [43, [-15, 1]~, 1, 1, [16, 1]~], [17, [20, 1]~, 1, 1, [-2, 1]~], [17, [15, |
6.497131103528062011 E-114*I, -54.878404098312329644822020875673145627 + 9.4 |
1]~, 1, 1, [3, 1]~], [29, [14, 1]~, 1, 1, [-13, 1]~], [29, [-13, 1]~, 1, 1, |
247779607693797153879301498385086526*I, 404.44153844676787690336623107514389 |
[14, 1]~], [31, [39, 1]~, 1, 1, [-7, 1]~], [31, [24, 1]~, 1, 1, [8, 1]~], [ |
175 + 9.4247779607693797153879301498385086526*I, -232.8098237435981789001149 |
41, [7, 1]~, 1, 1, [-6, 1]~], [41, [-6, 1]~, 1, 1, [7, 1]~], [43, [16, 1]~, |
0485449930607 + 3.1415926535897932384626433832795028842*I, 668.8089996367148 |
1, 1, [-15, 1]~], [23, [-6, 1]~, 1, 1, [7, 1]~]], 0, [x^2 - x - 100000, [2, |
3856204802764462926790 + 6.2831853071795864769252867665590057684*I, -367.356 |
0], 400001, 1, [[1, -316.72816130129840161392089489603747004; 1, 315.7281613 |
83481950538594888487746203445803 + 3.1415926535897932384626433832795028842*I |
0129840161392089489603747004], [1, -316.72816130129840161392089489603747004; |
, 1214.0716092619656173892944003952818868 + 3.141592653589793238462643383279 |
1, 315.72816130129840161392089489603747004], 0, [2, -1; -1, 200001], [40000 |
5028842*I, 125.94415646756187210316334148291471657 + 6.283185307179586476925 |
1, 200001; 0, 1], [200001, 1; 1, 2], [400001, [200001, 1]~]], [-315.72816130 |
2867665590057684*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2, [2, 1]~, 1, 1, [1, 1] |
129840161392089489603747004, 316.72816130129840161392089489603747004], [1, x |
~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-1, 1]~], [7, [3, 1]~, |
- 1], [1, 1; 0, 1], [1, 0, 0, 100000; 0, 1, 1, -1]], [[5, [5], [[2, 0; 0, 1 |
2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5, 1]~, 1, 1, [-6, 1]~] |
]]], 129.82045011403975460991182396195022419, 0.9876536979069047228, [2, -1] |
, [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [-7, 1 |
, [379554884019013781006303254896369154068336082609238336*x + 11983616564425 |
]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [-14, 1]~, 1, 1, [13 |
0789990462835950022871665178127611316131167], 185], [Mat(1), [[0, 0]], [[-41 |
, 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~, 1, 1, [7, 1]~], [31, |
.811264589129943393339502258694361489 + 6.2831853071795864769252867665590057 |
[38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1]~], [41, [6, 1]~, 1, |
684*I, 41.811264589129943393339502258694361489]]], 0] |
1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [15, 1]~, 1, 1, [-16, 1] |
|
~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18], [ |
|
x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.72816130129840161392089489603 |
|
747004; 1, 316.72816130129840161392089489603747004], [1, 1; -315.72816130129 |
|
840161392089489603747004, 316.72816130129840161392089489603747004], [2, 1.00 |
|
00000000000000000000000000000000000; 1.0000000000000000000000000000000000000 |
|
, 200001.00000000000000000000000000000000], [2, 1; 1, 200001], [400001, 2000 |
|
00; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~]], [-315.7281613012984 |
|
0161392089489603747004, 316.72816130129840161392089489603747004], [1, x], [1 |
|
, 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.8 |
|
2045011403975460991182396195022419, 0.9876536979069047239, [2, -1], [3795548 |
|
84019013781006303254896369154068336082609238336*x + 119836165644250789990462 |
|
835950022871665178127611316131167], 186], [Mat(1), [[0, 0]], [[-41.811264589 |
|
129943393339502258694361489 + 8.121413879410077514 E-115*I, 41.8112645891299 |
|
43393339502258694361489 + 6.2831853071795864769252867665590057684*I]]], 0] |
|
? \p19 |
? \p19 |
realprecision = 19 significant digits |
realprecision = 19 significant digits |
? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3) |
? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3) |
[x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071 |
[x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2 - x - 9], [-3.233732695981516672 |
82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0, |
, -0.07182350902743636344, 4.305556205008953036], [10889, 5698, 8994; 0, 1, |
1], Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 10, 69, 33, 39, |
0; 0, 0, 1], Mat(2), Mat([1, 1, 0, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 39, 10, |
57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, 3, -1, 2, 3, 11, 1, - |
33, 57, 69], [2, [-1, 0, 0]~], [[0, 1, 0]~, [5, 3, 1]~], [-4, -1, 2, 3, 10, |
1, -7; 1, 1, 1, 1, 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]] |
3, 1, 7, 2; 1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]] |
? \p38 |
? \p38 |
realprecision = 38 significant digits |
realprecision = 38 significant digits |
? bnrinit(bnf,[[5,3;0,1],[1,0]],1) |
? bnrinit(bnf,[[5,4;0,1],[1,0]],1) |
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 |
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 |
061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 |
061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 |
808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767 |
808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306 |
22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1 |
52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70 |
.2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122 |
148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133 |
634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659 |
9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157 |
095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337 |
8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358 |
698160660239595315877930058147543 + 9.4247779607693797153879301498385086526* |
97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3. |
I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498 |
1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639 |
385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153 |
0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368 |
879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265 |
492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697 |
35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + |
7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014 |
0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 |
8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339 |
433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 |
071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414 |
5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 |
38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974 |
47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 |
7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3, |
12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932 |
[0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1, |
384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592 |
[2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [ |
6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + |
2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [ |
3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934 |
-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [ |
24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438 |
x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058; |
988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1 |
1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593 |
415926535897932384626433832795028842*I, -24.47836604854184150431328408777833 |
10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, |
4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, |
115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107 |
1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1] |
