Annotation of OpenXM_contrib/pari-2.2/src/test/64/nfields, Revision 1.2
1.1 noro 1: echo = 1 (on)
2: ? nfpol=x^5-5*x^3+5*x+25
3: x^5 - 5*x^3 + 5*x + 25
4: ? qpol=y^3-y-1;un=Mod(1,qpol);w=Mod(y,qpol);p=un*(x^5-5*x+w)
5: Mod(1, y^3 - y - 1)*x^5 + Mod(-5, y^3 - y - 1)*x + Mod(y, y^3 - y - 1)
6: ? p2=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
7: x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
8: 2057
9: ? fa=[11699,6;2392997,2;4987333019653,2]
10:
11: [11699 6]
12:
13: [2392997 2]
14:
15: [4987333019653 2]
16:
17: ? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8));
18: ? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8));
19: ? nf=nfinit(nfpol)
1.2 ! noro 20: [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -1.08911514572050482502495
! 21: 27946671612684, -2.4285174907194186068992069565359418364, 0.7194669112891317
! 22: 8943997506477288225733, -2.5558200350691694950646071159426779971; 1, -0.1383
! 23: 8372073406036365047976417441696637 - 0.4918163765776864349975328551474152510
! 24: 7*I, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940822
! 25: 19556466857*I, -0.072312766896812300380582649294307897121 + 2.19808037538462
! 26: 76641195195160383234877*I, -0.98796319352507039803950539735452837194 + 1.570
! 27: 1452385894131769052374806001981108*I; 1, 1.682941293594312776162956161507997
! 28: 6005 + 2.0500351226010726172974286983598602163*I, -0.75045317576910401286427
! 29: 186094108607489 + 1.3101462685358123283560773619310445915*I, -0.787420688747
! 30: 75359433940488309213323154 + 2.1336633893126618034168454610457936017*I, 1.26
! 31: 58732110596551455718089553258673705 - 2.716479010374315056657802803578983483
! 32: 4*I], [1, -1.0891151457205048250249527946671612684, -2.428517490719418606899
! 33: 2069565359418364, 0.71946691128913178943997506477288225733, -2.5558200350691
! 34: 694950646071159426779971; 1.4142135623730950488016887242096980785, -0.195704
! 35: 13467375904264179382543977540673, 2.7785222450164664309920925654093065576, -
! 36: 0.10226569567819614506098907018896260035, -1.3971909474085893198147151262541
! 37: 540506; 0, -0.69553338995335755797766403996841143190, 1.14510982744395651299
! 38: 26149974389115722, 3.1085550780550843138423672171643499921, 2.22052069130868
! 39: 72788181483285734827868; 1.4142135623730950488016887242096980785, 2.38003840
! 40: 20787979181834702019470475018, -1.0613010590986270398182318786558994412, -1.
! 41: 1135810173202366904448352912286604470, 1.79021506332534372536778891648110361
! 42: 60; 0, 2.8991874737236275652408825679737171586, 1.85282662165584876344468105
! 43: 12816401036, 3.0174557027049114270734649132936867272, -3.8416814583731999185
! 44: 306312841432940661], 0, [5, 2, 0, -1, -2; 2, -2, -5, -10, 20; 0, -5, 10, -10
! 45: , 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 0, 200, 110, 177; 0, 345
! 46: , 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5175, 0
! 47: , -10350, -15525; 5175, 13800, -8625, -1725, 27600; 0, -8625, 37950, -17250,
! 48: 0; -10350, -1725, -17250, -24150, -15525; -15525, 27600, 0, -15525, -3450],
! 49: [595125, [238050, -296700, 91425, 1725, 0]~]], [-2.428517490719418606899206
! 50: 9565359418364, 1.9647119211288133163138753392090569931 + 0.80971492418897895
! 51: 128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.31014
! 52: 62685358123283560773619310445915*I], [1, 1/15*x^4 - 2/3*x^2 + 1/3*x + 4/3, x
! 53: , 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 -
! 54: 2/3], [1, 0, 3, 1, 10; 0, 0, -2, 1, -5; 0, 1, 0, 3, -5; 0, 0, 1, 1, 10; 0, 0
! 55: , 0, 3, 0], [1, 0, 0, 0, 0, 0, -1, -1, -2, 4, 0, -1, 3, -1, 1, 0, -2, -1, -3
! 56: , -1, 0, 4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, -1, -1, 1, 0, -1, -2, -1, 1, 0,
! 57: -1, -1, -1, 3, 0, 1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, -2
! 58: , 0, 1, 0, -1, -1, 0, -1, -2, -1, -1; 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1,
! 59: 1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1; 0, 0, 0, 0, 1, 0, -1, -1, -1, 1, 0, -1
! 60: , 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1]]
1.1 noro 61: ? nf1=nfinit(nfpol,2)
62: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
1.2 ! noro 63: 7205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.71
! 64: 946691128913178943997506477288225733, 2.555820035069169495064607115942677997
! 65: 1; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
! 66: 85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
! 67: 7895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.1
! 68: 980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
! 69: 7194 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
! 70: 9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
! 71: 10401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.78
! 72: 742068874775359433940488309213323154 - 2.13366338931266180341684546104579360
! 73: 17*I, -1.2658732110596551455718089553258673705 + 2.7164790103743150566578028
! 74: 035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
! 75: 94186068992069565359418364, -0.71946691128913178943997506477288225733, 2.555
! 76: 8200350691694950646071159426779971; 1.4142135623730950488016887242096980785,
! 77: -0.19570413467375904264179382543977540674, -2.77852224501646643099209256540
! 78: 93065576, 0.10226569567819614506098907018896260035, 1.3971909474085893198147
! 79: 151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
! 80: 9565129926149974389115722, 3.1085550780550843138423672171643499922, 2.220520
! 81: 6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
! 82: 3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
! 83: 12, 1.1135810173202366904448352912286604470, -1.7902150633253437253677889164
! 84: 811036160; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
! 85: 4446810512816401036, -3.0174557027049114270734649132936867272, 3.84168145837
! 86: 31999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10,
! 87: -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3
! 88: 45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51
! 89: 75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250
! 90: , 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
! 91: [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527
! 92: 946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864
! 93: 3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
! 94: 1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x
! 95: - 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], [
! 96: 1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0,
! 97: 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1
! 98: , 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1
! 99: , -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1
! 100: , 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
! 101: 1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1
! 102: , 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]]
1.1 noro 103: ? nfinit(nfpol,3)
104: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
1.2 ! noro 105: 57205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.7
! 106: 1946691128913178943997506477288225733, 2.55582003506916949506460711594267799
! 107: 71; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
! 108: 285514741525107*I, -1.9647119211288133163138753392090569931 + 0.809714924188
! 109: 97895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.
! 110: 1980803753846276641195195160383234877*I, 0.987963193525070398039505397354528
! 111: 37194 + 1.5701452385894131769052374806001981108*I; 1, 1.68294129359431277616
! 112: 29561615079976005 + 2.0500351226010726172974286983598602163*I, 0.75045317576
! 113: 910401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.7
! 114: 8742068874775359433940488309213323154 - 2.1336633893126618034168454610457936
! 115: 017*I, -1.2658732110596551455718089553258673705 + 2.716479010374315056657802
! 116: 8035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.4285174907
! 117: 194186068992069565359418364, -0.71946691128913178943997506477288225733, 2.55
! 118: 58200350691694950646071159426779971; 1.4142135623730950488016887242096980785
! 119: , -0.19570413467375904264179382543977540674, -2.7785222450164664309920925654
! 120: 093065576, 0.10226569567819614506098907018896260035, 1.397190947408589319814
! 121: 7151262541540506; 0, 0.69553338995335755797766403996841143190, 1.14510982744
! 122: 39565129926149974389115722, 3.1085550780550843138423672171643499922, 2.22052
! 123: 06913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2
! 124: .3800384020787979181834702019470475018, 1.0613010590986270398182318786558994
! 125: 412, 1.1135810173202366904448352912286604470, -1.790215063325343725367788916
! 126: 4811036160; 0, 2.8991874737236275652408825679737171587, -1.85282662165584876
! 127: 34446810512816401036, -3.0174557027049114270734649132936867272, 3.8416814583
! 128: 731999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10
! 129: , -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0,
! 130: 345, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5
! 131: 175, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -1725
! 132: 0, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
! 133: [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.089115145720504825024952
! 134: 7946671612684, -0.13838372073406036365047976417441696637 + 0.491816376577686
! 135: 43499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.05003
! 136: 51226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*
! 137: 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],
! 138: [1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0
! 139: , 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -
! 140: 1, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -
! 141: 1, -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0,
! 142: 1, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
! 143: 1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -
! 144: 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
! 145: *x + 1, x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
1.1 noro 146: ? nfinit(nfpol,4)
147: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
1.2 ! noro 148: 7205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.71
! 149: 946691128913178943997506477288225733, 2.555820035069169495064607115942677997
! 150: 1; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
! 151: 85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
! 152: 7895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.1
! 153: 980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
! 154: 7194 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
! 155: 9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
! 156: 10401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.78
! 157: 742068874775359433940488309213323154 - 2.13366338931266180341684546104579360
! 158: 17*I, -1.2658732110596551455718089553258673705 + 2.7164790103743150566578028
! 159: 035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
! 160: 94186068992069565359418364, -0.71946691128913178943997506477288225733, 2.555
! 161: 8200350691694950646071159426779971; 1.4142135623730950488016887242096980785,
! 162: -0.19570413467375904264179382543977540674, -2.77852224501646643099209256540
! 163: 93065576, 0.10226569567819614506098907018896260035, 1.3971909474085893198147
! 164: 151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
! 165: 9565129926149974389115722, 3.1085550780550843138423672171643499922, 2.220520
! 166: 6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
! 167: 3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
! 168: 12, 1.1135810173202366904448352912286604470, -1.7902150633253437253677889164
! 169: 811036160; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
! 170: 4446810512816401036, -3.0174557027049114270734649132936867272, 3.84168145837
! 171: 31999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10,
! 172: -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3
! 173: 45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51
! 174: 75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250
! 175: , 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
! 176: [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527
! 177: 946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864
! 178: 3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
! 179: 1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x
! 180: - 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], [
! 181: 1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0,
! 182: 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1
! 183: , 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1
! 184: , -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1
! 185: , 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
! 186: 1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1
! 187: , 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]]
1.1 noro 188: ? nf3=nfinit(x^6+108);
189: ? nf4=nfinit(x^3-10*x+8)
1.2 ! noro 190: [x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -0.36332823793268357037416860931988791
! 191: 960, -3.1413361156553641347759399165844441383; 1, -1.76155718183189058754537
! 192: 11274124874988, 2.6261980685272936133764995500786243868; 1, 3.12488541976457
! 193: 41579195397367323754183, -0.48486195287192947860055963349418024846], [1, -0.
