File: [local] / OpenXM_contrib / pari-2.2 / src / test / 64 / Attic / nfields (download)
Revision 1.2, Wed Sep 11 07:27:12 2002 UTC (21 years, 9 months ago) by noro
Branch: MAIN
CVS Tags: RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2
Changes since 1.1: +614 -726
lines
Upgraded pari-2.2 to pari-2.2.4.
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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, -1.08911514572050482502495
27946671612684, -2.4285174907194186068992069565359418364, 0.7194669112891317
8943997506477288225733, -2.5558200350691694950646071159426779971; 1, -0.1383
8372073406036365047976417441696637 - 0.4918163765776864349975328551474152510
7*I, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940822
19556466857*I, -0.072312766896812300380582649294307897121 + 2.19808037538462
76641195195160383234877*I, -0.98796319352507039803950539735452837194 + 1.570
1452385894131769052374806001981108*I; 1, 1.682941293594312776162956161507997
6005 + 2.0500351226010726172974286983598602163*I, -0.75045317576910401286427
186094108607489 + 1.3101462685358123283560773619310445915*I, -0.787420688747
75359433940488309213323154 + 2.1336633893126618034168454610457936017*I, 1.26
58732110596551455718089553258673705 - 2.716479010374315056657802803578983483
4*I], [1, -1.0891151457205048250249527946671612684, -2.428517490719418606899
2069565359418364, 0.71946691128913178943997506477288225733, -2.5558200350691
694950646071159426779971; 1.4142135623730950488016887242096980785, -0.195704
13467375904264179382543977540673, 2.7785222450164664309920925654093065576, -
0.10226569567819614506098907018896260035, -1.3971909474085893198147151262541
540506; 0, -0.69553338995335755797766403996841143190, 1.14510982744395651299
26149974389115722, 3.1085550780550843138423672171643499921, 2.22052069130868
72788181483285734827868; 1.4142135623730950488016887242096980785, 2.38003840
20787979181834702019470475018, -1.0613010590986270398182318786558994412, -1.
1135810173202366904448352912286604470, 1.79021506332534372536778891648110361
60; 0, 2.8991874737236275652408825679737171586, 1.85282662165584876344468105
12816401036, 3.0174557027049114270734649132936867272, -3.8416814583731999185
306312841432940661], 0, [5, 2, 0, -1, -2; 2, -2, -5, -10, 20; 0, -5, 10, -10
, 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 0, 200, 110, 177; 0, 345
, 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5175, 0
, -10350, -15525; 5175, 13800, -8625, -1725, 27600; 0, -8625, 37950, -17250,
0; -10350, -1725, -17250, -24150, -15525; -15525, 27600, 0, -15525, -3450],
[595125, [238050, -296700, 91425, 1725, 0]~]], [-2.428517490719418606899206
9565359418364, 1.9647119211288133163138753392090569931 + 0.80971492418897895
128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.31014
62685358123283560773619310445915*I], [1, 1/15*x^4 - 2/3*x^2 + 1/3*x + 4/3, x
, 2/15*x^4 - 1/3*x^2 + 2/3*x - 1/3, -1/15*x^4 + 1/3*x^3 + 1/3*x^2 - 4/3*x -
2/3], [1, 0, 3, 1, 10; 0, 0, -2, 1, -5; 0, 1, 0, 3, -5; 0, 0, 1, 1, 10; 0, 0
, 0, 3, 0], [1, 0, 0, 0, 0, 0, -1, -1, -2, 4, 0, -1, 3, -1, 1, 0, -2, -1, -3
, -1, 0, 4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, -1, -1, 1, 0, -1, -2, -1, 1, 0,
-1, -1, -1, 3, 0, 1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, -2
, 0, 1, 0, -1, -1, 0, -1, -2, -1, -1; 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1,
1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1; 0, 0, 0, 0, 1, 0, -1, -1, -1, 1, 0, -1
, 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1]]
? 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, 2.4285174907194186068992069565359418364, -0.71
946691128913178943997506477288225733, 2.555820035069169495064607115942677997
1; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
7895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.1
980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
7194 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
10401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.78
742068874775359433940488309213323154 - 2.13366338931266180341684546104579360
17*I, -1.2658732110596551455718089553258673705 + 2.7164790103743150566578028
035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
94186068992069565359418364, -0.71946691128913178943997506477288225733, 2.555
8200350691694950646071159426779971; 1.4142135623730950488016887242096980785,
-0.19570413467375904264179382543977540674, -2.77852224501646643099209256540
93065576, 0.10226569567819614506098907018896260035, 1.3971909474085893198147
151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
9565129926149974389115722, 3.1085550780550843138423672171643499922, 2.220520
6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
12, 1.1135810173202366904448352912286604470, -1.7902150633253437253677889164
811036160; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
4446810512816401036, -3.0174557027049114270734649132936867272, 3.84168145837
31999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10,
-10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3
45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51
75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250
, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
[595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527
946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864
3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x
- 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2], [
1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0,
1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1
, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1
, -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1
, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1
, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]]
? 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, 2.4285174907194186068992069565359418364, -0.7
1946691128913178943997506477288225733, 2.55582003506916949506460711594267799
71; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
285514741525107*I, -1.9647119211288133163138753392090569931 + 0.809714924188
97895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.
