Annotation of OpenXM_contrib/pari-2.2/src/test/32/nfields, Revision 1.2
1.1 noro 1: realprecision = 38 significant digits
2: echo = 1 (on)
3: ? nfpol=x^5-5*x^3+5*x+25
4: x^5 - 5*x^3 + 5*x + 25
5: ? qpol=y^3-y-1;un=Mod(1,qpol);w=Mod(y,qpol);p=un*(x^5-5*x+w)
6: Mod(1, y^3 - y - 1)*x^5 + Mod(-5, y^3 - y - 1)*x + Mod(y, y^3 - y - 1)
7: ? p2=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
8: x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
9: 2057
10: ? fa=[11699,6;2392997,2;4987333019653,2]
11:
12: [11699 6]
13:
14: [2392997 2]
15:
16: [4987333019653 2]
17:
18: ? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8));
19: ? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8));
20: ? nf=nfinit(nfpol)
1.2 ! noro 21: [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -1.08911514572050482502495
! 22: 27946671612683, -2.4285174907194186068992069565359418364, 0.7194669112891317
! 23: 8943997506477288225728, -2.5558200350691694950646071159426779970; 1, -0.1383
! 24: 8372073406036365047976417441696635 - 0.4918163765776864349975328551474152510
! 25: 7*I, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940822
! 26: 19556466856*I, -0.072312766896812300380582649294307897098 + 2.19808037538462
! 27: 76641195195160383234877*I, -0.98796319352507039803950539735452837196 + 1.570
! 28: 1452385894131769052374806001981108*I; 1, 1.682941293594312776162956161507997
! 29: 6005 + 2.0500351226010726172974286983598602163*I, -0.75045317576910401286427
! 30: 186094108607489 + 1.3101462685358123283560773619310445915*I, -0.787420688747
! 31: 75359433940488309213323154 + 2.1336633893126618034168454610457936017*I, 1.26
! 32: 58732110596551455718089553258673705 - 2.716479010374315056657802803578983483
! 33: 4*I], [1, -1.0891151457205048250249527946671612683, -2.428517490719418606899
! 34: 2069565359418364, 0.71946691128913178943997506477288225728, -2.5558200350691
! 35: 694950646071159426779970; 1.4142135623730950488016887242096980785, -0.195704
! 36: 13467375904264179382543977540672, 2.7785222450164664309920925654093065576, -
! 37: 0.10226569567819614506098907018896260032, -1.3971909474085893198147151262541
! 38: 540506; 0, -0.69553338995335755797766403996841143190, 1.14510982744395651299
! 39: 26149974389115722, 3.1085550780550843138423672171643499921, 2.22052069130868
! 40: 72788181483285734827868; 1.4142135623730950488016887242096980785, 2.38003840
! 41: 20787979181834702019470475018, -1.0613010590986270398182318786558994412, -1.
! 42: 1135810173202366904448352912286604470, 1.79021506332534372536778891648110361
! 43: 60; 0, 2.8991874737236275652408825679737171586, 1.85282662165584876344468105
! 44: 12816401036, 3.0174557027049114270734649132936867272, -3.8416814583731999185
! 45: 306312841432940660], 0, [5, 2, 0, -1, -2; 2, -2, -5, -10, 20; 0, -5, 10, -10
! 46: , 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 0, 200, 110, 177; 0, 345
! 47: , 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5175, 0
! 48: , -10350, -15525; 5175, 13800, -8625, -1725, 27600; 0, -8625, 37950, -17250,
! 49: 0; -10350, -1725, -17250, -24150, -15525; -15525, 27600, 0, -15525, -3450],
! 50: [595125, [238050, -296700, 91425, 1725, 0]~]], [-2.428517490719418606899206
! 51: 9565359418364, 1.9647119211288133163138753392090569931 + 0.80971492418897895
! 52: 128294082219556466856*I, -0.75045317576910401286427186094108607489 + 1.31014
! 53: 62685358123283560773619310445915*I], [1, 1/15*x^4 - 2/3*x^2 + 1/3*x + 4/3, x
! 54: , 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 -
! 55: 2/3], [1, 0, 3, 1, 10; 0, 0, -2, 1, -5; 0, 1, 0, 3, -5; 0, 0, 1, 1, 10; 0, 0
! 56: , 0, 3, 0], [1, 0, 0, 0, 0, 0, -1, -1, -2, 4, 0, -1, 3, -1, 1, 0, -2, -1, -3
! 57: , -1, 0, 4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, -1, -1, 1, 0, -1, -2, -1, 1, 0,
! 58: -1, -1, -1, 3, 0, 1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, -2
! 59: , 0, 1, 0, -1, -1, 0, -1, -2, -1, -1; 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1,
! 60: 1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1; 0, 0, 0, 0, 1, 0, -1, -1, -1, 1, 0, -1
! 61: , 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1]]
1.1 noro 62: ? nf1=nfinit(nfpol,2)
63: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
1.2 ! noro 64: 7205048250249527946671612684, 2.4285174907194186068992069565359418363, -0.71
! 65: 946691128913178943997506477288225737, 2.555820035069169495064607115942677997
! 66: 0; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
! 67: 85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
! 68: 7895128294082219556466856*I, 0.072312766896812300380582649294307897128 + 2.1
! 69: 980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
! 70: 7195 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
! 71: 9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
! 72: 10401286427186094108607491 - 1.3101462685358123283560773619310445914*I, 0.78
! 73: 742068874775359433940488309213323161 - 2.13366338931266180341684546104579360
! 74: 16*I, -1.2658732110596551455718089553258673704 + 2.7164790103743150566578028
! 75: 035789834835*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
! 76: 94186068992069565359418363, -0.71946691128913178943997506477288225737, 2.555
! 77: 8200350691694950646071159426779970; 1.4142135623730950488016887242096980785,
! 78: -0.19570413467375904264179382543977540673, -2.77852224501646643099209256540
! 79: 93065576, 0.10226569567819614506098907018896260036, 1.3971909474085893198147
! 80: 151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
! 81: 9565129926149974389115722, 3.1085550780550843138423672171643499921, 2.220520
! 82: 6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
! 83: 3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
! 84: 13, 1.1135810173202366904448352912286604471, -1.7902150633253437253677889164
! 85: 811036159; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
! 86: 4446810512816401034, -3.0174557027049114270734649132936867271, 3.84168145837
! 87: 31999185306312841432940662], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10,
! 88: -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3
! 89: 45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51
! 90: 75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250
! 91: , 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
! 92: [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527
! 93: 946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864
! 94: 3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
! 95: 1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x
! 96: - 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], [
! 97: 1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0,
! 98: 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1
! 99: , 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1
! 100: , -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1
! 101: , 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
! 102: 1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1
! 103: , 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]]
1.1 noro 104: ? nfinit(nfpol,3)
105: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
1.2 ! noro 106: 57205048250249527946671612684, 2.4285174907194186068992069565359418363, -0.7
! 107: 1946691128913178943997506477288225737, 2.55582003506916949506460711594267799
! 108: 70; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
! 109: 285514741525107*I, -1.9647119211288133163138753392090569931 + 0.809714924188
! 110: 97895128294082219556466856*I, 0.072312766896812300380582649294307897128 + 2.
! 111: 1980803753846276641195195160383234877*I, 0.987963193525070398039505397354528
! 112: 37195 + 1.5701452385894131769052374806001981108*I; 1, 1.68294129359431277616
! 113: 29561615079976005 + 2.0500351226010726172974286983598602163*I, 0.75045317576
! 114: 910401286427186094108607491 - 1.3101462685358123283560773619310445914*I, 0.7
! 115: 8742068874775359433940488309213323161 - 2.1336633893126618034168454610457936
! 116: 016*I, -1.2658732110596551455718089553258673704 + 2.716479010374315056657802
! 117: 8035789834835*I], [1, -1.0891151457205048250249527946671612684, 2.4285174907
! 118: 194186068992069565359418363, -0.71946691128913178943997506477288225737, 2.55
! 119: 58200350691694950646071159426779970; 1.4142135623730950488016887242096980785
! 120: , -0.19570413467375904264179382543977540673, -2.7785222450164664309920925654
! 121: 093065576, 0.10226569567819614506098907018896260036, 1.397190947408589319814
! 122: 7151262541540506; 0, 0.69553338995335755797766403996841143190, 1.14510982744
! 123: 39565129926149974389115722, 3.1085550780550843138423672171643499921, 2.22052
! 124: 06913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2
! 125: .3800384020787979181834702019470475018, 1.0613010590986270398182318786558994
! 126: 413, 1.1135810173202366904448352912286604471, -1.790215063325343725367788916
! 127: 4811036159; 0, 2.8991874737236275652408825679737171587, -1.85282662165584876
! 128: 34446810512816401034, -3.0174557027049114270734649132936867271, 3.8416814583
! 129: 731999185306312841432940662], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10
! 130: , -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0,
! 131: 345, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5
! 132: 175, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -1725
! 133: 0, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
! 134: [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.089115145720504825024952
! 135: 7946671612684, -0.13838372073406036365047976417441696637 + 0.491816376577686
! 136: 43499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.05003
! 137: 51226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*
! 138: 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],
! 139: [1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0
! 140: , 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -
! 141: 1, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -
! 142: 1, -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0,
! 143: 1, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
! 144: 1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -
! 145: 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
! 146: *x + 1, x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
1.1 noro 147: ? nfinit(nfpol,4)
148: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
1.2 ! noro 149: 7205048250249527946671612684, 2.4285174907194186068992069565359418363, -0.71
! 150: 946691128913178943997506477288225737, 2.555820035069169495064607115942677997
! 151: 0; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
! 152: 85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
! 153: 7895128294082219556466856*I, 0.072312766896812300380582649294307897128 + 2.1
! 154: 980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
! 155: 7195 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
! 156: 9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
! 157: 10401286427186094108607491 - 1.3101462685358123283560773619310445914*I, 0.78
! 158: 742068874775359433940488309213323161 - 2.13366338931266180341684546104579360
! 159: 16*I, -1.2658732110596551455718089553258673704 + 2.7164790103743150566578028
! 160: 035789834835*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
! 161: 94186068992069565359418363, -0.71946691128913178943997506477288225737, 2.555
! 162: 8200350691694950646071159426779970; 1.4142135623730950488016887242096980785,
! 163: -0.19570413467375904264179382543977540673, -2.77852224501646643099209256540
! 164: 93065576, 0.10226569567819614506098907018896260036, 1.3971909474085893198147
! 165: 151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
! 166: 9565129926149974389115722, 3.1085550780550843138423672171643499921, 2.220520
! 167: 6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
! 168: 3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
! 169: 13, 1.1135810173202366904448352912286604471, -1.7902150633253437253677889164
! 170: 811036159; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
! 171: 4446810512816401034, -3.0174557027049114270734649132936867271, 3.84168145837
! 172: 31999185306312841432940662], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10,
! 173: -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3
! 174: 45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51
! 175: 75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250
! 176: , 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
! 177: [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527
! 178: 946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864
! 179: 3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
! 180: 1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x
! 181: - 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], [
! 182: 1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0,
! 183: 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1
! 184: , 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1
! 185: , -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1
! 186: , 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
! 187: 1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1
! 188: , 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]]
1.1 noro 189: ? nf3=nfinit(x^6+108);
190: ? nf4=nfinit(x^3-10*x+8)
1.2 ! noro 191: [x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -0.36332823793268357037416860931988791
! 192: 960, -3.1413361156553641347759399165844441383; 1, -1.76155718183189058754537
! 193: 11274124874988, 2.6261980685272936133764995500786243868; 1, 3.12488541976457
! 194: 41579195397367323754183, -0.48486195287192947860055963349418024846], [1, -0.
