OpenXM_contrib/pari-2.2/src/test/64/nfields - view

Return to nfields CVS log

Up to [local] / OpenXM_contrib / pari-2.2 / src / test / 64

File: [local] / OpenXM_contrib / pari-2.2 / src / test / 64 / Attic / nfields (download)

Revision 1.1.1.1 (vendor branch), Tue Oct 2 11:17:13 2001 UTC (22 years, 9 months ago) by noro
Branch: NORO
CVS Tags: RELEASE_1_2_1, PARI_2_2
Changes since 1.1: +0 -0 lines

Imported pari-2.2.1(alpha).

   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, 0.E-77, 10.0000000000000000000000000000000
00000, -5.0000000000000000000000000000000000000, 7.0000000000000000000000000
000000000000; 0.E-77, 19.488486013650707197449403270536023970, 2.07268045322
2666710 E-76, 19.488486013650707197449403270536023970, 4.1504592246706085588
902013976045703227; 10.000000000000000000000000000000000000, 2.0726804532226
66710 E-76, 85.960217420851846480305133936577594605, -36.0342682914829798382
67056239752434596, 53.576130452511107888183080361946556763; -5.0000000000000
000000000000000000000000, 19.488486013650707197449403270536023970, -36.03426
8291482979838267056239752434596, 60.916248374441986300937507618575151517, -1
8.470101750219179344070032346246890434; 7.0000000000000000000000000000000000
000, 4.1504592246706085588902013976045703227, 53.576130452511107888183080361
946556763, -18.470101750219179344070032346246890434, 37.97015289284236734089
7384258599214282], [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, 41400, 3450, -43125; -5175, 41400, -41400
, -15525, 51750; 27600, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -86
250], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.42851749071941860689
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)
[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]~]], [-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)
[[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]~]], [-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)
[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]~]], [-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);
? 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, -3.454467422037777850 E-77, 10.0000000000000000000
00000000000000000; -3.454467422037777850 E-77, 20.00000000000000000000000000
0000000000, -12.000000000000000000000000000000000000; 10.0000000000000000000
00000000000000000, -12.000000000000000000000000000000000000, 50.000000000000
000000000000000000000000], [3, 0, 10; 0, 20, -12; 10, -12, 50], [284, 168, 2
35; 0, 2, 0; 0, 0, 1], [856, -120, -200; -120, 50, 36; -200, 36, 60], [568, 
[-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);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], [9.927737672
2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1.
2897619530652735025030086072395031017 + 0.E-57*I, -2.01097980249891575621226
34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590
95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376
98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I
, -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983
85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538
79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653
5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0
.E-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264
33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795
864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424
7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061
2 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.14159265358979323
84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926
535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + 
3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342
4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389
88786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.14
15926535897932384626433832795028842*I, -24.478366048541841504313284087778334
822 + 3.1415926535897932384626433832795028842*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], 229, 1, [[1, -7.0663729752107779635959310
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)
[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 - 12.56637061435917295385057353
3118011536*I], [-41.811264589129943393339502258694361489 + 8.121413879410077
514 E-115*I, 9.2399004147902289816376260438840931575 + 3.1415926535897932384
626433832795028842*I, -11.874609881075406725097315997431161032 + 9.424777960
7693797153879301498385086526*I, 389.46135034211926382973547188585067257 + 12
.566370614359172953850573533118011536*I, -440.512515346039436204712600188429
12722 + 0.E-113*I, -324.55112528509938652477955990487556047 + 6.283185307179
5864769252867665590057684*I, 229.70424552002497255158146166263724792 + 3.141
5926535897932384626433832795028842*I, -785.660451862534215720251179722755983
25 + 6.2831853071795864769252867665590057684*I, -554.35531386699327377220656
215544062014 + 6.2831853071795864769252867665590057684*I, -47.66831907156823
3997332918482707687879 + 9.4247779607693797153879301498385086526*I, 177.4887
6918560798860724474244465791207 + 6.497131103528062011 E-114*I, -875.6123693