779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - |
~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, |
1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2. |
1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1 |
7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + |
, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7 |
7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7 |
, 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931 |
903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[5, 4; |
0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372 |
0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], Mat([[5, [-1, 1]~, 1, 1, [ |
9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [ |
2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[0, |
2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000 |
1]~], Mat(1)]], [1, 0; 0, 1]], [1], Mat([1, -3, -6]), [12, [12], [[3, 0; 0, |
0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114 |
1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]] |
; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102 |
? bnr=bnrclass(bnf,[[5,4;0,1],[1,0]],2) |
46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], |
|
[1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974 |
|
6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1), |
|
[[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384 |
|
626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307 |
|
1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1] |
|
, [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1] |
|
~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~] |
|
, Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[ |
|
3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]] |
|
? bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2) |
|
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 |
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 |
061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 |
061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 |
808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767 |
808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306 |
22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1 |
52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70 |
.2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122 |
148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133 |
634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659 |
9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157 |
095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337 |
8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358 |
698160660239595315877930058147543 + 9.4247779607693797153879301498385086526* |
97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3. |
I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498 |
1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639 |
385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153 |
0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368 |
879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265 |
492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697 |
35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + |
7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014 |
0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 |
8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339 |
433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 |
071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414 |
5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 |
38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974 |
47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 |
7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3, |
12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932 |
[0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1, |
384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592 |
[2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [ |
6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + |
2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [ |
3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934 |
-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [ |
24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438 |
x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058; |
988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1 |
1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593 |
415926535897932384626433832795028842*I, -24.47836604854184150431328408777833 |
10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, |
4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, |
115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107 |
1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1] |
779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - |
~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, |
1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2. |
1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1 |
7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + |
, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7 |
7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7 |
, 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931 |
903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[5, 4; |
0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372 |
0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], Mat([[5, [-1, 1]~, 1, 1, [ |
9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [ |
2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[0, |
2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000 |
1]~], Mat(1)]], [1, 0; 0, 1]], [1], Mat([1, -3, -6]), [12, [12], [[3, 0; 0, |
0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114 |
1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]] |
; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102 |
|
46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], |
|
[1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974 |
|
6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1), |
|
[[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384 |
|
626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307 |
|
1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1] |
|
, [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1] |
|
~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~] |
|
, Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[ |
|
3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]] |
|
? rnfinit(nf2,x^5-x-2) |
? rnfinit(nf2,x^5-x-2) |
[x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3 |
[x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3 |
109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914 |
109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914 |
Line 591 I, -1.0672071180669977537495893497477340535 - 1.390957 |
|
Line 490 I, -1.0672071180669977537495893497477340535 - 1.390957 |
|
0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [M |
0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [M |
od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1 |
od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1 |
, y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^ |
, y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^ |
3 - y - 1)], [], [y^3 - y - 1, [1, 1], -23, 1, [[1, 1.3247179572447460259609 |
3 - y - 1)], [], [y^3 - y - 1, [1, 1], -23, 1, [[1, 0.7548776662466927600495 |
088544780973407, 1.7548776662466927600495088963585286918; 1, -0.662358978622 |
0889635852869189, 1.3247179572447460259609088544780973407; 1, -0.87743883312 |
37301298045442723904867036 + 0.56227951206230124389918214490937306149*I, 0.1 |
