Annotation of OpenXM_contrib/pari-2.2/src/test/64/nfields, Revision 1.1
1.1 ! noro 1: echo = 1 (on)
! 2: ? nfpol=x^5-5*x^3+5*x+25
! 3: x^5 - 5*x^3 + 5*x + 25
! 4: ? qpol=y^3-y-1;un=Mod(1,qpol);w=Mod(y,qpol);p=un*(x^5-5*x+w)
! 5: Mod(1, y^3 - y - 1)*x^5 + Mod(-5, y^3 - y - 1)*x + Mod(y, y^3 - y - 1)
! 6: ? p2=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
! 7: x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 385389051407
! 8: 2057
! 9: ? fa=[11699,6;2392997,2;4987333019653,2]
! 10:
! 11: [11699 6]
! 12:
! 13: [2392997 2]
! 14:
! 15: [4987333019653 2]
! 16:
! 17: ? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8));
! 18: ? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8));
! 19: ? nf=nfinit(nfpol)
! 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: 2666710 E-76, 19.488486013650707197449403270536023970, 4.1504592246706085588
! 47: 902013976045703227; 10.000000000000000000000000000000000000, 2.0726804532226
! 48: 66710 E-76, 85.960217420851846480305133936577594605, -36.0342682914829798382
! 49: 67056239752434596, 53.576130452511107888183080361946556763; -5.0000000000000
! 50: 000000000000000000000000, 19.488486013650707197449403270536023970, -36.03426
! 51: 8291482979838267056239752434596, 60.916248374441986300937507618575151517, -1
! 52: 8.470101750219179344070032346246890434; 7.0000000000000000000000000000000000
! 53: 000, 4.1504592246706085588902013976045703227, 53.576130452511107888183080361
! 54: 946556763, -18.470101750219179344070032346246890434, 37.97015289284236734089
! 55: 7384258599214282], [5, 0, 10, -5, 7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; -
! 56: 5, 10, -55, 45, -39; 7, -5, 20, -39, 9], [345, 0, 340, 167, 150; 0, 345, 110
! 57: , 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [132825, -18975, -
! 58: 5175, 27600, 17250; -18975, 34500, 41400, 3450, -43125; -5175, 41400, -41400
! 59: , -15525, 51750; 27600, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -86
! 60: 250], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.42851749071941860689
! 61: 92069565359418364, 1.9647119211288133163138753392090569931 + 0.8097149241889
! 62: 7895128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.3
! 63: 101462685358123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3
! 64: , 1/15*x^4 + 1/3*x^2 + 1/3*x + 1/3], [1, 0, 0, 1, -5; 0, 1, 0, 0, -5; 0, 0,
! 65: 1, 1, -5; 0, 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0
! 66: , 1, -5, -5, -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0
! 67: , -2, 0, 0, 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0
! 68: , 1, 1, -2, 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1
! 69: , 0, 0, 0, 3, -1, 2, 0, 3, 0, 5, 1, 1, -1, 5, -4, 3, 0, 2, 1, 3, 1; 0, 0, 0,
! 70: 0, 1, 0, 0, 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]]
! 71: ? nf1=nfinit(nfpol,2)
! 72: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
! 73: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
! 74: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
! 75: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
! 76: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
! 77: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
! 78: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
! 79: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
! 80: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
! 81: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
! 82: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
! 83: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
! 84: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
! 85: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
! 86: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
! 87: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
! 88: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
! 89: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
! 90: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
! 91: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
! 92: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
! 93: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
! 94: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
! 95: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
! 96: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
! 97: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
! 98: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
! 99: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
! 100: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
! 101: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
! 102: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
! 103: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
! 104: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
! 105: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
! 106: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
! 107: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
! 108: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
! 109: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
! 110: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
! 111: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
! 112: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
! 113: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
! 114: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
! 115: 0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504
! 116: 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359
! 117: 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1,
! 118: x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1,
! 119: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0,
! 120: 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
! 121: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14;
! 122: 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
! 123: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -
! 124: 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3
! 125: , 4, -4, 1, 2, 1, -4, -21]]
! 126: ? nfinit(nfpol,3)
! 127: [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
! 128: 57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5
! 129: 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894
! 130: 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975
! 131: 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602
! 132: 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +
! 133: 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835
! 134: 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431
! 135: 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703
! 136: 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*
! 137: I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301
! 138: 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354
! 139: 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,
! 140: -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294
! 141: 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459
! 142: 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821
! 143: 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2
! 144: .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927
! 145: 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753
! 146: 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573
! 147: 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1
! 148: 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052
! 149: 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346
! 150: 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000
! 151: 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17
! 152: .000000000000000000000000000000000000, -44.000000000000000000000000000000000
! 153: 000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471
! 154: 283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499
! 155: 932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000
! 156: 00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912
! 157: 62388960975827806174040462368, 143.93295090847353519436673793501057176, -55.
! 158: 842564718082452641322500190813370023; -17.0000000000000000000000000000000000
! 159: 00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935
! 160: 01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201
! 161: 80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084
! 162: 1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400
! 163: 38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
! 164: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -
! 165: 101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215
! 166: , 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125,
! 167: -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670
! 168: 0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89
! 169: 700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725
! 170: , 0]~]], [-1.0891151457205048250249527946671612684, -0.138383720734060363650
! 171: 47976417441696637 + 0.49181637657768643499753285514741525107*I, 1.6829412935
! 172: 943127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1
! 173: , x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1,
! 174: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0
! 175: , 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
! 176: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14
! 177: ; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
! 178: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9,
! 179: -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1,
! 180: 3, 4, -4, 1, 2, 1, -4, -21]], Mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2*x + 1, x^
! 181: 5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
! 182: ? nfinit(nfpol,4)
! 183: [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
! 184: 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59
! 185: 741050929194782733001765987770358483, 0.158944197453903762065494816710718942
! 186: 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
! 187: 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021
! 188: 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0
! 189: .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357
! 190: 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312
! 191: 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035
! 192: 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I
! 193: , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013
! 194: 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544
! 195: 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -
! 196: 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948
! 197: 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594
! 198: 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211
! 199: 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.
! 200: 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274
! 201: 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539
! 202: 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732
! 203: 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15
! 204: 894419745390376206549481671071894289, -0.10730191731399545071859505671520521
! 205: 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468
! 206: 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000
! 207: 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.