1980803753846276641195195160383234877*I, 0.987963193525070398039505397354528
37194 + 1.5701452385894131769052374806001981108*I; 1, 1.68294129359431277616
29561615079976005 + 2.0500351226010726172974286983598602163*I, 0.75045317576
910401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.7
8742068874775359433940488309213323154 - 2.1336633893126618034168454610457936
017*I, -1.2658732110596551455718089553258673705 + 2.716479010374315056657802
8035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.4285174907
194186068992069565359418364, -0.71946691128913178943997506477288225733, 2.55
58200350691694950646071159426779971; 1.4142135623730950488016887242096980785
, -0.19570413467375904264179382543977540674, -2.7785222450164664309920925654
093065576, 0.10226569567819614506098907018896260035, 1.397190947408589319814
7151262541540506; 0, 0.69553338995335755797766403996841143190, 1.14510982744
39565129926149974389115722, 3.1085550780550843138423672171643499922, 2.22052
06913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2
.3800384020787979181834702019470475018, 1.0613010590986270398182318786558994
412, 1.1135810173202366904448352912286604470, -1.790215063325343725367788916
4811036160; 0, 2.8991874737236275652408825679737171587, -1.85282662165584876
34446810512816401036, -3.0174557027049114270734649132936867272, 3.8416814583
731999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10
, -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0,
345, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5
175, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -1725
0, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
[595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.089115145720504825024952
7946671612684, -0.13838372073406036365047976417441696637 + 0.491816376577686
43499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.05003
51226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*
x - 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2],
[1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0
, 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -
1, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -
1, -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0,
1, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -
1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]], Mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2
*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, 2.4285174907194186068992069565359418364, -0.71
946691128913178943997506477288225733, 2.555820035069169495064607115942677997
1; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
7895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.1
980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
7194 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
10401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.78
742068874775359433940488309213323154 - 2.13366338931266180341684546104579360
17*I, -1.2658732110596551455718089553258673705 + 2.7164790103743150566578028
035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
94186068992069565359418364, -0.71946691128913178943997506477288225733, 2.555
8200350691694950646071159426779971; 1.4142135623730950488016887242096980785,
-0.19570413467375904264179382543977540674, -2.77852224501646643099209256540
93065576, 0.10226569567819614506098907018896260035, 1.3971909474085893198147
151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
9565129926149974389115722, 3.1085550780550843138423672171643499922, 2.220520
6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
12, 1.1135810173202366904448352912286604470, -1.7902150633253437253677889164
811036160; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
4446810512816401036, -3.0174557027049114270734649132936867272, 3.84168145837
31999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10,
-10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3
45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51
75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250
, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
[595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527
946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864
3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x
- 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2], [
1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0,
1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1
, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1
, -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1
, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1
, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]]
? nf3=nfinit(x^6+108);
? nf4=nfinit(x^3-10*x+8)
[x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -0.36332823793268357037416860931988791
960, -3.1413361156553641347759399165844441383; 1, -1.76155718183189058754537
11274124874988, 2.6261980685272936133764995500786243868; 1, 3.12488541976457
41579195397367323754183, -0.48486195287192947860055963349418024846], [1, -0.