! 195: 36332823793268357037416860931988791960, -3.141336115655364134775939916584444
! 196: 1383; 1, -1.7615571818318905875453711274124874988, 2.62619806852729361337649
! 197: 95500786243868; 1, 3.1248854197645741579195397367323754183, -0.4848619528719
! 198: 2947860055963349418024846], 0, [3, 1, -1; 1, 13, -5; -1, -5, 17], [284, 76,
! 199: 46; 0, 2, 0; 0, 0, 1], [196, -12, 8; -12, 50, 14; 8, 14, 38], [568, [120, 21
! 200: 0, 2]~]], [-3.5046643535880477051501085259043320579, 0.864640886695403025831
! 201: 12842266613688800, 2.6400234668926446793189801032381951699], [1, 1/2*x^2 + x
! 202: - 3, -1/2*x^2 + 3], [1, 0, 6; 0, 1, 0; 0, 1, -2], [1, 0, 0, 0, 4, -2, 0, -2
! 203: , 6; 0, 1, 0, 1, 2, 0, 0, 0, -2; 0, 0, 1, 0, 1, -1, 1, -1, -1]]
1.1 noro 204: ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];
205: ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
206: [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
1.2 ! noro 207: 61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
! 208: 08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065
! 209: 2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701
! 210: 48550268542821846861610071436900868, -1.36845553 E-48, 0.5005798036324558738
! 211: 2620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254
! 212: 0123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.14
! 213: 15926535897932384626433832795028842*I, -0.3432876442770270943898878667334192
! 214: 1876 + 3.1415926535897932384626433832795028842*I, 2.133629400974756470719099
! 215: 7873636390948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745
! 216: 732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790
! 217: 3417566977293763292119206302198760, -1.2897619530652735025030086072395031017
! 218: , -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.50057980363
! 219: 245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.72
! 220: 41634548149836441438434283070556826, 0.3432876442770270943898878667334192187
! 221: 6, -2.1336294009747564707190997873636390948, -0.0661783018827457321853684923
! 222: 23164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [1
! 223: 1, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1,
! 224: [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17
! 225: , [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
! 226: 1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.06637297521077796359
! 227: 59310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.06637
! 228: 29752107779635959310246705326058; 1, 7.0663729752107779635959310246705326058
! 229: ], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]],
! 230: [-7.0663729752107779635959310246705326058, 8.066372975210777963595931024670
! 231: 5326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [
! 232: [3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.88144225126545793
! 233: 64, [2, -1], [x + 7], 155], [Mat(1), [[0, 0]], [[1.7903417566977293763292119
! 234: 206302198761, -1.7903417566977293763292119206302198760]]], 0]
1.1 noro 235: ? setrand(1);bnfinit(x^2-x-100000,1)
1.2 ! noro 236: [Mat(5), Mat([3, 2, 1, 2, 0, 3, 0, 2, 2, 3, 1, 4, 3, 2, 2, 3, 3, 0]), [-129.
! 237: 82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
! 238: 4*I; 129.82045011403975460991182396195022419], [-41.811264589129943393339502
! 239: 258694361489 + 6.2831853071795864769252867665590057684*I, 9.2399004147902289
! 240: 816376260438840931575 + 3.1415926535897932384626433832795028842*I, -11.87460
! 241: 9881075406725097315997431161032 + 3.1415926535897932384626433832795028842*I,
! 242: 0.E-67, -51.051165003920172374977128302578454646 + 3.1415926535897932384626
! 243: 433832795028842*I, -64.910225057019877304955911980975112095 + 3.141592653589
! 244: 7932384626433832795028842*I, -29.936654708054536668242186261263200456 + 3.14
! 245: 15926535897932384626433832795028842*I, -47.668319071568233997332918482707687
! 246: 878 + 6.2831853071795864769252867665590057684*I, 3.8762936464778825067484824
! 247: 790355076166, -6.7377511782956880607802359510546381087 + 3.14159265358979323
! 248: 84626433832795028842*I, -35.073513410834255332559266307639723380 + 3.1415926
! 249: 535897932384626433832795028842*I, 33.130781426597481571750300827582717074 +
! 250: 2.96736492 E-67*I, 54.878404098312329644822020875673145627 + 5.93472984 E-67
! 251: *I, -14.980188104648613073630759189293219180 + 3.141592653589793238462643383
! 252: 2795028842*I, -26.831076484481330319708743069401142308 + 3.14159265358979323
! 253: 84626433832795028842*I, -19.706749066516065512488907834878146944 + 3.1415926
! 254: 535897932384626433832795028842*I, -22.104515522613877880850594423816214544 +
! 255: 3.1415926535897932384626433832795028842*I, -45.6875582356078259000879847377
! 256: 29869105 + 6.2831853071795864769252867665590057684*I, 47.6683190715682339973
! 257: 32918482707687879 + 1.18694596 E-66*I; 41.8112645891299433933395022586943614
! 258: 89, -9.2399004147902289816376260438840931575, 11.874609881075406725097315997
! 259: 431161032, 0.E-67, 51.051165003920172374977128302578454646, 64.9102250570198
! 260: 77304955911980975112095, 29.936654708054536668242186261263200456, 47.6683190
! 261: 71568233997332918482707687879, -3.8762936464778825067484824790355076166, 6.7
! 262: 377511782956880607802359510546381087, 35.07351341083425533255926630763972338
! 263: 0, -33.130781426597481571750300827582717074, -54.878404098312329644822020875
! 264: 673145627, 14.980188104648613073630759189293219180, 26.831076484481330319708
! 265: 743069401142309, 19.706749066516065512488907834878146944, 22.104515522613877
! 266: 880850594423816214544, 45.687558235607825900087984737729869105, -47.66831907
! 267: 1568233997332918482707687878], [[2, [2, 1]~, 1, 1, [1, 1]~], [5, [5, 1]~, 1,
! 268: 1, [1, 1]~], [13, [-5, 1]~, 1, 1, [6, 1]~], [2, [3, 1]~, 1, 1, [0, 1]~], [5
! 269: , [6, 1]~, 1, 1, [0, 1]~], [7, [4, 1]~, 2, 1, [-3, 1]~], [13, [6, 1]~, 1, 1,
! 270: [-5, 1]~], [23, [7, 1]~, 1, 1, [-6, 1]~], [43, [-15, 1]~, 1, 1, [16, 1]~],
! 271: [17, [20, 1]~, 1, 1, [-2, 1]~], [17, [15, 1]~, 1, 1, [3, 1]~], [29, [14, 1]~
! 272: , 1, 1, [-13, 1]~], [29, [-13, 1]~, 1, 1, [14, 1]~], [31, [39, 1]~, 1, 1, [-
! 273: 7, 1]~], [31, [24, 1]~, 1, 1, [8, 1]~], [41, [7, 1]~, 1, 1, [-6, 1]~], [41,
! 274: [-6, 1]~, 1, 1, [7, 1]~], [43, [16, 1]~, 1, 1, [-15, 1]~], [23, [-6, 1]~, 1,
! 275: 1, [7, 1]~]], 0, [x^2 - x - 100000, [2, 0], 400001, 1, [[1, -316.7281613012
! 276: 9840161392089489603747004; 1, 315.72816130129840161392089489603747004], [1,
! 277: -316.72816130129840161392089489603747004; 1, 315.728161301298401613920894896
! 278: 03747004], 0, [2, -1; -1, 200001], [400001, 200001; 0, 1], [200001, 1; 1, 2]
! 279: , [400001, [200001, 1]~]], [-315.72816130129840161392089489603747004, 316.72
! 280: 816130129840161392089489603747004], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 1000
! 281: 00; 0, 1, 1, -1]], [[5, [5], [[2, 0; 0, 1]]], 129.82045011403975460991182396
! 282: 195022419, 0.9876536979069047228, [2, -1], [37955488401901378100630325489636
! 283: 9154068336082609238336*x + 1198361656442507899904628359500228716651781276113
! 284: 16131167], 24], [Mat(1), [[0, 0]], [[-41.81126458912994339333950225869436148
! 285: 9 + 6.2831853071795864769252867665590057684*I, 41.81126458912994339333950225
! 286: 8694361489]]], 0]
1.1 noro 287: ? \p19
288: realprecision = 19 significant digits
289: ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
1.2 ! noro 290: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2 - x - 9], [-3.233732695981516672
! 291: , -0.07182350902743636344, 4.305556205008953036], [10889, 5698, 8994; 0, 1,
! 292: 0; 0, 0, 1], Mat(2), Mat([1, 1, 0, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 39, 10,
! 293: 33, 57, 69], [2, [-1, 0, 0]~], [[0, 1, 0]~, [5, 3, 1]~], [-4, -1, 2, 3, 10,
! 294: 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 295: ? \p38
296: realprecision = 38 significant digits
1.2 ! noro 297: ? bnrinit(bnf,[[5,4;0,1],[1,0]],1)
1.1 noro 298: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
1.2 ! noro 299: 061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 300: 808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
! 301: 52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
! 302: 148550268542821846861610071436900868, -1.36845553 E-48, 0.500579803632455873
! 303: 82620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.08885625
! 304: 40123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.1
! 305: 415926535897932384626433832795028842*I, -0.343287644277027094389887866733419
! 306: 21876 + 3.1415926535897932384626433832795028842*I, 2.13362940097475647071909
! 307: 97873636390948 + 3.1415926535897932384626433832795028842*I, 0.06617830188274
! 308: 5732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.79
! 309: 03417566977293763292119206302198760, -1.289761953065273502503008607239503101
! 310: 7, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.5005798036
! 311: 3245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.7
! 312: 241634548149836441438434283070556826, 0.343287644277027094389887866733419218
! 313: 76, -2.1336294009747564707190997873636390948, -0.066178301882745732185368492
! 314: 323164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [
! 315: 11, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1
! 316: , [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [1
! 317: 7, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
! 318: 1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635
! 319: 959310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.0663
! 320: 729752107779635959310246705326058; 1, 7.066372975210777963595931024670532605
! 321: 8], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]]
! 322: , [-7.0663729752107779635959310246705326058, 8.06637297521077796359593102467
! 323: 05326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3],
! 324: [[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512654579
! 325: 364, [2, -1], [x + 7], 155], [Mat(1), [[0, 0]], [[1.790341756697729376329211
! 326: 9206302198761, -1.7903417566977293763292119206302198760]]], [0, [Mat([[6, 1]
! 327: ~, 1])]]], [[[5, 4; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], Mat([[5
! 328: , [-1, 1]~, 1, 1, [2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~
! 329: ], 1]], [[2], [[0, 1]~], Mat(1)]], [1, 0; 0, 1]], [1], Mat([1, -3, -6]), [12
! 330: , [12], [[3, 0; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
! 331: ? bnr=bnrclass(bnf,[[5,4;0,1],[1,0]],2)
1.1 noro 332: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
1.2 ! noro 333: 061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 334: 808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
! 335: 52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
! 336: 148550268542821846861610071436900868, -1.36845553 E-48, 0.500579803632455873
! 337: 82620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.08885625
! 338: 40123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.1
! 339: 415926535897932384626433832795028842*I, -0.343287644277027094389887866733419
! 340: 21876 + 3.1415926535897932384626433832795028842*I, 2.13362940097475647071909
! 341: 97873636390948 + 3.1415926535897932384626433832795028842*I, 0.06617830188274
! 342: 5732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.79
! 343: 03417566977293763292119206302198760, -1.289761953065273502503008607239503101
! 344: 7, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.5005798036
! 345: 3245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.7
! 346: 241634548149836441438434283070556826, 0.343287644277027094389887866733419218
! 347: 76, -2.1336294009747564707190997873636390948, -0.066178301882745732185368492
! 348: 323164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [
! 349: 11, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1
! 350: , [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [1
! 351: 7, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
! 352: 1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635
! 353: 959310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.0663
! 354: 729752107779635959310246705326058; 1, 7.066372975210777963595931024670532605
! 355: 8], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]]
! 356: , [-7.0663729752107779635959310246705326058, 8.06637297521077796359593102467
! 357: 05326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3],
! 358: [[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512654579
! 359: 364, [2, -1], [x + 7], 155], [Mat(1), [[0, 0]], [[1.790341756697729376329211
! 360: 9206302198761, -1.7903417566977293763292119206302198760]]], [0, [Mat([[6, 1]
! 361: ~, 1])]]], [[[5, 4; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], Mat([[5
! 362: , [-1, 1]~, 1, 1, [2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~
! 363: ], 1]], [[2], [[0, 1]~], Mat(1)]], [1, 0; 0, 1]], [1], Mat([1, -3, -6]), [12
! 364: , [12], [[3, 0; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
1.1 noro 365: ? rnfinit(nf2,x^5-x-2)
366: [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3
367: 109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914
368: 279776896412, 1.6057155120361619195949075151301679393, 2.0347118029638523119
369: 874445717108994866, 2.5783223055935536544757871909285592749; 1, 0.2609638803
370: 8645528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -1
371: .3177592693689352747870763902256347904 + 0.614427010164338838041906608641467
372: 31824*I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524
373: 673160314582604*I, 1.3589689411882615753626439480614001936 - 1.6193337759893
374: 970298359887428575174472*I; 1, -0.89454803265751744362901306471557966872 + 0
375: .53414854617473272670874609150394379949*I, 0.5149015133508543149896226326605
376: 5082078 - 0.95564306225496055080453352211847466685*I, 0.04985121658507159775
377: 5867063892284310224 + 1.1299025160425089918993024639913611785*I, -0.64813009
378: 398503840260053754352567983115 - 0.98412411795664774269323431620030610541*I]
379: , [1, 1.2671683045421243172528914279776896412 + 0.E-38*I, 1.6057155120361619
380: 195949075151301679393 + 0.E-38*I, 2.0347118029638523119874445717108994866 +
381: 0.E-37*I, 2.5783223055935536544757871909285592749 + 0.E-37*I; 1, 0.260963880
382: 38645528500256735072673484811 - 1.1772261533941944394700286585617926513*I, -
383: 1.3177592693689352747870763902256347904 - 0.61442701016433883804190660864146
384: 731824*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921652
385: 4673160314582604*I, 1.3589689411882615753626439480614001936 + 1.619333775989
386: 3970298359887428575174472*I; 1, 0.26096388038645528500256735072673484811 + 1
387: .1772261533941944394700286585617926513*I, -1.3177592693689352747870763902256
388: 347904 + 0.61442701016433883804190660864146731824*I, -1.06720711806699775374
389: 95893497477340535 - 1.3909574189920019216524673160314582604*I, 1.35896894118
390: 82615753626439480614001936 - 1.6193337759893970298359887428575174472*I; 1, -
391: 0.89454803265751744362901306471557966872 - 0.5341485461747327267087460915039
392: 4379949*I, 0.51490151335085431498962263266055082078 + 0.95564306225496055080
393: 453352211847466685*I, 0.049851216585071597755867063892284310224 - 1.12990251
394: 60425089918993024639913611785*I, -0.64813009398503840260053754352567983115 +
395: 0.98412411795664774269323431620030610541*I; 1, -0.8945480326575174436290130
396: 6471557966872 + 0.53414854617473272670874609150394379949*I, 0.51490151335085
397: 431498962263266055082078 - 0.95564306225496055080453352211847466685*I, 0.049
398: 851216585071597755867063892284310224 + 1.12990251604250899189930246399136117
399: 85*I, -0.64813009398503840260053754352567983115 - 0.984124117956647742693234
400: 31620030610541*I]], [[1, 2, 2; 1.2671683045421243172528914279776896412, 0.52
401: 192776077291057000513470145346969622 - 2.35445230678838887894005731712358530
402: 26*I, -1.7890960653150348872580261294311593374 - 1.0682970923494654534174921
403: 830078875989*I; 1.6057155120361619195949075151301679393, -2.6355185387378705
404: 495741527804512695809 - 1.2288540203286776760838132172829346364*I, 1.0298030
405: 267017086299792452653211016415 + 1.9112861245099211016090670442369493337*I;
406: 2.0347118029638523119874445717108994866, -2.13441423613399550749917869949546
407: 81070 + 2.7819148379840038433049346320629165208*I, 0.09970243317014319551173
408: 4127784568620449 - 2.2598050320850179837986049279827223571*I; 2.578322305593
409: 5536544757871909285592749, 2.7179378823765231507252878961228003872 + 3.23866
410: 75519787940596719774857150348944*I, -1.2962601879700768052010750870513596623
411: + 1.9682482359132954853864686324006122108*I], [1, 1, 1, 1, 1; 1.26716830454
412: 21243172528914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484
413: 811 + 1.1772261533941944394700286585617926513*I, 0.2609638803864552850025673
414: 5072673484811 - 1.1772261533941944394700286585617926513*I, -0.89454803265751
415: 744362901306471557966872 + 0.53414854617473272670874609150394379949*I, -0.89
416: 454803265751744362901306471557966872 - 0.53414854617473272670874609150394379
417: 949*I; 1.6057155120361619195949075151301679393 + 0.E-38*I, -1.31775926936893
418: 52747870763902256347904 + 0.61442701016433883804190660864146731824*I, -1.317
419: 7592693689352747870763902256347904 - 0.6144270101643388380419066086414673182
420: 4*I, 0.51490151335085431498962263266055082078 - 0.95564306225496055080453352
421: 211847466685*I, 0.51490151335085431498962263266055082078 + 0.955643062254960
422: 55080453352211847466685*I; 2.0347118029638523119874445717108994866 + 0.E-37*
423: I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524673160
424: 314582604*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921
425: 6524673160314582604*I, 0.049851216585071597755867063892284310224 + 1.1299025
426: 160425089918993024639913611785*I, 0.049851216585071597755867063892284310224
427: - 1.1299025160425089918993024639913611785*I; 2.57832230559355365447578719092
428: 85592749 + 0.E-37*I, 1.3589689411882615753626439480614001936 - 1.61933377598
429: 93970298359887428575174472*I, 1.3589689411882615753626439480614001936 + 1.61
430: 93337759893970298359887428575174472*I, -0.6481300939850384026005375435256798
431: 3115 - 0.98412411795664774269323431620030610541*I, -0.6481300939850384026005
432: 3754352567983115 + 0.98412411795664774269323431620030610541*I]], [[5, -5.877
433: 47175 E-39 + 3.4227493991378543323575495001314729016*I, 2.35098870 E-38 - 0.