! 208: 000000000000000000000000000000000000, -44.0000000000000000000000000000000000
! 209: 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712
! 210: 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999
! 211: 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000
! 212: 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126
! 213: 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8
! 214: 42564718082452641322500190813370023; -17.00000000000000000000000000000000000
! 215: 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350
! 216: 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018
! 217: 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841
! 218: 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003
! 219: 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,
! 220: 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1
! 221: 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,
! 222: 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -
! 223: 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700
! 224: , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897
! 225: 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,
! 226: 0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504
! 227: 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359
! 228: 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1,
! 229: x, x^2, 1/2*x^3 + 1/2*x^2 + 1/2*x, 1/2*x^4 + 1/2*x], [1, 0, 0, 0, 0; 0, 1,
! 230: 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0,
! 231: 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,
! 232: 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14;
! 233: 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,
! 234: -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -
! 235: 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3
! 236: , 4, -4, 1, 2, 1, -4, -21]]
! 237: ? nf3=nfinit(x^6+108);
! 238: ? nf4=nfinit(x^3-10*x+8)
! 239: [x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -3.50466435358804770515010852590433205
! 240: 79, 6.1413361156553641347759399165844441383; 1, 0.86464088669540302583112842
! 241: 266613688800, 0.37380193147270638662350044992137561317; 1, 2.640023466892644
! 242: 6793189801032381951699, 3.4848619528719294786005596334941802484], [1, 1, 1;
! 243: -3.5046643535880477051501085259043320579, 0.86464088669540302583112842266613
! 244: 688800, 2.6400234668926446793189801032381951699; 6.1413361156553641347759399
! 245: 165844441383, 0.37380193147270638662350044992137561317, 3.484861952871929478
! 246: 6005596334941802484], [3, -3.454467422037777850 E-77, 10.0000000000000000000
! 247: 00000000000000000; -3.454467422037777850 E-77, 20.00000000000000000000000000
! 248: 0000000000, -12.000000000000000000000000000000000000; 10.0000000000000000000
! 249: 00000000000000000, -12.000000000000000000000000000000000000, 50.000000000000
! 250: 000000000000000000000000], [3, 0, 10; 0, 20, -12; 10, -12, 50], [284, 168, 2
! 251: 35; 0, 2, 0; 0, 0, 1], [856, -120, -200; -120, 50, 36; -200, 36, 60], [568,
! 252: [-216, 90, 8]~]], [-3.5046643535880477051501085259043320579, 0.8646408866954
! 253: 0302583112842266613688800, 2.6400234668926446793189801032381951699], [1, x,
! 254: 1/2*x^2], [1, 0, 0; 0, 1, 0; 0, 0, 2], [1, 0, 0, 0, 0, -4, 0, -4, 0; 0, 1, 0
! 255: , 1, 0, 5, 0, 5, -2; 0, 0, 1, 0, 2, 0, 1, 0, 5]]
! 256: ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];
! 257: ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
! 258: [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
! 259: 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
! 260: 08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672
! 261: 2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1.
! 262: 2897619530652735025030086072395031017 + 0.E-57*I, -2.01097980249891575621226
! 263: 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590
! 264: 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376
! 265: 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I
! 266: , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983
! 267: 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538
! 268: 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653
! 269: 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0
! 270: .E-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264
! 271: 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795
! 272: 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424
! 273: 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061
! 274: 2 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.14159265358979323
! 275: 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926
! 276: 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
! 277: 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342
! 278: 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389
! 279: 88786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.14
! 280: 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334
! 281: 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1
! 282: ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~
! 283: , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1
! 284: ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1,
! 285: 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7,
! 286: 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310
! 287: 246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729
! 288: 752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2
! 289: , 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000
! 290: 000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114;
! 291: 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.066372975210777963595931024
! 292: 6705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
! 293: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746
! 294: 808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),
! 295: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846
! 296: 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071
! 297: 795864769252867665590057684*I]]], 0]
! 298: ? setrand(1);bnfinit(x^2-x-100000,1)
! 299: [Mat(5), Mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129.
! 300: 82045011403975460991182396195022419 - 6.283185307179586476925286766559005768
! 301: 4*I; 129.82045011403975460991182396195022419 - 12.56637061435917295385057353
! 302: 3118011536*I], [-41.811264589129943393339502258694361489 + 8.121413879410077
! 303: 514 E-115*I, 9.2399004147902289816376260438840931575 + 3.1415926535897932384
! 304: 626433832795028842*I, -11.874609881075406725097315997431161032 + 9.424777960
! 305: 7693797153879301498385086526*I, 389.46135034211926382973547188585067257 + 12
! 306: .566370614359172953850573533118011536*I, -440.512515346039436204712600188429
! 307: 12722 + 0.E-113*I, -324.55112528509938652477955990487556047 + 6.283185307179
! 308: 5864769252867665590057684*I, 229.70424552002497255158146166263724792 + 3.141
! 309: 5926535897932384626433832795028842*I, -785.660451862534215720251179722755983
! 310: 25 + 6.2831853071795864769252867665590057684*I, -554.35531386699327377220656
! 311: 215544062014 + 6.2831853071795864769252867665590057684*I, -47.66831907156823
! 312: 3997332918482707687879 + 9.4247779607693797153879301498385086526*I, 177.4887
! 313: 6918560798860724474244465791207 + 6.497131103528062011 E-114*I, -875.6123693
! 314: 7168080069763246690606885226 + 2.598852441411224804 E-113*I, 54.878404098312
! 315: 329644822020875673145627 + 9.4247779607693797153879301498385086526*I, -404.4
! 316: 4153844676787690336623107514389175 + 0.E-113*I, 232.809823743598178900114904
! 317: 85449930607 + 6.2831853071795864769252867665590057684*I, -668.80899963671483
! 318: 856204802764462926790 + 9.4247779607693797153879301498385086526*I, 367.35683