36332823793268357037416860931988791960, -3.141336115655364134775939916584444
1383; 1, -1.7615571818318905875453711274124874988, 2.62619806852729361337649
95500786243868; 1, 3.1248854197645741579195397367323754183, -0.4848619528719
2947860055963349418024846], 0, [3, 1, -1; 1, 13, -5; -1, -5, 17], [284, 76,
46; 0, 2, 0; 0, 0, 1], [196, -12, 8; -12, 50, 14; 8, 14, 38], [568, [120, 21
0, 2]~]], [-3.5046643535880477051501085259043320579, 0.864640886695403025831
12842266613688800, 2.6400234668926446793189801032381951699], [1, 1/2*x^2 + x
- 3, -1/2*x^2 + 3], [1, 0, 6; 0, 1, 0; 0, 1, -2], [1, 0, 0, 0, 4, -2, 0, -2
, 6; 0, 1, 0, 1, 2, 0, 0, 0, -2; 0, 0, 1, 0, 1, -1, 1, -1, -1]]
? 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
61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065
2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701
48550268542821846861610071436900868, 0.E-57, 0.50057980363245587382620331339
071677436 + 3.1415926535897932384626433832795028842*I, 1.0888562540123011578
605958199158508674, 1.7241634548149836441438434283070556826 + 3.141592653589
7932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.1
415926535897932384626433832795028842*I, 2.1336294009747564707190997873636390
948 + 3.1415926535897932384626433832795028842*I, 0.0661783018827457321853684
92323164193433 + 3.1415926535897932384626433832795028842*I; -1.7903417566977
293763292119206302198760, -1.2897619530652735025030086072395031017, -0.70148
550268542821846861610071436900868, 0.E-57, -0.500579803632455873826203313390
71677436, -1.0888562540123011578605958199158508674, -1.724163454814983644143
8434283070556826, 0.34328764427702709438988786673341921876, -2.1336294009747
564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
[0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
[2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [2
, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [-
2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [x
^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
1, 7.0663729752107779635959310246705326058], [1, -8.066372975210777963595931
0246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, 1
15], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.06637297521077
79635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - 1
], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.7
124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + 7
], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.79
03417566977293763292119206302198760]]], 0]
? setrand(1);bnfinit(x^2-x-100000,1)
[Mat(5), Mat([3, 2, 1, 2, 0, 3, 0, 2, 2, 3, 1, 4, 3, 2, 2, 3, 3, 0]), [-129.
82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
4*I; 129.82045011403975460991182396195022419], [-41.811264589129943393339502
258694361489 + 6.2831853071795864769252867665590057684*I, 9.2399004147902289
816376260438840931575 + 3.1415926535897932384626433832795028842*I, -11.87460
9881075406725097315997431161032 + 3.1415926535897932384626433832795028842*I,
0.E-115, -51.051165003920172374977128302578454646 + 3.141592653589793238462
6433832795028842*I, -64.910225057019877304955911980975112095 + 3.14159265358
97932384626433832795028842*I, -29.936654708054536668242186261263200456 + 3.1
415926535897932384626433832795028842*I, -47.66831907156823399733291848270768
7878 + 6.2831853071795864769252867665590057684*I, 3.876293646477882506748482
4790355076166, -6.7377511782956880607802359510546381087 + 3.1415926535897932
384626433832795028842*I, -35.073513410834255332559266307639723380 + 3.141592
6535897932384626433832795028842*I, 33.130781426597481571750300827582717074 +
2.030353469852519378 E-115*I, 54.878404098312329644822020875673145627 + 4.0
60706939705038757 E-115*I, -14.980188104648613073630759189293219180 + 3.1415
926535897932384626433832795028842*I, -26.83107648448133031970874306940114230
8 + 3.1415926535897932384626433832795028842*I, -19.7067490665160655124889078
34878146944 + 3.1415926535897932384626433832795028842*I, -22.104515522613877
880850594423816214544 + 3.1415926535897932384626433832795028842*I, -45.68755
8235607825900087984737729869105 + 6.2831853071795864769252867665590057684*I,
47.668319071568233997332918482707687879 + 8.121413879410077514 E-115*I; 41.
811264589129943393339502258694361489, -9.23990041479022898163762604388409315
75, 11.874609881075406725097315997431161032, 0.E-115, 51.0511650039201723749
77128302578454646, 64.910225057019877304955911980975112095, 29.9366547080545
36668242186261263200456, 47.668319071568233997332918482707687879, -3.8762936
464778825067484824790355076166, 6.7377511782956880607802359510546381087, 35.