! 194: 36332823793268357037416860931988791960, -3.141336115655364134775939916584444
! 195: 1383; 1, -1.7615571818318905875453711274124874988, 2.62619806852729361337649
! 196: 95500786243868; 1, 3.1248854197645741579195397367323754183, -0.4848619528719
! 197: 2947860055963349418024846], 0, [3, 1, -1; 1, 13, -5; -1, -5, 17], [284, 76,
! 198: 46; 0, 2, 0; 0, 0, 1], [196, -12, 8; -12, 50, 14; 8, 14, 38], [568, [120, 21
! 199: 0, 2]~]], [-3.5046643535880477051501085259043320579, 0.864640886695403025831
! 200: 12842266613688800, 2.6400234668926446793189801032381951699], [1, 1/2*x^2 + x
! 201: - 3, -1/2*x^2 + 3], [1, 0, 6; 0, 1, 0; 0, 1, -2], [1, 0, 0, 0, 4, -2, 0, -2
! 202: , 6; 0, 1, 0, 1, 2, 0, 0, 0, -2; 0, 0, 1, 0, 1, -1, 1, -1, -1]]
1.1 noro 203: ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];
204: ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
205: [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
1.2 ! noro 206: 61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
! 207: 08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065
! 208: 2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701
! 209: 48550268542821846861610071436900868, 0.E-57, 0.50057980363245587382620331339
! 210: 071677436 + 3.1415926535897932384626433832795028842*I, 1.0888562540123011578
! 211: 605958199158508674, 1.7241634548149836441438434283070556826 + 3.141592653589
! 212: 7932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.1
! 213: 415926535897932384626433832795028842*I, 2.1336294009747564707190997873636390
! 214: 948 + 3.1415926535897932384626433832795028842*I, 0.0661783018827457321853684
! 215: 92323164193433 + 3.1415926535897932384626433832795028842*I; -1.7903417566977
! 216: 293763292119206302198760, -1.2897619530652735025030086072395031017, -0.70148
! 217: 550268542821846861610071436900868, 0.E-57, -0.500579803632455873826203313390
! 218: 71677436, -1.0888562540123011578605958199158508674, -1.724163454814983644143
! 219: 8434283070556826, 0.34328764427702709438988786673341921876, -2.1336294009747
! 220: 564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
! 221: [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
! 222: [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [2
! 223: , 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [-
! 224: 2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [x
! 225: ^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
! 226: 1, 7.0663729752107779635959310246705326058], [1, -8.066372975210777963595931
! 227: 0246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, 1
! 228: 15], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.06637297521077
! 229: 79635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - 1
! 230: ], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.7
! 231: 124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + 7
! 232: ], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.79
! 233: 03417566977293763292119206302198760]]], 0]
1.1 noro 234: ? setrand(1);bnfinit(x^2-x-100000,1)
1.2 ! noro 235: [Mat(5), Mat([3, 2, 1, 2, 0, 3, 0, 2, 2, 3, 1, 4, 3, 2, 2, 3, 3, 0]), [-129.
! 236: 82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
! 237: 4*I; 129.82045011403975460991182396195022419], [-41.811264589129943393339502
! 238: 258694361489 + 6.2831853071795864769252867665590057684*I, 9.2399004147902289
! 239: 816376260438840931575 + 3.1415926535897932384626433832795028842*I, -11.87460
! 240: 9881075406725097315997431161032 + 3.1415926535897932384626433832795028842*I,
! 241: 0.E-115, -51.051165003920172374977128302578454646 + 3.141592653589793238462
! 242: 6433832795028842*I, -64.910225057019877304955911980975112095 + 3.14159265358
! 243: 97932384626433832795028842*I, -29.936654708054536668242186261263200456 + 3.1
! 244: 415926535897932384626433832795028842*I, -47.66831907156823399733291848270768
! 245: 7878 + 6.2831853071795864769252867665590057684*I, 3.876293646477882506748482
! 246: 4790355076166, -6.7377511782956880607802359510546381087 + 3.1415926535897932
! 247: 384626433832795028842*I, -35.073513410834255332559266307639723380 + 3.141592
! 248: 6535897932384626433832795028842*I, 33.130781426597481571750300827582717074 +
! 249: 2.030353469852519378 E-115*I, 54.878404098312329644822020875673145627 + 4.0
! 250: 60706939705038757 E-115*I, -14.980188104648613073630759189293219180 + 3.1415
! 251: 926535897932384626433832795028842*I, -26.83107648448133031970874306940114230
! 252: 8 + 3.1415926535897932384626433832795028842*I, -19.7067490665160655124889078
! 253: 34878146944 + 3.1415926535897932384626433832795028842*I, -22.104515522613877
! 254: 880850594423816214544 + 3.1415926535897932384626433832795028842*I, -45.68755
! 255: 8235607825900087984737729869105 + 6.2831853071795864769252867665590057684*I,
! 256: 47.668319071568233997332918482707687879 + 8.121413879410077514 E-115*I; 41.
! 257: 811264589129943393339502258694361489, -9.23990041479022898163762604388409315
! 258: 75, 11.874609881075406725097315997431161032, 0.E-115, 51.0511650039201723749
! 259: 77128302578454646, 64.910225057019877304955911980975112095, 29.9366547080545
! 260: 36668242186261263200456, 47.668319071568233997332918482707687879, -3.8762936
! 261: 464778825067484824790355076166, 6.7377511782956880607802359510546381087, 35.