! 319: 481950538594888487746203445802 + 12.566370614359172953850573533118011536*I,
! 320: -1214.0716092619656173892944003952818868 + 9.4247779607693797153879301498385
! 321: 086526*I, -125.94415646756187210316334148291471657 + 6.283185307179586476925
! 322: 2867665590057684*I; 41.811264589129943393339502258694361489 + 6.283185307179
! 323: 5864769252867665590057684*I, -9.2399004147902289816376260438840931575 + 12.5
! 324: 66370614359172953850573533118011536*I, 11.8746098810754067250973159974311610
! 325: 32 + 8.121413879410077514 E-115*I, -389.46135034211926382973547188585067257
! 326: + 6.2831853071795864769252867665590057684*I, 440.512515346039436204712600188
! 327: 42912722 + 3.1415926535897932384626433832795028842*I, 324.551125285099386524
! 328: 77955990487556047 + 9.4247779607693797153879301498385086526*I, -229.70424552
! 329: 002497255158146166263724792 + 6.2831853071795864769252867665590057684*I, 785
! 330: .66045186253421572025117972275598325 + 9.42477796076937971538793014983850865
! 331: 26*I, 554.35531386699327377220656215544062014 + 3.14159265358979323846264338
! 332: 32795028842*I, 47.668319071568233997332918482707687878 + 3.14159265358979323
! 333: 84626433832795028842*I, -177.48876918560798860724474244465791207 + 6.2831853
! 334: 071795864769252867665590057684*I, 875.61236937168080069763246690606885226 +
! 335: 6.497131103528062011 E-114*I, -54.878404098312329644822020875673145627 + 9.4
! 336: 247779607693797153879301498385086526*I, 404.44153844676787690336623107514389
! 337: 175 + 9.4247779607693797153879301498385086526*I, -232.8098237435981789001149
! 338: 0485449930607 + 3.1415926535897932384626433832795028842*I, 668.8089996367148
! 339: 3856204802764462926790 + 6.2831853071795864769252867665590057684*I, -367.356
! 340: 83481950538594888487746203445803 + 3.1415926535897932384626433832795028842*I
! 341: , 1214.0716092619656173892944003952818868 + 3.141592653589793238462643383279
! 342: 5028842*I, 125.94415646756187210316334148291471657 + 6.283185307179586476925
! 343: 2867665590057684*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2, [2, 1]~, 1, 1, [1, 1]
! 344: ~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-1, 1]~], [7, [3, 1]~,
! 345: 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5, 1]~, 1, 1, [-6, 1]~]
! 346: , [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [-7, 1
! 347: ]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [-14, 1]~, 1, 1, [13
! 348: , 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~, 1, 1, [7, 1]~], [31,
! 349: [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1]~], [41, [6, 1]~, 1,
! 350: 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [15, 1]~, 1, 1, [-16, 1]
! 351: ~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18], [
! 352: x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.72816130129840161392089489603
! 353: 747004; 1, 316.72816130129840161392089489603747004], [1, 1; -315.72816130129
! 354: 840161392089489603747004, 316.72816130129840161392089489603747004], [2, 1.00
! 355: 00000000000000000000000000000000000; 1.0000000000000000000000000000000000000
! 356: , 200001.00000000000000000000000000000000], [2, 1; 1, 200001], [400001, 2000
! 357: 00; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~]], [-315.7281613012984
! 358: 0161392089489603747004, 316.72816130129840161392089489603747004], [1, x], [1
! 359: , 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.8
! 360: 2045011403975460991182396195022419, 0.9876536979069047239, [2, -1], [3795548
! 361: 84019013781006303254896369154068336082609238336*x + 119836165644250789990462
! 362: 835950022871665178127611316131167], 186], [Mat(1), [[0, 0]], [[-41.811264589
! 363: 129943393339502258694361489 + 8.121413879410077514 E-115*I, 41.8112645891299
! 364: 43393339502258694361489 + 6.2831853071795864769252867665590057684*I]]], 0]
! 365: ? \p19
! 366: realprecision = 19 significant digits
! 367: ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
! 368: [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071
! 369: 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,
! 370: 1], Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 10, 69, 33, 39,
! 371: 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, 3, -1, 2, 3, 11, 1, -
! 372: 1, -7; 1, 1, 1, 1, 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]
! 373: ? \p38
! 374: realprecision = 38 significant digits
! 375: ? bnrinit(bnf,[[5,3;0,1],[1,0]],1)
! 376: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
! 377: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 378: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
! 379: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
! 380: .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
! 381: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
! 382: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
! 383: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
! 384: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
! 385: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
! 386: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
! 387: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
! 388: 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
! 389: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
! 390: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
! 391: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
! 392: 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
! 393: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
! 394: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
! 395: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
! 396: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
! 397: 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
! 398: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
! 399: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
! 400: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
! 401: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
! 402: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
! 403: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
! 404: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
! 405: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
! 406: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
! 407: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
! 408: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
! 409: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
! 410: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
! 411: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
! 412: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),
! 413: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
! 414: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
! 415: 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1]
! 416: , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]
! 417: ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~]
! 418: , Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[
! 419: 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
! 420: ? bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2)
! 421: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
! 422: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 423: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
! 424: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
! 425: .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
! 426: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
! 427: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
! 428: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
! 429: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
! 430: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
! 431: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
