Annotation of OpenXM_contrib/pari/src/test/64/nfields, Revision 1.1
1.1 ! maekawa 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)
! 20: [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920
! 21: 69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929
! 22: 269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119
! 23: 211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I,
! 24: 3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331
! 25: 539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319
! 26: 06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196
! 27: 23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 +
! 28: 1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610
! 29: 81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887
! 30: 04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982
! 31: 34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I]
! 32: , [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262
! 33: 77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515
! 34: 382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8
! 35: 976972027301414394898806541072047941, 6.408909349142616853840753758109052071
! 36: 2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441
! 37: 22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929
! 38: 269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875
! 39: 724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 -
! 40: 1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400
! 41: 435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104
! 42: 7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231
! 43: 7837223883352537186677084*I], [5, 0.E-77, 10.0000000000000000000000000000000
! 44: 00000, -5.0000000000000000000000000000000000000, 7.0000000000000000000000000
! 45: 000000000000; 0.E-77, 19.488486013650707197449403270536023970, 2.07268045322
! 46: 26667100551498190000000000 E-76, 19.488486013650707197449403270536023970, 4.
! 47: 1504592246706085588902013976045703227; 10.0000000000000000000000000000000000
! 48: 00, 2.0726804532226667100551498190000000000 E-76, 85.96021742085184648030513
! 49: 3936577594605, -36.034268291482979838267056239752434596, 53.5761304525111078
! 50: 88183080361946556763; -5.0000000000000000000000000000000000000, 19.488486013
! 51: 650707197449403270536023970, -36.034268291482979838267056239752434596, 60.91
! 52: 6248374441986300937507618575151517, -18.470101750219179344070032346246890434
! 53: ; 7.0000000000000000000000000000000000000, 4.1504592246706085588902013976045
! 54: 703227, 53.576130452511107888183080361946556763, -18.47010175021917934407003
! 55: 2346246890434, 37.970152892842367340897384258599214282], [5, 0, 10, -5, 7; 0
! 56: , 10, 0, 10, -5; 10, 0, 30, -55, 20; -5, 10, -55, 45, -39; 7, -5, 20, -39, 9
! 57: ], [345, 0, 340, 167, 150; 0, 345, 110, 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1,
! 58: 0; 0, 0, 0, 0, 1], [132825, -18975, -5175, 27600, 17250; -18975, 34500, 414
! 59: 00, 3450, -43125; -5175, 41400, -41400, -15525, 51750; 27600, 3450, -15525,
! 60: -3450, 0; 17250, -43125, 51750, 0, -86250], [595125, [-120750, 63825, 113850
! 61: , 0, 8625]~, 125439056256992431640625]], [-2.4285174907194186068992069565359
! 62: 418364, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940
! 63: 82219556466857*I, -0.75045317576910401286427186094108607489 + 1.310146268535
! 64: 8123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3, 1/15*x^4
! 65: + 1/3*x^2 + 1/3*x + 1/3], [1, 0, 0, 1, -5; 0, 1, 0, 0, -5; 0, 0, 1, 1, -5; 0
! 66: , 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0, 1, -5, -5
! 67: , -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0, -2, 0, 0,
! 68: 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0, 1, 1, -2,
! 69: 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1, 0, 0, 0,
! 70: 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0, 0, 0, 1, 0, 0
! 71: , 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]]
! 72: ? nf1=nfinit(nfpol,2)
! 73: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
! 74: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
! 75: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
! 76: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
! 77: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
! 78: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
! 79: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
! 80: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
! 81: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
! 82: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
! 83: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
! 84: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
! 85: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
! 86: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
! 87: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
! 88: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
! 89: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
! 90: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
! 91: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
! 92: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
! 93: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
! 94: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
! 95: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
! 96: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
! 97: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
! 98: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
! 99: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
! 100: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
! 101: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
! 102: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
! 103: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
! 104: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
! 105: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
! 106: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
! 107: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
! 108: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
! 109: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
! 110: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
! 111: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
! 112: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
! 113: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
! 114: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
! 115: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
! 116: 0]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684,
! 117: -0.13838372073406036365047976417441696637 + 0.49181637657768643499753285514
! 118: 741525107*I, 1.6829412935943127761629561615079976005 + 2.0500351226010726172
! 119: 974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*
! 120: x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0,
! 121: 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0
! 122: , -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -
! 123: 2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3,
! 124: 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0
! 125: , -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1,
! 126: 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, -21]]
! 127: ? nfinit(nfpol,3)
! 128: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
! 129: 57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5
! 130: 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894
! 131: 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975
! 132: 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602
! 133: 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +
! 134: 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835
! 135: 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431
! 136: 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703
! 137: 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*
! 138: I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301
! 139: 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354
! 140: 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,
! 141: -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294
! 142: 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459
! 143: 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821
! 144: 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2
! 145: .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927
! 146: 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753
! 147: 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573
! 148: 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1
! 149: 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052
! 150: 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346
! 151: 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000
! 152: 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17
! 153: .000000000000000000000000000000000000, -44.000000000000000000000000000000000
! 154: 000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471
! 155: 283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499
! 156: 932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000
! 157: 00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912
! 158: 62388960975827806174040462368, 143.93295090847353519436673793501057176, -55.
! 159: 842564718082452641322500190813370023; -17.0000000000000000000000000000000000
! 160: 00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935
! 161: 01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201
! 162: 80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084
! 163: 1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400
! 164: 38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
! 165: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -
! 166: 101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215
! 167: , 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125,
! 168: -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670
! 169: 0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89
! 170: 700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725
! 171: , 0]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684
! 172: , -0.13838372073406036365047976417441696637 + 0.4918163765776864349975328551
! 173: 4741525107*I, 1.6829412935943127761629561615079976005 + 2.050035122601072617
! 174: 2974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2
! 175: *x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0
! 176: , 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2,
! 177: 0, -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1,
! 178: -2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3
! 179: , 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2,
! 180: 0, -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1
! 181: , 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, -21]], Mod(-1/2*x^4 + 3/2*x
! 182: ^3 - 5/2*x^2 - 2*x + 1, x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
! 183: ? nfinit(nfpol,4)
! 184: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
! 185: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
! 186: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
! 187: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
! 188: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
! 189: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
! 190: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
! 191: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
! 192: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
! 193: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
! 194: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
! 195: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
! 196: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
! 197: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
! 198: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
! 199: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
! 200: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
! 201: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
! 202: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
! 203: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
! 204: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
! 205: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
! 206: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
! 207: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
! 208: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
! 209: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
! 210: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
! 211: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
! 212: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
! 213: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
! 214: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
! 215: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
! 216: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
! 217: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
! 218: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
! 219: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
! 220: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
! 221: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
! 222: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
! 223: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
! 224: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
! 225: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
! 226: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
! 227: 0]~, 125439056256992431640625]], [-1.0891151457205048250249527946671612684,
! 228: -0.13838372073406036365047976417441696637 + 0.49181637657768643499753285514
! 229: 741525107*I, 1.6829412935943127761629561615079976005 + 2.0500351226010726172
! 230: 974286983598602163*I], [1, x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*
! 231: x], [1, 0, 0, 0, 0; 0, 1, 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0,
! 232: 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0
! 233: , -1, -2, -2, 5; 0, 1, 0, 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -
! 234: 2, -1, 7, 0, -1, 2, 7, 14; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3,
! 235: 0, 0, -3, -4, -1, 0, -2, -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0
! 236: , -2, -13, 1, 1, -2, -9, -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1,
! 237: 2, 0, 0, 2, 3, 1, 0, 1, 3, 4, -4, 1, 2, 1, -4, -21]]
! 238: ? nf3=nfinit(x^6+108);
! 239: ? nf4=nfinit(x^3-10*x+8)
! 240: [x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -3.50466435358804770515010852590433205
! 241: 79, 6.1413361156553641347759399165844441383; 1, 0.86464088669540302583112842
! 242: 266613688800, 0.37380193147270638662350044992137561317; 1, 2.640023466892644
! 243: 6793189801032381951699, 3.4848619528719294786005596334941802484], [1, 1, 1;
! 244: -3.5046643535880477051501085259043320579, 0.86464088669540302583112842266613
! 245: 688800, 2.6400234668926446793189801032381951699; 6.1413361156553641347759399
! 246: 165844441383, 0.37380193147270638662350044992137561317, 3.484861952871929478
! 247: 6005596334941802484], [3, -3.4544674220377778500919163650000000000 E-77, 10.