073513410834255332559266307639723380, -33.1307814265974815717503008275827170
74, -54.878404098312329644822020875673145627, 14.980188104648613073630759189
293219180, 26.831076484481330319708743069401142309, 19.706749066516065512488
907834878146944, 22.104515522613877880850594423816214544, 45.687558235607825
900087984737729869105, -47.668319071568233997332918482707687878], [[2, [2, 1
]~, 1, 1, [1, 1]~], [5, [5, 1]~, 1, 1, [1, 1]~], [13, [-5, 1]~, 1, 1, [6, 1]
~], [2, [3, 1]~, 1, 1, [0, 1]~], [5, [6, 1]~, 1, 1, [0, 1]~], [7, [4, 1]~, 2
, 1, [-3, 1]~], [13, [6, 1]~, 1, 1, [-5, 1]~], [23, [7, 1]~, 1, 1, [-6, 1]~]
, [43, [-15, 1]~, 1, 1, [16, 1]~], [17, [20, 1]~, 1, 1, [-2, 1]~], [17, [15,
1]~, 1, 1, [3, 1]~], [29, [14, 1]~, 1, 1, [-13, 1]~], [29, [-13, 1]~, 1, 1,
[14, 1]~], [31, [39, 1]~, 1, 1, [-7, 1]~], [31, [24, 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]~], [23, [-6, 1]~, 1, 1, [7, 1]~]], 0, [x^2 - x - 100000, [2,
0], 400001, 1, [[1, -316.72816130129840161392089489603747004; 1, 315.7281613
0129840161392089489603747004], [1, -316.72816130129840161392089489603747004;
1, 315.72816130129840161392089489603747004], 0, [2, -1; -1, 200001], [40000
1, 200001; 0, 1], [200001, 1; 1, 2], [400001, [200001, 1]~]], [-315.72816130
129840161392089489603747004, 316.72816130129840161392089489603747004], [1, x
- 1], [1, 1; 0, 1], [1, 0, 0, 100000; 0, 1, 1, -1]], [[5, [5], [[2, 0; 0, 1
]]], 129.82045011403975460991182396195022419, 0.9876536979069047228, [2, -1]
, [379554884019013781006303254896369154068336082609238336*x + 11983616564425
0789990462835950022871665178127611316131167], 185], [Mat(1), [[0, 0]], [[-41
.811264589129943393339502258694361489 + 6.2831853071795864769252867665590057
684*I, 41.811264589129943393339502258694361489]]], 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 - x - 9], [-3.233732695981516672
, -0.07182350902743636344, 4.305556205008953036], [10889, 5698, 8994; 0, 1,
0; 0, 0, 1], Mat(2), Mat([1, 1, 0, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 39, 10,
33, 57, 69], [2, [-1, 0, 0]~], [[0, 1, 0]~, [5, 3, 1]~], [-4, -1, 2, 3, 10,
3, 1, 7, 2; 1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
? \p38
realprecision = 38 significant digits
? bnrinit(bnf,[[5,4;0,1],[1,0]],1)
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
[0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
[2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[5, 4;
0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], Mat([[5, [-1, 1]~, 1, 1, [
2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[0,
1]~], Mat(1)]], [1, 0; 0, 1]], [1], Mat([1, -3, -6]), [12, [12], [[3, 0; 0,
1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
? bnr=bnrclass(bnf,[[5,4;0,1],[1,0]],2)
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
[0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
[2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[5, 4;
0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], Mat([[5, [-1, 1]~, 1, 1, [
2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[0,
1]~], Mat(1)]], [1, 0; 0, 1]], [1], Mat([1, -3, -6]), [12, [12], [[3, 0; 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, 0.7548776662466927600495
0889635852869189, 1.3247179572447460259609088544780973407; 1, -0.87743883312
334638002475444817926434594 - 0.74486176661974423659317042860439236723*I, -0
.66235897862237301298045442723904867036 + 0.56227951206230124389918214490937
306149*I], [1, 0.75487766624669276004950889635852869189, 1.32471795724474602
59609088544780973407; 1.4142135623730950488016887242096980785, -1.2408858979
558593537192653626096055786, -0.93671705072735084703311164961686101696; 0, -
1.0533936124468254335289038498031013275, 0.795183311803032710044767156296587
54002], 0, [3, -1, 0; -1, 1, 3; 0, 3, 2], [23, 16, 13; 0, 1, 0; 0, 0, 1], [-
7, 2, -3; 2, 6, -9; -3, -9, 2], [23, [10, 7, 1]~]], [1.324717957244746025960