7168080069763246690606885226 + 2.598852441411224804 E-113*I, 54.878404098312
329644822020875673145627 + 9.4247779607693797153879301498385086526*I, -404.4
4153844676787690336623107514389175 + 0.E-113*I, 232.809823743598178900114904
85449930607 + 6.2831853071795864769252867665590057684*I, -668.80899963671483
856204802764462926790 + 9.4247779607693797153879301498385086526*I, 367.35683
481950538594888487746203445802 + 12.566370614359172953850573533118011536*I, 
-1214.0716092619656173892944003952818868 + 9.4247779607693797153879301498385
086526*I, -125.94415646756187210316334148291471657 + 6.283185307179586476925
2867665590057684*I; 41.811264589129943393339502258694361489 + 6.283185307179
5864769252867665590057684*I, -9.2399004147902289816376260438840931575 + 12.5
66370614359172953850573533118011536*I, 11.8746098810754067250973159974311610
32 + 8.121413879410077514 E-115*I, -389.46135034211926382973547188585067257 
+ 6.2831853071795864769252867665590057684*I, 440.512515346039436204712600188
42912722 + 3.1415926535897932384626433832795028842*I, 324.551125285099386524
77955990487556047 + 9.4247779607693797153879301498385086526*I, -229.70424552
002497255158146166263724792 + 6.2831853071795864769252867665590057684*I, 785
.66045186253421572025117972275598325 + 9.42477796076937971538793014983850865
26*I, 554.35531386699327377220656215544062014 + 3.14159265358979323846264338
32795028842*I, 47.668319071568233997332918482707687878 + 3.14159265358979323
84626433832795028842*I, -177.48876918560798860724474244465791207 + 6.2831853
071795864769252867665590057684*I, 875.61236937168080069763246690606885226 + 
6.497131103528062011 E-114*I, -54.878404098312329644822020875673145627 + 9.4
247779607693797153879301498385086526*I, 404.44153844676787690336623107514389
175 + 9.4247779607693797153879301498385086526*I, -232.8098237435981789001149
0485449930607 + 3.1415926535897932384626433832795028842*I, 668.8089996367148
3856204802764462926790 + 6.2831853071795864769252867665590057684*I, -367.356
83481950538594888487746203445803 + 3.1415926535897932384626433832795028842*I
, 1214.0716092619656173892944003952818868 + 3.141592653589793238462643383279
5028842*I, 125.94415646756187210316334148291471657 + 6.283185307179586476925
2867665590057684*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, [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
   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, 1, 0, 1, 1]), [9, 15, 16, 17, 10, 69, 33, 39, 
57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-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
   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], [9.92773767
22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
.2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 
0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
4822 + 3.1415926535897932384626433832795028842*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], 229, 1, [[1, -7.066372975210777963595931
0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
; 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]]]
? 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], [9.92773767
22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
.2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 
0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
4822 + 3.1415926535897932384626433832795028842*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], 229, 1, [[1, -7.066372975210777963595931
0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
; 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)
[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
471754111437539 E-39 + 3.4227493991378543323575495001314729016*I, 2.35098870
1644575015 E-38 - 0.68243210418124342552525382695401469720*I, -2.35098870164
4575015 E-38 - 0.52210980589898585950632970408019416371*I, 3.999999999999999
9999999999999999999999 - 5.2069157878920895450584461181156471052*I; -5.87747
1754111437539 E-39 - 3.4227493991378543323575495001314729016*I, 6.6847043424
634879841147654217963674264 - 5.877471754111437539 E-39*I, 0.851456773407213
76574333983502938573598 + 4.5829573180978430291541592600601794652*I, -0.1357
4266252716976137461193821267520737 - 0.2880510854402577236173893646768205039
1*I, 0.27203784387468568916539788233281013320 - 1.59171472799429477189656508
59986677247*I; 2.350988701644575015 E-38 + 0.6824321041812434255252538269540
1469720*I, 0.85145677340721376574333983502938573598 - 4.58295731809784302915
41592600601794652*I, 9.1630968530221077951281598310681467898 + 0.E-38*I, 2.2
622987652095629453403849736225691490 + 6.23619279135585067657240470631807068
69*I, -0.21796409886496632254445901043974770643 + 0.345593689310632156861589
39748833975810*I; -2.350988701644575015 E-38 + 0.522109805898985859506329704
08019416371*I, -0.13574266252716976137461193821267520737 + 0.288051085440257
72361738936467682050392*I, 2.2622987652095629453403849736225691490 - 6.23619
27913558506765724047063180706869*I, 12.845768948832335511882696939380696155 
+ 1.175494350822287507 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 + 5.877471754111437539 E-39*I], 