434: 68243210418124342552525382695401469720*I, -2.35098870 E-38 - 0.5221098058989
435: 8585950632970408019416371*I, 3.9999999999999999999999999999999999999 - 5.206
436: 9157878920895450584461181156471052*I; -5.87747175 E-39 - 3.42274939913785433
437: 23575495001314729016*I, 6.6847043424634879841147654217963674264 - 5.87747175
438: E-39*I, 0.85145677340721376574333983502938573598 + 4.5829573180978430291541
439: 592600601794652*I, -0.13574266252716976137461193821267520737 - 0.28805108544
440: 025772361738936467682050391*I, 0.27203784387468568916539788233281013320 - 1.
441: 5917147279942947718965650859986677247*I; 2.35098870 E-38 + 0.682432104181243
442: 42552525382695401469720*I, 0.85145677340721376574333983502938573598 - 4.5829
443: 573180978430291541592600601794652*I, 9.1630968530221077951281598310681467898
444: + 0.E-38*I, 2.2622987652095629453403849736225691490 + 6.2361927913558506765
445: 724047063180706869*I, -0.21796409886496632254445901043974770643 + 0.34559368
446: 931063215686158939748833975810*I; -2.35098870 E-38 + 0.522109805898985859506
447: 32970408019416371*I, -0.13574266252716976137461193821267520737 + 0.288051085
448: 44025772361738936467682050392*I, 2.2622987652095629453403849736225691490 - 6
449: .2361927913558506765724047063180706869*I, 12.8457689488323355118826969393806
450: 96155 + 1.17549435 E-38*I, 4.5618400502378124720913214622468855074 + 8.60339
451: 30051068500425218923146793019614*I; 3.9999999999999999999999999999999999999
452: + 5.2069157878920895450584461181156471052*I, 0.27203784387468568916539788233
453: 281013320 + 1.5917147279942947718965650859986677247*I, -0.217964098864966322
454: 54445901043974770643 - 0.34559368931063215686158939748833975810*I, 4.5618400
455: 502378124720913214622468855074 - 8.6033930051068500425218923146793019615*I,
456: 18.362968630416114402425299186062892646 + 5.87747175 E-39*I], [5, -1.1754943
457: 5 E-38 + 0.E-38*I, 2.35098870 E-38 + 0.E-38*I, -1.76324152 E-38 + 0.E-38*I,
458: 3.9999999999999999999999999999999999998 + 0.E-38*I; -1.17549435 E-38 + 0.E-3
459: 8*I, 6.6847043424634879841147654217963674264 - 5.87747175 E-39*I, 0.85145677
460: 340721376574333983502938573597 + 5.87747175 E-39*I, -0.135742662527169761374
461: 61193821267520737 + 5.87747175 E-39*I, 0.27203784387468568916539788233281013
462: 314 - 5.87747175 E-39*I; 2.35098870 E-38 + 0.E-38*I, 0.851456773407213765743
463: 33983502938573597 + 5.87747175 E-39*I, 9.16309685302210779512815983106814678
464: 98 + 0.E-38*I, 2.2622987652095629453403849736225691490 + 2.35098870 E-38*I,
465: -0.21796409886496632254445901043974770651 + 0.E-38*I; -1.76324152 E-38 + 0.E
466: -38*I, -0.13574266252716976137461193821267520737 + 5.87747175 E-39*I, 2.2622
467: 987652095629453403849736225691490 + 2.35098870 E-38*I, 12.845768948832335511
468: 882696939380696155 + 0.E-37*I, 4.5618400502378124720913214622468855073 - 3.5
469: 2648305 E-38*I; 3.9999999999999999999999999999999999998 + 0.E-38*I, 0.272037
470: 84387468568916539788233281013314 - 5.87747175 E-39*I, -0.2179640988649663225
471: 4445901043974770651 + 0.E-38*I, 4.5618400502378124720913214622468855073 - 3.
472: 52648305 E-38*I, 18.362968630416114402425299186062892646 + 0.E-37*I]], [Mod(
473: 5, y^3 - y - 1), 0, 0, 0, Mod(4, y^3 - y - 1); 0, 0, 0, Mod(4, y^3 - y - 1),
474: Mod(10, y^3 - y - 1); 0, 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0; 0
475: , Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0, 0; Mod(4, y^3 - y - 1), Mod(
476: 10, y^3 - y - 1), 0, 0, Mod(4, y^3 - y - 1)], [;], [;], [;]], [[1.2671683045
477: 421243172528914279776896412, 0.26096388038645528500256735072673484811 + 1.17
478: 72261533941944394700286585617926513*I, -0.8945480326575174436290130647155796
479: 6872 + 0.53414854617473272670874609150394379949*I], [1.267168304542124317252
480: 8914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484811 - 1.17
481: 72261533941944394700286585617926513*I, 0.26096388038645528500256735072673484
482: 811 + 1.1772261533941944394700286585617926513*I, -0.894548032657517443629013
483: 06471557966872 - 0.53414854617473272670874609150394379949*I, -0.894548032657
484: 51744362901306471557966872 + 0.53414854617473272670874609150394379949*I]~],
485: [[Mod(1, y^3 - y - 1), Mod(1, y^3 - y - 1)*x, Mod(1, y^3 - y - 1)*x^2, Mod(1
486: , y^3 - y - 1)*x^3, Mod(1, y^3 - y - 1)*x^4], [[1, 0, 0; 0, 1, 0; 0, 0, 1],
487: [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0;
488: 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [Mod(1, y^3 - y - 1), 0, 0, 0, 0;
489: 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1, y^3 - y - 1), 0, 0; 0, 0, 0, M
490: od(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^3 - y - 1)], [], [y^3 - y - 1, [
1.2 ! noro 491: 1, 1], -23, 1, [[1, 0.75487766624669276004950889635852869189, 1.324717957244
! 492: 7460259609088544780973407; 1, -0.87743883312334638002475444817926434594 - 0.
! 493: 74486176661974423659317042860439236723*I, -0.6623589786223730129804544272390
! 494: 4867036 + 0.56227951206230124389918214490937306149*I], [1, 0.754877666246692
! 495: 76004950889635852869189, 1.3247179572447460259609088544780973407; 1.41421356
! 496: 23730950488016887242096980785, -1.2408858979558593537192653626096055786, -0.