9088544780973407, -0.66235897862237301298045442723904867036 + 0.562279512062
30124389918214490937306149*I], [1, y^2 - 1, y], [1, 0, 1; 0, 0, 1; 0, 1, 0],
[1, 0, 0, 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, -1, 0, 0, 0, 1; 0, 0, 1, 0, 1, 0, 1
, 0, 0]], [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(3951653
6165538345/83718587879473471*x^14 - 6500512476832995/83718587879473471*x^13
- 196215472046117185/83718587879473471*x^12 + 229902227480108910/83718587879
473471*x^11 + 237380704030959181/83718587879473471*x^10 - 106493198816077380
5/83718587879473471*x^9 - 20657086671714300/83718587879473471*x^8 + 17728852
05999206010/83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^
6 - 4838840187320655696/83718587879473471*x^5 + 5180390720553188700/83718587
879473471*x^4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040
221/83718587879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920
215718580450/83718587879473471, 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^1
3 - 4742392948888610/83718587879473471*x^12 - 9983523646123358/8371858787947
3471*x^11 + 40898955597139011/83718587879473471*x^10 + 29412692423971937/837
18587879473471*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075
066/83718587879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 2015290
5879672878/83718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 -
8471905745957397/83718587879473471*x^3 - 13395753879413605/83718587879473471
*x^2 + 27623037732247492/83718587879473471*x + 26306699661480593/83718587879
473471], [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, 8471905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -959164
3151927789; 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, 5017479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412
692423971937; 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, 20528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718
587879473471]]]
? 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 - 1]]
[[5, [5], [[2, 0; 0, 1]]]]
[129.82045011403975460991182396195022419]
[0.9876536979069047228]
[[2, -1]]
[[;]]
[0]
? setrand(1);bnfclassunit(x^2-x-100000,1)
[x^2 - x - 100000]
[[2, 0]]
[[400001, 1]]
[[1, x - 1]]
[[5, [5], [[2, 0; 0, 1]]]]
[129.82045011403975460991182396195022419]
[0.9876536979069047228]
[[2, -1]]
[[379554884019013781006303254896369154068336082609238336*x + 119836165644250
789990462835950022871665178127611316131167]]
[185]
? 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, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343, 17/1029*x^3 - 32/1029
*x^2 + 109/343*x + 2444/343, -11/343*x^3 + 163/1029*x^2 - 373/343*x - 4260/3
43]]
[[4, [4], [[7, 2, 4, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
[3.7941269688216589341408274220859400302]
[0.8826018286655581299]
[[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
[[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]
[365]
? 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, 2, 0, 5; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]
? bnrconductor(bnf,[[25,14;0,1],[1,1]])
[[5, 4; 0, 1], [1, 0]]
? bnrconductorofchar(bnr,[2])
[[5, 4; 0, 1], [0, 0]]
? bnfisprincipal(bnf,[5,2;0,1],0)
[1]~
? bnfisprincipal(bnf,[5,2;0,1])
[[1]~, [7/3, 1/3]~, 187]
? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
[-4, Mod(1, 2)]~
? \p19
realprecision = 19 significant digits
? bnfmake(sbnf)
[Mat(2), Mat([1, 1, 0, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
89793238*I, -4.562279014988837952 + 3.141592653589793238*I; -2.6335434327389
76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
1592653589793238*I, 0.5404006376129469727 + 3.141592653589793238*I, -0.69263
91142471042844 + 3.141592653589793238*I, -1.990056445584799713 + 3.141592653
589793238*I, -0.8305625946607188643 + 3.141592653589793238*I, 0.E-57, 0.0043