[5, -1.175494350822287507 E-38 + 0.E-38*I, 2.350988701644575015 E-38 + 0.E-3
8*I, -1.763241526233431261 E-38 + 0.E-38*I, 3.999999999999999999999999999999
9999998 + 0.E-38*I; -1.175494350822287507 E-38 + 0.E-38*I, 6.684704342463487
9841147654217963674264 - 5.877471754111437539 E-39*I, 0.85145677340721376574
333983502938573597 + 5.877471754111437539 E-39*I, -0.13574266252716976137461
193821267520737 + 5.877471754111437539 E-39*I, 0.272037843874685689165397882
33281013314 - 5.877471754111437539 E-39*I; 2.350988701644575015 E-38 + 0.E-3
8*I, 0.85145677340721376574333983502938573597 + 5.877471754111437539 E-39*I,
 9.1630968530221077951281598310681467898 + 0.E-38*I, 2.262298765209562945340
3849736225691490 + 2.350988701644575015 E-38*I, -0.2179640988649663225444590
1043974770651 + 0.E-38*I; -1.763241526233431261 E-38 + 0.E-38*I, -0.13574266
252716976137461193821267520737 + 5.877471754111437539 E-39*I, 2.262298765209
5629453403849736225691490 + 2.350988701644575015 E-38*I, 12.8457689488323355
11882696939380696155 + 0.E-37*I, 4.5618400502378124720913214622468855073 - 3
.526483052466862523 E-38*I; 3.9999999999999999999999999999999999998 + 0.E-38
*I, 0.27203784387468568916539788233281013314 - 5.877471754111437539 E-39*I, 
-0.21796409886496632254445901043974770651 + 0.E-38*I, 4.56184005023781247209
13214622468855073 - 3.526483052466862523 E-38*I, 18.362968630416114402425299
186062892646 + 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(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), Mod(10, y^3 - y - 1), 0, 0, Mod(4, y^3 - y - 1)]
, [;], [;], [;]], [[1.2671683045421243172528914279776896412, 0.2609638803864
5528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -0.89
454803265751744362901306471557966872 + 0.53414854617473272670874609150394379
949*I], [1.2671683045421243172528914279776896412 + 0.E-38*I, 0.2609638803864
5528500256735072673484811 - 1.1772261533941944394700286585617926513*I, 0.260
96388038645528500256735072673484811 + 1.177226153394194439470028658561792651
3*I, -0.89454803265751744362901306471557966872 - 0.5341485461747327267087460
9150394379949*I, -0.89454803265751744362901306471557966872 + 0.5341485461747
3272670874609150394379949*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]]], [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
, 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
088544780973407, 1.7548776662466927600495088963585286918; 1, -0.662358978622
37301298045442723904867036 + 0.56227951206230124389918214490937306149*I, 0.1
2256116687665361997524555182073565405 - 0.7448617666197442365931704286043923
6724*I], [1, 2; 1.3247179572447460259609088544780973407, -1.3247179572447460
259609088544780973407 - 1.1245590241246024877983642898187461229*I; 1.7548776
662466927600495088963585286918, 0.24512233375330723995049110364147130810 + 1
.4897235332394884731863408572087847344*I], [3, 0.E-96, 2.0000000000000000000
000000000000000000; 0.E-96, 3.2646329987400782801485266890755860756, 1.32471
79572447460259609088544780973407; 2.0000000000000000000000000000000000000, 1
.3247179572447460259609088544780973407, 4.2192762054875453178332176670757633
303], [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]~]], [1.3247179572447460259609088544
780973407, -0.66235897862237301298045442723904867036 + 0.5622795120623012438
9918214490937306149*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(39516536165538345/8
3718587879473471*x^14 - 6500512476832995/83718587879473471*x^13 - 1962154720
46117185/83718587879473471*x^12 + 229902227480108910/83718587879473471*x^11 
+ 237380704030959181/83718587879473471*x^10 - 1064931988160773805/8371858787
9473471*x^9 - 20657086671714300/83718587879473471*x^8 + 1772885205999206010/
83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^6 - 48388401
87320655696/83718587879473471*x^5 + 5180390720553188700/83718587879473471*x^
4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040221/83718587
879473471*x^2 + 4155976664123434381/83718587879473471*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 - 20528463024680133/83718587879473471*x^13 - 47423929
48888610/83718587879473471*x^12 - 9983523646123358/83718587879473471*x^11 + 
40898955597139011/83718587879473471*x^10 + 29412692423971937/837185878794734
71*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075066/83718587
879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 20152905879672878/8
3718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 - 847190574595
7397/83718587879473471*x^3 - 13395753879413605/83718587879473471*x^2 + 27623
037732247492/83718587879473471*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, -27623037732247492; 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, 847
1905745957397; 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, 2712810874903165; 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, 50
17479463612351; 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, 9983523646123358; 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, 20
528463024680133; 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], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]