! 497: 93671705072735084703311164961686101696; 0, -1.053393612446825433528903849803
! 498: 1013275, 0.79518331180303271004476715629658754002], 0, [3, -1, 0; -1, 1, 3;
! 499: 0, 3, 2], [23, 16, 13; 0, 1, 0; 0, 0, 1], [-7, 2, -3; 2, 6, -9; -3, -9, 2],
! 500: [23, [10, 7, 1]~]], [1.3247179572447460259609088544780973407, -0.66235897862
! 501: 237301298045442723904867036 + 0.56227951206230124389918214490937306149*I], [
! 502: 1, y^2 - 1, y], [1, 0, 1; 0, 0, 1; 0, 1, 0], [1, 0, 0, 0, 0, 1, 0, 1, 1; 0,
! 503: 1, 0, 1, -1, 0, 0, 0, 1; 0, 0, 1, 0, 1, 0, 1, 0, 0]], [x^15 - 5*x^13 + 5*x^1
! 504: 2 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4
! 505: + 189*x^3 + 144*x^2 + 25*x + 1, Mod(39516536165538345/83718587879473471*x^1
! 506: 4 - 6500512476832995/83718587879473471*x^13 - 196215472046117185/83718587879
! 507: 473471*x^12 + 229902227480108910/83718587879473471*x^11 + 237380704030959181
! 508: /83718587879473471*x^10 - 1064931988160773805/83718587879473471*x^9 - 206570
! 509: 86671714300/83718587879473471*x^8 + 1772885205999206010/83718587879473471*x^
! 510: 7 + 5952033217241102348/83718587879473471*x^6 - 4838840187320655696/83718587
! 511: 879473471*x^5 + 5180390720553188700/83718587879473471*x^4 - 8374015687535120
! 512: 430/83718587879473471*x^3 + 8907744727915040221/83718587879473471*x^2 + 4155
! 513: 976664123434381/83718587879473471*x + 318920215718580450/83718587879473471,
! 514: 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^
! 515: 6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), -1, [1, x, x^2, x^3,
! 516: x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, 1/83718587879473471*x^
! 517: 14 - 20528463024680133/83718587879473471*x^13 - 4742392948888610/83718587879
! 518: 473471*x^12 - 9983523646123358/83718587879473471*x^11 + 40898955597139011/83
! 519: 718587879473471*x^10 + 29412692423971937/83718587879473471*x^9 - 50174794636
! 520: 12351/83718587879473471*x^8 + 41014993230075066/83718587879473471*x^7 - 2712
! 521: 810874903165/83718587879473471*x^6 + 20152905879672878/83718587879473471*x^5
! 522: + 9591643151927789/83718587879473471*x^4 - 8471905745957397/837185878794734
! 523: 71*x^3 - 13395753879413605/83718587879473471*x^2 + 27623037732247492/8371858
! 524: 7879473471*x + 26306699661480593/83718587879473471], [1, 0, 0, 0, 0, 0, 0, 0
! 525: , 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
! 526: 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13395753
! 527: 879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8471905745957397; 0, 0,
! 528: 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789; 0, 0, 0, 0, 0, 1, 0,
! 529: 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0
! 530: , 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -4101499
! 531: 3230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5017479463612351; 0, 0
! 532: , 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937; 0, 0, 0, 0, 0, 0,
! 533: 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
! 534: 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 474239
! 535: 2948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20528463024680133; 0,
! 536: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471]]]
1.1 noro 537: ? bnfcertify(bnf)
538: 1
539: ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
540:
541: [x^4 - 7]
542:
543: [[2, 1]]
544:
545: [[-87808, 1]]
546:
547: [[1, x, x^2, x^3]]
548:
549: [[2, [2], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
550:
551: [14.229975145405511722395637833443108790]
552:
553: [1.121117107152756229]
554:
555: ? setrand(1);bnfclassunit(x^2-x-100000)
556: *** Warning: insufficient precision for fundamental units, not given.
557:
558: [x^2 - x - 100000]
559:
560: [[2, 0]]
561:
562: [[400001, 1]]
563:
1.2 ! noro 564: [[1, x - 1]]
1.1 noro 565:
1.2 ! noro 566: [[5, [5], [[2, 0; 0, 1]]]]
1.1 noro 567:
568: [129.82045011403975460991182396195022419]
569:
1.2 ! noro 570: [0.9876536979069047228]
1.1 noro 571:
572: [[2, -1]]
573:
574: [[;]]
575:
576: [-27]
577:
578: ? setrand(1);bnfclassunit(x^2-x-100000,1)
579:
580: [x^2 - x - 100000]
581:
582: [[2, 0]]
583:
584: [[400001, 1]]
585:
1.2 ! noro 586: [[1, x - 1]]
1.1 noro 587:
1.2 ! noro 588: [[5, [5], [[2, 0; 0, 1]]]]
1.1 noro 589:
590: [129.82045011403975460991182396195022419]
591:
1.2 ! noro 592: [0.9876536979069047228]
1.1 noro 593:
594: [[2, -1]]
595:
596: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
597: 789990462835950022871665178127611316131167]]
598:
1.2 ! noro 599: [24]
1.1 noro 600:
601: ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
602:
603: [x^4 + 24*x^2 + 585*x + 1791]
604:
605: [[0, 2]]
606:
607: [[18981, 3087]]
608:
1.2 ! noro 609: [[1, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343, 17/1029*x^3 - 32/1029
! 610: *x^2 + 109/343*x + 2444/343, -11/343*x^3 + 163/1029*x^2 - 373/343*x - 4260/3
! 611: 43]]
1.1 noro 612:
1.2 ! noro 613: [[4, [4], [[7, 2, 4, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
1.1 noro 614:
615: [3.7941269688216589341408274220859400302]
616:
1.2 ! noro 617: [0.8826018286655581299]
1.1 noro 618:
619: [[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
620:
1.2 ! noro 621: [[1/343*x^3 - 46/1029*x^2 - 122/343*x - 174/343]]
1.1 noro 622:
1.2 ! noro 623: [154]
1.1 noro 624:
625: ? setrand(1);bnfclgp(17)
626: [1, [], []]
627: ? setrand(1);bnfclgp(-31)
628: [3, [3], [Qfb(2, 1, 4)]]
629: ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791)
1.2 ! noro 630: [4, [4], [[7, 2, 0, 5; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]
! 631: ? bnrconductor(bnf,[[25,14;0,1],[1,1]])
! 632: [[5, 4; 0, 1], [1, 0]]
1.1 noro 633: ? bnrconductorofchar(bnr,[2])
1.2 ! noro 634: [[5, 4; 0, 1], [0, 0]]
! 635: ? bnfisprincipal(bnf,[5,2;0,1],0)
1.1 noro 636: [1]~
1.2 ! noro 637: ? bnfisprincipal(bnf,[5,2;0,1])
! 638: [[1]~, [7/3, 1/3]~, 155]
1.1 noro 639: ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
640: [-4, Mod(1, 2)]~
641: ? \p19
642: realprecision = 19 significant digits
643: ? bnfmake(sbnf)
1.2 ! noro 644: [Mat(2), Mat([1, 1, 0, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
! 645: 89793238*I, -4.562279014988837952 + 3.141592653589793238*I; -2.6335434327389
1.1 noro 646: 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
647: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
1.2 ! noro 648: 1592653589793238*I, 0.5404006376129469727 + 3.141592653589793238*I, -0.69263
! 649: 91142471042844 + 3.141592653589793238*I, -1.990056445584799713 + 3.141592653
! 650: 589793238*I, -0.8305625946607188643 + 3.141592653589793238*I, 0.E-57, 0.0043
! 651: 75616572659815433 + 3.141592653589793238*I, -1.977791147836553953, 0.3677262
! 652: 014027817708 + 3.141592653589793238*I; 0.6716827432867392938 + 3.14159265358
! 653: 9793238*I, -0.8333219883742404170 + 3.141592653589793238*I, -0.2461086674077
! 654: 943076, 0.5379005671092853269, -1.552661549868775853, 0.E-57, -0.87383180430
! 655: 71131263, 0.5774919091398324092, 0.9729063188316092380; -1.91802973262155845
! 656: 5, 0.2929213507612934444, 0.9387477816548985923, 1.452155878475514386, 2.383
! 657: 224144529494717, 0.E-57, 0.8694561877344533111, 1.400299238696721544, -1.340
! 658: 632520234391008], [[3, [-1, 1, 0]~, 1, 1, [1, 1, 1]~], [5, [-1, 1, 0]~, 1, 1
! 659: , [0, 1, 1]~], [5, [2, 1, 0]~, 1, 1, [1, -2, 1]~], [5, [3, 1, 0]~, 1, 1, [2,
! 660: 2, 1]~], [13, [19, 1, 0]~, 1, 1, [-2, -6, 1]~], [3, [10, 1, 1]~, 1, 2, [-1,
! 661: 1, 0]~], [11, [1, 1, 0]~, 1, 1, [-3, -1, 1]~], [19, [-6, 1, 0]~, 1, 1, [6,
! 662: 6, 1]~], [23, [-10, 1, 0]~, 1, 1, [-7, 10, 1]~]]~, 0, [x^3 - x^2 - 14*x - 1,
! 663: [3, 0], 10889, 1, [[1, -3.233732695981516672, 4.690759845041404811; 1, -0.0
! 664: 7182350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.23225
! 665: 8029482144592], [1, -3.233732695981516672, 4.690759845041404811; 1, -0.07182
! 666: 350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.232258029
! 667: 482144592], 0, [3, 1, 1; 1, 29, 8; 1, 8, 129], [10889, 5698, 8994; 0, 1, 0;
! 668: 0, 0, 1], [3677, -121, -21; -121, 386, -23; -21, -23, 86], [10889, [1899, 51
! 669: 91, 1]~]], [-3.233732695981516672, -0.07182350902743636344, 4.30555620500895
! 670: 3036], [1, x, x^2 - x - 9], [1, 0, 9; 0, 1, 1; 0, 0, 1], [1, 0, 0, 0, 9, 1,
! 671: 0, 1, 44; 0, 1, 0, 1, 1, 5, 0, 5, 1; 0, 0, 1, 0, 1, 0, 1, 0, -4]], [[2, [2],
! 672: [[3, 2, 0; 0, 1, 0; 0, 0, 1]]], 10.34800724602768011, 1.000000000000000000,
! 673: [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0.E-57, 0.E-57, 0.E-57]], [[
! 674: 1.246346989334819161 + 3.141592653589793238*I, 0.6716827432867392938 + 3.141
! 675: 592653589793238*I, -1.918029732621558455]]], [-4, -1, 2, 3, 10, 3, 1, 7, 2;
! 676: 1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
1.1 noro 677: ? \p38
678: realprecision = 38 significant digits