75616572659815433 + 3.141592653589793238*I, -1.977791147836553953, 0.3677262
014027817708 + 3.141592653589793238*I; 0.6716827432867392938 + 3.14159265358
9793238*I, -0.8333219883742404170 + 3.141592653589793238*I, -0.2461086674077
943076, 0.5379005671092853269, -1.552661549868775853, 0.E-57, -0.87383180430
71131263, 0.5774919091398324092, 0.9729063188316092380; -1.91802973262155845
5, 0.2929213507612934444, 0.9387477816548985923, 1.452155878475514386, 2.383
224144529494717, 0.E-57, 0.8694561877344533111, 1.400299238696721544, -1.340
632520234391008], [[3, [-1, 1, 0]~, 1, 1, [1, 1, 1]~], [5, [-1, 1, 0]~, 1, 1
, [0, 1, 1]~], [5, [2, 1, 0]~, 1, 1, [1, -2, 1]~], [5, [3, 1, 0]~, 1, 1, [2,
2, 1]~], [13, [19, 1, 0]~, 1, 1, [-2, -6, 1]~], [3, [10, 1, 1]~, 1, 2, [-1,
1, 0]~], [11, [1, 1, 0]~, 1, 1, [-3, -1, 1]~], [19, [-6, 1, 0]~, 1, 1, [6,
6, 1]~], [23, [-10, 1, 0]~, 1, 1, [-7, 10, 1]~]]~, 0, [x^3 - x^2 - 14*x - 1,
[3, 0], 10889, 1, [[1, -3.233732695981516672, 4.690759845041404811; 1, -0.0
7182350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.23225
8029482144592], [1, -3.233732695981516672, 4.690759845041404811; 1, -0.07182
350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.232258029
482144592], 0, [3, 1, 1; 1, 29, 8; 1, 8, 129], [10889, 5698, 8994; 0, 1, 0;
0, 0, 1], [3677, -121, -21; -121, 386, -23; -21, -23, 86], [10889, [1899, 51
91, 1]~]], [-3.233732695981516672, -0.07182350902743636344, 4.30555620500895
3036], [1, x, x^2 - x - 9], [1, 0, 9; 0, 1, 1; 0, 0, 1], [1, 0, 0, 0, 9, 1,
0, 1, 44; 0, 1, 0, 1, 1, 5, 0, 5, 1; 0, 0, 1, 0, 1, 0, 1, 0, -4]], [[2, [2],
[[3, 2, 0; 0, 1, 0; 0, 0, 1]]], 10.34800724602768011, 1.000000000000000000,
[2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0.E-57, 0.E-57, 0.E-57]], [[
1.246346989334819161 + 3.141592653589793238*I, 0.6716827432867392938 + 3.141
592653589793238*I, -1.918029732621558455]]], [-4, -1, 2, 3, 10, 3, 1, 7, 2;
1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
? \p38
realprecision = 38 significant digits
? bnfnarrow(bnf)
[3, [3], [[3, 0; 0, 1]]]
? bnfreg(x^2-x-57)
2.7124653051843439746808795106061300699
? bnfsignunit(bnf)
[-1]
[1]
? bnfunit(bnf)
[[x + 7], 187]
? bnrclass(bnf,[[5,4;0,1],[1,0]])
[12, [12], [[3, 0; 0, 1]]]
? bnr2=bnrclass(bnf,[[25,14;0,1],[1,1]],2)
[[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
[0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
[2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[25, 1
4; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [4, 2]~, [-2, -2]~]], Mat([[5,
[-1, 1]~, 1, 1, [2, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), M
od(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat(
[1/5, -14/5])]], [[2, 2], [[4, 2]~, [-2, -2]~], [1, 0; 0, 1]]], [1, -12, 0,
0; 0, 0, 1, 0; 0, 0, 0, 1]], [1], Mat([1, -3, -6, 0]), [12, [12], [[3, 0; 0,
1]]], [[1, -18, 9; -1/2, 10, -5], [-2, 0; 0, -10]]]
? bnrclassno(bnf,[[5,4;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, 14; 0, 1]]
? bnrdisc(bnr,,,1)
[12, 1, [1953125, 1160889; 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]~, [112595/19683, 13958/19683]~, 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, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~]
? idx=idealmul(nf,matid(5),vp)
[3 2 1 0 1]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
? idealinv(nf,idx)
[1 0 0 2/3 0]
[0 1 0 1/3 0]
[0 0 1 1/3 0]
[0 0 0 1/3 0]
[0 0 0 0 1]
? idy=idealred(nf,idx,[1,5,6])
[5 0 0 0 2]
[0 5 0 0 2]
[0 0 5 0 1]
[0 0 0 5 2]
[0 0 0 0 1]
? idx2=idealmul(nf,idx,idx)
[9 5 7 0 4]
[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 0]
[0 2 0 0 0]
[0 0 2 0 0]
[0 0 0 2 1]
[0 0 0 0 1]
? idz=idealintersect(nf,idx,idy)
[15 10 5 0 12]
[0 5 0 0 2]
[0 0 5 0 1]
[0 0 0 5 2]
[0 0 0 0 1]
? aid=[idx,idy,idz,matid(5),idx]
[[3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
, [5, 0, 0, 0, 2; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1