334638002475444817926434594 - 0.74486176661974423659317042860439236723*I, -0 |
2256116687665361997524555182073565405 - 0.7448617666197442365931704286043923 |
.66235897862237301298045442723904867036 + 0.56227951206230124389918214490937 |
6724*I], [1, 2; 1.3247179572447460259609088544780973407, -1.3247179572447460 |
306149*I], [1, 0.75487766624669276004950889635852869189, 1.32471795724474602 |
259609088544780973407 - 1.1245590241246024877983642898187461229*I; 1.7548776 |
59609088544780973407; 1.4142135623730950488016887242096980785, -1.2408858979 |
662466927600495088963585286918, 0.24512233375330723995049110364147130810 + 1 |
558593537192653626096055786, -0.93671705072735084703311164961686101696; 0, - |
.4897235332394884731863408572087847344*I], [3, 0.E-96, 2.0000000000000000000 |
1.0533936124468254335289038498031013275, 0.795183311803032710044767156296587 |
000000000000000000; 0.E-96, 3.2646329987400782801485266890755860756, 1.32471 |
54002], 0, [3, -1, 0; -1, 1, 3; 0, 3, 2], [23, 16, 13; 0, 1, 0; 0, 0, 1], [- |
79572447460259609088544780973407; 2.0000000000000000000000000000000000000, 1 |
7, 2, -3; 2, 6, -9; -3, -9, 2], [23, [10, 7, 1]~]], [1.324717957244746025960 |
.3247179572447460259609088544780973407, 4.2192762054875453178332176670757633 |
9088544780973407, -0.66235897862237301298045442723904867036 + 0.562279512062 |
303], [3, 0, 2; 0, 2, 3; 2, 3, 2], [23, 13, 15; 0, 1, 0; 0, 0, 1], [-5, 6, - |
30124389918214490937306149*I], [1, y^2 - 1, y], [1, 0, 1; 0, 0, 1; 0, 1, 0], |
4; 6, 2, -9; -4, -9, 6], [23, [7, 10, 1]~]], [1.3247179572447460259609088544 |
[1, 0, 0, 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, -1, 0, 0, 0, 1; 0, 0, 1, 0, 1, 0, 1 |
780973407, -0.66235897862237301298045442723904867036 + 0.5622795120623012438 |
, 0, 0]], [x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158* |
9918214490937306149*I], [1, y, y^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, |
x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1, Mod(3951653 |
0, 0, 1, 0, 1, 0; 0, 1, 0, 1, 0, 1, 0, 1, 1; 0, 0, 1, 0, 1, 0, 1, 0, 1]], [x |
6165538345/83718587879473471*x^14 - 6500512476832995/83718587879473471*x^13 |
^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 |
- 196215472046117185/83718587879473471*x^12 + 229902227480108910/83718587879 |
+ 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1, Mod(39516536165538345/8 |
473471*x^11 + 237380704030959181/83718587879473471*x^10 - 106493198816077380 |
3718587879473471*x^14 - 6500512476832995/83718587879473471*x^13 - 1962154720 |
5/83718587879473471*x^9 - 20657086671714300/83718587879473471*x^8 + 17728852 |
46117185/83718587879473471*x^12 + 229902227480108910/83718587879473471*x^11 |
05999206010/83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^ |
+ 237380704030959181/83718587879473471*x^10 - 1064931988160773805/8371858787 |
6 - 4838840187320655696/83718587879473471*x^5 + 5180390720553188700/83718587 |
9473471*x^9 - 20657086671714300/83718587879473471*x^8 + 1772885205999206010/ |
879473471*x^4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040 |
83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^6 - 48388401 |
221/83718587879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920 |
87320655696/83718587879473471*x^5 + 5180390720553188700/83718587879473471*x^ |
215718580450/83718587879473471, x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - |
4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040221/83718587 |
5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + |
879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920215718580450 |
25*x + 1), -1, [1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^ |
/83718587879473471, x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x |
12, x^13, 1/83718587879473471*x^14 - 20528463024680133/83718587879473471*x^1 |
^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), - |
3 - 4742392948888610/83718587879473471*x^12 - 9983523646123358/8371858787947 |
1, [1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, 1/ |
3471*x^11 + 40898955597139011/83718587879473471*x^10 + 29412692423971937/837 |
83718587879473471*x^14 - 20528463024680133/83718587879473471*x^13 - 47423929 |
18587879473471*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075 |
48888610/83718587879473471*x^12 - 9983523646123358/83718587879473471*x^11 + |
066/83718587879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 2015290 |
40898955597139011/83718587879473471*x^10 + 29412692423971937/837185878794734 |
5879672878/83718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 - |
71*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075066/83718587 |
8471905745957397/83718587879473471*x^3 - 13395753879413605/83718587879473471 |
879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 20152905879672878/8 |
*x^2 + 27623037732247492/83718587879473471*x + 26306699661480593/83718587879 |
3718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 - 847190574595 |
473471], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1 |
7397/83718587879473471*x^3 - 13395753879413605/83718587879473471*x^2 + 27623 |
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0, |
037732247492/83718587879473471*x + 26306699661480593/83718587879473471], [1, |
0, 0, 0, 0, 0, 0, 0, 0, 13395753879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0 |
0, 0, 0, 8471905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -959164 |
, 0, 0, 0, 0, 0, 0, 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, |
3151927789; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0, |
0, 0, 0, 0, 13395753879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 847 |
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0, |
1905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789; |
0, 1, 0, 0, 0, 0, 0, 0, -41014993230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, |
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0, |
0, 0, 0, 5017479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412 |
0, 1, 0, 0, 0, 0, 0, 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, |
692423971937; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011; |
0, 0, 0, 0, -41014993230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 50 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0 |
17479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937 |
, 0, 0, 0, 0, 0, 0, 1, 0, 4742392948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011; 0, 0, 0, 0, |
0, 0, 1, 20528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718 |
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
587879473471]]] |
, 0, 0, 1, 0, 4742392948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20 |
|
528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471 |
|
]]] |
|
? bnfcertify(bnf) |
? bnfcertify(bnf) |
1 |
1 |
? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2]) |
? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2]) |
Line 668 od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1) |
|
Line 564 od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1) |
|
|
|
[[400001, 1]] |
[[400001, 1]] |
|
|
[[1, x]] |
[[1, x - 1]] |
|
|
[[5, [5], [[2, 1; 0, 1]]]] |
[[5, [5], [[2, 0; 0, 1]]]] |
|
|
[129.82045011403975460991182396195022419] |
[129.82045011403975460991182396195022419] |
|
|
[0.9876536979069047239] |
[0.9876536979069047228] |
|
|
[[2, -1]] |
[[2, -1]] |
|
|
Line 690 od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1) |
|
Line 586 od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1) |
|
|
|
[[400001, 1]] |
[[400001, 1]] |
|
|
[[1, x]] |
[[1, x - 1]] |
|
|
[[5, [5], [[2, 1; 0, 1]]]] |
[[5, [5], [[2, 0; 0, 1]]]] |
|
|
[129.82045011403975460991182396195022419] |
[129.82045011403975460991182396195022419] |
|
|
[0.9876536979069047239] |
[0.9876536979069047228] |