679: ? bnfnarrow(bnf)
1.2 ! noro 680: [3, [3], [[3, 0; 0, 1]]]
1.1 noro 681: ? bnfreg(x^2-x-57)
682: 2.7124653051843439746808795106061300699
683: ? bnfsignunit(bnf)
684:
685: [-1]
686:
687: [1]
688:
689: ? bnfunit(bnf)
1.2 ! noro 690: [[x + 7], 155]
! 691: ? bnrclass(bnf,[[5,4;0,1],[1,0]])
! 692: [12, [12], [[3, 0; 0, 1]]]
! 693: ? bnr2=bnrclass(bnf,[[25,14;0,1],[1,1]],2)
1.1 noro 694: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
1.2 ! noro 695: 061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 696: 808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
! 697: 52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
! 698: 148550268542821846861610071436900868, -1.36845553 E-48, 0.500579803632455873
! 699: 82620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.08885625
! 700: 40123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.1
! 701: 415926535897932384626433832795028842*I, -0.343287644277027094389887866733419
! 702: 21876 + 3.1415926535897932384626433832795028842*I, 2.13362940097475647071909
! 703: 97873636390948 + 3.1415926535897932384626433832795028842*I, 0.06617830188274
! 704: 5732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.79
! 705: 03417566977293763292119206302198760, -1.289761953065273502503008607239503101
! 706: 7, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.5005798036
! 707: 3245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.7
! 708: 241634548149836441438434283070556826, 0.343287644277027094389887866733419218
! 709: 76, -2.1336294009747564707190997873636390948, -0.066178301882745732185368492
! 710: 323164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [
! 711: 11, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1
! 712: , [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [1
! 713: 7, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
! 714: 1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635
! 715: 959310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.0663
! 716: 729752107779635959310246705326058; 1, 7.066372975210777963595931024670532605
! 717: 8], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]]
! 718: , [-7.0663729752107779635959310246705326058, 8.06637297521077796359593102467
! 719: 05326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3],
! 720: [[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512654579
! 721: 364, [2, -1], [x + 7], 155], [Mat(1), [[0, 0]], [[1.790341756697729376329211
! 722: 9206302198761, -1.7903417566977293763292119206302198760]]], [0, [Mat([[6, 1]
! 723: ~, 1])]]], [[[25, 14; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [4, 2]~, [-
! 724: 2, -2]~]], Mat([[5, [-1, 1]~, 1, 1, [2, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0
! 725: ]~], [[Mod(0, 2), Mod(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2),
! 726: Mod(0, 2)]~], Mat([1/5, -14/5])]], [[2, 2], [[4, 2]~, [-2, -2]~], [1, 0; 0,
! 727: 1]]], [1, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [1], Mat([1, -3, -6, 0]), [1
! 728: 2, [12], [[3, 0; 0, 1]]], [[1, -18, 9; -1/2, 10, -5], [-2, 0; 0, -10]]]
! 729: ? bnrclassno(bnf,[[5,4;0,1],[1,0]])
1.1 noro 730: 12
731: ? lu=ideallist(bnf,55,3);
732: ? bnrclassnolist(bnf,lu)
733: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
734: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
735: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
736: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
737: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
738: ? bnrdisc(bnr,Mat(6))
739: [12, 12, 18026977100265125]
740: ? bnrdisc(bnr)
741: [24, 12, 40621487921685401825918161408203125]
742: ? bnrdisc(bnr2,,,2)
743: 0
744: ? bnrdisc(bnr,Mat(6),,1)
1.2 ! noro 745: [6, 2, [125, 14; 0, 1]]
1.1 noro 746: ? bnrdisc(bnr,,,1)
1.2 ! noro 747: [12, 1, [1953125, 1160889; 0, 1]]
1.1 noro 748: ? bnrdisc(bnr2,,,3)
749: 0
750: ? bnrdisclist(bnf,lu)
751: [[[6, 6, Mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
752: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
753: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
754: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
755: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
756: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
757: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
758: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
759: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
760: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
761: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
762: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
763: , []]]
764: ? bnrdisclist(bnf,20,,1)
765: [[[[matrix(0,2), [[6, 6, Mat([229, 3])], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]],
766: [], [[Mat([12, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [3, 3; 229, 6
767: ]]]], [Mat([13, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1, 1; 3, 3; 229, 6]],
768: [0, 0, 0]]]], [[Mat([10, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]
769: , [[Mat([20, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [0, 0, 0], [24, 0, [
770: 5, 9; 229, 12]]]], [Mat([21, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [24,
771: 12, [5, 9; 229, 12]], [0, 0, 0]]]], [], [], [], [[Mat([12, 2]), [[0, 0, 0],
772: [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1], [[0, 0, 0], [12, 6, [-1
773: , 1; 3, 6; 229, 6]], [0, 0, 0], [24, 0, [3, 12; 229, 12]]]], [Mat([13, 2]),
774: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([44, 1]), [[0, 0,
775: 0], [0, 0, 0], [12, 6, [-1, 1; 11, 3; 229, 6]], [0, 0, 0]]], [Mat([45, 1]),
776: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [11, 3; 229, 6]]]]], [[[10, 1; 12,
777: 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 13, 1], [[0, 0,
778: 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [], [[[12, 1; 20, 1], [[24, 24,
779: [3, 6; 5, 9; 229, 12]], [0, 0, 0], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 2
780: 4]]]], [[13, 1; 20, 1], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [24, 12
781: , [3, 6; 5, 6; 229, 12]], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1
782: ], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 0, [3, 12; 5
783: , 18; 229, 24]]]], [[13, 1; 21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0,
784: 0], [48, 24, [3, 12; 5, 18; 229, 24]], [0, 0, 0]]]], [[Mat([10, 2]), [[0, 0
785: , 0], [12, 6, [-1, 1; 2, 12; 229, 6]], [12, 6, [-1, 1; 2, 12; 229, 6]], [24,
786: 0, [2, 36; 229, 12]]]]], [[Mat([68, 1]), [[0, 0, 0], [12, 6, [-1, 1; 17, 3;
787: 229, 6]], [0, 0, 0], [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [12, 6, [-1, 1
788: ; 17, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [1
789: 9, 6; 229, 9]], [0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77
790: , 1]), [[18, 18, [19, 6; 229, 9]], [0, 0, 0], [36, 18, [-1, 1; 19, 15; 229,
791: 18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0,
792: 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]]
793: ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
1.2 ! noro 794: [[9]~, [112595/19683, 13958/19683]~, 192]
1.1 noro 795: ? dirzetak(nf4,30)
796: [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,
797: 0, 1, 0, 1, 0]
798: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
799:
800: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t, t^3 + t^2 - 2*t - 1) 1]
801:
802: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
803:
804: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
805:
806: ? vp=idealprimedec(nf,3)[1]
1.2 ! noro 807: [3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~]
1.1 noro 808: ? idx=idealmul(nf,matid(5),vp)
809:
1.2 ! noro 810: [3 2 1 0 1]
1.1 noro 811:
812: [0 1 0 0 0]
813:
814: [0 0 1 0 0]
815:
816: [0 0 0 1 0]
817:
818: [0 0 0 0 1]
819:
820: ? idealinv(nf,idx)
821:
1.2 ! noro 822: [1 0 0 2/3 0]
1.1 noro 823:
1.2 ! noro 824: [0 1 0 1/3 0]
1.1 noro 825:
1.2 ! noro 826: [0 0 1 1/3 0]
1.1 noro 827:
1.2 ! noro 828: [0 0 0 1/3 0]
1.1 noro 829:
830: [0 0 0 0 1]
831:
832: ? idy=idealred(nf,idx,[1,5,6])
833:
1.2 ! noro 834: [5 0 0 0 2]
1.1 noro 835:
1.2 ! noro 836: [0 5 0 0 2]
1.1 noro 837:
1.2 ! noro 838: [0 0 5 0 1]
1.1 noro 839:
1.2 ! noro 840: [0 0 0 5 2]
1.1 noro 841:
1.2 ! noro 842: [0 0 0 0 1]
1.1 noro 843:
844: ? idx2=idealmul(nf,idx,idx)
845:
1.2 ! noro 846: [9 5 7 0 4]
1.1 noro 847:
848: [0 1 0 0 0]
849:
850: [0 0 1 0 0]
851:
852: [0 0 0 1 0]
853:
854: [0 0 0 0 1]
855:
856: ? idt=idealmul(nf,idx,idx,1)
857:
1.2 ! noro 858: [2 0 0 0 0]
1.1 noro 859:
1.2 ! noro 860: [0 2 0 0 0]
1.1 noro 861:
862: [0 0 2 0 0]
863:
864: [0 0 0 2 1]
865:
866: [0 0 0 0 1]
867:
868: ? idz=idealintersect(nf,idx,idy)
869:
1.2 ! noro 870: [15 10 5 0 12]
1.1 noro 871:
1.2 ! noro 872: [0 5 0 0 2]
1.1 noro 873:
1.2 ! noro 874: [0 0 5 0 1]
1.1 noro 875:
1.2 ! noro 876: [0 0 0 5 2]
1.1 noro 877:
1.2 ! noro 878: [0 0 0 0 1]
1.1 noro 879:
880: ? aid=[idx,idy,idz,matid(5),idx]
1.2 ! noro 881: [[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]
! 882: , [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
! 883: ], [15, 10, 5, 0, 12; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0,
! 884: 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,
! 885: 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
! 886: , 0, 1]]
1.1 noro 887: ? bid=idealstar(nf2,54,1)
888: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
889: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1.2 ! noro 890: 2, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 0, 2]~], [[-27, 0, 2]
1.1 noro 891: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
892: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
893: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
894: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
1.2 ! noro 895: 0]]], [[], [], [;]]], [468, 469, 0, 0, -12194, 0, 0, -36582; 0, 0, 1, 0, -3
! 896: , -6, 0, 0; 0, 0, 0, 1, -4, 0, -6, -3]]
1.1 noro 897: ? vaid=[idx,idy,matid(5)]
1.2 ! noro 898: [[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]
! 899: , [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 900: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
901: 1]]
902: ? haid=[matid(5),matid(5),matid(5)]
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, 1]
904: , [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
905: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
906: 1]]
907: ? idealadd(nf,idx,idy)
908:
909: [1 0 0 0 0]
910:
911: [0 1 0 0 0]
912:
913: [0 0 1 0 0]
914:
915: [0 0 0 1 0]
916:
917: [0 0 0 0 1]
918:
919: ? idealaddtoone(nf,idx,idy)
1.2 ! noro 920: [[3, 2, 1, 2, 1]~, [-2, -2, -1, -2, -1]~]
1.1 noro 921: ? idealaddtoone(nf,[idy,idx])
922: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
923: ? idealappr(nf,idy)
1.2 ! noro 924: [-2, -2, -1, -2, -1]~
1.1 noro 925: ? idealappr(nf,idealfactor(nf,idy),1)
1.2 ! noro 926: [-2, -2, -1, -2, -1]~
1.1 noro 927: ? idealcoprime(nf,idx,idx)
1.2 ! noro 928: [1/3, -1/3, -1/3, -1/3, 0]~
1.1 noro 929: ? idealdiv(nf,idy,idt)
930:
1.2 ! noro 931: [5 0 5/2 0 1]
1.1 noro 932:
1.2 ! noro 933: [0 5/2 0 0 1]
1.1 noro 934:
1.2 ! noro 935: [0 0 5/2 0 1/2]
1.1 noro 936:
1.2 ! noro 937: [0 0 0 5/2 1]
1.1 noro 938:
1.2 ! noro 939: [0 0 0 0 1/2]
1.1 noro 940:
941: ? idealdiv(nf,idx2,idx,1)
942:
1.2 ! noro 943: [3 2 1 0 1]
1.1 noro 944:
945: [0 1 0 0 0]
946:
947: [0 0 1 0 0]
948:
949: [0 0 0 1 0]
950:
951: [0 0 0 0 1]
952:
953: ? idf=idealfactor(nf,idz)
954:
1.2 ! noro 955: [[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] 1]
1.1 noro 956:
1.2 ! noro 957: [[5, [-1, 0, 0, 0, 1]~, 1, 1, [2, 0, 3, 0, 1]~] 1]
1.1 noro 958:
1.2 ! noro 959: [[5, [2, 0, 0, 0, 1]~, 4, 1, [2, 2, 1, 2, 1]~] 3]
1.1 noro 960:
961: ? idealhnf(nf,vp)
962:
1.2 ! noro 963: [3 2 1 0 1]
1.1 noro 964:
965: [0 1 0 0 0]
966:
967: [0 0 1 0 0]
968:
969: [0 0 0 1 0]
970:
971: [0 0 0 0 1]
972:
973: ? idealhnf(nf,vp[2],3)
974:
1.2 ! noro 975: [3 2 1 0 1]
1.1 noro 976:
977: [0 1 0 0 0]
978:
979: [0 0 1 0 0]
980:
981: [0 0 0 1 0]
982:
983: [0 0 0 0 1]
984:
985: ? ideallist(bnf,20)
1.2 ! noro 986: [[[1, 0; 0, 1]], [], [[3, 0; 0, 1], [3, 1; 0, 1]], [[2, 0; 0, 2]], [[5, 4; 0
! 987: , 1], [5, 2; 0, 1]], [], [], [], [[9, 6; 0, 1], [3, 0; 0, 3], [9, 4; 0, 1]],
! 988: [], [[11, 10; 0, 1], [11, 2; 0, 1]], [[6, 0; 0, 2], [6, 2; 0, 2]], [], [],
! 989: [[15, 9; 0, 1], [15, 4; 0, 1], [15, 12; 0, 1], [15, 7; 0, 1]], [[4, 0; 0, 4]
! 990: ], [[17, 15; 0, 1], [17, 3; 0, 1]], [], [[19, 0; 0, 1], [19, 1; 0, 1]], [[10
! 991: , 8; 0, 2], [10, 4; 0, 2]]]
1.1 noro 992: ? ideallog(nf2,w,bid)
1.2 ! noro 993: [1184, 6, 2]~
1.1 noro 994: ? idealmin(nf,idx,[1,2,3])
1.2 ! noro 995: [[-2; 1; 1; 0; 1], [2.0885812311199768913287869744681966008 + 3.141592653589
! 996: 7932384626433832795028841*I, 1.5921096812520196555597562531657929784 + 4.244
1.1 noro 997: 7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160
1.2 ! noro 998: 209 + 2.5437460822678889883600220330800078854*I]]
1.1 noro 999: ? idealnorm(nf,idt)
1000: 16
1001: ? idp=idealpow(nf,idx,7)
1002:
1.2 ! noro 1003: [2187 1436 1807 630 1822]
1.1 noro 1004:
1005: [0 1 0 0 0]
1006:
1007: [0 0 1 0 0]
1008:
1009: [0 0 0 1 0]
1010:
1011: [0 0 0 0 1]
1012:
1013: ? idealpow(nf,idx,7,1)
1014:
1.2 ! noro 1015: [2 0 0 0 0]
1.1 noro 1016:
1.2 ! noro 1017: [0 2 0 0 0]
1.1 noro 1018:
1.2 ! noro 1019: [0 0 2 0 0]
1.1 noro 1020:
1.2 ! noro 1021: [0 0 0 2 1]
1.1 noro 1022:
1.2 ! noro 1023: [0 0 0 0 1]
1.1 noro 1024:
1025: ? idealprimedec(nf,2)
1.2 ! noro 1026: [[2, [3, 0, 1, 0, 0]~, 1, 1, [0, 0, 0, 1, 1]~], [2, [12, -4, -2, 11, 3]~, 1,
! 1027: 4, [1, 0, 1, 0, 0]~]]
1.1 noro 1028: ? idealprimedec(nf,3)
1.2 ! noro 1029: [[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~], [3, [-1, -1, -1, 0, 0]~,
! 1030: 2, 2, [0, 2, 2, 1, 0]~]]
1.1 noro 1031: ? idealprimedec(nf,11)
1032: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
1033: ? idealprincipal(nf,Mod(x^3+5,nfpol))
1034:
1035: [6]
1036:
1.2 ! noro 1037: [1]
! 1038:
! 1039: [3]
1.1 noro 1040:
1041: [1]
1042:
1043: [3]
1044:
1045: ? idealtwoelt(nf,idy)
1.2 ! noro 1046: [5, [2, 2, 1, 2, 1]~]
1.1 noro 1047: ? idealtwoelt(nf,idy,10)
1.2 ! noro 1048: [-2, -2, -1, -2, -1]~
1.1 noro 1049: ? idealstar(nf2,54)
1050: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
1051: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
1.2 ! noro 1052: 2, 1, 1]~], [[-26, -27, -27]~], [[]~], 1]], [[[26], [[0, 0, 2]~], [[-27, 0,
! 1053: 2]~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24,
! 1054: 0]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1
! 1055: /3, 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~
! 1056: , [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9,
! 1057: 0, 0]]], [[], [], [;]]], [468, 469, 0, 0, -12194, 0, 0, -36582; 0, 0, 1, 0,
! 1058: -3, -6, 0, 0; 0, 0, 0, 1, -4, 0, -6, -3]]
1.1 noro 1059: ? idealval(nf,idp,vp)
1060: 7
1061: ? ideleprincipal(nf,Mod(x^3+5,nfpol))
1.2 ! noro 1062: [[6; 1; 3; 1; 3], [2.2324480827796254080981385584384939684 + 3.1415926535897
! 1063: 932384626433832795028841*I, 5.0387659675158716386435353106610489967 + 1.5851
1.1 noro 1064: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
1.2 ! noro 1065: - 0.0083630478144368246110910258645462996226*I]]
1.1 noro 1066: ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
1.2 ! noro 1067: [6, 1, 3, 1, 3]~
1.1 noro 1068: ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
1.2 ! noro 1069: [1, 1, 4, 1, 3]~
1.1 noro 1070: ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
1071:
1.2 ! noro 1072: [[3, -2, 1, 1, 0]~]
1.1 noro 1073:
1.2 ! noro 1074: [[4, -2, 0, 1, 0]~]
1.1 noro 1075:
1076: ? matbasistoalg(nf,bc)
1077:
1078: [Mod(x^2 + x, x^5 - 5*x^3 + 5*x + 25)]
1079:
1080: [Mod(x^2 + 1, x^5 - 5*x^3 + 5*x + 25)]
1081:
1082: ? nfbasis(x^3+4*x+5)
1083: [1, x, 1/7*x^2 - 1/7*x - 2/7]
1084: ? nfbasis(x^3+4*x+5,2)
1085: [1, x, 1/7*x^2 - 1/7*x - 2/7]
1086: ? nfbasis(x^3+4*x+12,1)
1087: [1, x, 1/2*x^2]
1088: ? nfbasistoalg(nf,ba)
1089: Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
1090: ? nfbasis(p2,0,fa)
1091: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
1092: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
1093: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
1094: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
1095: ? da=nfdetint(nf,[a,aid])
1096:
1.2 ! noro 1097: [90 70 35 0 65]
1.1 noro 1098:
1099: [0 5 0 0 0]
1100:
1.2 ! noro 1101: [0 0 5 0 0]
1.1 noro 1102:
1.2 ! noro 1103: [0 0 0 5 0]
1.1 noro 1104:
1105: [0 0 0 0 5]
1106:
1107: ? nfdisc(x^3+4*x+12)
1108: -1036
1109: ? nfdisc(x^3+4*x+12,1)
1110: -1036
1111: ? nfdisc(p2,0,fa)
1112: 136866601
1113: ? nfeltdiv(nf,ba,bb)
1.2 ! noro 1114: [584/373, 66/373, -32/373, -105/373, 120/373]~
1.1 noro 1115: ? nfeltdiveuc(nf,ba,bb)
1.2 ! noro 1116: [2, 0, 0, 0, 0]~
1.1 noro 1117: ? nfeltdivrem(nf,ba,bb)
1.2 ! noro 1118: [[2, 0, 0, 0, 0]~, [4, -1, -5, -1, -3]~]
1.1 noro 1119: ? nfeltmod(nf,ba,bb)
1.2 ! noro 1120: [4, -1, -5, -1, -3]~
1.1 noro 1121: ? nfeltmul(nf,ba,bb)
1.2 ! noro 1122: [50, -15, -35, 60, 15]~
1.1 noro 1123: ? nfeltpow(nf,bb,5)
1.2 ! noro 1124: [-291920, 136855, 230560, -178520, 74190]~
1.1 noro 1125: ? nfeltreduce(nf,ba,idx)
1126: [1, 0, 0, 0, 0]~
1127: ? nfeltval(nf,ba,vp)
1128: 0
1129: ? nffactor(nf2,x^3+x)
1130:
1.2 ! noro 1131: [x 1]
1.1 noro 1132:
1.2 ! noro 1133: [x^2 + 1 1]
1.1 noro 1134:
1135: ? aut=nfgaloisconj(nf3)
1.2 ! noro 1136: [-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
! 1137: /2*x]~
1.1 noro 1138: ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
1.2 ! noro 1139: Mod(-1/2*x^5 + 9*x^2, x^6 + 108)
1.1 noro 1140: ? nfhilbert(nf,3,5)