! 248: 000000000000000000000000000000000000; -3.45446742203777785009191636500000000
! 249: 00 E-77, 20.000000000000000000000000000000000000, -12.0000000000000000000000
! 250: 00000000000000; 10.000000000000000000000000000000000000, -12.000000000000000
! 251: 000000000000000000000, 50.000000000000000000000000000000000000], [3, 0, 10;
! 252: 0, 20, -12; 10, -12, 50], [284, 168, 235; 0, 2, 0; 0, 0, 1], [856, -120, -20
! 253: 0; -120, 50, 36; -200, 36, 60], [568, [80, 14, -24]~, 322624]], [-3.50466435
! 254: 35880477051501085259043320579, 0.86464088669540302583112842266613688800, 2.6
! 255: 400234668926446793189801032381951699], [1, x, 1/2*x^2], [1, 0, 0; 0, 1, 0; 0
! 256: , 0, 2], [1, 0, 0, 0, 0, -4, 0, -4, 0; 0, 1, 0, 1, 0, 5, 0, 5, -2; 0, 0, 1,
! 257: 0, 2, 0, 1, 0, 5]]
! 258: ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];
! 259: ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
! 260: [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
! 261: 61300699 - 9.4247779607693797153879301498385086526*I; 2.71246530518434397468
! 262: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.97922
! 263: 3478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 86
! 264: 6.56619430687100142570357249059499540 + 6.2831853071795864769252867665590057
! 265: 684*I, 2881.3396396084587293295626563644245032 + 3.1415926535897932384626433
! 266: 832795028842*I, 27379.624790530768080428797780058276925 + 2.0880974297595278
! 267: 484866027080000000000 E-52*I, 57933.334567930851067108050790839116749 + 3.54
! 268: 97656305911973423188043860000000000 E-52*I, -34585.5562501515577199980340439
! 269: 18848670 + 9.4247779607693797153879301498385086526*I, 23348.3225111226233465
! 270: 49049047574325150 + 3.1415926535897932384626433832795028842*I, -0.3432876442
! 271: 7702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -4
! 272: 031.7117453543045067063239888430083582 + 9.424777960769379715387930149838508
! 273: 6526*I, 27379.690968832650826160983148550600089 + 9.424777960769379715387930
! 274: 1498385086526*I; -23347.979223478346319454659159707591731 + 9.42477796076937
! 275: 97153879301498385086526*I, -866.56619430687100142570357249059499540 + 8.1566
! 276: 305849981556577374397490000000000 E-55*I, -2881.3396396084587293295626563644
! 277: 245032 + 9.4247779607693797153879301498385086526*I, -27379.62479053076808042
! 278: 8797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.3345679
! 279: 30851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 3458
! 280: 5.556250151557719998034043918848670 + 6.283185307179586476925286766559005768
! 281: 4*I, -23348.322511122623346549049047574325150 + 9.42477796076937971538793014
! 282: 98385086526*I, 0.34328764427702709438988786673341921876 + 0.E-57*I, 4031.711
! 283: 7453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I,
! 284: -27379.690968832650826160983148550600089 + 6.283185307179586476925286766559
! 285: 0057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5,
! 286: [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1
! 287: , [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [1
! 288: 7, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1,
! 289: 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 22
! 290: 9, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.066372975210777963
! 291: 5959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.066
! 292: 3729752107779635959310246705326058], [2, 1.000000000000000000000000000000000
! 293: 0000; 1.0000000000000000000000000000000000000, 115.0000000000000000000000000
! 294: 0000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114,
! 295: 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.066372975210777963
! 296: 5959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3,
! 297: [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512
! 298: 6545793690341704100000000000, [2, -1], [x + 7], 162], [Mat(1), Mat(1), [[[3,
! 299: 2; 0, 1], [0, 0]]]], 0]
! 300: ? setrand(1);bnfinit(x^2-x-100000,1)
! 301: [Mat(5), Mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129.
! 302: 82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
! 303: 4*I; 129.82045011403975460991182396195022419 + 5.348345931263972060504263694
! 304: 0000000000 E-115*I], [2093832.2286247580721598744691800364716 + 9.4247779607
! 305: 693797153879301498385086526*I, 463727.88770776479369558667281813008490 + 6.2
! 306: 831853071795864769252867665590057684*I, 229510.68119174121074359900744873056
! 307: 520 + 3.1415926535897932384626433832795028842*I, -13814064.27618485624828610
! 308: 7275967161406 + 6.2831853071795864769252867665590057684*I, 10975229.44237614
! 309: 5014058790444262893275 + 9.4247779607693797153879301498385086526*I, 12628868
! 310: .476868730308574917279106536834 + 6.2831853071795864769252867665590057684*I,
! 311: 2595210.6815750606798700790306370856686 + 3.1415926535897932384626433832795
! 312: 028842*I, 21463208.279603014333968661075393279510 + 6.2831853071795864769252
! 313: 867665590057684*I, 9340416.4917416354701732132629720490406 + 9.4247779607693
! 314: 797153879301498385086526*I, 224801.35127844528675036994618361508061 + 12.566
! 315: 370614359172953850573533118011536*I, -224801.3512784452867503699461836150806
! 316: 1 + 9.6067672535041710996049808843552935572 E-110*I, 40271115.67885724271600
! 317: 3879014241558828 + 6.2831853071795864769252867665590057684*I, -10066612.2847
! 318: 88886379386747743460630561 + 4.3018790993764137358012770550502916873 E-108*I
! 319: , 10267873.880681641662748682261863339788 + 12.56637061435917295385057353311
! 320: 8011536*I, -4435991.6114732228963510067335229085617 + 6.28318530717958647692
! 321: 52867665590057684*I, 8361196.2032957779193404684451855312611 + 9.42477796076
! 322: 93797153879301498385086526*I, -10272584.501589374356405593568879583106 + 9.4
! 323: 247779607693797153879301498385086526*I, 41648172.195327314227598351804544361
! 324: 493 + 9.4247779607693797153879301498385086526*I, -2117367.665066341919805155
! 325: 1003369291210 + 9.0483757581445359017535541005707614256 E-109*I; -2093832.22
! 326: 86247580721598744691800364716 + 3.1415926535897932384626433832795028842*I, -
! 327: 463727.88770776479369558667281813008490 + 9.42477796076937971538793014983850
! 328: 86526*I, -229510.68119174121074359900744873056520 + 12.566370614359172953850
! 329: 573533118011536*I, 13814064.276184856248286107275967161405 + 5.6909456906323
! 330: 670696834504660000000000 E-110*I, -10975229.442376145014058790444262893275 +
! 331: 12.566370614359172953850573533118011536*I, -12628868.4768687303085749172791
! 332: 06536834 + 3.1415926535897932384626433832795028842*I, -2595210.6815750606798
! 333: 700790306370856686 + 12.566370614359172953850573533118011536*I, -21463208.27
! 334: 9603014333968661075393279510 + 9.4247779607693797153879301498385086526*I, -9
! 335: 340416.4917416354701732132629720490406 + 6.283185307179586476925286766559005
! 336: 7684*I, -224801.35127844528675036994618361508061 + 12.5663706143591729538505
! 337: 73533118011536*I, 224801.35127844528675036994618361508061 + 9.26104300469294
! 338: 36195130014290000000000 E-112*I, -40271115.678857242716003879014241558828 +
! 339: 12.566370614359172953850573533118011536*I, 10066612.284788886379386747743460
! 340: 630561 + 4.1471150755962714546179470600000000000 E-110*I, -10267873.88068164
! 341: 1662748682261863339788 + 3.1415926535897932384626433832795028842*I, 4435991.