|
|
[[2, -1]] |
[[2, -1]] |
|
|
[[379554884019013781006303254896369154068336082609238336*x + 119836165644250 |
[[379554884019013781006303254896369154068336082609238336*x + 119836165644250 |
789990462835950022871665178127611316131167]] |
789990462835950022871665178127611316131167]] |
|
|
[186] |
[185] |
|
|
? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1]) |
? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1]) |
|
|
Line 713 od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1) |
|
Line 609 od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1) |
|
|
|
[[18981, 3087]] |
[[18981, 3087]] |
|
|
[[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]] |
[[1, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343, 17/1029*x^3 - 32/1029 |
|
*x^2 + 109/343*x + 2444/343, -11/343*x^3 + 163/1029*x^2 - 373/343*x - 4260/3 |
|
43]] |
|
|
[[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]] |
[[4, [4], [[7, 2, 4, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]] |
|
|
[3.7941269688216589341408274220859400302] |
[3.7941269688216589341408274220859400302] |
|
|
[0.8826018286655581306] |
[0.8826018286655581299] |
|
|
[[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]] |
[[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]] |
|
|
[[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]] |
[[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]] |
|
|
[182] |
[365] |
|
|
? setrand(1);bnfclgp(17) |
? setrand(1);bnfclgp(17) |
[1, [], []] |
[1, [], []] |
? setrand(1);bnfclgp(-31) |
? setrand(1);bnfclgp(-31) |
[3, [3], [Qfb(2, 1, 4)]] |
[3, [3], [Qfb(2, 1, 4)]] |
? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791) |
? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791) |
[4, [4], [[7, 5, 1, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]] |
[4, [4], [[7, 2, 0, 5; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]] |
? bnrconductor(bnf,[[25,13;0,1],[1,1]]) |
? bnrconductor(bnf,[[25,14;0,1],[1,1]]) |
[[5, 3; 0, 1], [1, 0]] |
[[5, 4; 0, 1], [1, 0]] |
? bnrconductorofchar(bnr,[2]) |
? bnrconductorofchar(bnr,[2]) |
[[5, 3; 0, 1], [0, 0]] |
[[5, 4; 0, 1], [0, 0]] |
? bnfisprincipal(bnf,[5,1;0,1],0) |
? bnfisprincipal(bnf,[5,2;0,1],0) |
[1]~ |
[1]~ |
? bnfisprincipal(bnf,[5,1;0,1]) |
? bnfisprincipal(bnf,[5,2;0,1]) |
[[1]~, [-2, -1/3]~, 181] |
[[1]~, [7/3, 1/3]~, 187] |
? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57)) |
? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57)) |
[-4, Mod(1, 2)]~ |
[-4, Mod(1, 2)]~ |
? \p19 |
? \p19 |
realprecision = 19 significant digits |
realprecision = 19 significant digits |
? bnfmake(sbnf) |
? bnfmake(sbnf) |
[Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535 |
[Mat(2), Mat([1, 1, 0, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535 |
89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389 |
89793238*I, -4.562279014988837952 + 3.141592653589793238*I; -2.6335434327389 |
76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238* |
76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238* |
I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14 |
I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14 |
1592653589793238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400 |
1592653589793238*I, 0.5404006376129469727 + 3.141592653589793238*I, -0.69263 |
6376129469727 + 3.141592653589793238*I, -0.6926391142471042845 + 3.141592653 |
91142471042844 + 3.141592653589793238*I, -1.990056445584799713 + 3.141592653 |
589793238*I, 0.E-96, 0.3677262014027817705 + 3.141592653589793238*I, 0.00437 |
589793238*I, -0.8305625946607188643 + 3.141592653589793238*I, 0.E-57, 0.0043 |
5616572659815402 + 3.141592653589793238*I, -0.8305625946607188639, -1.977791 |
75616572659815433 + 3.141592653589793238*I, -1.977791147836553953, 0.3677262 |
147836553953 + 3.141592653589793238*I; 0.6716827432867392935 + 3.14159265358 |
014027817708 + 3.141592653589793238*I; 0.6716827432867392938 + 3.14159265358 |
9793238*I, 0.5379005671092853266, -0.8333219883742404172 + 3.141592653589793 |
9793238*I, -0.8333219883742404170 + 3.141592653589793238*I, -0.2461086674077 |
238*I, -0.2461086674077943078, 0.E-96, 0.9729063188316092378, -0.87383180430 |
943076, 0.5379005671092853269, -1.552661549868775853, 0.E-57, -0.87383180430 |
71131265, -1.552661549868775853 + 3.141592653589793238*I, 0.5774919091398324 |
71131263, 0.5774919091398324092, 0.9729063188316092380; -1.91802973262155845 |
092 + 3.141592653589793238*I; -1.918029732621558454, 1.452155878475514386, 0 |
5, 0.2929213507612934444, 0.9387477816548985923, 1.452155878475514386, 2.383 |
.2929213507612934444, 0.9387477816548985923, 0.E-96, -1.340632520234391008, |
224144529494717, 0.E-57, 0.8694561877344533111, 1.400299238696721544, -1.340 |
0.8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.4002 |
632520234391008], [[3, [-1, 1, 0]~, 1, 1, [1, 1, 1]~], [5, [-1, 1, 0]~, 1, 1 |
99238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]~ |
, [0, 1, 1]~], [5, [2, 1, 0]~, 1, 1, [1, -2, 1]~], [5, [3, 1, 0]~, 1, 1, [2, |
], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [ |
2, 1]~], [13, [19, 1, 0]~, 1, 1, [-2, -6, 1]~], [3, [10, 1, 1]~, 1, 2, [-1, |
5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [23, [ |
1, 0]~], [11, [1, 1, 0]~, 1, 1, [-3, -1, 1]~], [19, [-6, 1, 0]~, 1, 1, [6, |
-10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [13, [ |
6, 1]~], [23, [-10, 1, 0]~, 1, 1, [-7, 10, 1]~]]~, 0, [x^3 - x^2 - 14*x - 1, |
19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2 |
[3, 0], 10889, 1, [[1, -3.233732695981516672, 4.690759845041404811; 1, -0.0 |
, 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.23 |
7182350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.23225 |
3732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.005158 |
8029482144592], [1, -3.233732695981516672, 4.690759845041404811; 1, -0.07182 |
616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; - |
350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.232258029 |
3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.4570 |
482144592], 0, [3, 1, 1; 1, 29, 8; 1, 8, 129], [10889, 5698, 8994; 0, 1, 0; |
2714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.0000000 |
0, 0, 1], [3677, -121, -21; -121, 386, -23; -21, -23, 86], [10889, [1899, 51 |
00000000000, 29.00000000000000000; 1.000000000000000000, 29.0000000000000000 |
91, 1]~]], [-3.233732695981516672, -0.07182350902743636344, 4.30555620500895 |
0, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.000 |
3036], [1, x, x^2 - x - 9], [1, 0, 9; 0, 1, 1; 0, 0, 1], [1, 0, 0, 0, 9, 1, |
0000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1 |
0, 1, 44; 0, 1, 0, 1, 1, 5, 0, 5, 1; 0, 0, 1, 0, 1, 0, 1, 0, -4]], [[2, [2], |
, 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, [ |
[[3, 2, 0; 0, 1, 0; 0, 0, 1]]], 10.34800724602768011, 1.000000000000000000, |
1890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.305556 |
[2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0.E-57, 0.E-57, 0.E-57]], [[ |
205008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, |
1.246346989334819161 + 3.141592653589793238*I, 0.6716827432867392938 + 3.141 |
0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2 |
592653589793238*I, -1.918029732621558455]]], [-4, -1, 2, 3, 10, 3, 1, 7, 2; |
], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.00000000000000000 |
1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]] |
0, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0, 0, 0]], [[1.24634698933 |
|
4819161 + 3.141592653589793238*I, 0.6716827432867392935 + 3.1415926535897932 |
|
38*I, -1.918029732621558454]]], [-4, 3, -1, 2, 3, 11, 1, -1, -7; 1, 1, 1, 1, |
|
0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]] |
|
? \p38 |
? \p38 |