! 432: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
! 433: 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
! 434: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
! 435: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
! 436: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
! 437: 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
! 438: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
! 439: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
! 440: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
! 441: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
! 442: 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
! 443: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
! 444: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
! 445: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
! 446: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
! 447: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
! 448: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
! 449: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
! 450: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
! 451: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
! 452: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
! 453: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
! 454: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
! 455: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
! 456: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
! 457: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),
! 458: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
! 459: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
! 460: 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1]
! 461: , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]
! 462: ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~]
! 463: , Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[
! 464: 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
! 465: ? rnfinit(nf2,x^5-x-2)
! 466: [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3
! 467: 109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914
! 468: 279776896412, 1.6057155120361619195949075151301679393, 2.0347118029638523119
! 469: 874445717108994866, 2.5783223055935536544757871909285592749; 1, 0.2609638803
! 470: 8645528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -1
! 471: .3177592693689352747870763902256347904 + 0.614427010164338838041906608641467
! 472: 31824*I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524
! 473: 673160314582604*I, 1.3589689411882615753626439480614001936 - 1.6193337759893
! 474: 970298359887428575174472*I; 1, -0.89454803265751744362901306471557966872 + 0
! 475: .53414854617473272670874609150394379949*I, 0.5149015133508543149896226326605
! 476: 5082078 - 0.95564306225496055080453352211847466685*I, 0.04985121658507159775
! 477: 5867063892284310224 + 1.1299025160425089918993024639913611785*I, -0.64813009
! 478: 398503840260053754352567983115 - 0.98412411795664774269323431620030610541*I]
! 479: , [1, 1.2671683045421243172528914279776896412 + 0.E-38*I, 1.6057155120361619
! 480: 195949075151301679393 + 0.E-38*I, 2.0347118029638523119874445717108994866 +
! 481: 0.E-37*I, 2.5783223055935536544757871909285592749 + 0.E-37*I; 1, 0.260963880
! 482: 38645528500256735072673484811 - 1.1772261533941944394700286585617926513*I, -
! 483: 1.3177592693689352747870763902256347904 - 0.61442701016433883804190660864146
! 484: 731824*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921652
! 485: 4673160314582604*I, 1.3589689411882615753626439480614001936 + 1.619333775989
! 486: 3970298359887428575174472*I; 1, 0.26096388038645528500256735072673484811 + 1
! 487: .1772261533941944394700286585617926513*I, -1.3177592693689352747870763902256
! 488: 347904 + 0.61442701016433883804190660864146731824*I, -1.06720711806699775374
! 489: 95893497477340535 - 1.3909574189920019216524673160314582604*I, 1.35896894118
! 490: 82615753626439480614001936 - 1.6193337759893970298359887428575174472*I; 1, -
! 491: 0.89454803265751744362901306471557966872 - 0.5341485461747327267087460915039
! 492: 4379949*I, 0.51490151335085431498962263266055082078 + 0.95564306225496055080
! 493: 453352211847466685*I, 0.049851216585071597755867063892284310224 - 1.12990251
! 494: 60425089918993024639913611785*I, -0.64813009398503840260053754352567983115 +
! 495: 0.98412411795664774269323431620030610541*I; 1, -0.8945480326575174436290130
! 496: 6471557966872 + 0.53414854617473272670874609150394379949*I, 0.51490151335085
! 497: 431498962263266055082078 - 0.95564306225496055080453352211847466685*I, 0.049
! 498: 851216585071597755867063892284310224 + 1.12990251604250899189930246399136117
! 499: 85*I, -0.64813009398503840260053754352567983115 - 0.984124117956647742693234
! 500: 31620030610541*I]], [[1, 2, 2; 1.2671683045421243172528914279776896412, 0.52
! 501: 192776077291057000513470145346969622 - 2.35445230678838887894005731712358530
! 502: 26*I, -1.7890960653150348872580261294311593374 - 1.0682970923494654534174921
! 503: 830078875989*I; 1.6057155120361619195949075151301679393, -2.6355185387378705
! 504: 495741527804512695809 - 1.2288540203286776760838132172829346364*I, 1.0298030
! 505: 267017086299792452653211016415 + 1.9112861245099211016090670442369493337*I;
! 506: 2.0347118029638523119874445717108994866, -2.13441423613399550749917869949546
! 507: 81070 + 2.7819148379840038433049346320629165208*I, 0.09970243317014319551173
! 508: 4127784568620449 - 2.2598050320850179837986049279827223571*I; 2.578322305593
! 509: 5536544757871909285592749, 2.7179378823765231507252878961228003872 + 3.23866
! 510: 75519787940596719774857150348944*I, -1.2962601879700768052010750870513596623
! 511: + 1.9682482359132954853864686324006122108*I], [1, 1, 1, 1, 1; 1.26716830454
! 512: 21243172528914279776896412 + 0.E-38*I, 0.26096388038645528500256735072673484
! 513: 811 + 1.1772261533941944394700286585617926513*I, 0.2609638803864552850025673
! 514: 5072673484811 - 1.1772261533941944394700286585617926513*I, -0.89454803265751
! 515: 744362901306471557966872 + 0.53414854617473272670874609150394379949*I, -0.89
! 516: 454803265751744362901306471557966872 - 0.53414854617473272670874609150394379
! 517: 949*I; 1.6057155120361619195949075151301679393 + 0.E-38*I, -1.31775926936893
! 518: 52747870763902256347904 + 0.61442701016433883804190660864146731824*I, -1.317
! 519: 7592693689352747870763902256347904 - 0.6144270101643388380419066086414673182
! 520: 4*I, 0.51490151335085431498962263266055082078 - 0.95564306225496055080453352
! 521: 211847466685*I, 0.51490151335085431498962263266055082078 + 0.955643062254960
! 522: 55080453352211847466685*I; 2.0347118029638523119874445717108994866 + 0.E-37*
! 523: I, -1.0672071180669977537495893497477340535 - 1.3909574189920019216524673160
! 524: 314582604*I, -1.0672071180669977537495893497477340535 + 1.390957418992001921
! 525: 6524673160314582604*I, 0.049851216585071597755867063892284310224 + 1.1299025
! 526: 160425089918993024639913611785*I, 0.049851216585071597755867063892284310224
! 527: - 1.1299025160425089918993024639913611785*I; 2.57832230559355365447578719092
! 528: 85592749 + 0.E-37*I, 1.3589689411882615753626439480614001936 - 1.61933377598
! 529: 93970298359887428575174472*I, 1.3589689411882615753626439480614001936 + 1.61
! 530: 93337759893970298359887428575174472*I, -0.6481300939850384026005375435256798
! 531: 3115 - 0.98412411795664774269323431620030610541*I, -0.6481300939850384026005
! 532: 3754352567983115 + 0.98412411795664774269323431620030610541*I]], [[5, -5.877
! 533: 471754111437539 E-39 + 3.4227493991378543323575495001314729016*I, 2.35098870
! 534: 1644575015 E-38 - 0.68243210418124342552525382695401469720*I, -2.35098870164
! 535: 4575015 E-38 - 0.52210980589898585950632970408019416371*I, 3.999999999999999