[14.229975145405511722395637833443108790]

[1.121117107152756229]

? 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]

[0.9876536979069047239]

[[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]

[0.9876536979069047239]

[[2, -1]]

[[379554884019013781006303254896369154068336082609238336*x + 119836165644250
789990462835950022871665178127611316131167]]

[186]

? 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]

[0.8826018286655581306]

[[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]]

[[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]

[182]

? 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]~, 181]
? 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, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
1592653589793238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400
6376129469727 + 3.141592653589793238*I, -0.6926391142471042845 + 3.141592653
589793238*I, 0.E-96, 0.3677262014027817705 + 3.141592653589793238*I, 0.00437
5616572659815402 + 3.141592653589793238*I, -0.8305625946607188639, -1.977791
147836553953 + 3.141592653589793238*I; 0.6716827432867392935 + 3.14159265358
9793238*I, 0.5379005671092853266, -0.8333219883742404172 + 3.141592653589793
238*I, -0.2461086674077943078, 0.E-96, 0.9729063188316092378, -0.87383180430
71131265, -1.552661549868775853 + 3.141592653589793238*I, 0.5774919091398324
092 + 3.141592653589793238*I; -1.918029732621558454, 1.452155878475514386, 0
.2929213507612934444, 0.9387477816548985923, 0.E-96, -1.340632520234391008, 
0.8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.4002
99238696721544 + 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]~], [23, [
-10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 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, -3.23
3732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.005158
616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; -
3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.4570
2714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.0000000
00000000000, 29.00000000000000000; 1.000000000000000000, 29.0000000000000000
0, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.000
0000000000000], [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]~]], [-3.233732695981516673, -0.07182350902743636344, 4.305556
205008953036], [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, 15]], [[2, [2
], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.00000000000000000
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
   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], 185]
? 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], [9.92773767
22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
.2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 
0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
4822 + 3.1415926535897932384626433832795028842*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], 229, 1, [[1, -7.066372975210777963595931
0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
; 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])]]], [[[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
? 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]~, 256]
? 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])
[[-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)

[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]

? 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]~ [38/25, -33/25, 11/25]~ [-11, -4, 9]~]

[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-14/25, 24/25, -8/25]~ [28/5, 2/5, -24/5]
~]

[[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]~ [0, 0, 0]~ [9/25, 6/25, -2/25]~ [-4/5, -11/5, 2/5]~]

[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [8/25, -3/25, 1/25]~ [-9/5, -6/5, 7/5]~]

? 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]~, [38/25, -33/25, 11/25]~, [-27/125, 33/
125, -11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-14/25, 24/25, -8/25]~,
 [6/125, -24/125, 8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [57/25, -12/2
5, 4/25]~, [-53/125, 12/125, -4/125]~; [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, 
0, 0]~, [8/25, -3/25, 1/25]~, [-7/125, 3/125, -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, 21294
0625, 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
75377600233]
? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
[4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
5514, 0.9990369458964383232]
? sizebyte(%)
328
? getheap
[198, 120613]
? print("Total time spent: ",gettime);
Total time spent: 4836
? \q