realprecision = 38 significant digits |
realprecision = 38 significant digits |
? bnfnarrow(bnf) |
? bnfnarrow(bnf) |
[3, [3], [[3, 2; 0, 1]]] |
[3, [3], [[3, 0; 0, 1]]] |
? bnfreg(x^2-x-57) |
? bnfreg(x^2-x-57) |
2.7124653051843439746808795106061300699 |
2.7124653051843439746808795106061300699 |
? bnfsignunit(bnf) |
? bnfsignunit(bnf) |
Line 796 I; 1.459906329303914334, 3.141948414209350543], [1.246 |
|
Line 690 I; 1.459906329303914334, 3.141948414209350543], [1.246 |
|
[1] |
[1] |
|
|
? bnfunit(bnf) |
? bnfunit(bnf) |
[[x + 7], 185] |
[[x + 7], 187] |
? bnrclass(bnf,[[5,3;0,1],[1,0]]) |
? bnrclass(bnf,[[5,4;0,1],[1,0]]) |
[12, [12], [[3, 2; 0, 1]]] |
[12, [12], [[3, 0; 0, 1]]] |
? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2) |
? bnr2=bnrclass(bnf,[[25,14;0,1],[1,1]],2) |
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 |
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 |
061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 |
061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 |
808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767 |
808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306 |
22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1 |
52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70 |
.2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122 |
148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133 |
634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659 |
9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157 |
095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337 |
8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358 |
698160660239595315877930058147543 + 9.4247779607693797153879301498385086526* |
97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3. |
I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498 |
1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639 |
385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153 |
0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368 |
879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265 |
492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697 |
35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + |
7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014 |
0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 |
8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339 |
433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 |
071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414 |
5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 |
38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974 |
47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 |
7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3, |
12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932 |
[0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1, |
384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592 |
[2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [ |
6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + |
2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [ |
3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934 |
-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [ |
24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438 |
x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058; |
988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1 |
1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593 |
415926535897932384626433832795028842*I, -24.47836604854184150431328408777833 |
10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, |
4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, |
115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107 |
1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1] |
779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - |
~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, |
1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2. |
1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1 |
7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + |
, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7 |
7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7 |
, 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931 |
903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[25, 1 |
0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372 |
4; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [4, 2]~, [-2, -2]~]], Mat([[5, |
9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [ |
[-1, 1]~, 1, 1, [2, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), M |
2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000 |
od(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat( |
0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114 |
[1/5, -14/5])]], [[2, 2], [[4, 2]~, [-2, -2]~], [1, 0; 0, 1]]], [1, -12, 0, |
; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102 |
0; 0, 0, 1, 0; 0, 0, 0, 1]], [1], Mat([1, -3, -6, 0]), [12, [12], [[3, 0; 0, |
46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], |
1]]], [[1, -18, 9; -1/2, 10, -5], [-2, 0; 0, -10]]] |
[1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974 |
? bnrclassno(bnf,[[5,4;0,1],[1,0]]) |
6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1), |
|
[[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384 |
|
626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307 |
|
1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[25, 13; 0, |
|
1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [0, -2]~, [2, 2]~]], Mat([[5, [-2, 1 |
|
]~, 1, 1, [1, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), Mod(0, 2 |
|
)]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat([1/5, - |
|
13/5])]], [[2, 2], [[0, -2]~, [2, 2]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0, |
|
1, 0; 0, 0, 0, 1]], [1], [1, -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0] |
|
, [12, [12], [[3, 2; 0, 1]]], [[1, 9, -18; -1/2, -5, 10], [-2, 0; 0, 10]]] |
|
? bnrclassno(bnf,[[5,3;0,1],[1,0]]) |
|
12 |
12 |
? lu=ideallist(bnf,55,3); |
? lu=ideallist(bnf,55,3); |
? bnrclassnolist(bnf,lu) |
? bnrclassnolist(bnf,lu) |
Line 862 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
Line 745 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
? bnrdisc(bnr2,,,2) |
? bnrdisc(bnr2,,,2) |
0 |
0 |
? bnrdisc(bnr,Mat(6),,1) |
? bnrdisc(bnr,Mat(6),,1) |
[6, 2, [125, 13; 0, 1]] |
[6, 2, [125, 14; 0, 1]] |
? bnrdisc(bnr,,,1) |
? bnrdisc(bnr,,,1) |
[12, 1, [1953125, 1160888; 0, 1]] |
[12, 1, [1953125, 1160889; 0, 1]] |
? bnrdisc(bnr2,,,3) |
? bnrdisc(bnr2,,,3) |
0 |
0 |
? bnrdisclist(bnf,lu) |
? bnrdisclist(bnf,lu) |
Line 911 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
Line 794 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, |
18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, |
0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]] |
0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]] |
? bnrisprincipal(bnr,idealprimedec(bnf,7)[1]) |
? bnrisprincipal(bnr,idealprimedec(bnf,7)[1]) |
[[9]~, [-2170/6561, -931/19683]~, 256] |
[[9]~, [112595/19683, 13958/19683]~, 256] |
? dirzetak(nf4,30) |
? dirzetak(nf4,30) |
[1, 2, 0, 3, 1, 0, 0, 4, 0, 2, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 0, 2, 0, 0, 2, |
[1, 2, 0, 3, 1, 0, 0, 4, 0, 2, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 0, 2, 0, 0, 2, |
0, 1, 0, 1, 0] |
0, 1, 0, 1, 0] |
Line 924 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
Line 807 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
[Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1] |
[Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1] |
|
|
? vp=idealprimedec(nf,3)[1] |
? vp=idealprimedec(nf,3)[1] |
[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] |