! 262: 073513410834255332559266307639723380, -33.1307814265974815717503008275827170
! 263: 74, -54.878404098312329644822020875673145627, 14.980188104648613073630759189
! 264: 293219180, 26.831076484481330319708743069401142309, 19.706749066516065512488
! 265: 907834878146944, 22.104515522613877880850594423816214544, 45.687558235607825
! 266: 900087984737729869105, -47.668319071568233997332918482707687878], [[2, [2, 1
! 267: ]~, 1, 1, [1, 1]~], [5, [5, 1]~, 1, 1, [1, 1]~], [13, [-5, 1]~, 1, 1, [6, 1]
! 268: ~], [2, [3, 1]~, 1, 1, [0, 1]~], [5, [6, 1]~, 1, 1, [0, 1]~], [7, [4, 1]~, 2
! 269: , 1, [-3, 1]~], [13, [6, 1]~, 1, 1, [-5, 1]~], [23, [7, 1]~, 1, 1, [-6, 1]~]
! 270: , [43, [-15, 1]~, 1, 1, [16, 1]~], [17, [20, 1]~, 1, 1, [-2, 1]~], [17, [15,
! 271: 1]~, 1, 1, [3, 1]~], [29, [14, 1]~, 1, 1, [-13, 1]~], [29, [-13, 1]~, 1, 1,
! 272: [14, 1]~], [31, [39, 1]~, 1, 1, [-7, 1]~], [31, [24, 1]~, 1, 1, [8, 1]~], [
! 273: 41, [7, 1]~, 1, 1, [-6, 1]~], [41, [-6, 1]~, 1, 1, [7, 1]~], [43, [16, 1]~,
! 274: 1, 1, [-15, 1]~], [23, [-6, 1]~, 1, 1, [7, 1]~]], 0, [x^2 - x - 100000, [2,
! 275: 0], 400001, 1, [[1, -316.72816130129840161392089489603747004; 1, 315.7281613
! 276: 0129840161392089489603747004], [1, -316.72816130129840161392089489603747004;
! 277: 1, 315.72816130129840161392089489603747004], 0, [2, -1; -1, 200001], [40000
! 278: 1, 200001; 0, 1], [200001, 1; 1, 2], [400001, [200001, 1]~]], [-315.72816130
! 279: 129840161392089489603747004, 316.72816130129840161392089489603747004], [1, x
! 280: - 1], [1, 1; 0, 1], [1, 0, 0, 100000; 0, 1, 1, -1]], [[5, [5], [[2, 0; 0, 1
! 281: ]]], 129.82045011403975460991182396195022419, 0.9876536979069047228, [2, -1]
! 282: , [379554884019013781006303254896369154068336082609238336*x + 11983616564425
! 283: 0789990462835950022871665178127611316131167], 185], [Mat(1), [[0, 0]], [[-41
! 284: .811264589129943393339502258694361489 + 6.2831853071795864769252867665590057
! 285: 684*I, 41.811264589129943393339502258694361489]]], 0]
1.1 noro 286: ? \p19
287: realprecision = 19 significant digits
288: ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
1.2 ! noro 289: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2 - x - 9], [-3.233732695981516672
! 290: , -0.07182350902743636344, 4.305556205008953036], [10889, 5698, 8994; 0, 1,
! 291: 0; 0, 0, 1], Mat(2), Mat([1, 1, 0, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 39, 10,
! 292: 33, 57, 69], [2, [-1, 0, 0]~], [[0, 1, 0]~, [5, 3, 1]~], [-4, -1, 2, 3, 10,
! 293: 3, 1, 7, 2; 1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
1.1 noro 294: ? \p38
295: realprecision = 38 significant digits
1.2 ! noro 296: ? bnrinit(bnf,[[5,4;0,1],[1,0]],1)
1.1 noro 297: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
1.2 ! noro 298: 061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 299: 808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
! 300: 52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
! 301: 148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
! 302: 9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
! 303: 8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
! 304: 97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
! 305: 1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
! 306: 0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
! 307: 492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
! 308: 7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
! 309: 8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
! 310: 071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
! 311: 38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
! 312: 7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
! 313: [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
! 314: [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
! 315: 2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
! 316: -2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
! 317: x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
! 318: 1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
! 319: 10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
! 320: 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
! 321: 779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
! 322: 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
! 323: 7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
! 324: 7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
! 325: 903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[5, 4;
! 326: 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], Mat([[5, [-1, 1]~, 1, 1, [
! 327: 2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[0,
! 328: 1]~], Mat(1)]], [1, 0; 0, 1]], [1], Mat([1, -3, -6]), [12, [12], [[3, 0; 0,
! 329: 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
! 330: ? bnr=bnrclass(bnf,[[5,4;0,1],[1,0]],2)
1.1 noro 331: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
1.2 ! noro 332: 061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 333: 808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
! 334: 52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
! 335: 148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
! 336: 9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
! 337: 8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
! 338: 97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
! 339: 1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
! 340: 0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
! 341: 492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
! 342: 7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
! 343: 8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
! 344: 071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
! 345: 38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
! 346: 7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
! 347: [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
! 348: [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
! 349: 2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
! 350: -2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
! 351: x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
! 352: 1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
! 353: 10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
! 354: 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
! 355: 779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
! 356: 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
! 357: 7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
! 358: 7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
! 359: 903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[5, 4;
! 360: 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], Mat([[5, [-1, 1]~, 1, 1, [
! 361: 2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[0,
! 362: 1]~], Mat(1)]], [1, 0; 0, 1]], [1], Mat([1, -3, -6]), [12, [12], [[3, 0; 0,
! 363: 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
1.1 noro 364: ? rnfinit(nf2,x^5-x-2)
365: [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3
366: 109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914
367: 279776896412, 1.6057155120361619195949075151301679393, 2.0347118029638523119
368: 874445717108994866, 2.5783223055935536544757871909285592749; 1, 0.2609638803
369: 8645528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -1
370: .3177592693689352747870763902256347904 + 0.614427010164338838041906608641467
371: 31824*I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524
372: 673160314582604*I, 1.3589689411882615753626439480614001936 - 1.6193337759893
373: 970298359887428575174472*I; 1, -0.89454803265751744362901306471557966872 + 0
374: .53414854617473272670874609150394379949*I, 0.5149015133508543149896226326605
375: 5082078 - 0.95564306225496055080453352211847466685*I, 0.04985121658507159775
376: 5867063892284310224 + 1.1299025160425089918993024639913611785*I, -0.64813009
377: 398503840260053754352567983115 - 0.98412411795664774269323431620030610541*I]
378: , [1, 1.2671683045421243172528914279776896412 + 0.E-38*I, 1.6057155120361619
379: 195949075151301679393 + 0.E-38*I, 2.0347118029638523119874445717108994866 +
380: 0.E-37*I, 2.5783223055935536544757871909285592749 + 0.E-37*I; 1, 0.260963880
381: 38645528500256735072673484811 - 1.1772261533941944394700286585617926513*I, -
382: 1.3177592693689352747870763902256347904 - 0.61442701016433883804190660864146
383: 731824*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921652
384: 4673160314582604*I, 1.3589689411882615753626439480614001936 + 1.619333775989
385: 3970298359887428575174472*I; 1, 0.26096388038645528500256735072673484811 + 1
386: .1772261533941944394700286585617926513*I, -1.3177592693689352747870763902256
387: 347904 + 0.61442701016433883804190660864146731824*I, -1.06720711806699775374
388: 95893497477340535 - 1.3909574189920019216524673160314582604*I, 1.35896894118
389: 82615753626439480614001936 - 1.6193337759893970298359887428575174472*I; 1, -
390: 0.89454803265751744362901306471557966872 - 0.5341485461747327267087460915039
391: 4379949*I, 0.51490151335085431498962263266055082078 + 0.95564306225496055080
392: 453352211847466685*I, 0.049851216585071597755867063892284310224 - 1.12990251
393: 60425089918993024639913611785*I, -0.64813009398503840260053754352567983115 +
394: 0.98412411795664774269323431620030610541*I; 1, -0.8945480326575174436290130
395: 6471557966872 + 0.53414854617473272670874609150394379949*I, 0.51490151335085
396: 431498962263266055082078 - 0.95564306225496055080453352211847466685*I, 0.049
397: 851216585071597755867063892284310224 + 1.12990251604250899189930246399136117
398: 85*I, -0.64813009398503840260053754352567983115 - 0.984124117956647742693234
399: 31620030610541*I]], [[1, 2, 2; 1.2671683045421243172528914279776896412, 0.52
400: 192776077291057000513470145346969622 - 2.35445230678838887894005731712358530
401: 26*I, -1.7890960653150348872580261294311593374 - 1.0682970923494654534174921
402: 830078875989*I; 1.6057155120361619195949075151301679393, -2.6355185387378705
403: 495741527804512695809 - 1.2288540203286776760838132172829346364*I, 1.0298030
404: 267017086299792452653211016415 + 1.9112861245099211016090670442369493337*I;
405: 2.0347118029638523119874445717108994866, -2.13441423613399550749917869949546
406: 81070 + 2.7819148379840038433049346320629165208*I, 0.09970243317014319551173
407: 4127784568620449 - 2.2598050320850179837986049279827223571*I; 2.578322305593
408: 5536544757871909285592749, 2.7179378823765231507252878961228003872 + 3.23866
409: 75519787940596719774857150348944*I, -1.2962601879700768052010750870513596623
410: + 1.9682482359132954853864686324006122108*I], [1, 1, 1, 1, 1; 1.26716830454
411: 21243172528914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484
