File: [local] / OpenXM_contrib / pari / src / test / 32 / Attic / nfields (download)
Revision 1.1.1.1 (vendor branch), Sun Jan 9 17:35:34 2000 UTC (24 years, 5 months ago) by maekawa
Branch: PARI_GP
CVS Tags: maekawa-ipv6, VERSION_2_0_17_BETA, RELEASE_20000124, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, RELEASE_1_1_3, RELEASE_1_1_2
Changes since 1.1: +0 -0
lines
Import PARI/GP 2.0.17 beta.
|
realprecision = 38 significant digits
echo = 1 (on)
? nfpol=x^5-5*x^3+5*x+25
x^5 - 5*x^3 + 5*x + 25
? qpol=y^3-y-1;un=Mod(1,qpol);w=Mod(y,qpol);p=un*(x^5-5*x+w)
Mod(1, y^3 - y - 1)*x^5 + Mod(-5, y^3 - y - 1)*x + Mod(y, y^3 - y - 1)
? p2=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
2057
? fa=[11699,6;2392997,2;4987333019653,2]
[11699 6]
[2392997 2]
[4987333019653 2]
? 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));
? nf=nfinit(nfpol)
[x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920
69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929
269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119
211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I,
3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331
539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319
06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196
23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 +
1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610
81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887
04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982
34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I]
, [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262
77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515
382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8
976972027301414394898806541072047941, 6.408909349142616853840753758109052071
2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441
22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929
269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875
724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 -
1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400
435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104
7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231
7837223883352537186677084*I], [5, 4.0215293653309345240000000000000000000 E-
87, 10.000000000000000000000000000000000000, -5.0000000000000000000000000000
000000000, 7.0000000000000000000000000000000000000; 4.0215293653309345240000
000000000000000 E-87, 19.488486013650707197449403270536023970, 8.04305873066
18690490000000000000000000 E-86, 19.488486013650707197449403270536023970, 4.
1504592246706085588902013976045703227; 10.0000000000000000000000000000000000
00, 8.0430587306618690490000000000000000000 E-86, 85.96021742085184648030513
3936577594605, -36.034268291482979838267056239752434596, 53.5761304525111078
88183080361946556763; -5.0000000000000000000000000000000000000, 19.488486013
650707197449403270536023970, -36.034268291482979838267056239752434596, 60.91
6248374441986300937507618575151517, -18.470101750219179344070032346246890434
; 7.0000000000000000000000000000000000000, 4.1504592246706085588902013976045
703227, 53.576130452511107888183080361946556763, -18.47010175021917934407003
2346246890434, 37.970152892842367340897384258599214282], [5, 0, 10, -5, 7; 0
, 10, 0, 10, -5; 10, 0, 30, -55, 20; -5, 10, -55, 45, -39; 7, -5, 20, -39, 9
], [345, 0, 340, 167, 150; 0, 345, 110, 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1,
0; 0, 0, 0, 0, 1], [132825, -18975, -5175, 27600, 17250; -18975, 34500, 414
00, 3450, -43125; -5175, 41400, -41400, -15525, 51750; 27600, 3450, -15525,
-3450, 0; 17250, -43125, 51750, 0, -86250], [595125, [-120750, 63825, 113850
, 0, 8625]~, 125439056256992431640625]], [-2.4285174907194186068992069565359
418364, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940
82219556466857*I, -0.75045317576910401286427186094108607489 + 1.310146268535
8123283560773619310445915*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)
[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
741050929194782733001765987770358483, 0.158944197453903762065494816710718942
89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
.13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
, -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
894419745390376206549481671071894289, -0.10730191731399545071859505671520521
623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
000000000000000000000000000000000000, -44.0000000000000000000000000000000000
00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
42564718082452641322500190813370023; -17.00000000000000000000000000000000000
0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
0]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684,
-0.13838372073406036365047976417441696637 + 0.49181637657768643499753285514
741525107*I, 1.6829412935943127761629561615079976005 + 2.0500351226010726172
974286983598602163*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)
[[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
9741050929194782733001765987770358483, 0.15894419745390376206549481671071894
289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975
3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602
1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +
0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835
7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431
27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703
526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*
I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301
348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354
4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,
-0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294
83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459
48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821
160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2
.7407052124261919274965153538200060029 - 13.80035504457609895474415392596927
4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753
9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573
272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1
5894419745390376206549481671071894289, -0.1073019173139954507185950567152052
1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346
899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000
00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17
.000000000000000000000000000000000000, -44.000000000000000000000000000000000
000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471
283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499
932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000
00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912
62388960975827806174040462368, 143.93295090847353519436673793501057176, -55.
842564718082452641322500190813370023; -17.0000000000000000000000000000000000
00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935
01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201
80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084
1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400
38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -
101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215
, 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125,
-296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670
0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89
700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725
, 0]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684
, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975328551
4741525107*I, 1.6829412935943127761629561615079976005 + 2.050035122601072617
2974286983598602163*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)
[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
741050929194782733001765987770358483, 0.158944197453903762065494816710718942
89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
.13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
, -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
894419745390376206549481671071894289, -0.10730191731399545071859505671520521
623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
000000000000000000000000000000000000, -44.0000000000000000000000000000000000
00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
42564718082452641322500190813370023; -17.00000000000000000000000000000000000
0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
0]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684,
-0.13838372073406036365047976417441696637 + 0.49181637657768643499753285514
741525107*I, 1.6829412935943127761629561615079976005 + 2.0500351226010726172
974286983598602163*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);
? nf4=nfinit(x^3-10*x+8)
[x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -3.50466435358804770515010852590433205
79, 6.1413361156553641347759399165844441383; 1, 0.86464088669540302583112842
266613688800, 0.37380193147270638662350044992137561317; 1, 2.640023466892644
6793189801032381951699, 3.4848619528719294786005596334941802484], [1, 1, 1;
-3.5046643535880477051501085259043320579, 0.86464088669540302583112842266613
688800, 2.6400234668926446793189801032381951699; 6.1413361156553641347759399
165844441383, 0.37380193147270638662350044992137561317, 3.484861952871929478
6005596334941802484], [3, -3.4544674213975667950000000000000000000 E-77, 10.