1141: -1
1142: ? nfhilbert(nf,3,5,idf[1,1])
1143: -1
1144: ? nfhnf(nf,[a,aid])
1.2 ! noro 1145: [[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [
! 1146: 1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0
! 1147: , 0, 0, 0]~], [[10, 4, 5, 6, 7; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1148: 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
! 1149: ; 0, 0, 0, 0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1,
! 1150: 0; 0, 0, 0, 0, 1]]]
1.1 noro 1151: ? nfhnfmod(nf,[a,aid],da)
1.2 ! noro 1152: [[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [
! 1153: 1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0
! 1154: , 0, 0, 0]~], [[10, 4, 5, 6, 7; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1155: 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
! 1156: ; 0, 0, 0, 0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1,
! 1157: 0; 0, 0, 0, 0, 1]]]
! 1158: ? nfisideal(bnf[7],[5,2;0,1])
1.1 noro 1159: 1
1160: ? nfisincl(x^2+1,x^4+1)
1161: [-x^2, x^2]
1162: ? nfisincl(x^2+1,nfinit(x^4+1))
1163: [-x^2, x^2]
1164: ? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
1165: [x, -x^2 - x + 1, x^2 - 2]
1166: ? nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30))
1167: [-1/25*x^2 + 13/25*x - 2/5]
1168: ? nfroots(nf2,x+2)
1169: [Mod(-2, y^3 - y - 1)]
1170: ? nfrootsof1(nf)
1171: [2, [-1, 0, 0, 0, 0]~]
1172: ? nfsnf(nf,[as,haid,vaid])
1.2 ! noro 1173: [[2562748315629757085585610, 436545976069778274371140, 123799938628701108220
! 1174: 1405, 2356446991473627724963350, 801407102592194537169612; 0, 5, 0, 0, 2; 0,
! 1175: 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
! 1176: , 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0;
! 1177: 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
1.1 noro 1178: ? nfsubfields(nf)
1179: [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]]
1180: ? polcompositum(x^4-4*x+2,x^3-x-1)
1181: [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
1182: ^2 - 128*x - 5]
1183: ? polcompositum(x^4-4*x+2,x^3-x-1,1)
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*
1185: x^2 - 128*x - 5, Mod(-279140305176/29063006931199*x^11 + 129916611552/290630
1186: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
1187: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
1188: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
1189: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
1190: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
1191: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), M
1192: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
1193: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
1194: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
1195: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
1196: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
1197: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
1198: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
1199: ? polgalois(x^6-3*x^2-1)
1200: [12, 1, 1]
1201: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
1202: [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
1203: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
1204: ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
1205:
1206: [1 x - 1]
1207:
1208: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
1209:
1210: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
1211:
1212: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
1213:
1214: ? polred(x^4+576,1)
1215: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
1216: ? polred(x^4+576,3)
1217:
1218: [1 x - 1]
1219:
1220: [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
1221:
1222: [-1/24*x^2 x^2 + 1]
1223:
1224: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
1225:
1226: ? polred(p2,0,fa)
1227: [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
1228: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
1229: *x^3 - 197*x^2 - 273*x - 127]
1230: ? polred(p2,1,fa)
1231: [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
1232: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
1233: *x^3 - 197*x^2 - 273*x - 127]
1234: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
1235: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
1236: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
1237: [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 -
1238: x^4 + 2*x^3 - 4*x^2 + x - 1)]
1239: ? polredord(x^3-12*x+45*x-1)
1240: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
1241: ? polsubcyclo(31,5)
1242: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
1243: ? setrand(1);poltschirnhaus(x^5-x-1)
1244: x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289
1245: ? aa=rnfpseudobasis(nf2,p)
1246: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
1247: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
1248: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
1249: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
1250: ], [[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 1251: , 0; 0, 0, 1], [1, 0, 2/5; 0, 1, 3/5; 0, 0, 1/5], [1, 0, 22/25; 0, 1, 8/25;
! 1252: 0, 0, 1/25]], [416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1
! 1253: 275, 5, 5]~]
1.1 noro 1254: ? rnfbasis(bnf2,aa)
1255:
1.2 ! noro 1256: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-6/25, 66/25, 77/25]~ [-391/25, -699/25,
! 1257: 197/25]~]
1.1 noro 1258:
1.2 ! noro 1259: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [18/25, -48/25, -56/25]~ [268/25, 552/25,
! 1260: -206/25]~]
1.1 noro 1261:
1.2 ! noro 1262: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [41/25, 24/25, 28/25]~ [-194/25, -116/25,
! 1263: -127/25]~]
1.1 noro 1264:
1.2 ! noro 1265: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [17/25, -12/25, -14/25]~ [52/25, 178/25, -
! 1266: 109/25]~]
1.1 noro 1267:
1.2 ! noro 1268: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/25, 6/25, 7/25]~ [-41/25, -49/25, -3/25
! 1269: ]~]
1.1 noro 1270:
1271: ? rnfdisc(nf2,p)
1.2 ! noro 1272: [[416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
1.1 noro 1273: ? rnfequation(nf2,p)
1274: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
1275: ? rnfequation(nf2,p,1)
1276: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, Mod(-x^5 + 5*x, x^15 - 1
1277: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
1278: ? rnfhnfbasis(bnf2,aa)
1279:
1.2 ! noro 1280: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [6/5, 4/5, -2/5]~ [-22/25, -33/25, 99/25]~
1.1 noro 1281: ]
1282:
1.2 ! noro 1283: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-6/5, -4/5, 2/5]~ [16/25, 24/25, -72/25]~
! 1284: ]
1.1 noro 1285:
1.2 ! noro 1286: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-3/5, -2/5, 1/5]~ [-8/25, -12/25, 36/25]~
! 1287: ]
1.1 noro 1288:
1.2 ! noro 1289: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/5, -2/5, 1/5]~ [4/25, 6/25, -18/25]~]
1.1 noro 1290:
1.2 ! noro 1291: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/25, -3/25, 9/25]~]
1.1 noro 1292:
1293: ? rnfisfree(bnf2,aa)
1294: 1
1295: ? rnfsteinitz(nf2,aa)
1.2 ! noro 1296: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-6/25, 66/25, 77/25]~, [17/125, -66/1
! 1297: 25, -77/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [18/25, -48/25, -56/25]~,
! 1298: [-26/125, 48/125, 56/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [41/25, 24/
! 1299: 25, 28/25]~, [-37/125, -24/125, -28/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]
! 1300: ~, [17/25, -12/25, -14/25]~, [-19/125, 12/125, 14/125]~; [0, 0, 0]~, [0, 0,
! 1301: 0]~, [0, 0, 0]~, [4/25, 6/25, 7/25]~, [-3/125, -6/125, -7/125]~], [[1, 0, 0;
! 1302: 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]
! 1303: , [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0, 22; 0, 125, 108; 0, 0, 1]], [4161343
! 1304: 75, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
1.1 noro 1305: ? nfz=zetakinit(x^2-2);
1306: ? zetak(nfz,-3)
1307: 0.091666666666666666666666666666666666666
1308: ? zetak(nfz,1.5+3*I)
1309: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
1310: 7938845*I
1311: ? setrand(1);quadclassunit(1-10^7,,[1,1])
1312: *** Warning: not a fundamental discriminant in quadclassunit.
1.2 ! noro 1313: [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 1.00257481
! 1314: 6299307750]
1.1 noro 1315: ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
1316: [4, [4], [Qfb(3, 1, -83333333, 0.E-48)], 2800.625251907016076486370621737074
1.2 ! noro 1317: 5514, 0.9849577285369119736]
1.1 noro 1318: ? sizebyte(%)
1.2 ! noro 1319: 172
1.1 noro 1320: ? getheap
1.2 ! noro 1321: [199, 126852]
1.1 noro 1322: ? print("Total time spent: ",gettime);
1.2 ! noro 1323: Total time spent: 960
1.1 noro 1324: ? \q
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