[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] |
? idx=idealmul(nf,matid(5),vp) |
? idx=idealmul(nf,matid(5),vp) |
|
|
[3 1 2 2 2] |
[3 2 1 0 1] |
|
|
[0 1 0 0 0] |
[0 1 0 0 0] |
|
|
Line 939 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
Line 822 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
|
|
? idealinv(nf,idx) |
? idealinv(nf,idx) |
|
|
[1 0 2/3 0 0] |
[1 0 0 2/3 0] |
|
|
[0 1 1/3 0 0] |
[0 1 0 1/3 0] |
|
|
[0 0 1/3 0 0] |
[0 0 1 1/3 0] |
|
|
[0 0 0 1 0] |
[0 0 0 1/3 0] |
|
|
[0 0 0 0 1] |
[0 0 0 0 1] |
|
|
? idy=idealred(nf,idx,[1,5,6]) |
? idy=idealred(nf,idx,[1,5,6]) |
|
|
[5 0 0 2 0] |
[5 0 0 0 2] |
|
|
[0 5 0 0 0] |
[0 5 0 0 2] |
|
|
[0 0 5 2 0] |
[0 0 5 0 1] |
|
|
[0 0 0 1 0] |
[0 0 0 5 2] |
|
|
[0 0 0 0 5] |
[0 0 0 0 1] |
|
|
? idx2=idealmul(nf,idx,idx) |
? idx2=idealmul(nf,idx,idx) |
|
|
[9 7 5 8 2] |
[9 5 7 0 4] |
|
|
[0 1 0 0 0] |
[0 1 0 0 0] |
|
|
Line 975 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
Line 858 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
|
|
? idt=idealmul(nf,idx,idx,1) |
? idt=idealmul(nf,idx,idx,1) |
|
|
[2 0 0 0 1] |
[2 0 0 0 0] |
|
|
[0 2 0 0 1] |
[0 2 0 0 0] |
|
|
[0 0 2 0 0] |
[0 0 2 0 0] |
|
|
Line 987 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
Line 870 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
|
|
? idz=idealintersect(nf,idx,idy) |
? idz=idealintersect(nf,idx,idy) |
|
|
[15 5 10 12 10] |
[15 10 5 0 12] |
|
|
[0 5 0 0 0] |
[0 5 0 0 2] |
|
|
[0 0 5 2 0] |
[0 0 5 0 1] |
|
|
[0 0 0 1 0] |
[0 0 0 5 2] |
|
|
[0 0 0 0 5] |
[0 0 0 0 1] |
|
|
? aid=[idx,idy,idz,matid(5),idx] |
? aid=[idx,idy,idz,matid(5),idx] |
[[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1] |
[[3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1] |
, [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5 |
, [5, 0, 0, 0, 2; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1 |
], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, |
], [15, 10, 5, 0, 12; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, |
0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0 |
0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, |
, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, |
0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0 |
0, 0, 1]] |
, 0, 1]] |
? bid=idealstar(nf2,54,1) |
? bid=idealstar(nf2,54,1) |
[[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0, |
[[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0, |
0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[ |
0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[ |
0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0] |
1, 1, 0]~], [[1, -27, 0]~], [[]~], 1]], [[[26], [[2, 1, 0]~], [[-25, -26, 0] |
~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0 |
~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0 |
]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3 |
]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3 |
, 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~, |
, 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~, |
[1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0, |
[1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0, |
0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7 |
0]]], [[], [], [;]]], [2106, -77, 10556, 0, -4368, 12012, 0, -13104; 0, 0, |
, -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]] |
0, 1, -2, 0, -6, -6; -27, 1, -136, 0, 56, -156, 0, 168]] |
? vaid=[idx,idy,matid(5)] |
? vaid=[idx,idy,matid(5)] |
[[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1] |
[[3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1] |
, [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5 |
, [5, 0, 0, 0, 2; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1 |
], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, |
], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, |
1]] |
1]] |
? haid=[matid(5),matid(5),matid(5)] |
? haid=[matid(5),matid(5),matid(5)] |
Line 1037 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
Line 920 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
[0 0 0 0 1] |
[0 0 0 0 1] |
|
|
? idealaddtoone(nf,idx,idy) |
? idealaddtoone(nf,idx,idy) |
[[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~] |
[[3, 2, 1, 2, 1]~, [-2, -2, -1, -2, -1]~] |
? idealaddtoone(nf,[idy,idx]) |
? idealaddtoone(nf,[idy,idx]) |
[[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~] |
[[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~] |
? idealappr(nf,idy) |
? idealappr(nf,idy) |
[-2, 0, -2, 4, 0]~ |
[-2, -2, -1, -2, -1]~ |
? idealappr(nf,idealfactor(nf,idy),1) |
? idealappr(nf,idealfactor(nf,idy),1) |
[-2, 0, -2, 4, 0]~ |
[-2, -2, -1, -2, -1]~ |
? idealcoprime(nf,idx,idx) |
? idealcoprime(nf,idx,idx) |
[-2/3, 2/3, -1/3, 0, 0]~ |
[1/3, -1/3, -1/3, -1/3, 0]~ |
? idealdiv(nf,idy,idt) |
? idealdiv(nf,idy,idt) |
|
|
[5 5/2 5/2 7/2 0] |
[5 0 5/2 0 1] |
|
|
[0 5/2 0 0 0] |
[0 5/2 0 0 1] |
|
|
[0 0 5/2 1 0] |
[0 0 5/2 0 1/2] |
|
|
[0 0 0 1/2 0] |
[0 0 0 5/2 1] |
|
|
[0 0 0 0 5/2] |
[0 0 0 0 1/2] |
|
|
? idealdiv(nf,idx2,idx,1) |
? idealdiv(nf,idx2,idx,1) |
|
|
[3 1 2 2 2] |
[3 2 1 0 1] |
|
|
[0 1 0 0 0] |
[0 1 0 0 0] |
|
|
Line 1072 I, -20.610866187462450639586440264933189691 + 9.424777 |
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Line 955 I, -20.610866187462450639586440264933189691 + 9.424777 |
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|
|
? idf=idealfactor(nf,idz) |
? idf=idealfactor(nf,idz) |
|
|
[[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1] |
[[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] 1] |
|
|
[[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1] |
[[5, [-1, 0, 0, 0, 1]~, 1, 1, [2, 0, 3, 0, 1]~] 1] |
|
|
[[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3] |
[[5, [2, 0, 0, 0, 1]~, 4, 1, [2, 2, 1, 2, 1]~] 3] |
|
|
? idealhnf(nf,vp) |
? idealhnf(nf,vp) |
|
|
[3 1 2 2 2] |
[3 2 1 0 1] |
|
|
[0 1 0 0 0] |
[0 1 0 0 0] |
|
|
Line 1092 I, -20.610866187462450639586440264933189691 + 9.424777 |
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Line 975 I, -20.610866187462450639586440264933189691 + 9.424777 |
|
|
|
? idealhnf(nf,vp[2],3) |
? idealhnf(nf,vp[2],3) |
|
|
[3 1 2 2 2] |
[3 2 1 0 1] |
|
|
[0 1 0 0 0] |
[0 1 0 0 0] |
|
|
Line 1103 I, -20.610866187462450639586440264933189691 + 9.424777 |
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Line 986 I, -20.610866187462450639586440264933189691 + 9.424777 |
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[0 0 0 0 1] |
[0 0 0 0 1] |
|
|
? ideallist(bnf,20) |
? ideallist(bnf,20) |
[[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0 |
[[[1, 0; 0, 1]], [], [[3, 0; 0, 1], [3, 1; 0, 1]], [[2, 0; 0, 2]], [[5, 4; 0 |
, 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]], |
, 1], [5, 2; 0, 1]], [], [], [], [[9, 6; 0, 1], [3, 0; 0, 3], [9, 4; 0, 1]], |
[], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [ |
[], [[11, 10; 0, 1], [11, 2; 0, 1]], [[6, 0; 0, 2], [6, 2; 0, 2]], [], [], |
[15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]] |
[[15, 9; 0, 1], [15, 4; 0, 1], [15, 12; 0, 1], [15, 7; 0, 1]], [[4, 0; 0, 4] |
, [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10 |
], [[17, 15; 0, 1], [17, 3; 0, 1]], [], [[19, 0; 0, 1], [19, 1; 0, 1]], [[10 |
, 6; 0, 2], [10, 2; 0, 2]]] |
, 8; 0, 2], [10, 4; 0, 2]]] |
? ideallog(nf2,w,bid) |
? ideallog(nf2,w,bid) |
[1574, 8, 6]~ |
[486, 3, 7]~ |
? idealmin(nf,idx,[1,2,3]) |
? idealmin(nf,idx,[1,2,3]) |
[[-1; 0; 0; 1; 0], [2.0885812311199768913287869744681966008 + 3.141592653589 |
[[-2; 1; 1; 0; 1], [2.0885812311199768913287869744681966008 + 3.141592653589 |
7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244 |
7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244 |