! 536: 9999999999999999999999 - 5.2069157878920895450584461181156471052*I; -5.87747
! 537: 1754111437539 E-39 - 3.4227493991378543323575495001314729016*I, 6.6847043424
! 538: 634879841147654217963674264 - 5.877471754111437539 E-39*I, 0.851456773407213
! 539: 76574333983502938573598 + 4.5829573180978430291541592600601794652*I, -0.1357
! 540: 4266252716976137461193821267520737 - 0.2880510854402577236173893646768205039
! 541: 1*I, 0.27203784387468568916539788233281013320 - 1.59171472799429477189656508
! 542: 59986677247*I; 2.350988701644575015 E-38 + 0.6824321041812434255252538269540
! 543: 1469720*I, 0.85145677340721376574333983502938573598 - 4.58295731809784302915
! 544: 41592600601794652*I, 9.1630968530221077951281598310681467898 + 0.E-38*I, 2.2
! 545: 622987652095629453403849736225691490 + 6.23619279135585067657240470631807068
! 546: 69*I, -0.21796409886496632254445901043974770643 + 0.345593689310632156861589
! 547: 39748833975810*I; -2.350988701644575015 E-38 + 0.522109805898985859506329704
! 548: 08019416371*I, -0.13574266252716976137461193821267520737 + 0.288051085440257
! 549: 72361738936467682050392*I, 2.2622987652095629453403849736225691490 - 6.23619
! 550: 27913558506765724047063180706869*I, 12.845768948832335511882696939380696155
! 551: + 1.175494350822287507 E-38*I, 4.5618400502378124720913214622468855074 + 8.6
! 552: 033930051068500425218923146793019614*I; 3.9999999999999999999999999999999999
! 553: 999 + 5.2069157878920895450584461181156471052*I, 0.2720378438746856891653978
! 554: 8233281013320 + 1.5917147279942947718965650859986677247*I, -0.21796409886496
! 555: 632254445901043974770643 - 0.34559368931063215686158939748833975810*I, 4.561
! 556: 8400502378124720913214622468855074 - 8.6033930051068500425218923146793019615
! 557: *I, 18.362968630416114402425299186062892646 + 5.877471754111437539 E-39*I],
! 558: [5, -1.175494350822287507 E-38 + 0.E-38*I, 2.350988701644575015 E-38 + 0.E-3
! 559: 8*I, -1.763241526233431261 E-38 + 0.E-38*I, 3.999999999999999999999999999999
! 560: 9999998 + 0.E-38*I; -1.175494350822287507 E-38 + 0.E-38*I, 6.684704342463487
! 561: 9841147654217963674264 - 5.877471754111437539 E-39*I, 0.85145677340721376574
! 562: 333983502938573597 + 5.877471754111437539 E-39*I, -0.13574266252716976137461
! 563: 193821267520737 + 5.877471754111437539 E-39*I, 0.272037843874685689165397882
! 564: 33281013314 - 5.877471754111437539 E-39*I; 2.350988701644575015 E-38 + 0.E-3
! 565: 8*I, 0.85145677340721376574333983502938573597 + 5.877471754111437539 E-39*I,
! 566: 9.1630968530221077951281598310681467898 + 0.E-38*I, 2.262298765209562945340
! 567: 3849736225691490 + 2.350988701644575015 E-38*I, -0.2179640988649663225444590
! 568: 1043974770651 + 0.E-38*I; -1.763241526233431261 E-38 + 0.E-38*I, -0.13574266
! 569: 252716976137461193821267520737 + 5.877471754111437539 E-39*I, 2.262298765209
! 570: 5629453403849736225691490 + 2.350988701644575015 E-38*I, 12.8457689488323355
! 571: 11882696939380696155 + 0.E-37*I, 4.5618400502378124720913214622468855073 - 3
! 572: .526483052466862523 E-38*I; 3.9999999999999999999999999999999999998 + 0.E-38
! 573: *I, 0.27203784387468568916539788233281013314 - 5.877471754111437539 E-39*I,
! 574: -0.21796409886496632254445901043974770651 + 0.E-38*I, 4.56184005023781247209
! 575: 13214622468855073 - 3.526483052466862523 E-38*I, 18.362968630416114402425299
! 576: 186062892646 + 0.E-37*I]], [Mod(5, y^3 - y - 1), 0, 0, 0, Mod(4, y^3 - y - 1
! 577: ); 0, 0, 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1); 0, 0, Mod(4, y^3 - y
! 578: - 1), Mod(10, y^3 - y - 1), 0; 0, Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1),
! 579: 0, 0; Mod(4, y^3 - y - 1), Mod(10, y^3 - y - 1), 0, 0, Mod(4, y^3 - y - 1)]
! 580: , [;], [;], [;]], [[1.2671683045421243172528914279776896412, 0.2609638803864
! 581: 5528500256735072673484811 + 1.1772261533941944394700286585617926513*I, -0.89
! 582: 454803265751744362901306471557966872 + 0.53414854617473272670874609150394379
! 583: 949*I], [1.2671683045421243172528914279776896412 + 0.E-38*I, 0.2609638803864
! 584: 5528500256735072673484811 - 1.1772261533941944394700286585617926513*I, 0.260
! 585: 96388038645528500256735072673484811 + 1.177226153394194439470028658561792651
! 586: 3*I, -0.89454803265751744362901306471557966872 - 0.5341485461747327267087460
! 587: 9150394379949*I, -0.89454803265751744362901306471557966872 + 0.5341485461747
! 588: 3272670874609150394379949*I]~], [[Mod(1, y^3 - y - 1), Mod(1, y^3 - y - 1)*x
! 589: , Mod(1, y^3 - y - 1)*x^2, Mod(1, y^3 - y - 1)*x^3, Mod(1, y^3 - y - 1)*x^4]
! 590: , [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1,
! 591: 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [M
! 592: od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1
! 593: , y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^
! 594: 3 - y - 1)], [], [y^3 - y - 1, [1, 1], -23, 1, [[1, 1.3247179572447460259609
! 595: 088544780973407, 1.7548776662466927600495088963585286918; 1, -0.662358978622
! 596: 37301298045442723904867036 + 0.56227951206230124389918214490937306149*I, 0.1
! 597: 2256116687665361997524555182073565405 - 0.7448617666197442365931704286043923
! 598: 6724*I], [1, 2; 1.3247179572447460259609088544780973407, -1.3247179572447460
! 599: 259609088544780973407 - 1.1245590241246024877983642898187461229*I; 1.7548776
! 600: 662466927600495088963585286918, 0.24512233375330723995049110364147130810 + 1
! 601: .4897235332394884731863408572087847344*I], [3, 0.E-96, 2.0000000000000000000
! 602: 000000000000000000; 0.E-96, 3.2646329987400782801485266890755860756, 1.32471
! 603: 79572447460259609088544780973407; 2.0000000000000000000000000000000000000, 1
! 604: .3247179572447460259609088544780973407, 4.2192762054875453178332176670757633
! 605: 303], [3, 0, 2; 0, 2, 3; 2, 3, 2], [23, 13, 15; 0, 1, 0; 0, 0, 1], [-5, 6, -
! 606: 4; 6, 2, -9; -4, -9, 6], [23, [7, 10, 1]~]], [1.3247179572447460259609088544
! 607: 780973407, -0.66235897862237301298045442723904867036 + 0.5622795120623012438
! 608: 9918214490937306149*I], [1, y, y^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0,
! 609: 0, 0, 1, 0, 1, 0; 0, 1, 0, 1, 0, 1, 0, 1, 1; 0, 0, 1, 0, 1, 0, 1, 0, 1]], [x
! 610: ^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6
! 611: + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1, Mod(39516536165538345/8
! 612: 3718587879473471*x^14 - 6500512476832995/83718587879473471*x^13 - 1962154720
! 613: 46117185/83718587879473471*x^12 + 229902227480108910/83718587879473471*x^11
! 614: + 237380704030959181/83718587879473471*x^10 - 1064931988160773805/8371858787
! 615: 9473471*x^9 - 20657086671714300/83718587879473471*x^8 + 1772885205999206010/
! 616: 83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^6 - 48388401
! 617: 87320655696/83718587879473471*x^5 + 5180390720553188700/83718587879473471*x^
! 618: 4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040221/83718587
! 619: 879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920215718580450
! 620: /83718587879473471, x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x
! 621: ^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), -
! 622: 1, [1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, 1/
! 623: 83718587879473471*x^14 - 20528463024680133/83718587879473471*x^13 - 47423929
! 624: 48888610/83718587879473471*x^12 - 9983523646123358/83718587879473471*x^11 +
! 625: 40898955597139011/83718587879473471*x^10 + 29412692423971937/837185878794734
! 626: 71*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075066/83718587
! 627: 879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 20152905879672878/8
! 628: 3718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 - 847190574595
! 629: 7397/83718587879473471*x^3 - 13395753879413605/83718587879473471*x^2 + 27623