! 342: 6114732228963510067335229085617 + 9.4247779607693797153879301498385086526*I,
! 343: -8361196.2032957779193404684451855312611 + 12.56637061435917295385057353311
! 344: 8011536*I, 10272584.501589374356405593568879583106 + 4.231970404042868132057
! 345: 2257270000000000 E-110*I, -41648172.195327314227598351804544361493 + 3.14159
! 346: 26535897932384626433832795028842*I, 2117367.6650663419198051551003369291210
! 347: + 8.7228465941240376311377469060000000000 E-111*I], [[2, [1, 1]~, 1, 1, [0,
! 348: 1]~], [2, [2, 1]~, 1, 1, [1, 1]~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~,
! 349: 1, 1, [-1, 1]~], [7, [3, 1]~, 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~]
! 350: , [13, [5, 1]~, 1, 1, [-6, 1]~], [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]
! 351: ~, 1, 1, [-3, 1]~], [23, [-7, 1]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7,
! 352: 1]~], [29, [-14, 1]~, 1, 1, [13, 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31,
! 353: [23, 1]~, 1, 1, [7, 1]~], [31, [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1,
! 354: 1, [6, 1]~], [41, [6, 1]~, 1, 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~]
! 355: , [43, [15, 1]~, 1, 1, [-16, 1]~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13,
! 356: 12, 15, 14, 17, 16, 19, 18]~, [x^2 - x - 100000, [2, 0], 400001, 1, [[1, -3
! 357: 15.72816130129840161392089489603747004; 1, 316.72816130129840161392089489603
! 358: 747004], [1, 1; -315.72816130129840161392089489603747004, 316.72816130129840
! 359: 161392089489603747004], [2, 1.0000000000000000000000000000000000000; 1.00000
! 360: 00000000000000000000000000000000, 200001.00000000000000000000000000000000],
! 361: [2, 1; 1, 200001], [400001, 200000; 0, 1], [200001, -1; -1, 2], [400001, [20
! 362: 0000, 1]~, 400001]], [-315.72816130129840161392089489603747004, 316.72816130
! 363: 129840161392089489603747004], [1, x], [1, 0; 0, 1], [1, 0, 0, 100000; 0, 1,
! 364: 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.82045011403975460991182396195022419,
! 365: 0.98765369790690472391212970100000000000, [2, -1], [379554884019013781006303
! 366: 254896369154068336082609238336*x + 11983616564425078999046283595002287166517
! 367: 8127611316131167], 185], [Mat(1), Mat(1), [[[2, 1; 0, 1], [0, 0]]]], 0]
! 368: ? \p19
! 369: realprecision = 19 significant digits
! 370: ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
! 371: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071
! 372: 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,
! 373: 1], Mat(2), Mat([0, 1, 1, 1, 0, 1, 1, 1]), [9, 15, 16, 17, 10, 33, 69, 39,
! 374: 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [4, 3, 1, 2, 3, 1, 11, 1,
! 375: -7; -1, 1, -1, 1, 0, 1, 2, 4, -2; 0, 0, 0, 0, 0, 0, -1, 1, 0]]
! 376: ? \p38
! 377: realprecision = 38 significant digits
! 378: ? bnrinit(bnf,[[5,3;0,1],[1,0]],1)
! 379: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
! 380: 061300699 - 9.4247779607693797153879301498385086526*I; 2.7124653051843439746
! 381: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
! 382: 23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
! 383: 66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
! 384: 7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
! 385: 3832795028842*I, 27379.624790530768080428797780058276925 + 2.088097429759527
! 386: 8484866027080000000000 E-52*I, 57933.334567930851067108050790839116749 + 3.5
! 387: 497656305911973423188043860000000000 E-52*I, -34585.556250151557719998034043
! 388: 918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
! 389: 549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
! 390: 27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
! 391: 4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
! 392: 86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
! 393: 01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
! 394: 797153879301498385086526*I, -866.56619430687100142570357249059499540 + 8.156
! 395: 6305849981556577374397490000000000 E-55*I, -2881.339639608458729329562656364
! 396: 4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
! 397: 28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
! 398: 930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
! 399: 85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
! 400: 84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
! 401: 498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-57*I, 4031.71
! 402: 17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
! 403: , -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
! 404: 90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
! 405: , [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
! 406: 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
! 407: 17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
! 408: , 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
! 409: 29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
! 410: 35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
! 411: 63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
! 412: 00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
! 413: 00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
! 414: , 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
! 415: 35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
! 416: , [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
! 417: 26545793690341704100000000000, [2, -1], [x + 7], 162], [Mat(1), Mat(1), [[[3
! 418: , 2; 0, 1], [0, 0]]]], 0], [[[5, 3; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [-
! 419: 1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]
! 420: ~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~], Mat(1)]], [1, 0; 0, 1]], [[1, 0]~
! 421: ], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[3, 2; 0, 1]]], [[0, 0; 0, 1],
! 422: [1, -1; 1, 1]]]
! 423: ? bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2)
! 424: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
! 425: 061300699 - 9.4247779607693797153879301498385086526*I; 2.7124653051843439746
! 426: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
! 427: 23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
! 428: 66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
! 429: 7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
! 430: 3832795028842*I, 27379.624790530768080428797780058276925 + 2.088097429759527
! 431: 8484866027080000000000 E-52*I, 57933.334567930851067108050790839116749 + 3.5
! 432: 497656305911973423188043860000000000 E-52*I, -34585.556250151557719998034043
! 433: 918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
! 434: 549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
! 435: 27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
! 436: 4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
! 437: 86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
! 438: 01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
! 439: 797153879301498385086526*I, -866.56619430687100142570357249059499540 + 8.156
! 440: 6305849981556577374397490000000000 E-55*I, -2881.339639608458729329562656364
! 441: 4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
! 442: 28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
! 443: 930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
! 444: 85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
! 445: 84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
! 446: 498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-57*I, 4031.71
! 447: 17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
! 448: , -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
! 449: 90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
! 450: , [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
! 451: 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
! 452: 17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
! 453: , 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
! 454: 29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
! 455: 35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
! 456: 63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
! 457: 00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
! 458: 00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
! 459: , 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
! 460: 35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
! 461: , [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
! 462: 26545793690341704100000000000, [2, -1], [x + 7], 162], [Mat(1), Mat(1), [[[3
! 463: , 2; 0, 1], [0, 0]]]], 0], [[[5, 3; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [-
! 464: 1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]
! 465: ~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~], Mat(1)]], [1, 0; 0, 1]], [[1, 0]~
! 466: ], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[3, 2; 0, 1]]], [[0, 0; 0, 1],
! 467: [1, -1; 1, 1]]]
! 468: ? rnfinit(nf2,x^5-x-2)
! 469: [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3
! 470: 109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914
! 471: 279776896412, 1.6057155120361619195949075151301679393, 2.0347118029638523119
! 472: 874445717108994866, 2.5783223055935536544757871909285592749; 1, 0.2609638803