7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160 |
7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160 |
203 + 2.5437460822678889883600220330800078854*I]] |
207 + 2.5437460822678889883600220330800078854*I]] |
? idealnorm(nf,idt) |
? idealnorm(nf,idt) |
16 |
16 |
? idp=idealpow(nf,idx,7) |
? idp=idealpow(nf,idx,7) |
|
|
[2187 1807 2129 692 1379] |
[2187 1436 1807 630 1822] |
|
|
[0 1 0 0 0] |
[0 1 0 0 0] |
|
|
Line 1132 I, -20.610866187462450639586440264933189691 + 9.424777 |
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Line 1015 I, -20.610866187462450639586440264933189691 + 9.424777 |
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|
|
? idealpow(nf,idx,7,1) |
? idealpow(nf,idx,7,1) |
|
|
[5 0 0 2 0] |
[2 0 0 0 0] |
|
|
[0 5 0 0 0] |
[0 2 0 0 0] |
|
|
[0 0 5 2 0] |
[0 0 2 0 0] |
|
|
[0 0 0 1 0] |
[0 0 0 2 1] |
|
|
[0 0 0 0 5] |
[0 0 0 0 1] |
|
|
? idealprimedec(nf,2) |
? idealprimedec(nf,2) |
[[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1, |
[[2, [3, 0, 1, 0, 0]~, 1, 1, [0, 0, 0, 1, 1]~], [2, [12, -4, -2, 11, 3]~, 1, |
4, [1, 1, 0, 0, 0]~]] |
4, [1, 0, 1, 0, 0]~]] |
? idealprimedec(nf,3) |
? idealprimedec(nf,3) |
[[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2, |
[[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~], [3, [-1, -1, -1, 0, 0]~, |
2, [1, 2, 3, 1, 0]~]] |
2, 2, [0, 2, 2, 1, 0]~]] |
? idealprimedec(nf,11) |
? idealprimedec(nf,11) |
[[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]] |
[[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]] |
? idealprincipal(nf,Mod(x^3+5,nfpol)) |
? idealprincipal(nf,Mod(x^3+5,nfpol)) |
|
|
[6] |
[6] |
|
|
[0] |
|
|
|
[1] |
[1] |
|
|
[3] |
[3] |
|
|
[0] |
[1] |
|
|
|
[3] |
|
|
? idealtwoelt(nf,idy) |
? idealtwoelt(nf,idy) |
[5, [2, 0, 2, 1, 0]~] |
[5, [2, 2, 1, 2, 1]~] |
? idealtwoelt(nf,idy,10) |
? idealtwoelt(nf,idy,10) |
[-2, 0, -2, -1, 0]~ |
[-2, -2, -1, -2, -1]~ |
? idealstar(nf2,54) |
? idealstar(nf2,54) |
[[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0, |
[[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0, |
0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[ |
0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[ |
0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0] |
1, 0, 1]~], [[1, 0, -27]~], [[]~], 1]], [[[26], [[2, 2, 1]~], [[-25, 2, -26] |
~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0 |
~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0 |
]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3 |
]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3 |
, 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~, |
, 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~, |
[1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0, |
[1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0, |
0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7 |
0]]], [[], [], [;]]], [468, 469, 0, 0, -85358, 0, 0, -36582; 0, 0, 1, 0, -5 |
, -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]] |
, -6, 0, -6; 0, 0, 0, 1, -8, 0, -6, -6]] |
? idealval(nf,idp,vp) |
? idealval(nf,idp,vp) |
7 |
7 |
? ideleprincipal(nf,Mod(x^3+5,nfpol)) |
? ideleprincipal(nf,Mod(x^3+5,nfpol)) |
[[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897 |
[[6; 1; 3; 1; 3], [2.2324480827796254080981385584384939684 + 3.1415926535897 |
932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851 |
932384626433832795028841*I, 5.0387659675158716386435353106610489968 + 1.5851 |
760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173 |
760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173 |
- 0.0083630478144368246110910258645462996191*I]] |
- 0.0083630478144368246110910258645462996225*I]] |
? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol)) |
? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol)) |
[6, 0, 1, 3, 0]~ |
[6, 1, 3, 1, 3]~ |
? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol)) |
? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol)) |
[1, 1, 1, 3, 0]~ |
[1, 1, 4, 1, 3]~ |
? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)]) |
? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)]) |
|
|
[[0, 1, 1, 0, 0]~] |
[[3, -2, 1, 1, 0]~] |
|
|
[[1, 0, 1, 0, 0]~] |
[[4, -2, 0, 1, 0]~] |
|
|
? matbasistoalg(nf,bc) |
? matbasistoalg(nf,bc) |
|
|
Line 1214 Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25) |
|
Line 1097 Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25) |
|
4/139623738889203638909659*x - 13185339461968406/58346808996920447] |
4/139623738889203638909659*x - 13185339461968406/58346808996920447] |
? da=nfdetint(nf,[a,aid]) |
? da=nfdetint(nf,[a,aid]) |
|
|
[30 5 25 27 10] |
[90 70 35 0 65] |
|
|
[0 5 0 0 0] |
[0 5 0 0 0] |
|
|
[0 0 5 2 0] |
[0 0 5 0 0] |
|
|
[0 0 0 1 0] |
[0 0 0 5 0] |
|
|
[0 0 0 0 5] |
[0 0 0 0 5] |
|
|
Line 1231 Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25) |
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Line 1114 Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25) |
|
? nfdisc(p2,0,fa) |
? nfdisc(p2,0,fa) |
136866601 |
136866601 |
? nfeltdiv(nf,ba,bb) |
? nfeltdiv(nf,ba,bb) |
[755/373, -152/373, 159/373, 120/373, -264/373]~ |
[584/373, 66/373, -32/373, -105/373, 120/373]~ |
? nfeltdiveuc(nf,ba,bb) |
? nfeltdiveuc(nf,ba,bb) |
[2, 0, 0, 0, -1]~ |
[2, 0, 0, 0, 0]~ |
? nfeltdivrem(nf,ba,bb) |
? nfeltdivrem(nf,ba,bb) |
[[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~] |
[[2, 0, 0, 0, 0]~, [4, -1, -5, -1, -3]~] |
? nfeltmod(nf,ba,bb) |
? nfeltmod(nf,ba,bb) |
[-12, -7, 0, 9, 5]~ |
[4, -1, -5, -1, -3]~ |
? nfeltmul(nf,ba,bb) |
? nfeltmul(nf,ba,bb) |
[-25, -50, -30, 15, 90]~ |
[50, -15, -35, 60, 15]~ |
? nfeltpow(nf,bb,5) |
? nfeltpow(nf,bb,5) |
[23455, 156370, 115855, 74190, -294375]~ |
[-291920, 136855, 230560, -178520, 74190]~ |
? nfeltreduce(nf,ba,idx) |
? nfeltreduce(nf,ba,idx) |
[1, 0, 0, 0, 0]~ |
[1, 0, 0, 0, 0]~ |
? nfeltval(nf,ba,vp) |
? nfeltval(nf,ba,vp) |
0 |
0 |
? nffactor(nf2,x^3+x) |
? nffactor(nf2,x^3+x) |
|
|
[Mod(1, y^3 - y - 1)*x 1] |
[x 1] |
|
|
[Mod(1, y^3 - y - 1)*x^2 + Mod(1, y^3 - y - 1) 1] |
[x^2 + 1 1] |
|
|
? aut=nfgaloisconj(nf3) |
? aut=nfgaloisconj(nf3) |
[x, 1/12*x^4 - 1/2*x, -1/12*x^4 - 1/2*x, 1/12*x^4 + 1/2*x, -1/12*x^4 + 1/2*x |
[-x, x, -1/12*x^4 - 1/2*x, -1/12*x^4 + 1/2*x, 1/12*x^4 - 1/2*x, 1/12*x^4 + 1 |
, -x]~ |
/2*x]~ |
? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108)) |
? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108)) |
Mod(1/2*x^5 - 9*x^2, x^6 + 108) |
Mod(-1/2*x^5 + 9*x^2, x^6 + 108) |
? nfhilbert(nf,3,5) |
? nfhilbert(nf,3,5) |
-1 |
-1 |
? nfhilbert(nf,3,5,idf[1,1]) |
? nfhilbert(nf,3,5,idf[1,1]) |
-1 |
-1 |
? nfhnf(nf,[a,aid]) |
? nfhnf(nf,[a,aid]) |
[[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1 |
[[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [ |
, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0, |
1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0 |
0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0 |
, 0, 0, 0]~], [[10, 4, 5, 6, 7; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; |
, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; |
0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0 |
0, 0, 0, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; |
; 0, 0, 0, 0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, |
0, 0, 0, 0, 1]]] |
0; 0, 0, 0, 0, 1]]] |
? nfhnfmod(nf,[a,aid],da) |
? nfhnfmod(nf,[a,aid],da) |
[[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1 |
[[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [ |
, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0, |
1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0 |
0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0 |
, 0, 0, 0]~], [[10, 4, 5, 6, 7; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; |
, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; |
0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0 |
0, 0, 0, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; |
; 0, 0, 0, 0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, |
0, 0, 0, 0, 1]]] |
0; 0, 0, 0, 0, 1]]] |
? nfisideal(bnf[7],[5,1;0,1]) |
? nfisideal(bnf[7],[5,2;0,1]) |
1 |
1 |
? nfisincl(x^2+1,x^4+1) |
? nfisincl(x^2+1,x^4+1) |
[-x^2, x^2] |
[-x^2, x^2] |
Line 1290 Mod(1/2*x^5 - 9*x^2, x^6 + 108) |
|
Line 1173 Mod(1/2*x^5 - 9*x^2, x^6 + 108) |
|
? nfrootsof1(nf) |
? nfrootsof1(nf) |
[2, [-1, 0, 0, 0, 0]~] |
[2, [-1, 0, 0, 0, 0]~] |
? nfsnf(nf,[as,haid,vaid]) |
? nfsnf(nf,[as,haid,vaid]) |
[[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3 |
[[2562748315629757085585610, 436545976069778274371140, 123799938628701108220 |
910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; |
1405, 2356446991473627724963350, 801407102592194537169612; 0, 5, 0, 0, 2; 0, |
0, 0, 0, 1, 0; 0, 0, 0, 0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0 |
0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0 |
; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, |
, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; |
0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]] |
0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]] |
? nfsubfields(nf) |
? nfsubfields(nf) |
[[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]] |
[[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]] |
? polcompositum(x^4-4*x+2,x^3-x-1) |
? polcompositum(x^4-4*x+2,x^3-x-1) |
Line 1368 x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289 |
|
Line 1251 x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289 |
|
0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, |
0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, |
0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~ |
0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~ |
], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1 |
], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1 |
, 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25; |
, 0; 0, 0, 1], [1, 0, 2/5; 0, 1, 3/5; 0, 0, 1/5], [1, 0, 22/25; 0, 1, 8/25; |
0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1 |
0, 0, 1/25]], [416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1 |
280, 5, 5]~] |
275, 5, 5]~] |
? rnfbasis(bnf2,aa) |
? rnfbasis(bnf2,aa) |
|
|
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [38/25, -33/25, 11/25]~ [-11, -4, 9]~] |
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-6/25, 66/25, 77/25]~ [-391/25, -699/25, |
|
197/25]~] |
|
|
[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-14/25, 24/25, -8/25]~ [28/5, 2/5, -24/5] |
[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [18/25, -48/25, -56/25]~ [268/25, 552/25, |
~] |
-206/25]~] |
|
|
[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [57/25, -12/25, 4/25]~ [-58/5, -47/5, 44/5 |
[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [41/25, 24/25, 28/25]~ [-194/25, -116/25, |
]~] |
-127/25]~] |
|
|
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [9/25, 6/25, -2/25]~ [-4/5, -11/5, 2/5]~] |
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [17/25, -12/25, -14/25]~ [52/25, 178/25, - |
|
109/25]~] |
|
|
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [8/25, -3/25, 1/25]~ [-9/5, -6/5, 7/5]~] |
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/25, 6/25, 7/25]~ [-41/25, -49/25, -3/25 |
|
]~] |
|
|
? rnfdisc(nf2,p) |
? rnfdisc(nf2,p) |
[[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~] |
[[416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~] |
? rnfequation(nf2,p) |
? rnfequation(nf2,p) |
x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1 |
x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1 |
? rnfequation(nf2,p,1) |
? rnfequation(nf2,p,1) |
Line 1394 x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1 |
|
Line 1280 x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1 |
|
5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0] |
5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0] |
? rnfhnfbasis(bnf2,aa) |
? rnfhnfbasis(bnf2,aa) |
|
|
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~ |
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [6/5, 4/5, -2/5]~ [-22/25, -33/25, 99/25]~ |
] |
] |
|
|
[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~] |
[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-6/5, -4/5, 2/5]~ [16/25, 24/25, -72/25]~ |
|
] |
|
|
[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~] |
[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-3/5, -2/5, 1/5]~ [-8/25, -12/25, 36/25]~ |
|
] |
|
|
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~] |
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/5, -2/5, 1/5]~ [4/25, 6/25, -18/25]~] |
|
|
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~] |
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/25, -3/25, 9/25]~] |
|
|
? rnfisfree(bnf2,aa) |
? rnfisfree(bnf2,aa) |
1 |
1 |
? rnfsteinitz(nf2,aa) |
? rnfsteinitz(nf2,aa) |
[[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [38/25, -33/25, 11/25]~, [-27/125, 33/ |
[[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-6/25, 66/25, 77/25]~, [17/125, -66/1 |
125, -11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-14/25, 24/25, -8/25]~, |
25, -77/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [18/25, -48/25, -56/25]~, |
[6/125, -24/125, 8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [57/25, -12/2 |
[-26/125, 48/125, 56/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [41/25, 24/ |
5, 4/25]~, [-53/125, 12/125, -4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [ |
25, 28/25]~, [-37/125, -24/125, -28/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0] |
9/25, 6/25, -2/25]~, [-11/125, -6/125, 2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, |
~, [17/25, -12/25, -14/25]~, [-19/125, 12/125, 14/125]~; [0, 0, 0]~, [0, 0, |
0, 0]~, [8/25, -3/25, 1/25]~, [-7/125, 3/125, -1/125]~], [[1, 0, 0; 0, 1, 0; |
0]~, [0, 0, 0]~, [4/25, 6/25, 7/25]~, [-3/125, -6/125, -7/125]~], [[1, 0, 0; |
0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, |
0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1] |
0; 0, 1, 0; 0, 0, 1], [125, 0, 108; 0, 125, 22; 0, 0, 1]], [416134375, 21294 |
, [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0, 22; 0, 125, 108; 0, 0, 1]], [4161343 |
0625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~] |
75, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~] |
? nfz=zetakinit(x^2-2); |
? nfz=zetakinit(x^2-2); |
? zetak(nfz,-3) |
? zetak(nfz,-3) |
0.091666666666666666666666666666666666666 |
0.091666666666666666666666666666666666666 |
Line 1425 x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1 |
|
Line 1313 x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1 |
|
7938845*I |
7938845*I |
? setrand(1);quadclassunit(1-10^7,,[1,1]) |
? setrand(1);quadclassunit(1-10^7,,[1,1]) |
*** Warning: not a fundamental discriminant in quadclassunit. |
*** Warning: not a fundamental discriminant in quadclassunit. |
[2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99984980 |
[2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 1.00257481 |
75377600233] |
6299307750] |
? setrand(1);quadclassunit(10^9-3,,[0.5,0.5]) |
? setrand(1);quadclassunit(10^9-3,,[0.5,0.5]) |
[4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074 |
[4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074 |
5514, 0.9990369458964383232] |
5514, 0.9849577285369119736] |
? sizebyte(%) |
? sizebyte(%) |
328 |
320 |
? getheap |
? getheap |
[198, 120613] |
[199, 115764] |
? print("Total time spent: ",gettime); |
? print("Total time spent: ",gettime); |
Total time spent: 4836 |
Total time spent: 3629 |
? \q |
? \q |