412: 811 + 1.1772261533941944394700286585617926513*I, 0.2609638803864552850025673
413: 5072673484811 - 1.1772261533941944394700286585617926513*I, -0.89454803265751
414: 744362901306471557966872 + 0.53414854617473272670874609150394379949*I, -0.89
415: 454803265751744362901306471557966872 - 0.53414854617473272670874609150394379
416: 949*I; 1.6057155120361619195949075151301679393 + 0.E-38*I, -1.31775926936893
417: 52747870763902256347904 + 0.61442701016433883804190660864146731824*I, -1.317
418: 7592693689352747870763902256347904 - 0.6144270101643388380419066086414673182
419: 4*I, 0.51490151335085431498962263266055082078 - 0.95564306225496055080453352
420: 211847466685*I, 0.51490151335085431498962263266055082078 + 0.955643062254960
421: 55080453352211847466685*I; 2.0347118029638523119874445717108994866 + 0.E-37*
422: I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524673160
423: 314582604*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921
424: 6524673160314582604*I, 0.049851216585071597755867063892284310224 + 1.1299025
425: 160425089918993024639913611785*I, 0.049851216585071597755867063892284310224
426: - 1.1299025160425089918993024639913611785*I; 2.57832230559355365447578719092
427: 85592749 + 0.E-37*I, 1.3589689411882615753626439480614001936 - 1.61933377598
428: 93970298359887428575174472*I, 1.3589689411882615753626439480614001936 + 1.61
429: 93337759893970298359887428575174472*I, -0.6481300939850384026005375435256798
430: 3115 - 0.98412411795664774269323431620030610541*I, -0.6481300939850384026005
431: 3754352567983115 + 0.98412411795664774269323431620030610541*I]], [[5, -5.877
432: 471754111437539 E-39 + 3.4227493991378543323575495001314729016*I, 2.35098870
433: 1644575015 E-38 - 0.68243210418124342552525382695401469720*I, -2.35098870164
434: 4575015 E-38 - 0.52210980589898585950632970408019416371*I, 3.999999999999999
435: 9999999999999999999999 - 5.2069157878920895450584461181156471052*I; -5.87747
436: 1754111437539 E-39 - 3.4227493991378543323575495001314729016*I, 6.6847043424
437: 634879841147654217963674264 - 5.877471754111437539 E-39*I, 0.851456773407213
438: 76574333983502938573598 + 4.5829573180978430291541592600601794652*I, -0.1357
439: 4266252716976137461193821267520737 - 0.2880510854402577236173893646768205039
440: 1*I, 0.27203784387468568916539788233281013320 - 1.59171472799429477189656508
441: 59986677247*I; 2.350988701644575015 E-38 + 0.6824321041812434255252538269540
442: 1469720*I, 0.85145677340721376574333983502938573598 - 4.58295731809784302915
443: 41592600601794652*I, 9.1630968530221077951281598310681467898 + 0.E-38*I, 2.2
444: 622987652095629453403849736225691490 + 6.23619279135585067657240470631807068
445: 69*I, -0.21796409886496632254445901043974770643 + 0.345593689310632156861589
446: 39748833975810*I; -2.350988701644575015 E-38 + 0.522109805898985859506329704
447: 08019416371*I, -0.13574266252716976137461193821267520737 + 0.288051085440257
448: 72361738936467682050392*I, 2.2622987652095629453403849736225691490 - 6.23619
449: 27913558506765724047063180706869*I, 12.845768948832335511882696939380696155
450: + 1.175494350822287507 E-38*I, 4.5618400502378124720913214622468855074 + 8.6
451: 033930051068500425218923146793019614*I; 3.9999999999999999999999999999999999
452: 999 + 5.2069157878920895450584461181156471052*I, 0.2720378438746856891653978
453: 8233281013320 + 1.5917147279942947718965650859986677247*I, -0.21796409886496
454: 632254445901043974770643 - 0.34559368931063215686158939748833975810*I, 4.561
455: 8400502378124720913214622468855074 - 8.6033930051068500425218923146793019615
456: *I, 18.362968630416114402425299186062892646 + 5.877471754111437539 E-39*I],
457: [5, -1.175494350822287507 E-38 + 0.E-38*I, 2.350988701644575015 E-38 + 0.E-3
458: 8*I, -1.763241526233431261 E-38 + 0.E-38*I, 3.999999999999999999999999999999
459: 9999998 + 0.E-38*I; -1.175494350822287507 E-38 + 0.E-38*I, 6.684704342463487
460: 9841147654217963674264 - 5.877471754111437539 E-39*I, 0.85145677340721376574
461: 333983502938573597 + 5.877471754111437539 E-39*I, -0.13574266252716976137461
462: 193821267520737 + 5.877471754111437539 E-39*I, 0.272037843874685689165397882
463: 33281013314 - 5.877471754111437539 E-39*I; 2.350988701644575015 E-38 + 0.E-3
464: 8*I, 0.85145677340721376574333983502938573597 + 5.877471754111437539 E-39*I,
465: 9.1630968530221077951281598310681467898 + 0.E-38*I, 2.262298765209562945340
466: 3849736225691490 + 2.350988701644575015 E-38*I, -0.2179640988649663225444590
467: 1043974770651 + 0.E-38*I; -1.763241526233431261 E-38 + 0.E-38*I, -0.13574266
468: 252716976137461193821267520737 + 5.877471754111437539 E-39*I, 2.262298765209
469: 5629453403849736225691490 + 2.350988701644575015 E-38*I, 12.8457689488323355
470: 11882696939380696155 + 0.E-37*I, 4.5618400502378124720913214622468855073 - 3
471: .526483052466862523 E-38*I; 3.9999999999999999999999999999999999998 + 0.E-38
472: *I, 0.27203784387468568916539788233281013314 - 5.877471754111437539 E-39*I,
473: -0.21796409886496632254445901043974770651 + 0.E-38*I, 4.56184005023781247209
474: 13214622468855073 - 3.526483052466862523 E-38*I, 18.362968630416114402425299
475: 186062892646 + 0.E-37*I]], [Mod(5, y^3 - y - 1), 0, 0, 0, Mod(4, y^3 - y - 1
476: ); 0, 0, 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1); 0, 0, Mod(4, y^3 - y
477: - 1), Mod(10, y^3 - y - 1), 0; 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1),
478: 0, 0; Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0, 0, Mod(4, y^3 - y - 1)]
479: , [;], [;], [;]], [[1.2671683045421243172528914279776896412, 0.2609638803864
480: 5528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -0.89
481: 454803265751744362901306471557966872 + 0.53414854617473272670874609150394379
482: 949*I], [1.2671683045421243172528914279776896412 + 0.E-38*I, 0.2609638803864
483: 5528500256735072673484811 - 1.1772261533941944394700286585617926513*I, 0.260
484: 96388038645528500256735072673484811 + 1.177226153394194439470028658561792651
485: 3*I, -0.89454803265751744362901306471557966872 - 0.5341485461747327267087460
486: 9150394379949*I, -0.89454803265751744362901306471557966872 + 0.5341485461747
487: 3272670874609150394379949*I]~], [[Mod(1, y^3 - y - 1), Mod(1, y^3 - y - 1)*x
488: , Mod(1, y^3 - y - 1)*x^2, Mod(1, y^3 - y - 1)*x^3, Mod(1, y^3 - y - 1)*x^4]
489: , [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1,
490: 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [M
491: od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1
492: , y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^
1.2 ! noro 493: 3 - y - 1)], [], [y^3 - y - 1, [1, 1], -23, 1, [[1, 0.7548776662466927600495
! 494: 0889635852869189, 1.3247179572447460259609088544780973407; 1, -0.87743883312
! 495: 334638002475444817926434594 - 0.74486176661974423659317042860439236723*I, -0
! 496: .66235897862237301298045442723904867036 + 0.56227951206230124389918214490937
! 497: 306149*I], [1, 0.75487766624669276004950889635852869189, 1.32471795724474602
! 498: 59609088544780973407; 1.4142135623730950488016887242096980785, -1.2408858979
! 499: 558593537192653626096055786, -0.93671705072735084703311164961686101696; 0, -
! 500: 1.0533936124468254335289038498031013275, 0.795183311803032710044767156296587
! 501: 54002], 0, [3, -1, 0; -1, 1, 3; 0, 3, 2], [23, 16, 13; 0, 1, 0; 0, 0, 1], [-
! 502: 7, 2, -3; 2, 6, -9; -3, -9, 2], [23, [10, 7, 1]~]], [1.324717957244746025960
! 503: 9088544780973407, -0.66235897862237301298045442723904867036 + 0.562279512062
! 504: 30124389918214490937306149*I], [1, y^2 - 1, y], [1, 0, 1; 0, 0, 1; 0, 1, 0],
! 505: [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
! 506: , 0, 0]], [x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*
! 507: x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1, Mod(3951653
! 508: 6165538345/83718587879473471*x^14 - 6500512476832995/83718587879473471*x^13
! 509: - 196215472046117185/83718587879473471*x^12 + 229902227480108910/83718587879
! 510: 473471*x^11 + 237380704030959181/83718587879473471*x^10 - 106493198816077380
! 511: 5/83718587879473471*x^9 - 20657086671714300/83718587879473471*x^8 + 17728852
! 512: 05999206010/83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^
! 513: 6 - 4838840187320655696/83718587879473471*x^5 + 5180390720553188700/83718587
! 514: 879473471*x^4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040
! 515: 221/83718587879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920
! 516: 215718580450/83718587879473471, x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 -
! 517: 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 +
! 518: 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^
! 519: 12, x^13, 1/83718587879473471*x^14 - 20528463024680133/83718587879473471*x^1
! 520: 3 - 4742392948888610/83718587879473471*x^12 - 9983523646123358/8371858787947
! 521: 3471*x^11 + 40898955597139011/83718587879473471*x^10 + 29412692423971937/837
! 522: 18587879473471*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075
! 523: 066/83718587879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 2015290
! 524: 5879672878/83718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 -
! 525: 8471905745957397/83718587879473471*x^3 - 13395753879413605/83718587879473471
! 526: *x^2 + 27623037732247492/83718587879473471*x + 26306699661480593/83718587879
! 527: 473471], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1
! 528: , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0,
! 529: 0, 0, 0, 0, 0, 0, 0, 0, 13395753879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
! 530: 0, 0, 0, 8471905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -959164
! 531: 3151927789; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0,
! 532: 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0,
! 533: 0, 1, 0, 0, 0, 0, 0, 0, -41014993230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
! 534: 0, 0, 0, 5017479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412
! 535: 692423971937; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011;
! 536: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0
! 537: , 0, 0, 0, 0, 0, 0, 1, 0, 4742392948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
! 538: 0, 0, 1, 20528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718
! 539: 587879473471]]]
1.1 noro 540: ? bnfcertify(bnf)
541: 1
542: ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
543:
544: [x^4 - 7]
545:
546: [[2, 1]]
547:
548: [[-87808, 1]]
549:
550: [[1, x, x^2, x^3]]
551:
552: [[2, [2], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
553:
554: [14.229975145405511722395637833443108790]
555:
556: [1.121117107152756229]
557:
558: ? setrand(1);bnfclassunit(x^2-x-100000)
559: *** Warning: insufficient precision for fundamental units, not given.