000000000000000000000000000000000000; -3.45446742139756679500000000000000000
00 E-77, 20.000000000000000000000000000000000000, -12.0000000000000000000000
00000000000000; 10.000000000000000000000000000000000000, -12.000000000000000
000000000000000000000, 50.000000000000000000000000000000000000], [3, 0, 10;
0, 20, -12; 10, -12, 50], [284, 168, 235; 0, 2, 0; 0, 0, 1], [856, -120, -20
0; -120, 50, 36; -200, 36, 60], [568, [80, 14, -24]~, 322624]], [-3.50466435
35880477051501085259043320579, 0.86464088669540302583112842266613688800, 2.6
400234668926446793189801032381951699], [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);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
08795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.97922
3478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 86
6.56619430687100142570357249059499540 + 6.2831853071795864769252867665590057
684*I, 2881.3396396084587293295626563644245032 + 3.1415926535897932384626433
832795028842*I, 27379.624790530768080428797780058276925 + 1.9281866867095232
000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.69
04930509626865380000000000000000000 E-42*I, -34585.5562501515577199980340439
18848670 + 9.4247779607693797153879301498385086526*I, 23348.3225111226233465
49049047574325150 + 3.1415926535897932384626433832795028842*I, -0.3432876442
7702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -4
031.7117453543045067063239888430083582 + 9.424777960769379715387930149838508
6526*I, 27379.690968832650826160983148550600089 + 9.424777960769379715387930
1498385086526*I; -23347.979223478346319454659159707591731 + 9.42477796076937
97153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.1019
476959481835360000000000000000000 E-45*I, -2881.3396396084587293295626563644
245032 + 9.4247779607693797153879301498385086526*I, -27379.62479053076808042
8797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.3345679
30851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 3458
5.556250151557719998034043918848670 + 6.283185307179586476925286766559005768
4*I, -23348.322511122623346549049047574325150 + 9.42477796076937971538793014
98385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.711
7453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I,
-27379.690968832650826160983148550600089 + 6.283185307179586476925286766559
0057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5,
[-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1
, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [1
7, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1,
1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 22
9, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.066372975210777963
5959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.066
3729752107779635959310246705326058], [2, 1.000000000000000000000000000000000
0000; 1.0000000000000000000000000000000000000, 115.0000000000000000000000000
0000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114,
1]~, 229]], [-7.0663729752107779635959310246705326058, 8.066372975210777963
5959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3,
[3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512
6545793690341704100000000000, [2, -1], [x + 7], 130], [Mat(1), Mat(1), [[[3,
2; 0, 1], [0, 0]]]], 0]
? 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.
82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
4*I; 129.82045011403975460991182396195022419 + 4.907207226380705833000000000
0000000000 E-95*I], [2093832.2286247580721598744691800364716 + 9.42477796076
93797153879301498385086526*I, 463727.88770776479369558667281813008490 + 6.28
31853071795864769252867665590057684*I, 229510.681191741210743599007448730565
20 + 3.1415926535897932384626433832795028842*I, -13814064.276184856248286107
275967161406 + 6.2831853071795864769252867665590057684*I, 10975229.442376145
014058790444262893275 + 9.4247779607693797153879301498385086526*I, 12628868.
476868730308574917279106536834 + 6.2831853071795864769252867665590057684*I,
2595210.6815750606798700790306370856686 + 3.14159265358979323846264338327950
28842*I, 21463208.279603014333968661075393279510 + 6.28318530717958647692528
67665590057684*I, 9340416.4917416354701732132629720490406 + 9.42477796076937
97153879301498385086526*I, 224801.35127844528675036994618361508061 + 12.5663
70614359172953850573533118011536*I, -224801.35127844528675036994618361508061
+ 2.1125754163178543118626478980000000000 E-90*I, 40271115.6788572427160038
79014241558828 + 6.2831853071795864769252867665590057684*I, -10066612.284788
886379386747743460630561 + 9.4600667685469491310218392850000000000 E-89*I, 1
0267873.880681641662748682261863339788 + 12.56637061435917295385057353311801
1536*I, -4435991.6114732228963510067335229085617 + 6.28318530717958647692528
67665590057684*I, 8361196.2032957779193404684451855312611 + 9.42477796076937
97153879301498385086526*I, -10272584.501589374356405593568879583106 + 9.4247
779607693797153879301498385086526*I, 41648172.195327314227598351804544361493
+ 9.4247779607693797153879301498385086526*I, -2117367.665066341919805155100
3369291210 + 1.9897854874556092437572207830000000000 E-89*I; -2093832.228624
7580721598744691800364716 + 3.1415926535897932384626433832795028842*I, -4637
27.88770776479369558667281813008490 + 9.424777960769379715387930149838508652
6*I, -229510.68119174121074359900744873056520 + 12.5663706143591729538505735
33118011536*I, 13814064.276184856248286107275967161405 + 5.22154890000820159
90000000000000000000 E-90*I, -10975229.442376145014058790444262893275 + 12.5
66370614359172953850573533118011536*I, -12628868.476868730308574917279106536
834 + 3.1415926535897932384626433832795028842*I, -2595210.681575060679870079
0306370856686 + 12.566370614359172953850573533118011536*I, -21463208.2796030
14333968661075393279510 + 9.4247779607693797153879301498385086526*I, -934041
6.4917416354701732132629720490406 + 6.2831853071795864769252867665590057684*
I, -224801.35127844528675036994618361508061 + 12.566370614359172953850573533
118011536*I, 224801.35127844528675036994618361508061 + 8.4971798285841941830
000000000000000000 E-92*I, -40271115.678857242716003879014241558828 + 12.566
370614359172953850573533118011536*I, 10066612.284788886379386747743460630561
+ 3.8050554944202303880000000000000000000 E-90*I, -10267873.880681641662748
682261863339788 + 3.1415926535897932384626433832795028842*I, 4435991.6114732