], [15, 10, 5, 0, 12; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0,
0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0,
0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0
, 0, 1]]
? 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], [[
1, 1, 0]~], [[1, -27, 0]~], [[]~], 1]], [[[26], [[2, 1, 0]~], [[-25, -26, 0]
~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
]~, [1, 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]]], [[], [], [;]]], [2106, -77, 10556, 0, -4368, 12012, 0, -13104; 0, 0,
0, 1, -2, 0, -6, -6; -27, 1, -136, 0, 56, -156, 0, 168]]
? vaid=[idx,idy,matid(5)]
[[3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
, [5, 0, 0, 0, 2; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1
], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
1]]
? 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, 2, 1, 2, 1]~, [-2, -2, -1, -2, -1]~]
? idealaddtoone(nf,[idy,idx])
[[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
? idealappr(nf,idy)
[-2, -2, -1, -2, -1]~
? idealappr(nf,idealfactor(nf,idy),1)
[-2, -2, -1, -2, -1]~
? idealcoprime(nf,idx,idx)
[1/3, -1/3, -1/3, -1/3, 0]~
? idealdiv(nf,idy,idt)
[5 0 5/2 0 1]
[0 5/2 0 0 1]
[0 0 5/2 0 1/2]
[0 0 0 5/2 1]
[0 0 0 0 1/2]
? idealdiv(nf,idx2,idx,1)
[3 2 1 0 1]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
? idf=idealfactor(nf,idz)
[[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] 1]
[[5, [-1, 0, 0, 0, 1]~, 1, 1, [2, 0, 3, 0, 1]~] 1]
[[5, [2, 0, 0, 0, 1]~, 4, 1, [2, 2, 1, 2, 1]~] 3]
? idealhnf(nf,vp)
[3 2 1 0 1]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
? idealhnf(nf,vp[2],3)
[3 2 1 0 1]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]
[0 0 0 0 1]
? ideallist(bnf,20)
[[[1, 0; 0, 1]], [], [[3, 0; 0, 1], [3, 1; 0, 1]], [[2, 0; 0, 2]], [[5, 4; 0
, 1], [5, 2; 0, 1]], [], [], [], [[9, 6; 0, 1], [3, 0; 0, 3], [9, 4; 0, 1]],
[], [[11, 10; 0, 1], [11, 2; 0, 1]], [[6, 0; 0, 2], [6, 2; 0, 2]], [], [],
[[15, 9; 0, 1], [15, 4; 0, 1], [15, 12; 0, 1], [15, 7; 0, 1]], [[4, 0; 0, 4]
], [[17, 15; 0, 1], [17, 3; 0, 1]], [], [[19, 0; 0, 1], [19, 1; 0, 1]], [[10
, 8; 0, 2], [10, 4; 0, 2]]]
? ideallog(nf2,w,bid)
[486, 3, 7]~
? idealmin(nf,idx,[1,2,3])
[[-2; 1; 1; 0; 1], [2.0885812311199768913287869744681966008 + 3.141592653589
7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244
7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160
207 + 2.5437460822678889883600220330800078854*I]]
? idealnorm(nf,idt)
16
? idp=idealpow(nf,idx,7)
[2187 1436 1807 630 1822]
[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 0]
[0 2 0 0 0]
[0 0 2 0 0]
[0 0 0 2 1]
[0 0 0 0 1]
? idealprimedec(nf,2)
[[2, [3, 0, 1, 0, 0]~, 1, 1, [0, 0, 0, 1, 1]~], [2, [12, -4, -2, 11, 3]~, 1,
4, [1, 0, 1, 0, 0]~]]
? idealprimedec(nf,3)
[[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~], [3, [-1, -1, -1, 0, 0]~,
2, 2, [0, 2, 2, 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]
[1]
[3]
[1]
[3]
? idealtwoelt(nf,idy)
[5, [2, 2, 1, 2, 1]~]
? idealtwoelt(nf,idy,10)
[-2, -2, -1, -2, -1]~
? 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], [[
1, 0, 1]~], [[1, 0, -27]~], [[]~], 1]], [[[26], [[2, 2, 1]~], [[-25, 2, -26]
~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
]~, [1, 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, -85358, 0, 0, -36582; 0, 0, 1, 0, -5
, -6, 0, -6; 0, 0, 0, 1, -8, 0, -6, -6]]
? idealval(nf,idp,vp)
7
? ideleprincipal(nf,Mod(x^3+5,nfpol))
[[6; 1; 3; 1; 3], [2.2324480827796254080981385584384939684 + 3.1415926535897
932384626433832795028841*I, 5.0387659675158716386435353106610489968 + 1.5851
760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
- 0.0083630478144368246110910258645462996225*I]]
? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
[6, 1, 3, 1, 3]~
? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
[1, 1, 4, 1, 3]~
? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