! 473: 8645528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -1
! 474: .3177592693689352747870763902256347904 + 0.614427010164338838041906608641467
! 475: 31824*I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524
! 476: 673160314582604*I, 1.3589689411882615753626439480614001936 - 1.6193337759893
! 477: 970298359887428575174472*I; 1, -0.89454803265751744362901306471557966872 + 0
! 478: .53414854617473272670874609150394379949*I, 0.5149015133508543149896226326605
! 479: 5082078 - 0.95564306225496055080453352211847466685*I, 0.04985121658507159775
! 480: 5867063892284310224 + 1.1299025160425089918993024639913611785*I, -0.64813009
! 481: 398503840260053754352567983115 - 0.98412411795664774269323431620030610541*I]
! 482: , [1, 1.2671683045421243172528914279776896412 + 0.E-38*I, 1.6057155120361619
! 483: 195949075151301679393 + 0.E-38*I, 2.0347118029638523119874445717108994866 +
! 484: 0.E-37*I, 2.5783223055935536544757871909285592749 + 0.E-37*I; 1, 0.260963880
! 485: 38645528500256735072673484811 - 1.1772261533941944394700286585617926513*I, -
! 486: 1.3177592693689352747870763902256347904 - 0.61442701016433883804190660864146
! 487: 731824*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921652
! 488: 4673160314582604*I, 1.3589689411882615753626439480614001936 + 1.619333775989
! 489: 3970298359887428575174472*I; 1, 0.26096388038645528500256735072673484811 + 1
! 490: .1772261533941944394700286585617926513*I, -1.3177592693689352747870763902256
! 491: 347904 + 0.61442701016433883804190660864146731824*I, -1.06720711806699775374
! 492: 95893497477340535 - 1.3909574189920019216524673160314582604*I, 1.35896894118
! 493: 82615753626439480614001936 - 1.6193337759893970298359887428575174472*I; 1, -
! 494: 0.89454803265751744362901306471557966872 - 0.5341485461747327267087460915039
! 495: 4379949*I, 0.51490151335085431498962263266055082078 + 0.95564306225496055080
! 496: 453352211847466685*I, 0.049851216585071597755867063892284310224 - 1.12990251
! 497: 60425089918993024639913611785*I, -0.64813009398503840260053754352567983115 +
! 498: 0.98412411795664774269323431620030610541*I; 1, -0.8945480326575174436290130
! 499: 6471557966872 + 0.53414854617473272670874609150394379949*I, 0.51490151335085
! 500: 431498962263266055082078 - 0.95564306225496055080453352211847466685*I, 0.049
! 501: 851216585071597755867063892284310224 + 1.12990251604250899189930246399136117
! 502: 85*I, -0.64813009398503840260053754352567983115 - 0.984124117956647742693234
! 503: 31620030610541*I]], [[1, 2, 2; 1.2671683045421243172528914279776896412, 0.52
! 504: 192776077291057000513470145346969622 - 2.35445230678838887894005731712358530
! 505: 26*I, -1.7890960653150348872580261294311593374 - 1.0682970923494654534174921
! 506: 830078875989*I; 1.6057155120361619195949075151301679393, -2.6355185387378705
! 507: 495741527804512695809 - 1.2288540203286776760838132172829346364*I, 1.0298030
! 508: 267017086299792452653211016415 + 1.9112861245099211016090670442369493337*I;
! 509: 2.0347118029638523119874445717108994866, -2.13441423613399550749917869949546
! 510: 81070 + 2.7819148379840038433049346320629165208*I, 0.09970243317014319551173
! 511: 4127784568620449 - 2.2598050320850179837986049279827223571*I; 2.578322305593
! 512: 5536544757871909285592749, 2.7179378823765231507252878961228003872 + 3.23866
! 513: 75519787940596719774857150348944*I, -1.2962601879700768052010750870513596623
! 514: + 1.9682482359132954853864686324006122108*I], [1, 1, 1, 1, 1; 1.26716830454
! 515: 21243172528914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484
! 516: 811 + 1.1772261533941944394700286585617926513*I, 0.2609638803864552850025673
! 517: 5072673484811 - 1.1772261533941944394700286585617926513*I, -0.89454803265751
! 518: 744362901306471557966872 + 0.53414854617473272670874609150394379949*I, -0.89
! 519: 454803265751744362901306471557966872 - 0.53414854617473272670874609150394379
! 520: 949*I; 1.6057155120361619195949075151301679393 + 0.E-38*I, -1.31775926936893
! 521: 52747870763902256347904 + 0.61442701016433883804190660864146731824*I, -1.317
! 522: 7592693689352747870763902256347904 - 0.6144270101643388380419066086414673182
! 523: 4*I, 0.51490151335085431498962263266055082078 - 0.95564306225496055080453352
! 524: 211847466685*I, 0.51490151335085431498962263266055082078 + 0.955643062254960
! 525: 55080453352211847466685*I; 2.0347118029638523119874445717108994866 + 0.E-37*
! 526: I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524673160
! 527: 314582604*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921
! 528: 6524673160314582604*I, 0.049851216585071597755867063892284310224 + 1.1299025
! 529: 160425089918993024639913611785*I, 0.049851216585071597755867063892284310224
! 530: - 1.1299025160425089918993024639913611785*I; 2.57832230559355365447578719092
! 531: 85592749 + 0.E-37*I, 1.3589689411882615753626439480614001936 - 1.61933377598
! 532: 93970298359887428575174472*I, 1.3589689411882615753626439480614001936 + 1.61
! 533: 93337759893970298359887428575174472*I, -0.6481300939850384026005375435256798
! 534: 3115 - 0.98412411795664774269323431620030610541*I, -0.6481300939850384026005
! 535: 3754352567983115 + 0.98412411795664774269323431620030610541*I]], [[5, -5.877
! 536: 4717541114375398032809710000000000 E-39 + 3.42274939913785433235754950013147
! 537: 29016*I, 2.3509887016445750159213123880000000000 E-38 - 0.682432104181243425
! 538: 52525382695401469720*I, -2.3509887016445750159213123880000000000 E-38 - 0.52
! 539: 210980589898585950632970408019416371*I, 3.9999999999999999999999999999999999
! 540: 999 - 5.2069157878920895450584461181156471052*I; -5.877471754111437539803280
! 541: 9710000000000 E-39 - 3.4227493991378543323575495001314729016*I, 6.6847043424
! 542: 634879841147654217963674264 - 5.8774717541114375398032809710000000000 E-39*I
! 543: , 0.85145677340721376574333983502938573598 + 4.58295731809784302915415926006
! 544: 01794652*I, -0.13574266252716976137461193821267520737 - 0.288051085440257723
! 545: 61738936467682050391*I, 0.27203784387468568916539788233281013320 - 1.5917147
! 546: 279942947718965650859986677247*I; 2.3509887016445750159213123880000000000 E-
! 547: 38 + 0.68243210418124342552525382695401469720*I, 0.8514567734072137657433398
! 548: 3502938573598 - 4.5829573180978430291541592600601794652*I, 9.163096853022107
! 549: 7951281598310681467898 + 0.E-38*I, 2.2622987652095629453403849736225691490 +
! 550: 6.2361927913558506765724047063180706869*I, -0.21796409886496632254445901043
! 551: 974770643 + 0.34559368931063215686158939748833975810*I; -2.35098870164457501
! 552: 59213123880000000000 E-38 + 0.52210980589898585950632970408019416371*I, -0.1
! 553: 3574266252716976137461193821267520737 + 0.2880510854402577236173893646768205
! 554: 0392*I, 2.2622987652095629453403849736225691490 - 6.236192791355850676572404
! 555: 7063180706869*I, 12.845768948832335511882696939380696155 + 1.175494350822287
! 556: 5079606561940000000000 E-38*I, 4.5618400502378124720913214622468855074 + 8.6
! 557: 033930051068500425218923146793019614*I; 3.9999999999999999999999999999999999
! 558: 999 + 5.2069157878920895450584461181156471052*I, 0.2720378438746856891653978
! 559: 8233281013320 + 1.5917147279942947718965650859986677247*I, -0.21796409886496
! 560: 632254445901043974770643 - 0.34559368931063215686158939748833975810*I, 4.561
! 561: 8400502378124720913214622468855074 - 8.6033930051068500425218923146793019615
! 562: *I, 18.362968630416114402425299186062892646 + 5.8774717541114375398032809710
! 563: 000000000 E-39*I], [5, -1.1754943508222875079606561940000000000 E-38 + 0.E-3
! 564: 8*I, 2.3509887016445750159213123880000000000 E-38 + 0.E-38*I, -1.76324152623
! 565: 34312619409842910000000000 E-38 + 0.E-38*I, 3.999999999999999999999999999999
! 566: 9999998 + 0.E-38*I; -1.1754943508222875079606561940000000000 E-38 + 0.E-38*I
! 567: , 6.6847043424634879841147654217963674264 - 5.877471754111437539803280971000
! 568: 0000000 E-39*I, 0.85145677340721376574333983502938573597 + 5.877471754111437
! 569: 5398032809710000000000 E-39*I, -0.13574266252716976137461193821267520737 + 5
! 570: .8774717541114375398032809710000000000 E-39*I, 0.272037843874685689165397882
! 571: 33281013314 - 5.8774717541114375398032809710000000000 E-39*I; 2.350988701644
! 572: 5750159213123880000000000 E-38 + 0.E-38*I, 0.8514567734072137657433398350293
! 573: 8573597 + 5.8774717541114375398032809710000000000 E-39*I, 9.1630968530221077
! 574: 951281598310681467898 + 0.E-38*I, 2.2622987652095629453403849736225691490 +
! 575: 2.3509887016445750159213123880000000000 E-38*I, -0.2179640988649663225444590
! 576: 1043974770651 + 0.E-38*I; -1.7632415262334312619409842910000000000 E-38 + 0.
! 577: E-38*I, -0.13574266252716976137461193821267520737 + 5.8774717541114375398032
! 578: 809710000000000 E-39*I, 2.2622987652095629453403849736225691490 + 2.35098870
! 579: 16445750159213123880000000000 E-38*I, 12.84576894883233551188269693938069615
! 580: 5 + 0.E-37*I, 4.5618400502378124720913214622468855073 - 3.526483052466862523
! 581: 8819685820000000000 E-38*I; 3.9999999999999999999999999999999999998 + 0.E-38
! 582: *I, 0.27203784387468568916539788233281013314 - 5.877471754111437539803280971
! 583: 0000000000 E-39*I, -0.21796409886496632254445901043974770651 + 0.E-38*I, 4.5