560:
561: [x^2 - x - 100000]
562:
563: [[2, 0]]
564:
565: [[400001, 1]]
566:
1.2 ! noro 567: [[1, x - 1]]
1.1 noro 568:
1.2 ! noro 569: [[5, [5], [[2, 0; 0, 1]]]]
1.1 noro 570:
571: [129.82045011403975460991182396195022419]
572:
1.2 ! noro 573: [0.9876536979069047228]
1.1 noro 574:
575: [[2, -1]]
576:
577: [[;]]
578:
579: [0]
580:
581: ? setrand(1);bnfclassunit(x^2-x-100000,1)
582:
583: [x^2 - x - 100000]
584:
585: [[2, 0]]
586:
587: [[400001, 1]]
588:
1.2 ! noro 589: [[1, x - 1]]
1.1 noro 590:
1.2 ! noro 591: [[5, [5], [[2, 0; 0, 1]]]]
1.1 noro 592:
593: [129.82045011403975460991182396195022419]
594:
1.2 ! noro 595: [0.9876536979069047228]
1.1 noro 596:
597: [[2, -1]]
598:
599: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
600: 789990462835950022871665178127611316131167]]
601:
1.2 ! noro 602: [185]
1.1 noro 603:
604: ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
605:
606: [x^4 + 24*x^2 + 585*x + 1791]
607:
608: [[0, 2]]
609:
610: [[18981, 3087]]
611:
1.2 ! noro 612: [[1, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343, 17/1029*x^3 - 32/1029
! 613: *x^2 + 109/343*x + 2444/343, -11/343*x^3 + 163/1029*x^2 - 373/343*x - 4260/3
! 614: 43]]
1.1 noro 615:
1.2 ! noro 616: [[4, [4], [[7, 2, 4, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
1.1 noro 617:
618: [3.7941269688216589341408274220859400302]
619:
1.2 ! noro 620: [0.8826018286655581299]
1.1 noro 621:
1.2 ! noro 622: [[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
1.1 noro 623:
624: [[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]
625:
1.2 ! noro 626: [365]
1.1 noro 627:
628: ? setrand(1);bnfclgp(17)
629: [1, [], []]
630: ? setrand(1);bnfclgp(-31)
631: [3, [3], [Qfb(2, 1, 4)]]
632: ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791)
1.2 ! noro 633: [4, [4], [[7, 2, 0, 5; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]
! 634: ? bnrconductor(bnf,[[25,14;0,1],[1,1]])
! 635: [[5, 4; 0, 1], [1, 0]]
1.1 noro 636: ? bnrconductorofchar(bnr,[2])
1.2 ! noro 637: [[5, 4; 0, 1], [0, 0]]
! 638: ? bnfisprincipal(bnf,[5,2;0,1],0)
1.1 noro 639: [1]~
1.2 ! noro 640: ? bnfisprincipal(bnf,[5,2;0,1])
! 641: [[1]~, [7/3, 1/3]~, 187]
1.1 noro 642: ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
643: [-4, Mod(1, 2)]~
644: ? \p19
645: realprecision = 19 significant digits
646: ? bnfmake(sbnf)
1.2 ! noro 647: [Mat(2), Mat([1, 1, 0, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
! 648: 89793238*I, -4.562279014988837952 + 3.141592653589793238*I; -2.6335434327389
1.1 noro 649: 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
650: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
1.2 ! noro 651: 1592653589793238*I, 0.5404006376129469727 + 3.141592653589793238*I, -0.69263
! 652: 91142471042844 + 3.141592653589793238*I, -1.990056445584799713 + 3.141592653
! 653: 589793238*I, -0.8305625946607188643 + 3.141592653589793238*I, 0.E-57, 0.0043
! 654: 75616572659815433 + 3.141592653589793238*I, -1.977791147836553953, 0.3677262
! 655: 014027817708 + 3.141592653589793238*I; 0.6716827432867392938 + 3.14159265358
! 656: 9793238*I, -0.8333219883742404170 + 3.141592653589793238*I, -0.2461086674077
! 657: 943076, 0.5379005671092853269, -1.552661549868775853, 0.E-57, -0.87383180430
! 658: 71131263, 0.5774919091398324092, 0.9729063188316092380; -1.91802973262155845
! 659: 5, 0.2929213507612934444, 0.9387477816548985923, 1.452155878475514386, 2.383
! 660: 224144529494717, 0.E-57, 0.8694561877344533111, 1.400299238696721544, -1.340
! 661: 632520234391008], [[3, [-1, 1, 0]~, 1, 1, [1, 1, 1]~], [5, [-1, 1, 0]~, 1, 1
! 662: , [0, 1, 1]~], [5, [2, 1, 0]~, 1, 1, [1, -2, 1]~], [5, [3, 1, 0]~, 1, 1, [2,
! 663: 2, 1]~], [13, [19, 1, 0]~, 1, 1, [-2, -6, 1]~], [3, [10, 1, 1]~, 1, 2, [-1,
! 664: 1, 0]~], [11, [1, 1, 0]~, 1, 1, [-3, -1, 1]~], [19, [-6, 1, 0]~, 1, 1, [6,
! 665: 6, 1]~], [23, [-10, 1, 0]~, 1, 1, [-7, 10, 1]~]]~, 0, [x^3 - x^2 - 14*x - 1,
! 666: [3, 0], 10889, 1, [[1, -3.233732695981516672, 4.690759845041404811; 1, -0.0
! 667: 7182350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.23225
! 668: 8029482144592], [1, -3.233732695981516672, 4.690759845041404811; 1, -0.07182
! 669: 350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.232258029
! 670: 482144592], 0, [3, 1, 1; 1, 29, 8; 1, 8, 129], [10889, 5698, 8994; 0, 1, 0;
! 671: 0, 0, 1], [3677, -121, -21; -121, 386, -23; -21, -23, 86], [10889, [1899, 51
! 672: 91, 1]~]], [-3.233732695981516672, -0.07182350902743636344, 4.30555620500895
! 673: 3036], [1, x, x^2 - x - 9], [1, 0, 9; 0, 1, 1; 0, 0, 1], [1, 0, 0, 0, 9, 1,
! 674: 0, 1, 44; 0, 1, 0, 1, 1, 5, 0, 5, 1; 0, 0, 1, 0, 1, 0, 1, 0, -4]], [[2, [2],
! 675: [[3, 2, 0; 0, 1, 0; 0, 0, 1]]], 10.34800724602768011, 1.000000000000000000,
! 676: [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0.E-57, 0.E-57, 0.E-57]], [[
! 677: 1.246346989334819161 + 3.141592653589793238*I, 0.6716827432867392938 + 3.141
! 678: 592653589793238*I, -1.918029732621558455]]], [-4, -1, 2, 3, 10, 3, 1, 7, 2;
! 679: 1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
1.1 noro 680: ? \p38
681: realprecision = 38 significant digits
682: ? bnfnarrow(bnf)
1.2 ! noro 683: [3, [3], [[3, 0; 0, 1]]]
1.1 noro 684: ? bnfreg(x^2-x-57)
685: 2.7124653051843439746808795106061300699
686: ? bnfsignunit(bnf)
687:
688: [-1]
689:
690: [1]
691:
692: ? bnfunit(bnf)
1.2 ! noro 693: [[x + 7], 187]
! 694: ? bnrclass(bnf,[[5,4;0,1],[1,0]])
! 695: [12, [12], [[3, 0; 0, 1]]]
! 696: ? bnr2=bnrclass(bnf,[[25,14;0,1],[1,1]],2)
1.1 noro 697: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
1.2 ! noro 698: 061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 699: 808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
! 700: 52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
! 701: 148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
! 702: 9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
! 703: 8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
! 704: 97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
! 705: 1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
! 706: 0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
! 707: 492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
! 708: 7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
! 709: 8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
! 710: 071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
! 711: 38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
! 712: 7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
! 713: [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
! 714: [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
! 715: 2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
! 716: -2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
! 717: x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
! 718: 1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
! 719: 10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
! 720: 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
! 721: 779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
! 722: 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
! 723: 7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
! 724: 7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
! 725: 903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[25, 1
! 726: 4; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [4, 2]~, [-2, -2]~]], Mat([[5,
! 727: [-1, 1]~, 1, 1, [2, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), M
! 728: od(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat(
! 729: [1/5, -14/5])]], [[2, 2], [[4, 2]~, [-2, -2]~], [1, 0; 0, 1]]], [1, -12, 0,
! 730: 0; 0, 0, 1, 0; 0, 0, 0, 1]], [1], Mat([1, -3, -6, 0]), [12, [12], [[3, 0; 0,