228963510067335229085617 + 9.4247779607693797153879301498385086526*I, -83611
96.2032957779193404684451855312611 + 12.566370614359172953850573533118011536
*I, 10272584.501589374356405593568879583106 + 3.8829118423163890830000000000
000000000 E-90*I, -41648172.195327314227598351804544361493 + 3.1415926535897
932384626433832795028842*I, 2117367.6650663419198051551003369291210 + 8.0033
745765686035150000000000000000000 E-91*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2,
[2, 1]~, 1, 1, [1, 1]~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-
1, 1]~], [7, [3, 1]~, 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5
, 1]~, 1, 1, [-6, 1]~], [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1,
[-3, 1]~], [23, [-7, 1]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29
, [-14, 1]~, 1, 1, [13, 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~
, 1, 1, [7, 1]~], [31, [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1
]~], [41, [6, 1]~, 1, 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [1
5, 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, -315.728161
30129840161392089489603747004; 1, 316.72816130129840161392089489603747004],
[1, 1; -315.72816130129840161392089489603747004, 316.72816130129840161392089
489603747004], [2, 1.0000000000000000000000000000000000000; 1.00000000000000
00000000000000000000000, 200001.00000000000000000000000000000000], [2, 1; 1,
200001], [400001, 200000; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~
, 400001]], [-315.72816130129840161392089489603747004, 316.72816130129840161
392089489603747004], [1, x], [1, 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [
[5, [5], [[2, 1; 0, 1]]], 129.82045011403975460991182396195022419, 0.9876536
9790690472391212970100000000000, [2, -1], [379554884019013781006303254896369
154068336082609238336*x + 11983616564425078999046283595002287166517812761131
6131167], 124], [Mat(1), Mat(1), [[[2, 1; 0, 1], [0, 0]]]], 0]
? \p19
realprecision = 19 significant digits
? 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
82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,
1], Mat(2), Mat([0, 1, 1, 1, 0, 1, 1, 1]), [9, 15, 16, 17, 10, 33, 69, 39,
57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [4, 3, 1, 2, 3, 1, 11, 1,
-7; -1, 1, -1, 1, 0, 1, 2, 4, -2; 0, 0, 0, 0, 0, 0, -1, 1, 0]]
? \p38
realprecision = 38 significant digits
? bnrinit(bnf,[[5,3;0,1],[1,0]],1)
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
3832795028842*I, 27379.624790530768080428797780058276925 + 1.928186686709523
2000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.6
904930509626865380000000000000000000 E-42*I, -34585.556250151557719998034043
918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
797153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.101
9476959481835360000000000000000000 E-45*I, -2881.339639608458729329562656364
4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.71
17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
, -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
, 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
, [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
26545793690341704100000000000, [2, -1], [x + 7], 130], [Mat(1), Mat(1), [[[3
, 2; 0, 1], [0, 0]]]], 0], [[[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, 0]~
], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[3, 2; 0, 1]]], [[0, 0; 0, 1],
[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
061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
3832795028842*I, 27379.624790530768080428797780058276925 + 1.928186686709523
2000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.6
904930509626865380000000000000000000 E-42*I, -34585.556250151557719998034043
918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
797153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.101
9476959481835360000000000000000000 E-45*I, -2881.339639608458729329562656364
4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.71
17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
, -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
, 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
, [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
26545793690341704100000000000, [2, -1], [x + 7], 130], [Mat(1), Mat(1), [[[3
, 2; 0, 1], [0, 0]]]], 0], [[[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, 0]~
], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[3, 2; 0, 1]]], [[0, 0; 0, 1],
[1, -1; 1, 1]]]
? rnfinit(nf2,x^5-x-2)
[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
279776896412, 1.6057155120361619195949075151301679393, 2.0347118029638523119
874445717108994866, 2.5783223055935536544757871909285592749; 1, 0.2609638803
8645528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -1
.3177592693689352747870763902256347904 + 0.614427010164338838041906608641467
31824*I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524
673160314582604*I, 1.3589689411882615753626439480614001936 - 1.6193337759893
970298359887428575174472*I; 1, -0.89454803265751744362901306471557966872 + 0
.53414854617473272670874609150394379949*I, 0.5149015133508543149896226326605
5082078 - 0.95564306225496055080453352211847466685*I, 0.04985121658507159775
5867063892284310224 + 1.1299025160425089918993024639913611785*I, -0.64813009
398503840260053754352567983115 - 0.98412411795664774269323431620030610541*I]
, [1, 1.2671683045421243172528914279776896412 + 0.E-38*I, 1.6057155120361619
195949075151301679393 + 0.E-38*I, 2.0347118029638523119874445717108994866 +
0.E-37*I, 2.5783223055935536544757871909285592749 + 0.E-37*I; 1, 0.260963880
38645528500256735072673484811 - 1.1772261533941944394700286585617926513*I, -
1.3177592693689352747870763902256347904 - 0.61442701016433883804190660864146
731824*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921652
4673160314582604*I, 1.3589689411882615753626439480614001936 + 1.619333775989
3970298359887428575174472*I; 1, 0.26096388038645528500256735072673484811 + 1
.1772261533941944394700286585617926513*I, -1.3177592693689352747870763902256
347904 + 0.61442701016433883804190660864146731824*I, -1.06720711806699775374
95893497477340535 - 1.3909574189920019216524673160314582604*I, 1.35896894118
82615753626439480614001936 - 1.6193337759893970298359887428575174472*I; 1, -