! 630: 037732247492/83718587879473471*x + 26306699661480593/83718587879473471], [1,
! 631: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0
! 632: , 0, 0, 0, 0, 0, 0, 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
! 633: 0, 0, 0, 0, 13395753879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 847
! 634: 1905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789;
! 635: 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0,
! 636: 0, 1, 0, 0, 0, 0, 0, 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
! 637: 0, 0, 0, 0, -41014993230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 50
! 638: 17479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937
! 639: ; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011; 0, 0, 0, 0,
! 640: 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
! 641: , 0, 0, 1, 0, 4742392948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20
! 642: 528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471
! 643: ]]]
! 644: ? bnfcertify(bnf)
! 645: 1
! 646: ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
! 647:
! 648: [x^4 - 7]
! 649:
! 650: [[2, 1]]
! 651:
! 652: [[-87808, 1]]
! 653:
! 654: [[1, x, x^2, x^3]]
! 655:
! 656: [[2, [2], [[3, 1, 2, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
! 657:
! 658: [14.229975145405511722395637833443108790]
! 659:
! 660: [1.121117107152756229]
! 661:
! 662: ? setrand(1);bnfclassunit(x^2-x-100000)
! 663: *** Warning: insufficient precision for fundamental units, not given.
! 664:
! 665: [x^2 - x - 100000]
! 666:
! 667: [[2, 0]]
! 668:
! 669: [[400001, 1]]
! 670:
! 671: [[1, x]]
! 672:
! 673: [[5, [5], [[2, 1; 0, 1]]]]
! 674:
! 675: [129.82045011403975460991182396195022419]
! 676:
! 677: [0.9876536979069047239]
! 678:
! 679: [[2, -1]]
! 680:
! 681: [[;]]
! 682:
! 683: [0]
! 684:
! 685: ? setrand(1);bnfclassunit(x^2-x-100000,1)
! 686:
! 687: [x^2 - x - 100000]
! 688:
! 689: [[2, 0]]
! 690:
! 691: [[400001, 1]]
! 692:
! 693: [[1, x]]
! 694:
! 695: [[5, [5], [[2, 1; 0, 1]]]]
! 696:
! 697: [129.82045011403975460991182396195022419]
! 698:
! 699: [0.9876536979069047239]
! 700:
! 701: [[2, -1]]
! 702:
! 703: [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
! 704: 789990462835950022871665178127611316131167]]
! 705:
! 706: [186]
! 707:
! 708: ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
! 709:
! 710: [x^4 + 24*x^2 + 585*x + 1791]
! 711:
! 712: [[0, 2]]
! 713:
! 714: [[18981, 3087]]
! 715:
! 716: [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]
! 717:
! 718: [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
! 719:
! 720: [3.7941269688216589341408274220859400302]
! 721:
! 722: [0.8826018286655581306]
! 723:
! 724: [[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]]
! 725:
! 726: [[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]
! 727:
! 728: [182]
! 729:
! 730: ? setrand(1);bnfclgp(17)
! 731: [1, [], []]
! 732: ? setrand(1);bnfclgp(-31)
! 733: [3, [3], [Qfb(2, 1, 4)]]
! 734: ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791)
! 735: [4, [4], [[7, 5, 1, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]
! 736: ? bnrconductor(bnf,[[25,13;0,1],[1,1]])
! 737: [[5, 3; 0, 1], [1, 0]]
! 738: ? bnrconductorofchar(bnr,[2])
! 739: [[5, 3; 0, 1], [0, 0]]
! 740: ? bnfisprincipal(bnf,[5,1;0,1],0)
! 741: [1]~
! 742: ? bnfisprincipal(bnf,[5,1;0,1])
! 743: [[1]~, [-2, -1/3]~, 181]
! 744: ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
! 745: [-4, Mod(1, 2)]~
! 746: ? \p19
! 747: realprecision = 19 significant digits
! 748: ? bnfmake(sbnf)
! 749: [Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
! 750: 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389
! 751: 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
! 752: I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
! 753: 1592653589793238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400
! 754: 6376129469727 + 3.141592653589793238*I, -0.6926391142471042845 + 3.141592653
! 755: 589793238*I, 0.E-96, 0.3677262014027817705 + 3.141592653589793238*I, 0.00437
! 756: 5616572659815402 + 3.141592653589793238*I, -0.8305625946607188639, -1.977791
! 757: 147836553953 + 3.141592653589793238*I; 0.6716827432867392935 + 3.14159265358
! 758: 9793238*I, 0.5379005671092853266, -0.8333219883742404172 + 3.141592653589793
! 759: 238*I, -0.2461086674077943078, 0.E-96, 0.9729063188316092378, -0.87383180430
! 760: 71131265, -1.552661549868775853 + 3.141592653589793238*I, 0.5774919091398324
! 761: 092 + 3.141592653589793238*I; -1.918029732621558454, 1.452155878475514386, 0
! 762: .2929213507612934444, 0.9387477816548985923, 0.E-96, -1.340632520234391008,
! 763: 0.8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.4002
! 764: 99238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]~
! 765: ], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [
! 766: 5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [23, [
! 767: -10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [13, [
! 768: 19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2
! 769: , 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.23
! 770: 3732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.005158
! 771: 616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; -
! 772: 3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.4570
! 773: 2714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.0000000
! 774: 00000000000, 29.00000000000000000; 1.000000000000000000, 29.0000000000000000
! 775: 0, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.000
! 776: 0000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1
! 777: , 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, [
! 778: 1890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.305556
! 779: 205008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1,
! 780: 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2
! 781: ], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.00000000000000000
! 782: 0, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0, 0, 0]], [[1.24634698933
! 783: 4819161 + 3.141592653589793238*I, 0.6716827432867392935 + 3.1415926535897932
! 784: 38*I, -1.918029732621558454]]], [-4, 3, -1, 2, 3, 11, 1, -1, -7; 1, 1, 1, 1,
! 785: 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]
! 786: ? \p38
! 787: realprecision = 38 significant digits
! 788: ? bnfnarrow(bnf)
! 789: [3, [3], [[3, 2; 0, 1]]]
! 790: ? bnfreg(x^2-x-57)
! 791: 2.7124653051843439746808795106061300699
! 792: ? bnfsignunit(bnf)
! 793:
! 794: [-1]
! 795:
! 796: [1]
! 797:
! 798: ? bnfunit(bnf)
! 799: [[x + 7], 185]
! 800: ? bnrclass(bnf,[[5,3;0,1],[1,0]])
! 801: [12, [12], [[3, 2; 0, 1]]]
! 802: ? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2)
! 803: [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
! 804: 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
! 805: 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767
! 806: 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1
! 807: .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122
! 808: 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659
! 809: 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337
! 810: 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*
! 811: I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498
! 812: 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153
! 813: 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265
! 814: 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +
! 815: 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626
! 816: 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179
! 817: 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42
! 818: 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106
! 819: 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932