! 731: 1]]], [[1, -18, 9; -1/2, 10, -5], [-2, 0; 0, -10]]]
! 732: ? bnrclassno(bnf,[[5,4;0,1],[1,0]])
1.1 noro 733: 12
734: ? lu=ideallist(bnf,55,3);
735: ? bnrclassnolist(bnf,lu)
736: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
737: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
738: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
739: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
740: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
741: ? bnrdisc(bnr,Mat(6))
742: [12, 12, 18026977100265125]
743: ? bnrdisc(bnr)
744: [24, 12, 40621487921685401825918161408203125]
745: ? bnrdisc(bnr2,,,2)
746: 0
747: ? bnrdisc(bnr,Mat(6),,1)
1.2 ! noro 748: [6, 2, [125, 14; 0, 1]]
1.1 noro 749: ? bnrdisc(bnr,,,1)
1.2 ! noro 750: [12, 1, [1953125, 1160889; 0, 1]]
1.1 noro 751: ? bnrdisc(bnr2,,,3)
752: 0
753: ? bnrdisclist(bnf,lu)
754: [[[6, 6, Mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
755: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
756: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
757: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
758: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
759: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
760: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
761: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
762: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
763: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
764: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
765: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
766: , []]]
767: ? bnrdisclist(bnf,20,,1)
768: [[[[matrix(0,2), [[6, 6, Mat([229, 3])], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]],
769: [], [[Mat([12, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [3, 3; 229, 6
770: ]]]], [Mat([13, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1, 1; 3, 3; 229, 6]],
771: [0, 0, 0]]]], [[Mat([10, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]
772: , [[Mat([20, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [0, 0, 0], [24, 0, [
773: 5, 9; 229, 12]]]], [Mat([21, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [24,
774: 12, [5, 9; 229, 12]], [0, 0, 0]]]], [], [], [], [[Mat([12, 2]), [[0, 0, 0],
775: [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1], [[0, 0, 0], [12, 6, [-1
776: , 1; 3, 6; 229, 6]], [0, 0, 0], [24, 0, [3, 12; 229, 12]]]], [Mat([13, 2]),
777: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([44, 1]), [[0, 0,
778: 0], [0, 0, 0], [12, 6, [-1, 1; 11, 3; 229, 6]], [0, 0, 0]]], [Mat([45, 1]),
779: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [11, 3; 229, 6]]]]], [[[10, 1; 12,
780: 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 13, 1], [[0, 0,
781: 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [], [[[12, 1; 20, 1], [[24, 24,
782: [3, 6; 5, 9; 229, 12]], [0, 0, 0], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 2
783: 4]]]], [[13, 1; 20, 1], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [24, 12
784: , [3, 6; 5, 6; 229, 12]], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1
785: ], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 0, [3, 12; 5
786: , 18; 229, 24]]]], [[13, 1; 21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0,
787: 0], [48, 24, [3, 12; 5, 18; 229, 24]], [0, 0, 0]]]], [[Mat([10, 2]), [[0, 0
788: , 0], [12, 6, [-1, 1; 2, 12; 229, 6]], [12, 6, [-1, 1; 2, 12; 229, 6]], [24,
789: 0, [2, 36; 229, 12]]]]], [[Mat([68, 1]), [[0, 0, 0], [12, 6, [-1, 1; 17, 3;
790: 229, 6]], [0, 0, 0], [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [12, 6, [-1, 1
791: ; 17, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [1
792: 9, 6; 229, 9]], [0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77
793: , 1]), [[18, 18, [19, 6; 229, 9]], [0, 0, 0], [36, 18, [-1, 1; 19, 15; 229,
794: 18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0,
795: 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]]
796: ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
1.2 ! noro 797: [[9]~, [112595/19683, 13958/19683]~, 256]
1.1 noro 798: ? dirzetak(nf4,30)
799: [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,
800: 0, 1, 0, 1, 0]
801: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
802:
803: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t, t^3 + t^2 - 2*t - 1) 1]
804:
805: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
806:
807: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
808:
809: ? vp=idealprimedec(nf,3)[1]
1.2 ! noro 810: [3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~]
1.1 noro 811: ? idx=idealmul(nf,matid(5),vp)
812:
1.2 ! noro 813: [3 2 1 0 1]
1.1 noro 814:
815: [0 1 0 0 0]
816:
817: [0 0 1 0 0]
818:
819: [0 0 0 1 0]
820:
821: [0 0 0 0 1]
822:
823: ? idealinv(nf,idx)
824:
1.2 ! noro 825: [1 0 0 2/3 0]
1.1 noro 826:
1.2 ! noro 827: [0 1 0 1/3 0]
1.1 noro 828:
1.2 ! noro 829: [0 0 1 1/3 0]
1.1 noro 830:
1.2 ! noro 831: [0 0 0 1/3 0]
1.1 noro 832:
833: [0 0 0 0 1]
834:
835: ? idy=idealred(nf,idx,[1,5,6])
836:
1.2 ! noro 837: [5 0 0 0 2]
1.1 noro 838:
1.2 ! noro 839: [0 5 0 0 2]
1.1 noro 840:
1.2 ! noro 841: [0 0 5 0 1]
1.1 noro 842:
1.2 ! noro 843: [0 0 0 5 2]
1.1 noro 844:
1.2 ! noro 845: [0 0 0 0 1]
1.1 noro 846:
847: ? idx2=idealmul(nf,idx,idx)
848:
1.2 ! noro 849: [9 5 7 0 4]
1.1 noro 850:
851: [0 1 0 0 0]
852:
853: [0 0 1 0 0]
854:
855: [0 0 0 1 0]
856:
857: [0 0 0 0 1]
858:
859: ? idt=idealmul(nf,idx,idx,1)
860:
1.2 ! noro 861: [2 0 0 0 0]
1.1 noro 862:
1.2 ! noro 863: [0 2 0 0 0]
1.1 noro 864:
865: [0 0 2 0 0]
866:
867: [0 0 0 2 1]
868:
869: [0 0 0 0 1]
870:
871: ? idz=idealintersect(nf,idx,idy)
872:
1.2 ! noro 873: [15 10 5 0 12]
1.1 noro 874:
1.2 ! noro 875: [0 5 0 0 2]
1.1 noro 876:
1.2 ! noro 877: [0 0 5 0 1]
1.1 noro 878:
1.2 ! noro 879: [0 0 0 5 2]
1.1 noro 880:
1.2 ! noro 881: [0 0 0 0 1]
1.1 noro 882:
883: ? aid=[idx,idy,idz,matid(5),idx]
1.2 ! noro 884: [[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]
! 885: , [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
! 886: ], [15, 10, 5, 0, 12; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0,
! 887: 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,
! 888: 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
! 889: , 0, 1]]
1.1 noro 890: ? bid=idealstar(nf2,54,1)
891: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
892: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1.2 ! noro 893: 1, 1, 0]~], [[1, -27, 0]~], [[]~], 1]], [[[26], [[2, 1, 0]~], [[-25, -26, 0]
1.1 noro 894: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
895: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
896: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
897: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
1.2 ! noro 898: 0]]], [[], [], [;]]], [2106, -77, 10556, 0, -4368, 12012, 0, -13104; 0, 0,
! 899: 0, 1, -2, 0, -6, -6; -27, 1, -136, 0, 56, -156, 0, 168]]
1.1 noro 900: ? vaid=[idx,idy,matid(5)]
1.2 ! noro 901: [[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]
! 902: , [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
1.1 noro 903: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
904: 1]]
905: ? haid=[matid(5),matid(5),matid(5)]
906: [[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]
907: , [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
908: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
909: 1]]
910: ? idealadd(nf,idx,idy)
911:
912: [1 0 0 0 0]
913:
914: [0 1 0 0 0]
915:
916: [0 0 1 0 0]
917:
918: [0 0 0 1 0]
919:
920: [0 0 0 0 1]
921:
922: ? idealaddtoone(nf,idx,idy)
1.2 ! noro 923: [[3, 2, 1, 2, 1]~, [-2, -2, -1, -2, -1]~]
1.1 noro 924: ? idealaddtoone(nf,[idy,idx])
925: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
926: ? idealappr(nf,idy)
1.2 ! noro 927: [-2, -2, -1, -2, -1]~