[[3, -2, 1, 1, 0]~]
[[4, -2, 0, 1, 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])
[90 70 35 0 65]
[0 5 0 0 0]
[0 0 5 0 0]
[0 0 0 5 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)
[584/373, 66/373, -32/373, -105/373, 120/373]~
? nfeltdiveuc(nf,ba,bb)
[2, 0, 0, 0, 0]~
? nfeltdivrem(nf,ba,bb)
[[2, 0, 0, 0, 0]~, [4, -1, -5, -1, -3]~]
? nfeltmod(nf,ba,bb)
[4, -1, -5, -1, -3]~
? nfeltmul(nf,ba,bb)
[50, -15, -35, 60, 15]~
? nfeltpow(nf,bb,5)
[-291920, 136855, 230560, -178520, 74190]~
? nfeltreduce(nf,ba,idx)
[1, 0, 0, 0, 0]~
? nfeltval(nf,ba,vp)
0
? nffactor(nf2,x^3+x)
[x 1]
[x^2 + 1 1]
? aut=nfgaloisconj(nf3)
[-x, x, -1/12*x^4 - 1/2*x, -1/12*x^4 + 1/2*x, 1/12*x^4 - 1/2*x, 1/12*x^4 + 1
/2*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]~, [-2, 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]~], [[10, 4, 5, 6, 7; 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, 2, 1, 0, 1; 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]~, [-2, 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]~], [[10, 4, 5, 6, 7; 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, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1,
0; 0, 0, 0, 0, 1]]]
? nfisideal(bnf[7],[5,2;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])
[[2562748315629757085585610, 436545976069778274371140, 123799938628701108220
1405, 2356446991473627724963350, 801407102592194537169612; 0, 5, 0, 0, 2; 0,
0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0
, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [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, 2/5; 0, 1, 3/5; 0, 0, 1/5], [1, 0, 22/25; 0, 1, 8/25;
0, 0, 1/25]], [416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1
275, 5, 5]~]
? rnfbasis(bnf2,aa)
[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-6/25, 66/25, 77/25]~ [-391/25, -699/25,
197/25]~]
[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [18/25, -48/25, -56/25]~ [268/25, 552/25,
-206/25]~]
[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [41/25, 24/25, 28/25]~ [-194/25, -116/25,
-127/25]~]
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [17/25, -12/25, -14/25]~ [52/25, 178/25, -
109/25]~]
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/25, 6/25, 7/25]~ [-41/25, -49/25, -3/25
]~]
? rnfdisc(nf2,p)
[[416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 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]~ [6/5, 4/5, -2/5]~ [-22/25, -33/25, 99/25]~
]
[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-6/5, -4/5, 2/5]~ [16/25, 24/25, -72/25]~
]
[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-3/5, -2/5, 1/5]~ [-8/25, -12/25, 36/25]~
]
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/5, -2/5, 1/5]~ [4/25, 6/25, -18/25]~]
[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/25, -3/25, 9/25]~]
? rnfisfree(bnf2,aa)
1
? rnfsteinitz(nf2,aa)
[[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-6/25, 66/25, 77/25]~, [17/125, -66/1
25, -77/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [18/25, -48/25, -56/25]~,
[-26/125, 48/125, 56/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [41/25, 24/
25, 28/25]~, [-37/125, -24/125, -28/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]
~, [17/25, -12/25, -14/25]~, [-19/125, 12/125, 14/125]~; [0, 0, 0]~, [0, 0,
0]~, [0, 0, 0]~, [4/25, 6/25, 7/25]~, [-3/125, -6/125, -7/125]~], [[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, 22; 0, 125, 108; 0, 0, 1]], [4161343
75, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 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, 1.00257481
6299307750]
? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
[4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
5514, 0.9849577285369119736]
? sizebyte(%)
320
? getheap
[199, 115764]
? print("Total time spent: ",gettime);
Total time spent: 3629
? \q
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