! 584: 618400502378124720913214622468855073 - 3.52648305246686252388196858200000000
! 585: 00 E-38*I, 18.362968630416114402425299186062892646 + 0.E-37*I]], [Mod(5, y^3
! 586: - y - 1), 0, 0, 0, Mod(4, y^3 - y - 1); 0, 0, 0, Mod(4, y^3 - y - 1), Mod(1
! 587: 0, y^3 - y - 1); 0, 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0; 0, Mod(
! 588: 4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0, 0; Mod(4, y^3 - y - 1), Mod(10, y^
! 589: 3 - y - 1), 0, 0, Mod(4, y^3 - y - 1)], [;], [;], [;]], [[1.2671683045421243
! 590: 172528914279776896412, 0.26096388038645528500256735072673484811 + 1.17722615
! 591: 33941944394700286585617926513*I, -0.89454803265751744362901306471557966872 +
! 592: 0.53414854617473272670874609150394379949*I], [1.267168304542124317252891427
! 593: 9776896412 + 0.E-38*I, 0.26096388038645528500256735072673484811 - 1.17722615
! 594: 33941944394700286585617926513*I, 0.26096388038645528500256735072673484811 +
! 595: 1.1772261533941944394700286585617926513*I, -0.894548032657517443629013064715
! 596: 57966872 - 0.53414854617473272670874609150394379949*I, -0.894548032657517443
! 597: 62901306471557966872 + 0.53414854617473272670874609150394379949*I]~], [[Mod(
! 598: 1, y^3 - y - 1), Mod(1, y^3 - y - 1)*x, Mod(1, y^3 - y - 1)*x^2, Mod(1, y^3
! 599: - y - 1)*x^3, Mod(1, y^3 - y - 1)*x^4], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,
! 600: 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0,
! 601: 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [Mod(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod
! 602: (1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1, y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1,
! 603: y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^3 - y - 1)], [], [y^3 - y - 1, [1, 1],
! 604: -23, 1, [[1, 1.3247179572447460259609088544780973407, 1.7548776662466927600
! 605: 495088963585286918; 1, -0.66235897862237301298045442723904867036 + 0.5622795
! 606: 1206230124389918214490937306149*I, 0.12256116687665361997524555182073565405
! 607: - 0.74486176661974423659317042860439236724*I], [1, 2; 1.32471795724474602596
! 608: 09088544780973407, -1.3247179572447460259609088544780973407 - 1.124559024124
! 609: 6024877983642898187461229*I; 1.7548776662466927600495088963585286918, 0.2451
! 610: 2233375330723995049110364147130810 + 1.4897235332394884731863408572087847344
! 611: *I], [3, 0.E-96, 2.0000000000000000000000000000000000000; 0.E-96, 3.26463299
! 612: 87400782801485266890755860756, 1.3247179572447460259609088544780973407; 2.00
! 613: 00000000000000000000000000000000000, 1.3247179572447460259609088544780973407
! 614: , 4.2192762054875453178332176670757633303], [3, 0, 2; 0, 2, 3; 2, 3, 2], [23
! 615: , 13, 15; 0, 1, 0; 0, 0, 1], [-5, 6, -4; 6, 2, -9; -4, -9, 6], [23, [7, 10,
! 616: 1]~, 529]], [1.3247179572447460259609088544780973407, -0.6623589786223730129
! 617: 8045442723904867036 + 0.56227951206230124389918214490937306149*I], [1, y, y^
! 618: 2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0, 1, 0; 0, 1, 0, 1, 0,
! 619: 1, 0, 1, 1; 0, 0, 1, 0, 1, 0, 1, 0, 1]], [x^15 - 5*x^13 + 5*x^12 + 7*x^11 -
! 620: 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 +
! 621: 144*x^2 + 25*x + 1, Mod(39516536165538345/83718587879473471*x^14 - 650051247
! 622: 6832995/83718587879473471*x^13 - 196215472046117185/83718587879473471*x^12 +
! 623: 229902227480108910/83718587879473471*x^11 + 237380704030959181/837185878794
! 624: 73471*x^10 - 1064931988160773805/83718587879473471*x^9 - 20657086671714300/8
! 625: 3718587879473471*x^8 + 1772885205999206010/83718587879473471*x^7 + 595203321
! 626: 7241102348/83718587879473471*x^6 - 4838840187320655696/83718587879473471*x^5
! 627: + 5180390720553188700/83718587879473471*x^4 - 8374015687535120430/837185878
! 628: 79473471*x^3 + 8907744727915040221/83718587879473471*x^2 + 41559766641234343
! 629: 81/83718587879473471*x + 318920215718580450/83718587879473471, x^15 - 5*x^13
! 630: + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 -
! 631: 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), -1, [1, x, x^2, x^3, x^4, x^5, x^6
! 632: , x^7, x^8, x^9, x^10, x^11, x^12, x^13, 1/83718587879473471*x^14 - 20528463
! 633: 024680133/83718587879473471*x^13 - 4742392948888610/83718587879473471*x^12 -
! 634: 9983523646123358/83718587879473471*x^11 + 40898955597139011/837185878794734
! 635: 71*x^10 + 29412692423971937/83718587879473471*x^9 - 5017479463612351/8371858
! 636: 7879473471*x^8 + 41014993230075066/83718587879473471*x^7 - 2712810874903165/
! 637: 83718587879473471*x^6 + 20152905879672878/83718587879473471*x^5 + 9591643151
! 638: 927789/83718587879473471*x^4 - 8471905745957397/83718587879473471*x^3 - 1339
! 639: 5753879413605/83718587879473471*x^2 + 27623037732247492/83718587879473471*x
! 640: + 26306699661480593/83718587879473471], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
! 641: 0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -276230
! 642: 37732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13395753879413605; 0,
! 643: 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8471905745957397; 0, 0, 0, 0, 1, 0,
! 644: 0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
! 645: 0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 27128
! 646: 10874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -41014993230075066; 0
! 647: , 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5017479463612351; 0, 0, 0, 0, 0, 0,
! 648: 0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
! 649: , 0, 0, 0, -40898955597139011; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 998
! 650: 3523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4742392948888610; 0
! 651: , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20528463024680133; 0, 0, 0, 0, 0, 0
! 652: , 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471]]]
! 653: ? bnfcertify(bnf)
! 654: 1
! 655: ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
! 656:
! 657: [x^4 - 7]
! 658:
! 659: [[2, 1]]
! 660:
! 661: [[-87808, 1]]
! 662:
! 663: [[1, x, x^2, x^3]]
! 664:
! 665: [[2, [2], [[2, 1, 1, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
! 666:
! 667: [14.229975145405511722395637833443108790]
! 668:
! 669: [1.1211171071527562299744232290000000000]
! 670:
! 671: ? setrand(1);bnfclassunit(x^2-x-100000)
! 672: *** Warning: fundamental units too large, not given.
! 673:
! 674: [x^2 - x - 100000]
! 675:
! 676: [[2, 0]]
! 677:
! 678: [[400001, 1]]
! 679:
! 680: [[1, x]]
! 681:
! 682: [[5, [5], [[2, 1; 0, 1]]]]
! 683:
! 684: [129.82045011403975460991182396195022419]
! 685:
! 686: [0.98765369790690472391212970100000000000]
! 687:
! 688: [[2, -1]]
! 689:
! 690: [[;]]
! 691:
! 692: [0]
! 693:
! 694: ? setrand(1);bnfclassunit(x^2-x-100000,1)
! 695:
! 696: [x^2 - x - 100000]
! 697:
! 698: [[2, 0]]
! 699:
! 700: [[400001, 1]]
! 701:
! 702: [[1, x]]
! 703:
! 704: [[5, [5], [[2, 1; 0, 1]]]]
! 705:
! 706: [129.82045011403975460991182396195022419]
! 707:
! 708: [0.98765369790690472391212970100000000000]
! 709:
! 710: [[2, -1]]
! 711:
! 712: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
! 713: 789990462835950022871665178127611316131167]]
! 714:
! 715: [185]
! 716:
! 717: ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
! 718:
! 719: [x^4 + 24*x^2 + 585*x + 1791]
! 720:
! 721: [[0, 2]]
! 722:
! 723: [[18981, 3087]]
! 724:
! 725: [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]
! 726:
! 727: [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
! 728:
! 729: [3.7941269688216589341408274220859400302]
! 730:
! 731: [0.88260182866555813061644128400000000000]
! 732:
! 733: [[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]]
! 734:
! 735: [[4/1029*x^3 + 53/1029*x^2 + 66/343*x + 111/343]]
! 736:
! 737: [140]
! 738:
! 739: ? setrand(1);bnfclgp(17)
! 740: [1, [], []]
! 741: ? setrand(1);bnfclgp(-31)
! 742: [3, [3], [Qfb(2, 1, 4)]]
! 743: ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791)
! 744: [4, [4], [[7, 5, 1, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]
! 745: ? bnrconductor(bnf,[[25,13;0,1],[1,1]])
! 746: [[5, 3; 0, 1], [1, 0]]
! 747: ? bnrconductorofchar(bnr,[2])
! 748: [[5, 3; 0, 1], [0, 0]]
! 749: ? bnfisprincipal(bnf,[5,1;0,1],0)
! 750: [1]~
! 751: ? bnfisprincipal(bnf,[5,1;0,1])
! 752: [[1]~, [2, 1/3]~, 151]
! 753: ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
! 754: [-4, Mod(1, 2)]~
! 755: ? \p19
! 756: realprecision = 19 significant digits
! 757: ? bnfmake(sbnf)
! 758: [Mat(2), Mat([0, 1, 1, 1, 0, 1, 1, 1]), [1.173637103435061715 + 3.1415926535
! 759: 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
! 760: 76049 + 3.141592653589793238*I, 1.420330600779487358 + 3.141592653589793238*
! 761: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161, -1.99
! 762: 0056445584799713 + 3.141592653589793238*I, 0.5404006376129469727, -0.6926391
! 763: 142471042845 + 3.141592653589793238*I, 0.E-96, 0.004375616572659815402 + 3.1
! 764: 41592653589793238*I, 0.3677262014027817705 + 3.141592653589793238*I, -0.8305
! 765: 625946607188639 + 3.141592653589793238*I, -1.977791147836553953 + 3.14159265
! 766: 3589793238*I; 0.6716827432867392935, 0.5379005671092853266, -0.8333219883742
! 767: 404172, -0.2461086674077943078, 0.E-96, -0.8738318043071131265, 0.9729063188