1.1 noro 928: ? idealappr(nf,idealfactor(nf,idy),1)
1.2 ! noro 929: [-2, -2, -1, -2, -1]~
1.1 noro 930: ? idealcoprime(nf,idx,idx)
1.2 ! noro 931: [1/3, -1/3, -1/3, -1/3, 0]~
1.1 noro 932: ? idealdiv(nf,idy,idt)
933:
1.2 ! noro 934: [5 0 5/2 0 1]
1.1 noro 935:
1.2 ! noro 936: [0 5/2 0 0 1]
1.1 noro 937:
1.2 ! noro 938: [0 0 5/2 0 1/2]
1.1 noro 939:
1.2 ! noro 940: [0 0 0 5/2 1]
1.1 noro 941:
1.2 ! noro 942: [0 0 0 0 1/2]
1.1 noro 943:
944: ? idealdiv(nf,idx2,idx,1)
945:
1.2 ! noro 946: [3 2 1 0 1]
1.1 noro 947:
948: [0 1 0 0 0]
949:
950: [0 0 1 0 0]
951:
952: [0 0 0 1 0]
953:
954: [0 0 0 0 1]
955:
956: ? idf=idealfactor(nf,idz)
957:
1.2 ! noro 958: [[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] 1]
1.1 noro 959:
1.2 ! noro 960: [[5, [-1, 0, 0, 0, 1]~, 1, 1, [2, 0, 3, 0, 1]~] 1]
1.1 noro 961:
1.2 ! noro 962: [[5, [2, 0, 0, 0, 1]~, 4, 1, [2, 2, 1, 2, 1]~] 3]
1.1 noro 963:
964: ? idealhnf(nf,vp)
965:
1.2 ! noro 966: [3 2 1 0 1]
1.1 noro 967:
968: [0 1 0 0 0]
969:
970: [0 0 1 0 0]
971:
972: [0 0 0 1 0]
973:
974: [0 0 0 0 1]
975:
976: ? idealhnf(nf,vp[2],3)
977:
1.2 ! noro 978: [3 2 1 0 1]
1.1 noro 979:
980: [0 1 0 0 0]
981:
982: [0 0 1 0 0]
983:
984: [0 0 0 1 0]
985:
986: [0 0 0 0 1]
987:
988: ? ideallist(bnf,20)
1.2 ! noro 989: [[[1, 0; 0, 1]], [], [[3, 0; 0, 1], [3, 1; 0, 1]], [[2, 0; 0, 2]], [[5, 4; 0
! 990: , 1], [5, 2; 0, 1]], [], [], [], [[9, 6; 0, 1], [3, 0; 0, 3], [9, 4; 0, 1]],
! 991: [], [[11, 10; 0, 1], [11, 2; 0, 1]], [[6, 0; 0, 2], [6, 2; 0, 2]], [], [],
! 992: [[15, 9; 0, 1], [15, 4; 0, 1], [15, 12; 0, 1], [15, 7; 0, 1]], [[4, 0; 0, 4]
! 993: ], [[17, 15; 0, 1], [17, 3; 0, 1]], [], [[19, 0; 0, 1], [19, 1; 0, 1]], [[10
! 994: , 8; 0, 2], [10, 4; 0, 2]]]
1.1 noro 995: ? ideallog(nf2,w,bid)
1.2 ! noro 996: [486, 3, 7]~
1.1 noro 997: ? idealmin(nf,idx,[1,2,3])
1.2 ! noro 998: [[-2; 1; 1; 0; 1], [2.0885812311199768913287869744681966008 + 3.141592653589
1.1 noro 999: 7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244
1000: 7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160
1.2 ! noro 1001: 207 + 2.5437460822678889883600220330800078854*I]]
1.1 noro 1002: ? idealnorm(nf,idt)
1003: 16
1004: ? idp=idealpow(nf,idx,7)
1005:
1.2 ! noro 1006: [2187 1436 1807 630 1822]
1.1 noro 1007:
1008: [0 1 0 0 0]
1009:
1010: [0 0 1 0 0]
1011:
1012: [0 0 0 1 0]
1013:
1014: [0 0 0 0 1]
1015:
1016: ? idealpow(nf,idx,7,1)
1017:
1.2 ! noro 1018: [2 0 0 0 0]
1.1 noro 1019:
1.2 ! noro 1020: [0 2 0 0 0]
1.1 noro 1021:
1.2 ! noro 1022: [0 0 2 0 0]
1.1 noro 1023:
1.2 ! noro 1024: [0 0 0 2 1]
1.1 noro 1025:
1.2 ! noro 1026: [0 0 0 0 1]
1.1 noro 1027:
1028: ? idealprimedec(nf,2)
1.2 ! noro 1029: [[2, [3, 0, 1, 0, 0]~, 1, 1, [0, 0, 0, 1, 1]~], [2, [12, -4, -2, 11, 3]~, 1,
! 1030: 4, [1, 0, 1, 0, 0]~]]
1.1 noro 1031: ? idealprimedec(nf,3)
1.2 ! noro 1032: [[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~], [3, [-1, -1, -1, 0, 0]~,
! 1033: 2, 2, [0, 2, 2, 1, 0]~]]
1.1 noro 1034: ? idealprimedec(nf,11)
1035: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
1036: ? idealprincipal(nf,Mod(x^3+5,nfpol))
1037:
1038: [6]
1039:
1.2 ! noro 1040: [1]
! 1041:
! 1042: [3]
1.1 noro 1043:
1044: [1]
1045:
1046: [3]
1047:
1048: ? idealtwoelt(nf,idy)
1.2 ! noro 1049: [5, [2, 2, 1, 2, 1]~]
1.1 noro 1050: ? idealtwoelt(nf,idy,10)
1.2 ! noro 1051: [-2, -2, -1, -2, -1]~
1.1 noro 1052: ? idealstar(nf2,54)
1053: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
1054: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1.2 ! noro 1055: 1, 0, 1]~], [[1, 0, -27]~], [[]~], 1]], [[[26], [[2, 2, 1]~], [[-25, 2, -26]
1.1 noro 1056: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
1057: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
1058: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
1059: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
1.2 ! noro 1060: 0]]], [[], [], [;]]], [468, 469, 0, 0, -85358, 0, 0, -36582; 0, 0, 1, 0, -5
! 1061: , -6, 0, -6; 0, 0, 0, 1, -8, 0, -6, -6]]
1.1 noro 1062: ? idealval(nf,idp,vp)
1063: 7
1064: ? ideleprincipal(nf,Mod(x^3+5,nfpol))
1.2 ! noro 1065: [[6; 1; 3; 1; 3], [2.2324480827796254080981385584384939684 + 3.1415926535897
! 1066: 932384626433832795028841*I, 5.0387659675158716386435353106610489968 + 1.5851
1.1 noro 1067: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
1.2 ! noro 1068: - 0.0083630478144368246110910258645462996225*I]]
1.1 noro 1069: ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
1.2 ! noro 1070: [6, 1, 3, 1, 3]~
1.1 noro 1071: ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
1.2 ! noro 1072: [1, 1, 4, 1, 3]~
1.1 noro 1073: ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
1074:
1.2 ! noro 1075: [[3, -2, 1, 1, 0]~]
1.1 noro 1076:
1.2 ! noro 1077: [[4, -2, 0, 1, 0]~]
1.1 noro 1078:
1079: ? matbasistoalg(nf,bc)
1080:
1081: [Mod(x^2 + x, x^5 - 5*x^3 + 5*x + 25)]
1082:
1083: [Mod(x^2 + 1, x^5 - 5*x^3 + 5*x + 25)]
1084:
1085: ? nfbasis(x^3+4*x+5)
1086: [1, x, 1/7*x^2 - 1/7*x - 2/7]
1087: ? nfbasis(x^3+4*x+5,2)
1088: [1, x, 1/7*x^2 - 1/7*x - 2/7]
1089: ? nfbasis(x^3+4*x+12,1)
1090: [1, x, 1/2*x^2]
1091: ? nfbasistoalg(nf,ba)
1092: Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
1093: ? nfbasis(p2,0,fa)
1094: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
1095: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
1096: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
1097: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
1098: ? da=nfdetint(nf,[a,aid])
1099:
1.2 ! noro 1100: [90 70 35 0 65]
1.1 noro 1101:
1102: [0 5 0 0 0]
1103:
1.2 ! noro 1104: [0 0 5 0 0]
1.1 noro 1105:
1.2 ! noro 1106: [0 0 0 5 0]
1.1 noro 1107:
1108: [0 0 0 0 5]
1109:
1110: ? nfdisc(x^3+4*x+12)
1111: -1036
1112: ? nfdisc(x^3+4*x+12,1)
1113: -1036
1114: ? nfdisc(p2,0,fa)
1115: 136866601
1116: ? nfeltdiv(nf,ba,bb)
1.2 ! noro 1117: [584/373, 66/373, -32/373, -105/373, 120/373]~
1.1 noro 1118: ? nfeltdiveuc(nf,ba,bb)
1.2 ! noro 1119: [2, 0, 0, 0, 0]~
1.1 noro 1120: ? nfeltdivrem(nf,ba,bb)
1.2 ! noro 1121: [[2, 0, 0, 0, 0]~, [4, -1, -5, -1, -3]~]
1.1 noro 1122: ? nfeltmod(nf,ba,bb)
1.2 ! noro 1123: [4, -1, -5, -1, -3]~
1.1 noro 1124: ? nfeltmul(nf,ba,bb)
1.2 ! noro 1125: [50, -15, -35, 60, 15]~
1.1 noro 1126: ? nfeltpow(nf,bb,5)
1.2 ! noro 1127: [-291920, 136855, 230560, -178520, 74190]~
1.1 noro 1128: ? nfeltreduce(nf,ba,idx)
1129: [1, 0, 0, 0, 0]~
1130: ? nfeltval(nf,ba,vp)
1131: 0
1132: ? nffactor(nf2,x^3+x)
1133:
1.2 ! noro 1134: [x 1]
1.1 noro 1135:
1.2 ! noro 1136: [x^2 + 1 1]
1.1 noro 1137:
1138: ? aut=nfgaloisconj(nf3)
1.2 ! noro 1139: [-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
! 1140: /2*x]~
1.1 noro 1141: ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
1.2 ! noro 1142: Mod(-1/2*x^5 + 9*x^2, x^6 + 108)
1.1 noro 1143: ? nfhilbert(nf,3,5)
1144: -1
1145: ? nfhilbert(nf,3,5,idf[1,1])
1146: -1
1147: ? nfhnf(nf,[a,aid])
1.2 ! noro 1148: [[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [
! 1149: 1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0
! 1150: , 0, 0, 0]~], [[10, 4, 5, 6, 7; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1151: 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
! 1152: ; 0, 0, 0, 0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1,
! 1153: 0; 0, 0, 0, 0, 1]]]
1.1 noro 1154: ? nfhnfmod(nf,[a,aid],da)
1.2 ! noro 1155: [[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [
! 1156: 1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0
! 1157: , 0, 0, 0]~], [[10, 4, 5, 6, 7; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1158: 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
! 1159: ; 0, 0, 0, 0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1,
! 1160: 0; 0, 0, 0, 0, 1]]]
! 1161: ? nfisideal(bnf[7],[5,2;0,1])
1.1 noro 1162: 1
1163: ? nfisincl(x^2+1,x^4+1)
1164: [-x^2, x^2]