0.89454803265751744362901306471557966872 - 0.5341485461747327267087460915039
4379949*I, 0.51490151335085431498962263266055082078 + 0.95564306225496055080
453352211847466685*I, 0.049851216585071597755867063892284310224 - 1.12990251
60425089918993024639913611785*I, -0.64813009398503840260053754352567983115 +
0.98412411795664774269323431620030610541*I; 1, -0.8945480326575174436290130
6471557966872 + 0.53414854617473272670874609150394379949*I, 0.51490151335085
431498962263266055082078 - 0.95564306225496055080453352211847466685*I, 0.049
851216585071597755867063892284310224 + 1.12990251604250899189930246399136117
85*I, -0.64813009398503840260053754352567983115 - 0.984124117956647742693234
31620030610541*I]], [[1, 2, 2; 1.2671683045421243172528914279776896412, 0.52
192776077291057000513470145346969622 - 2.35445230678838887894005731712358530
26*I, -1.7890960653150348872580261294311593374 - 1.0682970923494654534174921
830078875989*I; 1.6057155120361619195949075151301679393, -2.6355185387378705
495741527804512695809 - 1.2288540203286776760838132172829346364*I, 1.0298030
267017086299792452653211016415 + 1.9112861245099211016090670442369493337*I;
2.0347118029638523119874445717108994866, -2.13441423613399550749917869949546
81070 + 2.7819148379840038433049346320629165208*I, 0.09970243317014319551173
4127784568620449 - 2.2598050320850179837986049279827223571*I; 2.578322305593
5536544757871909285592749, 2.7179378823765231507252878961228003872 + 3.23866
75519787940596719774857150348944*I, -1.2962601879700768052010750870513596623
+ 1.9682482359132954853864686324006122108*I], [1, 1, 1, 1, 1; 1.26716830454
21243172528914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484
811 + 1.1772261533941944394700286585617926513*I, 0.2609638803864552850025673
5072673484811 - 1.1772261533941944394700286585617926513*I, -0.89454803265751
744362901306471557966872 + 0.53414854617473272670874609150394379949*I, -0.89
454803265751744362901306471557966872 - 0.53414854617473272670874609150394379
949*I; 1.6057155120361619195949075151301679393 + 0.E-38*I, -1.31775926936893
52747870763902256347904 + 0.61442701016433883804190660864146731824*I, -1.317
7592693689352747870763902256347904 - 0.6144270101643388380419066086414673182
4*I, 0.51490151335085431498962263266055082078 - 0.95564306225496055080453352
211847466685*I, 0.51490151335085431498962263266055082078 + 0.955643062254960
55080453352211847466685*I; 2.0347118029638523119874445717108994866 + 0.E-37*
I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524673160
314582604*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921
6524673160314582604*I, 0.049851216585071597755867063892284310224 + 1.1299025
160425089918993024639913611785*I, 0.049851216585071597755867063892284310224
- 1.1299025160425089918993024639913611785*I; 2.57832230559355365447578719092
85592749 + 0.E-37*I, 1.3589689411882615753626439480614001936 - 1.61933377598
93970298359887428575174472*I, 1.3589689411882615753626439480614001936 + 1.61
93337759893970298359887428575174472*I, -0.6481300939850384026005375435256798
3115 - 0.98412411795664774269323431620030610541*I, -0.6481300939850384026005
3754352567983115 + 0.98412411795664774269323431620030610541*I]], [[5, -5.877
4717524647712700000000000000000000 E-39 + 3.42274939913785433235754950013147
29016*I, 2.3509887009859085080000000000000000000 E-38 - 0.682432104181243425
52525382695401469720*I, -2.3509887009859085080000000000000000000 E-38 - 0.52
210980589898585950632970408019416371*I, 3.9999999999999999999999999999999999
999 - 5.2069157878920895450584461181156471052*I; -5.877471752464771270000000
0000000000000 E-39 - 3.4227493991378543323575495001314729016*I, 6.6847043424
634879841147654217963674264 - 5.8774717524647712700000000000000000000 E-39*I
, 0.85145677340721376574333983502938573598 + 4.58295731809784302915415926006
01794652*I, -0.13574266252716976137461193821267520737 - 0.288051085440257723
61738936467682050391*I, 0.27203784387468568916539788233281013320 - 1.5917147
279942947718965650859986677247*I; 2.3509887009859085080000000000000000000 E-
38 + 0.68243210418124342552525382695401469720*I, 0.8514567734072137657433398
3502938573598 - 4.5829573180978430291541592600601794652*I, 9.163096853022107
7951281598310681467898 + 0.E-38*I, 2.2622987652095629453403849736225691490 +
6.2361927913558506765724047063180706869*I, -0.21796409886496632254445901043
974770643 + 0.34559368931063215686158939748833975810*I; -2.35098870098590850
80000000000000000000 E-38 + 0.52210980589898585950632970408019416371*I, -0.1
3574266252716976137461193821267520737 + 0.2880510854402577236173893646768205
0392*I, 2.2622987652095629453403849736225691490 - 6.236192791355850676572404
7063180706869*I, 12.845768948832335511882696939380696155 + 1.175494350492954
2540000000000000000000 E-38*I, 4.5618400502378124720913214622468855074 + 8.6
033930051068500425218923146793019614*I; 3.9999999999999999999999999999999999
999 + 5.2069157878920895450584461181156471052*I, 0.2720378438746856891653978
8233281013320 + 1.5917147279942947718965650859986677247*I, -0.21796409886496
632254445901043974770643 - 0.34559368931063215686158939748833975810*I, 4.561
8400502378124720913214622468855074 - 8.6033930051068500425218923146793019615
*I, 18.362968630416114402425299186062892646 + 5.8774717524647712700000000000
000000000 E-39*I], [5, -1.1754943504929542540000000000000000000 E-38 + 0.E-3
8*I, 2.3509887009859085080000000000000000000 E-38 + 0.E-38*I, -1.76324152620
50926680000000000000000000 E-38 + 0.E-38*I, 3.999999999999999999999999999999
9999998 + 0.E-38*I; -1.1754943504929542540000000000000000000 E-38 + 0.E-38*I
, 6.6847043424634879841147654217963674264 - 5.877471752464771270000000000000
0000000 E-39*I, 0.85145677340721376574333983502938573597 + 5.877471752464771
2700000000000000000000 E-39*I, -0.13574266252716976137461193821267520737 + 5
.8774717524647712700000000000000000000 E-39*I, 0.272037843874685689165397882
33281013314 - 5.8774717524647712700000000000000000000 E-39*I; 2.350988700985
9085080000000000000000000 E-38 + 0.E-38*I, 0.8514567734072137657433398350293
8573597 + 5.8774717524647712700000000000000000000 E-39*I, 9.1630968530221077
951281598310681467898 + 0.E-38*I, 2.2622987652095629453403849736225691490 +
2.3509887009859085080000000000000000000 E-38*I, -0.2179640988649663225444590
1043974770651 + 0.E-38*I; -1.7632415262050926680000000000000000000 E-38 + 0.