! 768: 316092378, -1.552661549868775853, 0.5774919091398324092 + 3.1415926535897932
! 769: 38*I; -1.918029732621558454 + 3.141592653589793238*I, 1.452155878475514386,
! 770: 0.2929213507612934444 + 3.141592653589793238*I, 0.9387477816548985923, 0.E-9
! 771: 6, 0.8694561877344533111, -1.340632520234391008, 2.383224144529494717, 1.400
! 772: 299238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]
! 773: ~], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~],
! 774: [5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [11,
! 775: [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [23, [-10, 1, 0]~, 1, 1, [7, 9, 1]~], [13,
! 776: [19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1,
! 777: 2, 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.2
! 778: 33732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.00515
! 779: 8616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1;
! 780: -3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.457
! 781: 02714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.000000
! 782: 000000000000, 29.00000000000000000; 1.000000000000000000, 29.000000000000000
! 783: 00, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.00
! 784: 00000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0,
! 785: 1, 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889,
! 786: [1890, 5190, 1]~, 118570321]], [-3.233732695981516673, -0.071823509027436363
! 787: 44, 4.305556205008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,
! 788: 0, 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 1
! 789: 5]], [[2, [2], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.00000
! 790: 0000000000000, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), Mat(1), [[[3, 2,
! 791: 2; 0, 1, 0; 0, 0, 1], [0, 0, 0]]]], 0]
! 792: ? \p38
! 793: realprecision = 38 significant digits
! 794: ? bnfnarrow(bnf)
! 795: [3, [3], [[3, 2; 0, 1]]]
! 796: ? bnfreg(x^2-x-57)
! 797: 2.7124653051843439746808795106061300699
! 798: ? bnfsignunit(bnf)
! 799:
! 800: [-1]
! 801:
! 802: [1]
! 803:
! 804: ? bnfunit(bnf)
! 805: [[x + 7], 162]
! 806: ? bnrclass(bnf,[[5,3;0,1],[1,0]])
! 807: [12, [12], [[3, 2; 0, 1]]]
! 808: ? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2)
! 809: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
! 810: 061300699 - 9.4247779607693797153879301498385086526*I; 2.7124653051843439746
! 811: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [23347.9792
! 812: 23478346319454659159707591731 + 6.2831853071795864769252867665590057684*I, 8
! 813: 66.56619430687100142570357249059499540 + 6.283185307179586476925286766559005
! 814: 7684*I, 2881.3396396084587293295626563644245032 + 3.141592653589793238462643
! 815: 3832795028842*I, 27379.624790530768080428797780058276925 + 2.088097429759527
! 816: 8484866027080000000000 E-52*I, 57933.334567930851067108050790839116749 + 3.5
! 817: 497656305911973423188043860000000000 E-52*I, -34585.556250151557719998034043
! 818: 918848670 + 9.4247779607693797153879301498385086526*I, 23348.322511122623346
! 819: 549049047574325150 + 3.1415926535897932384626433832795028842*I, -0.343287644
! 820: 27702709438988786673341921876 + 3.1415926535897932384626433832795028842*I, -
! 821: 4031.7117453543045067063239888430083582 + 9.42477796076937971538793014983850
! 822: 86526*I, 27379.690968832650826160983148550600089 + 9.42477796076937971538793
! 823: 01498385086526*I; -23347.979223478346319454659159707591731 + 9.4247779607693
! 824: 797153879301498385086526*I, -866.56619430687100142570357249059499540 + 8.156
! 825: 6305849981556577374397490000000000 E-55*I, -2881.339639608458729329562656364
! 826: 4245032 + 9.4247779607693797153879301498385086526*I, -27379.6247905307680804
! 827: 28797780058276925 + 6.2831853071795864769252867665590057684*I, -57933.334567
! 828: 930851067108050790839116749 + 3.1415926535897932384626433832795028842*I, 345
! 829: 85.556250151557719998034043918848670 + 6.28318530717958647692528676655900576
! 830: 84*I, -23348.322511122623346549049047574325150 + 9.4247779607693797153879301
! 831: 498385086526*I, 0.34328764427702709438988786673341921876 + 0.E-57*I, 4031.71
! 832: 17453543045067063239888430083582 + 3.1415926535897932384626433832795028842*I
! 833: , -27379.690968832650826160983148550600089 + 6.28318530717958647692528676655
! 834: 90057684*I], [[3, [-1, 1]~, 1, 1, [0, 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5
! 835: , [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1,
! 836: 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [
! 837: 17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1
! 838: , 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, 8, 10, 9]~, [x^2 - x - 57, [2, 0], 2
! 839: 29, 1, [[1, -7.0663729752107779635959310246705326058; 1, 8.06637297521077796
! 840: 35959310246705326058], [1, 1; -7.0663729752107779635959310246705326058, 8.06
! 841: 63729752107779635959310246705326058], [2, 1.00000000000000000000000000000000
! 842: 00000; 1.0000000000000000000000000000000000000, 115.000000000000000000000000
! 843: 00000000000], [2, 1; 1, 115], [229, 114; 0, 1], [115, -1; -1, 2], [229, [114
! 844: , 1]~, 229]], [-7.0663729752107779635959310246705326058, 8.06637297521077796
! 845: 35959310246705326058], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3
! 846: , [3], [[3, 2; 0, 1]]], 2.7124653051843439746808795106061300699, 0.881442251
! 847: 26545793690341704100000000000, [2, -1], [x + 7], 162], [Mat(1), Mat(1), [[[3
! 848: , 2; 0, 1], [0, 0]]]], 0], [[[25, 13; 0, 1], [1, 1]], [80, [20, 2, 2], [[2,
! 849: 0]~, [0, -2]~, [2, 2]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]~], 2]), [[[[4], [[
! 850: 2, 0]~], [[2, 0]~], [[Mod(0, 2), Mod(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~
! 851: ], [[Mod(0, 2), Mod(0, 2)]~], Mat([1/5, -13/5])]], [[2, 2], [[0, -2]~, [2, 2
! 852: ]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [[1, 0]~], [1,
! 853: -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0], [12, [12], [[3, 2; 0, 1]]],
! 854: [[1/2, 5, -9; -1/2, -5, 10], [-2, 0; 0, 10]]]
! 855: ? bnrclassno(bnf,[[5,3;0,1],[1,0]])
! 856: 12
! 857: ? lu=ideallist(bnf,55,3);
! 858: ? bnrclassnolist(bnf,lu)
! 859: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
! 860: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
! 861: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
! 862: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
! 863: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
! 864: ? bnrdisc(bnr,Mat(6))
! 865: [12, 12, 18026977100265125]
! 866: ? bnrdisc(bnr)
! 867: [24, 12, 40621487921685401825918161408203125]
! 868: ? bnrdisc(bnr2,,,2)
! 869: 0
! 870: ? bnrdisc(bnr,Mat(6),,1)
! 871: [6, 2, [125, 13; 0, 1]]
! 872: ? bnrdisc(bnr,,,1)
! 873: [12, 1, [1953125, 1160888; 0, 1]]
! 874: ? bnrdisc(bnr2,,,3)
! 875: 0
! 876: ? bnrdisclist(bnf,lu)
! 877: [[[6, 6, Mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
! 878: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
! 879: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
! 880: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
! 881: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
! 882: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
! 883: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
! 884: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
! 885: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
! 886: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
! 887: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
! 888: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
! 889: , []]]
! 890: ? bnrdisclist(bnf,20,,1)
! 891: [[[[matrix(0,2), [[6, 6, Mat([229, 3])], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]],
! 892: [], [[Mat([12, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [3, 3; 229, 6
! 893: ]]]], [Mat([13, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1, 1; 3, 3; 229, 6]],
! 894: [0, 0, 0]]]], [[Mat([10, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]
! 895: , [[Mat([20, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [0, 0, 0], [24, 0, [
! 896: 5, 9; 229, 12]]]], [Mat([21, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [24,
! 897: 12, [5, 9; 229, 12]], [0, 0, 0]]]], [], [], [], [[Mat([12, 2]), [[0, 0, 0],
! 898: [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1], [[0, 0, 0], [12, 6, [-1
! 899: , 1; 3, 6; 229, 6]], [0, 0, 0], [24, 0, [3, 12; 229, 12]]]], [Mat([13, 2]),
! 900: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([44, 1]), [[0, 0,
! 901: 0], [0, 0, 0], [12, 6, [-1, 1; 11, 3; 229, 6]], [0, 0, 0]]], [Mat([45, 1]),
! 902: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [11, 3; 229, 6]]]]], [[[10, 1; 12,
! 903: 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 13, 1], [[0, 0,
! 904: 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [], [[[12, 1; 20, 1], [[24, 24,
! 905: [3, 6; 5, 9; 229, 12]], [0, 0, 0], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 2
! 906: 4]]]], [[13, 1; 20, 1], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [24, 12
! 907: , [3, 6; 5, 6; 229, 12]], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1
! 908: ], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 0, [3, 12; 5
! 909: , 18; 229, 24]]]], [[13, 1; 21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0,