1165: ? nfisincl(x^2+1,nfinit(x^4+1))
1166: [-x^2, x^2]
1167: ? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
1168: [x, -x^2 - x + 1, x^2 - 2]
1169: ? nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30))
1170: [-1/25*x^2 + 13/25*x - 2/5]
1171: ? nfroots(nf2,x+2)
1172: [Mod(-2, y^3 - y - 1)]
1173: ? nfrootsof1(nf)
1174: [2, [-1, 0, 0, 0, 0]~]
1175: ? nfsnf(nf,[as,haid,vaid])
1.2 ! noro 1176: [[2562748315629757085585610, 436545976069778274371140, 123799938628701108220
! 1177: 1405, 2356446991473627724963350, 801407102592194537169612; 0, 5, 0, 0, 2; 0,
! 1178: 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
! 1179: , 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0;
! 1180: 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
1.1 noro 1181: ? nfsubfields(nf)
1182: [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]]
1183: ? polcompositum(x^4-4*x+2,x^3-x-1)
1184: [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
1185: ^2 - 128*x - 5]
1186: ? polcompositum(x^4-4*x+2,x^3-x-1,1)
1187: [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
1188: x^2 - 128*x - 5, Mod(-279140305176/29063006931199*x^11 + 129916611552/290630
1189: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
1190: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
1191: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
1192: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
1193: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
1194: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), M
1195: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
1196: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
1197: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
1198: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
1199: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
1200: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
1201: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
1202: ? polgalois(x^6-3*x^2-1)
1203: [12, 1, 1]
1204: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
1205: [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
1206: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
1207: ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
1208:
1209: [1 x - 1]
1210:
1211: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
1212:
1213: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
1214:
1215: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
1216:
1217: ? polred(x^4+576,1)
1218: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
1219: ? polred(x^4+576,3)
1220:
1221: [1 x - 1]
1222:
1223: [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
1224:
1225: [-1/24*x^2 x^2 + 1]
1226:
1227: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
1228:
1229: ? polred(p2,0,fa)
1230: [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
1231: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
1232: *x^3 - 197*x^2 - 273*x - 127]
1233: ? polred(p2,1,fa)
1234: [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
1235: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
1236: *x^3 - 197*x^2 - 273*x - 127]
1237: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
1238: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
1239: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
1240: [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 -
1241: x^4 + 2*x^3 - 4*x^2 + x - 1)]
1242: ? polredord(x^3-12*x+45*x-1)
1243: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
1244: ? polsubcyclo(31,5)
1245: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
1246: ? setrand(1);poltschirnhaus(x^5-x-1)
1247: x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289
1248: ? aa=rnfpseudobasis(nf2,p)
1249: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
1250: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
1251: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
1252: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
1253: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
1.2 ! noro 1254: , 0; 0, 0, 1], [1, 0, 2/5; 0, 1, 3/5; 0, 0, 1/5], [1, 0, 22/25; 0, 1, 8/25;
! 1255: 0, 0, 1/25]], [416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1
! 1256: 275, 5, 5]~]
1.1 noro 1257: ? rnfbasis(bnf2,aa)
1258:
1.2 ! noro 1259: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-6/25, 66/25, 77/25]~ [-391/25, -699/25,
! 1260: 197/25]~]
1.1 noro 1261:
1.2 ! noro 1262: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [18/25, -48/25, -56/25]~ [268/25, 552/25,
! 1263: -206/25]~]
1.1 noro 1264:
1.2 ! noro 1265: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [41/25, 24/25, 28/25]~ [-194/25, -116/25,
! 1266: -127/25]~]
1.1 noro 1267:
1.2 ! noro 1268: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [17/25, -12/25, -14/25]~ [52/25, 178/25, -
! 1269: 109/25]~]
1.1 noro 1270:
1.2 ! noro 1271: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/25, 6/25, 7/25]~ [-41/25, -49/25, -3/25
! 1272: ]~]
1.1 noro 1273:
1274: ? rnfdisc(nf2,p)
1.2 ! noro 1275: [[416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
1.1 noro 1276: ? rnfequation(nf2,p)
1277: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
1278: ? rnfequation(nf2,p,1)
1279: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, Mod(-x^5 + 5*x, x^15 - 1
1280: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
1281: ? rnfhnfbasis(bnf2,aa)
1282:
1.2 ! noro 1283: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [6/5, 4/5, -2/5]~ [-22/25, -33/25, 99/25]~
1.1 noro 1284: ]
1285:
1.2 ! noro 1286: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-6/5, -4/5, 2/5]~ [16/25, 24/25, -72/25]~
! 1287: ]
1.1 noro 1288:
1.2 ! noro 1289: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-3/5, -2/5, 1/5]~ [-8/25, -12/25, 36/25]~
! 1290: ]
1.1 noro 1291:
1.2 ! noro 1292: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/5, -2/5, 1/5]~ [4/25, 6/25, -18/25]~]
1.1 noro 1293:
1.2 ! noro 1294: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/25, -3/25, 9/25]~]
1.1 noro 1295:
1296: ? rnfisfree(bnf2,aa)
1297: 1
1298: ? rnfsteinitz(nf2,aa)
1.2 ! noro 1299: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-6/25, 66/25, 77/25]~, [17/125, -66/1
! 1300: 25, -77/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [18/25, -48/25, -56/25]~,
! 1301: [-26/125, 48/125, 56/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [41/25, 24/
! 1302: 25, 28/25]~, [-37/125, -24/125, -28/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]
! 1303: ~, [17/25, -12/25, -14/25]~, [-19/125, 12/125, 14/125]~; [0, 0, 0]~, [0, 0,
! 1304: 0]~, [0, 0, 0]~, [4/25, 6/25, 7/25]~, [-3/125, -6/125, -7/125]~], [[1, 0, 0;
! 1305: 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]
! 1306: , [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0, 22; 0, 125, 108; 0, 0, 1]], [4161343
! 1307: 75, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
1.1 noro 1308: ? nfz=zetakinit(x^2-2);
1309: ? zetak(nfz,-3)
1310: 0.091666666666666666666666666666666666666
1311: ? zetak(nfz,1.5+3*I)
1312: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
1313: 7938845*I
1314: ? setrand(1);quadclassunit(1-10^7,,[1,1])
1315: *** Warning: not a fundamental discriminant in quadclassunit.
1.2 ! noro 1316: [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 1.00257481
! 1317: 6299307750]
1.1 noro 1318: ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
1319: [4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
1.2 ! noro 1320: 5514, 0.9849577285369119736]
1.1 noro 1321: ? sizebyte(%)
1.2 ! noro 1322: 320
1.1 noro 1323: ? getheap
1.2 ! noro 1324: [199, 115764]
1.1 noro 1325: ? print("Total time spent: ",gettime);
1.2 ! noro 1326: Total time spent: 3629
1.1 noro 1327: ? \q
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