E-38*I, -0.13574266252716976137461193821267520737 + 5.8774717524647712700000
000000000000000 E-39*I, 2.2622987652095629453403849736225691490 + 2.35098870
09859085080000000000000000000 E-38*I, 12.84576894883233551188269693938069615
5 + 0.E-37*I, 4.5618400502378124720913214622468855073 - 3.526483052410185337
0000000000000000000 E-38*I; 3.9999999999999999999999999999999999998 + 0.E-38
*I, 0.27203784387468568916539788233281013314 - 5.877471752464771270000000000
0000000000 E-39*I, -0.21796409886496632254445901043974770651 + 0.E-38*I, 4.5
618400502378124720913214622468855073 - 3.52648305241018533700000000000000000
00 E-38*I, 18.362968630416114402425299186062892646 + 0.E-37*I]], [Mod(5, y^3
- y - 1), 0, 0, 0, Mod(4, y^3 - y - 1); 0, 0, 0, Mod(4, y^3 - y - 1), Mod(1
0, y^3 - y - 1); 0, 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0; 0, Mod(
4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0, 0; Mod(4, y^3 - y - 1), Mod(10, y^
3 - y - 1), 0, 0, Mod(4, y^3 - y - 1)], [;], [;], [;]], [[1.2671683045421243
172528914279776896412, 0.26096388038645528500256735072673484811 + 1.17722615
33941944394700286585617926513*I, -0.89454803265751744362901306471557966872 +
0.53414854617473272670874609150394379949*I], [1.267168304542124317252891427
9776896412 + 0.E-38*I, 0.26096388038645528500256735072673484811 - 1.17722615
33941944394700286585617926513*I, 0.26096388038645528500256735072673484811 +
1.1772261533941944394700286585617926513*I, -0.894548032657517443629013064715
57966872 - 0.53414854617473272670874609150394379949*I, -0.894548032657517443
62901306471557966872 + 0.53414854617473272670874609150394379949*I]~], [[Mod(
1, y^3 - y - 1), Mod(1, y^3 - y - 1)*x, Mod(1, y^3 - y - 1)*x^2, Mod(1, y^3
- y - 1)*x^3, Mod(1, y^3 - y - 1)*x^4], [[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, 0; 0, 1, 0; 0, 0,
1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [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^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^3 - y - 1)], [], [y^3 - y - 1, [1, 1],
-23, 1, [[1, 1.3247179572447460259609088544780973407, 1.7548776662466927600
495088963585286918; 1, -0.66235897862237301298045442723904867036 + 0.5622795
1206230124389918214490937306149*I, 0.12256116687665361997524555182073565405
- 0.74486176661974423659317042860439236724*I], [1, 2; 1.32471795724474602596
09088544780973407, -1.3247179572447460259609088544780973407 - 1.124559024124
6024877983642898187461229*I; 1.7548776662466927600495088963585286918, 0.2451
2233375330723995049110364147130810 + 1.4897235332394884731863408572087847344
*I], [3, 0.E-96, 2.0000000000000000000000000000000000000; 0.E-96, 3.26463299
87400782801485266890755860756, 1.3247179572447460259609088544780973407; 2.00
00000000000000000000000000000000000, 1.3247179572447460259609088544780973407
, 4.2192762054875453178332176670757633303], [3, 0, 2; 0, 2, 3; 2, 3, 2], [23
, 13, 15; 0, 1, 0; 0, 0, 1], [-5, 6, -4; 6, 2, -9; -4, -9, 6], [23, [7, 10,
1]~, 529]], [1.3247179572447460259609088544780973407, -0.6623589786223730129
8045442723904867036 + 0.56227951206230124389918214490937306149*I], [1, y, y^
2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 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^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 + 110*x^5 - 190*x^4 + 189*x^3 +
144*x^2 + 25*x + 1, Mod(39516536165538345/83718587879473471*x^14 - 650051247
6832995/83718587879473471*x^13 - 196215472046117185/83718587879473471*x^12 +
229902227480108910/83718587879473471*x^11 + 237380704030959181/837185878794
73471*x^10 - 1064931988160773805/83718587879473471*x^9 - 20657086671714300/8
3718587879473471*x^8 + 1772885205999206010/83718587879473471*x^7 + 595203321
7241102348/83718587879473471*x^6 - 4838840187320655696/83718587879473471*x^5
+ 5180390720553188700/83718587879473471*x^4 - 8374015687535120430/837185878
79473471*x^3 + 8907744727915040221/83718587879473471*x^2 + 41559766641234343
81/83718587879473471*x + 318920215718580450/83718587879473471, x^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 + 110*x^5 -
190*x^4 + 189*x^3 + 144*x^2 + 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^12, x^13, 1/83718587879473471*x^14 - 20528463
024680133/83718587879473471*x^13 - 4742392948888610/83718587879473471*x^12 -
9983523646123358/83718587879473471*x^11 + 40898955597139011/837185878794734
71*x^10 + 29412692423971937/83718587879473471*x^9 - 5017479463612351/8371858
7879473471*x^8 + 41014993230075066/83718587879473471*x^7 - 2712810874903165/
83718587879473471*x^6 + 20152905879672878/83718587879473471*x^5 + 9591643151
927789/83718587879473471*x^4 - 8471905745957397/83718587879473471*x^3 - 1339
5753879413605/83718587879473471*x^2 + 27623037732247492/83718587879473471*x
+ 26306699661480593/83718587879473471], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -276230
37732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13395753879413605; 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8471905745957397; 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 27128
10874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -41014993230075066; 0
, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5017479463612351; 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
, 0, 0, 0, -40898955597139011; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 998
3523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4742392948888610; 0
, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20528463024680133; 0, 0, 0, 0, 0, 0
, 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471]]]
? bnfcertify(bnf)
1
? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
[x^4 - 7]
[[2, 1]]
[[-87808, 1]]
[[1, x, x^2, x^3]]
[[2, [2], [[2, 1, 1, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
[14.229975145405511722395637833443108790]
[1.1211171071527562299744232290000000000]
? setrand(1);bnfclassunit(x^2-x-100000)