! 910: 0], [48, 24, [3, 12; 5, 18; 229, 24]], [0, 0, 0]]]], [[Mat([10, 2]), [[0, 0
! 911: , 0], [12, 6, [-1, 1; 2, 12; 229, 6]], [12, 6, [-1, 1; 2, 12; 229, 6]], [24,
! 912: 0, [2, 36; 229, 12]]]]], [[Mat([68, 1]), [[0, 0, 0], [12, 6, [-1, 1; 17, 3;
! 913: 229, 6]], [0, 0, 0], [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [12, 6, [-1, 1
! 914: ; 17, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [1
! 915: 9, 6; 229, 9]], [0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77
! 916: , 1]), [[18, 18, [19, 6; 229, 9]], [0, 0, 0], [36, 18, [-1, 1; 19, 15; 229,
! 917: 18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0,
! 918: 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]]
! 919: ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
! 920: [[9]~, [-2170/6561, -931/19683]~, 148]
! 921: ? dirzetak(nf4,30)
! 922: [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,
! 923: 0, 1, 0, 1, 0]
! 924: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
! 925:
! 926: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t, t^3 + t^2 - 2*t - 1) 1]
! 927:
! 928: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
! 929:
! 930: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
! 931:
! 932: ? vp=idealprimedec(nf,3)[1]
! 933: [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
! 934: ? idx=idealmul(nf,matid(5),vp)
! 935:
! 936: [3 1 2 2 2]
! 937:
! 938: [0 1 0 0 0]
! 939:
! 940: [0 0 1 0 0]
! 941:
! 942: [0 0 0 1 0]
! 943:
! 944: [0 0 0 0 1]
! 945:
! 946: ? idealinv(nf,idx)
! 947:
! 948: [1 0 2/3 0 0]
! 949:
! 950: [0 1 1/3 0 0]
! 951:
! 952: [0 0 1/3 0 0]
! 953:
! 954: [0 0 0 1 0]
! 955:
! 956: [0 0 0 0 1]
! 957:
! 958: ? idy=idealred(nf,idx,[1,5,6])
! 959:
! 960: [5 0 0 2 0]
! 961:
! 962: [0 5 0 0 0]
! 963:
! 964: [0 0 5 2 0]
! 965:
! 966: [0 0 0 1 0]
! 967:
! 968: [0 0 0 0 5]
! 969:
! 970: ? idx2=idealmul(nf,idx,idx)
! 971:
! 972: [9 7 5 8 2]
! 973:
! 974: [0 1 0 0 0]
! 975:
! 976: [0 0 1 0 0]
! 977:
! 978: [0 0 0 1 0]
! 979:
! 980: [0 0 0 0 1]
! 981:
! 982: ? idt=idealmul(nf,idx,idx,1)
! 983:
! 984: [2 0 0 0 1]
! 985:
! 986: [0 2 0 0 1]
! 987:
! 988: [0 0 2 0 0]
! 989:
! 990: [0 0 0 2 1]
! 991:
! 992: [0 0 0 0 1]
! 993:
! 994: ? idz=idealintersect(nf,idx,idy)
! 995:
! 996: [15 5 10 12 10]
! 997:
! 998: [0 5 0 0 0]
! 999:
! 1000: [0 0 5 2 0]
! 1001:
! 1002: [0 0 0 1 0]
! 1003:
! 1004: [0 0 0 0 5]
! 1005:
! 1006: ? aid=[idx,idy,idz,matid(5),idx]
! 1007: [[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
! 1008: , [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5
! 1009: ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0,
! 1010: 0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0
! 1011: , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,
! 1012: 0, 0, 1]]
! 1013: ? bid=idealstar(nf2,54,1)
! 1014: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
! 1015: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
! 1016: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
! 1017: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
! 1018: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
! 1019: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
! 1020: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
! 1021: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
! 1022: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
! 1023: ? vaid=[idx,idy,matid(5)]
! 1024: [[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
! 1025: , [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5
! 1026: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
! 1027: 1]]
! 1028: ? haid=[matid(5),matid(5),matid(5)]
! 1029: [[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]
! 1030: , [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
! 1031: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
! 1032: 1]]
! 1033: ? idealadd(nf,idx,idy)
! 1034:
! 1035: [1 0 0 0 0]
! 1036:
! 1037: [0 1 0 0 0]
! 1038:
! 1039: [0 0 1 0 0]
! 1040:
! 1041: [0 0 0 1 0]
! 1042:
! 1043: [0 0 0 0 1]
! 1044:
! 1045: ? idealaddtoone(nf,idx,idy)
! 1046: [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
! 1047: ? idealaddtoone(nf,[idy,idx])
! 1048: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
! 1049: ? idealappr(nf,idy)
! 1050: [-2, 0, -2, 4, 0]~
! 1051: ? idealappr(nf,idealfactor(nf,idy),1)
! 1052: [-2, 0, -2, 4, 0]~
! 1053: ? idealcoprime(nf,idx,idx)
! 1054: [-2/3, 2/3, -1/3, 0, 0]~
! 1055: ? idealdiv(nf,idy,idt)
! 1056:
! 1057: [5 5/2 5/2 7/2 0]
! 1058:
! 1059: [0 5/2 0 0 0]
! 1060:
! 1061: [0 0 5/2 1 0]
! 1062:
! 1063: [0 0 0 1/2 0]
! 1064:
! 1065: [0 0 0 0 5/2]
! 1066:
! 1067: ? idealdiv(nf,idx2,idx,1)
! 1068:
! 1069: [3 1 2 2 2]
! 1070:
! 1071: [0 1 0 0 0]
! 1072:
! 1073: [0 0 1 0 0]
! 1074:
! 1075: [0 0 0 1 0]
! 1076:
! 1077: [0 0 0 0 1]
! 1078:
! 1079: ? idf=idealfactor(nf,idz)
! 1080:
! 1081: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]
! 1082:
! 1083: [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]
! 1084:
! 1085: [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]
! 1086:
! 1087: ? idealhnf(nf,vp)
! 1088:
! 1089: [3 1 2 2 2]
! 1090:
! 1091: [0 1 0 0 0]
! 1092:
! 1093: [0 0 1 0 0]
! 1094:
! 1095: [0 0 0 1 0]
! 1096:
! 1097: [0 0 0 0 1]
! 1098:
! 1099: ? idealhnf(nf,vp[2],3)
! 1100:
! 1101: [3 1 2 2 2]
! 1102:
! 1103: [0 1 0 0 0]
! 1104:
! 1105: [0 0 1 0 0]
! 1106:
! 1107: [0 0 0 1 0]
! 1108:
! 1109: [0 0 0 0 1]
! 1110:
! 1111: ? ideallist(bnf,20)
! 1112: [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
! 1113: , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
! 1114: [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
! 1115: [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
! 1116: , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
! 1117: , 6; 0, 2], [10, 2; 0, 2]]]
! 1118: ? ideallog(nf2,w,bid)
! 1119: [1574, 8, 6]~
! 1120: ? idealmin(nf,idx,[1,2,3,4,5])
! 1121: [[-1; 0; 0; 1; 0], [2.0885812311199768913287869744681966008 + 3.141592653589
! 1122: 7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244
! 1123: 7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160
! 1124: 203 + 2.5437460822678889883600220330800078854*I]]
! 1125: ? idealnorm(nf,idt)
! 1126: 16
! 1127: ? idp=idealpow(nf,idx,7)
! 1128:
! 1129: [2187 1807 2129 692 1379]
! 1130:
! 1131: [0 1 0 0 0]
! 1132:
! 1133: [0 0 1 0 0]
! 1134:
! 1135: [0 0 0 1 0]
! 1136:
! 1137: [0 0 0 0 1]
! 1138:
! 1139: ? idealpow(nf,idx,7,1)
! 1140:
! 1141: [2 0 0 0 1]
! 1142:
! 1143: [0 2 0 0 1]
! 1144:
! 1145: [0 0 2 0 0]
! 1146:
! 1147: [0 0 0 2 1]
! 1148:
! 1149: [0 0 0 0 1]
! 1150:
! 1151: ? idealprimedec(nf,2)
! 1152: [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,
! 1153: 4, [1, 1, 0, 0, 0]~]]
! 1154: ? idealprimedec(nf,3)
! 1155: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,
! 1156: 2, [1, 2, 3, 1, 0]~]]
! 1157: ? idealprimedec(nf,11)
! 1158: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
! 1159: ? idealprincipal(nf,Mod(x^3+5,nfpol))
! 1160:
! 1161: [6]
! 1162:
! 1163: [0]
! 1164:
! 1165: [1]
! 1166:
! 1167: [3]
! 1168:
! 1169: [0]
! 1170:
! 1171: ? idealtwoelt(nf,idy)
! 1172: [5, [2, 0, 2, 1, 0]~]
! 1173: ? idealtwoelt(nf,idy,10)
! 1174: [-2, 0, -2, -1, 0]~
! 1175: ? idealstar(nf2,54)
! 1176: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
! 1177: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
! 1178: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
! 1179: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
! 1180: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
! 1181: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
! 1182: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
! 1183: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
! 1184: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
! 1185: ? idealval(nf,idp,vp)
! 1186: 7
! 1187: ? ideleprincipal(nf,Mod(x^3+5,nfpol))
! 1188: [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897
! 1189: 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851
! 1190: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
! 1191: - 0.0083630478144368246110910258645462996191*I]]
! 1192: ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
! 1193: [6, 0, 1, 3, 0]~
! 1194: ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
! 1195: [1, 1, 1, 3, 0]~
! 1196: ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
! 1197:
! 1198: [[0, 1, 1, 0, 0]~]
! 1199:
! 1200: [[1, 0, 1, 0, 0]~]
! 1201:
! 1202: ? matbasistoalg(nf,bc)
! 1203:
! 1204: [Mod(x^2 + x, x^5 - 5*x^3 + 5*x + 25)]
! 1205:
! 1206: [Mod(x^2 + 1, x^5 - 5*x^3 + 5*x + 25)]
! 1207:
! 1208: ? nfbasis(x^3+4*x+5)
! 1209: [1, x, 1/7*x^2 - 1/7*x - 2/7]
! 1210: ? nfbasis(x^3+4*x+5,2)
! 1211: [1, x, 1/7*x^2 - 1/7*x - 2/7]
! 1212: ? nfbasis(x^3+4*x+12,1)
! 1213: [1, x, 1/2*x^2]
! 1214: ? nfbasistoalg(nf,ba)
! 1215: Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
! 1216: ? nfbasis(p2,0,fa)
! 1217: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
! 1218: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
! 1219: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
! 1220: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
! 1221: ? da=nfdetint(nf,[a,aid])
! 1222:
! 1223: [30 5 25 27 10]
! 1224:
! 1225: [0 5 0 0 0]
! 1226:
! 1227: [0 0 5 2 0]
! 1228:
! 1229: [0 0 0 1 0]
! 1230:
! 1231: [0 0 0 0 5]
! 1232:
! 1233: ? nfdisc(x^3+4*x+12)
! 1234: -1036
! 1235: ? nfdisc(x^3+4*x+12,1)
! 1236: -1036
! 1237: ? nfdisc(p2,0,fa)
! 1238: 136866601
! 1239: ? nfeltdiv(nf,ba,bb)
! 1240: [755/373, -152/373, 159/373, 120/373, -264/373]~
! 1241: ? nfeltdiveuc(nf,ba,bb)
! 1242: [2, 0, 0, 0, -1]~
! 1243: ? nfeltdivrem(nf,ba,bb)
! 1244: [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
! 1245: ? nfeltmod(nf,ba,bb)
! 1246: [-12, -7, 0, 9, 5]~
! 1247: ? nfeltmul(nf,ba,bb)
! 1248: [-25, -50, -30, 15, 90]~
! 1249: ? nfeltpow(nf,bb,5)
! 1250: [23455, 156370, 115855, 74190, -294375]~
! 1251: ? nfeltreduce(nf,ba,idx)
! 1252: [1, 0, 0, 0, 0]~
! 1253: ? nfeltval(nf,ba,vp)
! 1254: 0
! 1255: ? nffactor(nf2,x^3+x)
! 1256:
! 1257: [Mod(1, y^3 - y - 1)*x 1]
! 1258:
! 1259: [Mod(1, y^3 - y - 1)*x^2 + Mod(1, y^3 - y - 1) 1]
! 1260:
! 1261: ? aut=nfgaloisconj(nf3)
! 1262: [x, 1/12*x^4 - 1/2*x, -1/12*x^4 - 1/2*x, 1/12*x^4 + 1/2*x, -1/12*x^4 + 1/2*x
! 1263: , -x]~
! 1264: ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
! 1265: Mod(1/2*x^5 - 9*x^2, x^6 + 108)
! 1266: ? nfhilbert(nf,3,5)
! 1267: -1
! 1268: ? nfhilbert(nf,3,5,idf[1,1])
! 1269: -1
! 1270: ? nfhnf(nf,[a,aid])
! 1271: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
! 1272: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
! 1273: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
! 1274: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1275: 0, 0, 0, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1276: 0, 0, 0, 0, 1]]]
! 1277: ? nfhnfmod(nf,[a,aid],da)
! 1278: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
! 1279: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
! 1280: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
! 1281: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1282: 0, 0, 0, 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1283: 0, 0, 0, 0, 1]]]
! 1284: ? nfisideal(bnf[7],[5,1;0,1])
! 1285: 1
! 1286: ? nfisincl(x^2+1,x^4+1)
! 1287: [-x^2, x^2]
! 1288: ? nfisincl(x^2+1,nfinit(x^4+1))
! 1289: [-x^2, x^2]
! 1290: ? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
! 1291: [x, -x^2 - x + 1, x^2 - 2]
! 1292: ? nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30))
! 1293: [-1/25*x^2 + 13/25*x - 2/5]
! 1294: ? nfroots(nf2,x+2)
! 1295: [Mod(-2, y^3 - y - 1)]
! 1296: ? nfrootsof1(nf)
! 1297: [2, [-1, 0, 0, 0, 0]~]
! 1298: ? nfsnf(nf,[as,haid,vaid])
! 1299: [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3
! 1300: 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0;
! 1301: 0, 0, 0, 1, 0; 0, 0, 0, 0, 5], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0
! 1302: ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0,
! 1303: 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
! 1304: ? nfsubfields(nf)
! 1305: [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]]
! 1306: ? polcompositum(x^4-4*x+2,x^3-x-1)
! 1307: [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
! 1308: ^2 - 128*x - 5]~
! 1309: ? polcompositum(x^4-4*x+2,x^3-x-1,1)
! 1310: [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
! 1311: x^2 - 128*x - 5, Mod(-279140305176/29063006931199*x^11 + 129916611552/290630
! 1312: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
! 1313: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
! 1314: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
! 1315: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
! 1316: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
! 1317: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), M
! 1318: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
! 1319: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
! 1320: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
! 1321: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
! 1322: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
! 1323: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
! 1324: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
! 1325: ? polgalois(x^6-3*x^2-1)
! 1326: [12, 1, 1]
! 1327: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
! 1328: [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
! 1329: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
! 1330: ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
! 1331:
! 1332: [1 x - 1]
! 1333:
! 1334: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
! 1335:
! 1336: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
! 1337:
! 1338: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
! 1339:
! 1340: ? polred(x^4+576,1)
! 1341: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
! 1342: ? polred(x^4+576,3)
! 1343:
! 1344: [1 x - 1]
! 1345:
! 1346: [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
! 1347:
! 1348: [-1/24*x^2 x^2 + 1]
! 1349:
! 1350: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
! 1351:
! 1352: ? polred(p2,0,fa)
! 1353: [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
! 1354: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
! 1355: *x^3 - 197*x^2 - 273*x - 127]
! 1356: ? polred(p2,1,fa)
! 1357: [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
! 1358: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
! 1359: *x^3 - 197*x^2 - 273*x - 127]
! 1360: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
! 1361: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
! 1362: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
! 1363: [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 -
! 1364: x^4 + 2*x^3 - 4*x^2 + x - 1)]
! 1365: ? polredord(x^3-12*x+45*x-1)
! 1366: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
! 1367: ? polsubcyclo(31,5)
! 1368: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
! 1369: ? setrand(1);poltschirnhaus(x^5-x-1)
! 1370: x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289
! 1371: ? aa=rnfpseudobasis(nf2,p)
! 1372: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
! 1373: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
! 1374: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
! 1375: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
! 1376: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
! 1377: , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25;
! 1378: 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1
! 1379: 280, 5, 5]~]
! 1380: ? rnfbasis(bnf2,aa)
! 1381:
! 1382: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/5, -4/5, -2/5]~ [187/25, 208/25, -61/25
! 1383: ]~]
! 1384:
! 1385: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-4/5, 4/5, 2/5]~ [-196/25, -214/25, 88/25
! 1386: ]~]
! 1387:
! 1388: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-2/5, 2/5, 1/5]~ [-122/25, -123/25, 116/2
! 1389: 5]~]
! 1390:
! 1391: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, 1/5]~ [-104/25, -111/25, 62/25
! 1392: ]~]
! 1393:
! 1394: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/25, -2/25, 9/25]~]
! 1395:
! 1396: ? rnfdisc(nf2,p)
! 1397: [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
! 1398: ? rnfequation(nf2,p)
! 1399: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
! 1400: ? rnfequation(nf2,p,1)
! 1401: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, Mod(-x^5 + 5*x, x^15 - 1
! 1402: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
! 1403: ? rnfhnfbasis(bnf2,aa)
! 1404:
! 1405: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~
! 1406: ]
! 1407:
! 1408: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]
! 1409:
! 1410: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]
! 1411:
! 1412: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~]
! 1413:
! 1414: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]
! 1415:
! 1416: ? rnfisfree(bnf2,aa)
! 1417: 1
! 1418: ? rnfsteinitz(nf2,aa)
! 1419: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [4/5, -4/5, -2/5]~, [39/125, 11/125, 1
! 1420: 1/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-4/5, 4/5, 2/5]~, [-42/125, -8
! 1421: /125, -8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [-2/5, 2/5, 1/5]~, [-29/
! 1422: 125, 4/125, 4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2/5, 2/5, 1/5]~,
! 1423: [-23/125, -2/125, -2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~,
! 1424: [-1/125, 1/125, 1/125]~], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0
! 1425: , 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0,
! 1426: 108; 0, 125, 22; 0, 0, 1]], [416134375, 212940625, 388649575; 0, 3125, 550;
! 1427: 0, 0, 25], [-1280, 5, 5]~]
! 1428: ? nfz=zetakinit(x^2-2);
! 1429: ? zetak(nfz,-3)
! 1430: 0.091666666666666666666666666666666666666
! 1431: ? zetak(nfz,1.5+3*I)
! 1432: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
! 1433: 7938845*I
! 1434: ? setrand(1);quadclassunit(1-10^7,,[1,1])
! 1435: *** Warning: not a fundamental discriminant in quadclassunit.
! 1436: [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99984980
! 1437: 753776002339750644800000000000]
! 1438: ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
! 1439: [4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
! 1440: 5514, 0.99903694589643832327024650000000000000]
! 1441: ? sizebyte(%)
! 1442: 328
! 1443: ? getheap
! 1444: [197, 120501]
! 1445: ? print("Total time spent: ",gettime);
! 1446: Total time spent: 6424
! 1447: ? \q
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