*** Warning: insufficient precision for fundamental units, not given.
[x^2 - x - 100000]
[[2, 0]]
[[400001, 1]]
[[1, x]]
[[5, [5], [[2, 1; 0, 1]]]]
[129.82045011403975460991182396195022419]
[0.98765369790690472391212970100000000000]
[[2, -1]]
[[;]]
[0]
? setrand(1);bnfclassunit(x^2-x-100000,1)
[x^2 - x - 100000]
[[2, 0]]
[[400001, 1]]
[[1, x]]
[[5, [5], [[2, 1; 0, 1]]]]
[129.82045011403975460991182396195022419]
[0.98765369790690472391212970100000000000]
[[2, -1]]
[[379554884019013781006303254896369154068336082609238336*x + 119836165644250
789990462835950022871665178127611316131167]]
[124]
? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
[x^4 + 24*x^2 + 585*x + 1791]
[[0, 2]]
[[18981, 3087]]
[[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]
[[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
[3.7941269688216589341408274220859400302]
[0.88260182866555813061644128400000000000]
[[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
[[4/1029*x^3 + 53/1029*x^2 + 66/343*x + 111/343]]
[103]
? setrand(1);bnfclgp(17)
[1, [], []]
? setrand(1);bnfclgp(-31)
[3, [3], [Qfb(2, 1, 4)]]
? 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]]]
? bnrconductor(bnf,[[25,13;0,1],[1,1]])
[[5, 3; 0, 1], [1, 0]]
? bnrconductorofchar(bnr,[2])
[[5, 3; 0, 1], [0, 0]]
? bnfisprincipal(bnf,[5,1;0,1],0)
[1]~
? bnfisprincipal(bnf,[5,1;0,1])
[[1]~, [2, 1/3]~, 117]
? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
[-4, Mod(1, 2)]~
? \p19
realprecision = 19 significant digits
? bnfmake(sbnf)
[Mat(2), Mat([0, 1, 1, 1, 0, 1, 1, 1]), [1.173637103435061715 + 3.1415926535
89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
76049 + 3.141592653589793238*I, 1.420330600779487358 + 3.141592653589793238*
I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161, -1.99
0056445584799713 + 3.141592653589793238*I, 0.5404006376129469727, -0.6926391
142471042845 + 3.141592653589793238*I, 0.E-96, 0.004375616572659815402 + 3.1
41592653589793238*I, 0.3677262014027817705 + 3.141592653589793238*I, -0.8305
625946607188639 + 3.141592653589793238*I, -1.977791147836553953 + 3.14159265
3589793238*I; 0.6716827432867392935, 0.5379005671092853266, -0.8333219883742
404172, -0.2461086674077943078, 0.E-96, -0.8738318043071131265, 0.9729063188
316092378, -1.552661549868775853, 0.5774919091398324092 + 3.1415926535897932
38*I; -1.918029732621558454 + 3.141592653589793238*I, 1.452155878475514386,
0.2929213507612934444 + 3.141592653589793238*I, 0.9387477816548985923, 0.E-9
6, 0.8694561877344533111, -1.340632520234391008, 2.383224144529494717, 1.400
299238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]
~], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~],
[5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [11,
[1, 1, 0]~, 1, 1, [-1, -2, 1]~], [23, [-10, 1, 0]~, 1, 1, [7, 9, 1]~], [13,
[19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1,
2, 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.2
33732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.00515
8616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1;
-3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.457
02714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.000000
000000000000, 29.00000000000000000; 1.000000000000000000, 29.000000000000000
00, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.00
00000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0,
1, 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889,
[1890, 5190, 1]~, 118570321]], [-3.233732695981516673, -0.071823509027436363
44, 4.305556205008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,
0, 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 1
5]], [[2, [2], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.00000
0000000000000, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), Mat(1), [[[3, 2,
2; 0, 1, 0; 0, 0, 1], [0, 0, 0]]]], 0]
? \p38
realprecision = 38 significant digits
? bnfnarrow(bnf)
[3, [3], [[3, 2; 0, 1]]]
? bnfreg(x^2-x-57)
2.7124653051843439746808795106061300699
? bnfsignunit(bnf)
[-1]
[1]
? bnfunit(bnf)
[[x + 7], 130]
? bnrclass(bnf,[[5,3;0,1],[1,0]])
[12, [12], [[3, 2; 0, 1]]]
? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2)
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
3832795028842*I, 27379.624790530768080428797780058276925 + 1.928186686709523
2000000000000000000000 E-42*I, 57933.334567930851067108050790839116749 + 2.6
904930509626865380000000000000000000 E-42*I, -34585.556250151557719998034043
918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
797153879301498385086526*I, -866.56619430687100142570357249059499540 + 2.101
9476959481835360000000000000000000 E-45*I, -2881.339639608458729329562656364
4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-48*I, 4031.71
17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
, -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
, 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
, [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
26545793690341704100000000000, [2, -1], [x + 7], 130], [Mat(1), Mat(1), [[[3
, 2; 0, 1], [0, 0]]]], 0], [[[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, 0]~], [1,
-3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0], [12, [12], [[3, 2; 0, 1]]],
[[1/2, 5, -9; -1/2, -5, 10], [-2, 0; 0, 10]]]
? bnrclassno(bnf,[[5,3;0,1],[1,0]])
12
? lu=ideallist(bnf,55,3);
? bnrclassnolist(bnf,lu)
[[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
, [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
, [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
, [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
? bnrdisc(bnr,Mat(6))
[12, 12, 18026977100265125]
? bnrdisc(bnr)
[24, 12, 40621487921685401825918161408203125]
? bnrdisc(bnr2,,,2)
0
? bnrdisc(bnr,Mat(6),,1)
[6, 2, [125, 13; 0, 1]]
? bnrdisc(bnr,,,1)
[12, 1, [1953125, 1160888; 0, 1]]
? bnrdisc(bnr2,,,3)
0
? bnrdisclist(bnf,lu)
[[[6, 6, Mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
, 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
, [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
[], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
, []]]
? bnrdisclist(bnf,20,,1)
[[[[matrix(0,2), [[6, 6, Mat([229, 3])], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]],
[], [[Mat([12, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [3, 3; 229, 6
]]]], [Mat([13, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1, 1; 3, 3; 229, 6]],
[0, 0, 0]]]], [[Mat([10, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]
, [[Mat([20, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [0, 0, 0], [24, 0, [
5, 9; 229, 12]]]], [Mat([21, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [24,
12, [5, 9; 229, 12]], [0, 0, 0]]]], [], [], [], [[Mat([12, 2]), [[0, 0, 0],
[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1], [[0, 0, 0], [12, 6, [-1
, 1; 3, 6; 229, 6]], [0, 0, 0], [24, 0, [3, 12; 229, 12]]]], [Mat([13, 2]),
[[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([44, 1]), [[0, 0,
0], [0, 0, 0], [12, 6, [-1, 1; 11, 3; 229, 6]], [0, 0, 0]]], [Mat([45, 1]),
[[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [11, 3; 229, 6]]]]], [[[10, 1; 12,
1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 13, 1], [[0, 0,
0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [], [[[12, 1; 20, 1], [[24, 24,
[3, 6; 5, 9; 229, 12]], [0, 0, 0], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 2
4]]]], [[13, 1; 20, 1], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [24, 12
, [3, 6; 5, 6; 229, 12]], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1
], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 0, [3, 12; 5
, 18; 229, 24]]]], [[13, 1; 21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0,
0], [48, 24, [3, 12; 5, 18; 229, 24]], [0, 0, 0]]]], [[Mat([10, 2]), [[0, 0
, 0], [12, 6, [-1, 1; 2, 12; 229, 6]], [12, 6, [-1, 1; 2, 12; 229, 6]], [24,
0, [2, 36; 229, 12]]]]], [[Mat([68, 1]), [[0, 0, 0], [12, 6, [-1, 1; 17, 3;
229, 6]], [0, 0, 0], [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [12, 6, [-1, 1
; 17, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [1
9, 6; 229, 9]], [0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77
, 1]), [[18, 18, [19, 6; 229, 9]], [0, 0, 0], [36, 18, [-1, 1; 19, 15; 229,
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]]]]]]
? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
[[9]~, [-2170/6561, -931/19683]~, 113]
? 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,
0, 1, 0, 1, 0]
? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
[Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t, t^3 + t^2 - 2*t - 1) 1]
[Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t^2 + 2, 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]
[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
? idx=idealmul(nf,matid(5),vp)
[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]
? idealinv(nf,idx)
[1 0 2/3 0 0]
[0 1 1/3 0 0]
[0 0 1/3 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
? idy=idealred(nf,idx,[1,5,6])
[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]
? idx2=idealmul(nf,idx,idx)
[9 7 5 8 2]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
? idt=idealmul(nf,idx,idx,1)
[2 0 0 0 1]
[0 2 0 0 1]
[0 0 2 0 0]
[0 0 0 2 1]
[0 0 0 0 1]
? idz=idealintersect(nf,idx,idy)
[15 5 10 12 10]
[0 5 0 0 0]
[0 0 5 2 0]
[0 0 0 1 0]
[0 0 0 0 5]
? 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]
, [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
], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 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, 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]]
? bid=idealstar(nf2,54,1)
[[[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, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 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
, 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,
0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
, -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
? 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]
, [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
], [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]]
? haid=[matid(5),matid(5),matid(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
], [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]]
? idealadd(nf,idx,idy)
[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]
? idealaddtoone(nf,idx,idy)
[[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
? idealaddtoone(nf,[idy,idx])
[[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
? idealappr(nf,idy)
[-2, 0, -2, 4, 0]~
? idealappr(nf,idealfactor(nf,idy),1)
[-2, 0, -2, 4, 0]~
? idealcoprime(nf,idx,idx)
[-2/3, 2/3, -1/3, 0, 0]~
? idealdiv(nf,idy,idt)
[5 5/2 5/2 7/2 0]
[0 5/2 0 0 0]
[0 0 5/2 1 0]
[0 0 0 1/2 0]
[0 0 0 0 5/2]
? idealdiv(nf,idx2,idx,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]
? idf=idealfactor(nf,idz)
[[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]
[[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]
[[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]
? idealhnf(nf,vp)
[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]
? idealhnf(nf,vp[2],3)
[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]
? ideallist(bnf,20)
[[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
, 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
[], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
[15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
, [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
, 6; 0, 2], [10, 2; 0, 2]]]
? ideallog(nf2,w,bid)
[1574, 8, 6]~
? idealmin(nf,idx,[1,2,3,4,5])
[[-1; 0; 0; 1; 0], [2.0885812311199768913287869744681966008 + 3.141592653589
7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244
7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160
203 + 2.5437460822678889883600220330800078854*I]]
? idealnorm(nf,idt)
16
? idp=idealpow(nf,idx,7)
[2187 1807 2129 692 1379]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
? idealpow(nf,idx,7,1)
[2 0 0 0 1]
[0 2 0 0 1]
[0 0 2 0 0]
[0 0 0 2 1]
[0 0 0 0 1]
? idealprimedec(nf,2)
[[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,
4, [1, 1, 0, 0, 0]~]]
? idealprimedec(nf,3)
[[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,
2, [1, 2, 3, 1, 0]~]]
? idealprimedec(nf,11)
[[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
? idealprincipal(nf,Mod(x^3+5,nfpol))
[6]
[0]
[1]
[3]
[0]
? idealtwoelt(nf,idy)
[5, [2, 0, 2, 1, 0]~]
? idealtwoelt(nf,idy,10)
[-2, 0, -2, -1, 0]~
? idealstar(nf2,54)
[[[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, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 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
, 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,
0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
, -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
? idealval(nf,idp,vp)
7
? ideleprincipal(nf,Mod(x^3+5,nfpol))
[[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897
932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851
760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
- 0.0083630478144368246110910258645462996191*I]]
? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
[6, 0, 1, 3, 0]~
? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
[1, 1, 1, 3, 0]~
? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
[[0, 1, 1, 0, 0]~]
[[1, 0, 1, 0, 0]~]
? matbasistoalg(nf,bc)
[Mod(x^2 + x, x^5 - 5*x^3 + 5*x + 25)]
[Mod(x^2 + 1, x^5 - 5*x^3 + 5*x + 25)]
? nfbasis(x^3+4*x+5)
[1, x, 1/7*x^2 - 1/7*x - 2/7]
? nfbasis(x^3+4*x+5,2)
[1, x, 1/7*x^2 - 1/7*x - 2/7]
? nfbasis(x^3+4*x+12,1)
[1, x, 1/2*x^2]
? nfbasistoalg(nf,ba)
Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
? nfbasis(p2,0,fa)
[1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
4/139623738889203638909659*x - 13185339461968406/58346808996920447]
? da=nfdetint(nf,[a,aid])
[30 5 25 27 10]
[0 5 0 0 0]
[0 0 5 2 0]
[0 0 0 1 0]
[0 0 0 0 5]
? nfdisc(x^3+4*x+12)
-1036
? nfdisc(x^3+4*x+12,1)
-1036
? nfdisc(p2,0,fa)
136866601
? nfeltdiv(nf,ba,bb)
[755/373, -152/373, 159/373, 120/373, -264/373]~
? nfeltdiveuc(nf,ba,bb)
[2, 0, 0, 0, -1]~
? nfeltdivrem(nf,ba,bb)
[[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
? nfeltmod(nf,ba,bb)
[-12, -7, 0, 9, 5]~
? nfeltmul(nf,ba,bb)
[-25, -50, -30, 15, 90]~
? nfeltpow(nf,bb,5)
[23455, 156370, 115855, 74190, -294375]~
? nfeltreduce(nf,ba,idx)
[1, 0, 0, 0, 0]~
? nfeltval(nf,ba,vp)
0
? nffactor(nf2,x^3+x)
[Mod(1, y^3 - y - 1)*x 1]
[Mod(1, y^3 - y - 1)*x^2 + Mod(1, y^3 - y - 1) 1]
? 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]~
? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
Mod(1/2*x^5 - 9*x^2, x^6 + 108)
? nfhilbert(nf,3,5)
-1
? nfhilbert(nf,3,5,idf[1,1])
-1
? 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
, 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, 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]]]
? 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
, 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, 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]]]
? nfisideal(bnf[7],[5,1;0,1])
1
? nfisincl(x^2+1,x^4+1)
[-x^2, x^2]
? nfisincl(x^2+1,nfinit(x^4+1))
[-x^2, x^2]
? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
[x, -x^2 - x + 1, x^2 - 2]
? nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30))
[-1/25*x^2 + 13/25*x - 2/5]
? nfroots(nf2,x+2)
[Mod(-2, y^3 - y - 1)]
? nfrootsof1(nf)
[2, [-1, 0, 0, 0, 0]~]
? nfsnf(nf,[as,haid,vaid])
[[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3
910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 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, 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]]
? nfsubfields(nf)
[[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)
[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x
^2 - 128*x - 5]~
? polcompositum(x^4-4*x+2,x^3-x-1,1)
[[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
x^2 - 128*x - 5, Mod(-279140305176/29063006931199*x^11 + 129916611552/290630
06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
- 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), M
od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
? polgalois(x^6-3*x^2-1)
[12, 1, 1]
? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
[x - 1, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5, x^5 - x^4 + 2*x^3 - 4*x^2 + x
- 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
? polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
[1 x - 1]
[1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
[3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
[1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
? polred(x^4+576,1)
[x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
? polred(x^4+576,3)
[1 x - 1]
[1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
[-1/24*x^2 x^2 + 1]
[-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
? polred(p2,0,fa)
[x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46
*x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
*x^3 - 197*x^2 - 273*x - 127]
? polred(p2,1,fa)
[x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46
*x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
*x^3 - 197*x^2 - 273*x - 127]
? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
[x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1, Mod(2*x^4 - x^3 + 3*x^2 - 3*x - 1, x^5 -
x^4 + 2*x^3 - 4*x^2 + x - 1)]
? polredord(x^3-12*x+45*x-1)
[x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
? polsubcyclo(31,5)
x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
? setrand(1);poltschirnhaus(x^5-x-1)
x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289
? aa=rnfpseudobasis(nf2,p)
[[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
[1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
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]~
], [[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, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1
280, 5, 5]~]
? rnfbasis(bnf2,aa)
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/5, -4/5, -2/5]~ [187/25, 208/25, -61/25
]~]
[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-4/5, 4/5, 2/5]~ [-196/25, -214/25, 88/25
]~]
[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-2/5, 2/5, 1/5]~ [-122/25, -123/25, 116/2
5]~]
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, 1/5]~ [-104/25, -111/25, 62/25
]~]
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/25, -2/25, 9/25]~]
? rnfdisc(nf2,p)
[[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
? rnfequation(nf2,p)
x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
? rnfequation(nf2,p,1)
[x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, Mod(-x^5 + 5*x, x^15 - 1
5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
? rnfhnfbasis(bnf2,aa)
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~
]
[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]
[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]
[[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]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]
? rnfisfree(bnf2,aa)
1
? rnfsteinitz(nf2,aa)
[[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [4/5, -4/5, -2/5]~, [39/125, 11/125, 1
1/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-4/5, 4/5, 2/5]~, [-42/125, -8
/125, -8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [-2/5, 2/5, 1/5]~, [-29/
125, 4/125, 4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2/5, 2/5, 1/5]~,
[-23/125, -2/125, -2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~,
[-1/125, 1/125, 1/125]~], [[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, 0; 0, 1, 0; 0, 0, 1], [125, 0,
108; 0, 125, 22; 0, 0, 1]], [416134375, 212940625, 388649575; 0, 3125, 550;
0, 0, 25], [-1280, 5, 5]~]
? nfz=zetakinit(x^2-2);
? zetak(nfz,-3)
0.091666666666666666666666666666666666666
? zetak(nfz,1.5+3*I)
0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
7938845*I
? setrand(1);quadclassunit(1-10^7,,[1,1])
*** Warning: not a fundamental discriminant in quadclassunit.
[2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99984980
753776002339750644800000000000]
? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
[4, [4], [Qfb(3, 1, -83333333, 0.E-48)], 2800.625251907016076486370621737074
5513, 0.99903694589643832327024650000000000000]
? sizebyte(%)
176
? getheap
[197, 135005]
? print("Total time spent: ",gettime);
Total time spent: 8590
? \q
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