! 820: 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592
! 821: 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +
! 822: 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934
! 823: 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438
! 824: 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1
! 825: 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833
! 826: 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,
! 827: 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]
! 828: ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,
! 829: 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1
! 830: , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7
! 831: , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931
! 832: 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372
! 833: 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [
! 834: 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000
! 835: 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114
! 836: ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102
! 837: 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],
! 838: [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974
! 839: 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),
! 840: [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384
! 841: 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307
! 842: 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[25, 13; 0,
! 843: 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [0, -2]~, [2, 2]~]], Mat([[5, [-2, 1
! 844: ]~, 1, 1, [1, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), Mod(0, 2
! 845: )]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat([1/5, -
! 846: 13/5])]], [[2, 2], [[0, -2]~, [2, 2]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0,
! 847: 1, 0; 0, 0, 0, 1]], [1], [1, -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0]
! 848: , [12, [12], [[3, 2; 0, 1]]], [[1, 9, -18; -1/2, -5, 10], [-2, 0; 0, 10]]]
! 849: ? bnrclassno(bnf,[[5,3;0,1],[1,0]])
! 850: 12
! 851: ? lu=ideallist(bnf,55,3);
! 852: ? bnrclassnolist(bnf,lu)
! 853: [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
! 854: , [], [12, 6, 6, 12], [3], [3, 3], [], [9, 9], [6, 6], [], [], [], [], [6, 1
! 855: 2, 6], [], [3, 3, 3, 3], [], [], [], [], [], [3, 6, 6, 3], [], [], [9, 3, 9]
! 856: , [6, 6], [], [], [], [], [], [3, 3], [3, 3], [12, 12, 6, 6, 12, 12], [], []
! 857: , [6, 6], [9], [], [3, 3, 3, 3], [], [3, 3], [], [6, 12, 12, 6]]
! 858: ? bnrdisc(bnr,Mat(6))
! 859: [12, 12, 18026977100265125]
! 860: ? bnrdisc(bnr)
! 861: [24, 12, 40621487921685401825918161408203125]
! 862: ? bnrdisc(bnr2,,,2)
! 863: 0
! 864: ? bnrdisc(bnr,Mat(6),,1)
! 865: [6, 2, [125, 13; 0, 1]]
! 866: ? bnrdisc(bnr,,,1)
! 867: [12, 1, [1953125, 1160888; 0, 1]]
! 868: ? bnrdisc(bnr2,,,3)
! 869: 0
! 870: ? bnrdisclist(bnf,lu)
! 871: [[[6, 6, Mat([229, 3])]], [], [[], []], [[]], [[12, 12, [5, 3; 229, 6]], [12
! 872: , 12, [5, 3; 229, 6]]], [], [], [], [[], [], []], [], [[], []], [[], []], []
! 873: , [], [[24, 24, [3, 6; 5, 9; 229, 12]], [], [], [24, 24, [3, 6; 5, 9; 229, 1
! 874: 2]]], [[]], [[], []], [], [[18, 18, [19, 6; 229, 9]], [18, 18, [19, 6; 229,
! 875: 9]]], [[], []], [], [], [], [], [[], [24, 24, [5, 12; 229, 12]], []], [], [[
! 876: ], [], [], []], [], [], [], [], [], [[], [12, 12, [3, 3; 11, 3; 229, 6]], [1
! 877: 2, 12, [3, 3; 11, 3; 229, 6]], []], [], [], [[18, 18, [2, 12; 3, 12; 229, 9]
! 878: ], [], [18, 18, [2, 12; 3, 12; 229, 9]]], [[12, 12, [37, 3; 229, 6]], [12, 1
! 879: 2, [37, 3; 229, 6]]], [], [], [], [], [], [[], []], [[], []], [[], [], [], [
! 880: ], [], []], [], [], [[12, 12, [2, 12; 3, 3; 229, 6]], [12, 12, [2, 12; 3, 3;
! 881: 229, 6]]], [[18, 18, [7, 12; 229, 9]]], [], [[], [], [], []], [], [[], []],
! 882: [], [[], [24, 24, [5, 9; 11, 6; 229, 12]], [24, 24, [5, 9; 11, 6; 229, 12]]
! 883: , []]]
! 884: ? bnrdisclist(bnf,20,,1)
! 885: [[[[matrix(0,2), [[6, 6, Mat([229, 3])], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]],
! 886: [], [[Mat([12, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [3, 3; 229, 6
! 887: ]]]], [Mat([13, 1]), [[0, 0, 0], [0, 0, 0], [12, 6, [-1, 1; 3, 3; 229, 6]],
! 888: [0, 0, 0]]]], [[Mat([10, 1]), [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]
! 889: , [[Mat([20, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [0, 0, 0], [24, 0, [
! 890: 5, 9; 229, 12]]]], [Mat([21, 1]), [[12, 12, [5, 3; 229, 6]], [0, 0, 0], [24,
! 891: 12, [5, 9; 229, 12]], [0, 0, 0]]]], [], [], [], [[Mat([12, 2]), [[0, 0, 0],
! 892: [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[12, 1; 13, 1], [[0, 0, 0], [12, 6, [-1
! 893: , 1; 3, 6; 229, 6]], [0, 0, 0], [24, 0, [3, 12; 229, 12]]]], [Mat([13, 2]),
! 894: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([44, 1]), [[0, 0,
! 895: 0], [0, 0, 0], [12, 6, [-1, 1; 11, 3; 229, 6]], [0, 0, 0]]], [Mat([45, 1]),
! 896: [[0, 0, 0], [0, 0, 0], [0, 0, 0], [12, 0, [11, 3; 229, 6]]]]], [[[10, 1; 12,
! 897: 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 13, 1], [[0, 0,
! 898: 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]], [], [], [[[12, 1; 20, 1], [[24, 24,
! 899: [3, 6; 5, 9; 229, 12]], [0, 0, 0], [0, 0, 0], [48, 0, [3, 12; 5, 18; 229, 2
! 900: 4]]]], [[13, 1; 20, 1], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [24, 12
! 901: , [3, 6; 5, 6; 229, 12]], [48, 0, [3, 12; 5, 18; 229, 24]]]], [[12, 1; 21, 1
! 902: ], [[0, 0, 0], [24, 12, [3, 6; 5, 9; 229, 12]], [0, 0, 0], [48, 0, [3, 12; 5
! 903: , 18; 229, 24]]]], [[13, 1; 21, 1], [[24, 24, [3, 6; 5, 9; 229, 12]], [0, 0,
! 904: 0], [48, 24, [3, 12; 5, 18; 229, 24]], [0, 0, 0]]]], [[Mat([10, 2]), [[0, 0
! 905: , 0], [12, 6, [-1, 1; 2, 12; 229, 6]], [12, 6, [-1, 1; 2, 12; 229, 6]], [24,
! 906: 0, [2, 36; 229, 12]]]]], [[Mat([68, 1]), [[0, 0, 0], [12, 6, [-1, 1; 17, 3;
! 907: 229, 6]], [0, 0, 0], [0, 0, 0]]], [Mat([69, 1]), [[0, 0, 0], [12, 6, [-1, 1
! 908: ; 17, 3; 229, 6]], [0, 0, 0], [0, 0, 0]]]], [], [[Mat([76, 1]), [[18, 18, [1
! 909: 9, 6; 229, 9]], [0, 0, 0], [0, 0, 0], [36, 0, [19, 15; 229, 18]]]], [Mat([77
! 910: , 1]), [[18, 18, [19, 6; 229, 9]], [0, 0, 0], [36, 18, [-1, 1; 19, 15; 229,
! 911: 18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0,
! 912: 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]]
! 913: ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
! 914: [[9]~, [-2170/6561, -931/19683]~, 256]
! 915: ? dirzetak(nf4,30)
! 916: [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,
! 917: 0, 1, 0, 1, 0]
! 918: ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
! 919:
! 920: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t, t^3 + t^2 - 2*t - 1) 1]
! 921:
! 922: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]
! 923:
! 924: [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
! 925:
! 926: ? vp=idealprimedec(nf,3)[1]
! 927: [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]
! 928: ? idx=idealmul(nf,matid(5),vp)
! 929:
! 930: [3 1 2 2 2]
! 931:
! 932: [0 1 0 0 0]
! 933:
! 934: [0 0 1 0 0]
! 935:
! 936: [0 0 0 1 0]
! 937:
! 938: [0 0 0 0 1]
! 939:
! 940: ? idealinv(nf,idx)
! 941:
! 942: [1 0 2/3 0 0]
! 943:
! 944: [0 1 1/3 0 0]
! 945:
! 946: [0 0 1/3 0 0]
! 947:
! 948: [0 0 0 1 0]
! 949:
! 950: [0 0 0 0 1]
! 951:
! 952: ? idy=idealred(nf,idx,[1,5,6])
! 953:
! 954: [5 0 0 2 0]
! 955:
! 956: [0 5 0 0 0]
! 957:
! 958: [0 0 5 2 0]
! 959:
! 960: [0 0 0 1 0]
! 961:
! 962: [0 0 0 0 5]
! 963:
! 964: ? idx2=idealmul(nf,idx,idx)
! 965:
! 966: [9 7 5 8 2]
! 967:
! 968: [0 1 0 0 0]
! 969:
! 970: [0 0 1 0 0]
! 971:
! 972: [0 0 0 1 0]
! 973:
! 974: [0 0 0 0 1]
! 975:
! 976: ? idt=idealmul(nf,idx,idx,1)
! 977:
! 978: [2 0 0 0 1]
! 979:
! 980: [0 2 0 0 1]
! 981:
! 982: [0 0 2 0 0]
! 983:
! 984: [0 0 0 2 1]
! 985:
! 986: [0 0 0 0 1]
! 987:
! 988: ? idz=idealintersect(nf,idx,idy)
! 989:
! 990: [15 5 10 12 10]
! 991:
! 992: [0 5 0 0 0]
! 993:
! 994: [0 0 5 2 0]
! 995:
! 996: [0 0 0 1 0]
! 997:
! 998: [0 0 0 0 5]
! 999:
! 1000: ? aid=[idx,idy,idz,matid(5),idx]
! 1001: [[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]
! 1002: , [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
! 1003: ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0,
! 1004: 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
! 1005: , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,
! 1006: 0, 0, 1]]
! 1007: ? bid=idealstar(nf2,54,1)
! 1008: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
! 1009: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
! 1010: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
! 1011: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
! 1012: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
! 1013: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
! 1014: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
! 1015: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
! 1016: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
! 1017: ? vaid=[idx,idy,matid(5)]
! 1018: [[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]
! 1019: , [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
! 1020: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
! 1021: 1]]
! 1022: ? haid=[matid(5),matid(5),matid(5)]
! 1023: [[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]
! 1024: , [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
! 1025: ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
! 1026: 1]]
! 1027: ? idealadd(nf,idx,idy)
! 1028:
! 1029: [1 0 0 0 0]
! 1030:
! 1031: [0 1 0 0 0]
! 1032:
! 1033: [0 0 1 0 0]
! 1034:
! 1035: [0 0 0 1 0]
! 1036:
! 1037: [0 0 0 0 1]
! 1038:
! 1039: ? idealaddtoone(nf,idx,idy)
! 1040: [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]
! 1041: ? idealaddtoone(nf,[idy,idx])
! 1042: [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
! 1043: ? idealappr(nf,idy)
! 1044: [-2, 0, -2, 4, 0]~
! 1045: ? idealappr(nf,idealfactor(nf,idy),1)
! 1046: [-2, 0, -2, 4, 0]~
! 1047: ? idealcoprime(nf,idx,idx)
! 1048: [-2/3, 2/3, -1/3, 0, 0]~
! 1049: ? idealdiv(nf,idy,idt)
! 1050:
! 1051: [5 5/2 5/2 7/2 0]
! 1052:
! 1053: [0 5/2 0 0 0]
! 1054:
! 1055: [0 0 5/2 1 0]
! 1056:
! 1057: [0 0 0 1/2 0]
! 1058:
! 1059: [0 0 0 0 5/2]
! 1060:
! 1061: ? idealdiv(nf,idx2,idx,1)
! 1062:
! 1063: [3 1 2 2 2]
! 1064:
! 1065: [0 1 0 0 0]
! 1066:
! 1067: [0 0 1 0 0]
! 1068:
! 1069: [0 0 0 1 0]
! 1070:
! 1071: [0 0 0 0 1]
! 1072:
! 1073: ? idf=idealfactor(nf,idz)
! 1074:
! 1075: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]
! 1076:
! 1077: [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]
! 1078:
! 1079: [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]
! 1080:
! 1081: ? idealhnf(nf,vp)
! 1082:
! 1083: [3 1 2 2 2]
! 1084:
! 1085: [0 1 0 0 0]
! 1086:
! 1087: [0 0 1 0 0]
! 1088:
! 1089: [0 0 0 1 0]
! 1090:
! 1091: [0 0 0 0 1]
! 1092:
! 1093: ? idealhnf(nf,vp[2],3)
! 1094:
! 1095: [3 1 2 2 2]
! 1096:
! 1097: [0 1 0 0 0]
! 1098:
! 1099: [0 0 1 0 0]
! 1100:
! 1101: [0 0 0 1 0]
! 1102:
! 1103: [0 0 0 0 1]
! 1104:
! 1105: ? ideallist(bnf,20)
! 1106: [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0
! 1107: , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],
! 1108: [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [
! 1109: [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]
! 1110: , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10
! 1111: , 6; 0, 2], [10, 2; 0, 2]]]
! 1112: ? ideallog(nf2,w,bid)
! 1113: [1574, 8, 6]~
! 1114: ? idealmin(nf,idx,[1,2,3])
! 1115: [[-1; 0; 0; 1; 0], [2.0885812311199768913287869744681966008 + 3.141592653589
! 1116: 7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244
! 1117: 7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160
! 1118: 203 + 2.5437460822678889883600220330800078854*I]]
! 1119: ? idealnorm(nf,idt)
! 1120: 16
! 1121: ? idp=idealpow(nf,idx,7)
! 1122:
! 1123: [2187 1807 2129 692 1379]
! 1124:
! 1125: [0 1 0 0 0]
! 1126:
! 1127: [0 0 1 0 0]
! 1128:
! 1129: [0 0 0 1 0]
! 1130:
! 1131: [0 0 0 0 1]
! 1132:
! 1133: ? idealpow(nf,idx,7,1)
! 1134:
! 1135: [5 0 0 2 0]
! 1136:
! 1137: [0 5 0 0 0]
! 1138:
! 1139: [0 0 5 2 0]
! 1140:
! 1141: [0 0 0 1 0]
! 1142:
! 1143: [0 0 0 0 5]
! 1144:
! 1145: ? idealprimedec(nf,2)
! 1146: [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,
! 1147: 4, [1, 1, 0, 0, 0]~]]
! 1148: ? idealprimedec(nf,3)
! 1149: [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,
! 1150: 2, [1, 2, 3, 1, 0]~]]
! 1151: ? idealprimedec(nf,11)
! 1152: [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
! 1153: ? idealprincipal(nf,Mod(x^3+5,nfpol))
! 1154:
! 1155: [6]
! 1156:
! 1157: [0]
! 1158:
! 1159: [1]
! 1160:
! 1161: [3]
! 1162:
! 1163: [0]
! 1164:
! 1165: ? idealtwoelt(nf,idy)
! 1166: [5, [2, 0, 2, 1, 0]~]
! 1167: ? idealtwoelt(nf,idy,10)
! 1168: [-2, 0, -2, -1, 0]~
! 1169: ? idealstar(nf2,54)
! 1170: [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
! 1171: 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
! 1172: 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]
! 1173: ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
! 1174: ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
! 1175: , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
! 1176: [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
! 1177: 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7
! 1178: , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]
! 1179: ? idealval(nf,idp,vp)
! 1180: 7
! 1181: ? ideleprincipal(nf,Mod(x^3+5,nfpol))
! 1182: [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897
! 1183: 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851
! 1184: 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
! 1185: - 0.0083630478144368246110910258645462996191*I]]
! 1186: ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
! 1187: [6, 0, 1, 3, 0]~
! 1188: ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
! 1189: [1, 1, 1, 3, 0]~
! 1190: ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
! 1191:
! 1192: [[0, 1, 1, 0, 0]~]
! 1193:
! 1194: [[1, 0, 1, 0, 0]~]
! 1195:
! 1196: ? matbasistoalg(nf,bc)
! 1197:
! 1198: [Mod(x^2 + x, x^5 - 5*x^3 + 5*x + 25)]
! 1199:
! 1200: [Mod(x^2 + 1, x^5 - 5*x^3 + 5*x + 25)]
! 1201:
! 1202: ? nfbasis(x^3+4*x+5)
! 1203: [1, x, 1/7*x^2 - 1/7*x - 2/7]
! 1204: ? nfbasis(x^3+4*x+5,2)
! 1205: [1, x, 1/7*x^2 - 1/7*x - 2/7]
! 1206: ? nfbasis(x^3+4*x+12,1)
! 1207: [1, x, 1/2*x^2]
! 1208: ? nfbasistoalg(nf,ba)
! 1209: Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
! 1210: ? nfbasis(p2,0,fa)
! 1211: [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/13962
! 1212: 3738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 +
! 1213: 418509858130821123141/139623738889203638909659*x^2 - 6810913798507599407313
! 1214: 4/139623738889203638909659*x - 13185339461968406/58346808996920447]
! 1215: ? da=nfdetint(nf,[a,aid])
! 1216:
! 1217: [30 5 25 27 10]
! 1218:
! 1219: [0 5 0 0 0]
! 1220:
! 1221: [0 0 5 2 0]
! 1222:
! 1223: [0 0 0 1 0]
! 1224:
! 1225: [0 0 0 0 5]
! 1226:
! 1227: ? nfdisc(x^3+4*x+12)
! 1228: -1036
! 1229: ? nfdisc(x^3+4*x+12,1)
! 1230: -1036
! 1231: ? nfdisc(p2,0,fa)
! 1232: 136866601
! 1233: ? nfeltdiv(nf,ba,bb)
! 1234: [755/373, -152/373, 159/373, 120/373, -264/373]~
! 1235: ? nfeltdiveuc(nf,ba,bb)
! 1236: [2, 0, 0, 0, -1]~
! 1237: ? nfeltdivrem(nf,ba,bb)
! 1238: [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]
! 1239: ? nfeltmod(nf,ba,bb)
! 1240: [-12, -7, 0, 9, 5]~
! 1241: ? nfeltmul(nf,ba,bb)
! 1242: [-25, -50, -30, 15, 90]~
! 1243: ? nfeltpow(nf,bb,5)
! 1244: [23455, 156370, 115855, 74190, -294375]~
! 1245: ? nfeltreduce(nf,ba,idx)
! 1246: [1, 0, 0, 0, 0]~
! 1247: ? nfeltval(nf,ba,vp)
! 1248: 0
! 1249: ? nffactor(nf2,x^3+x)
! 1250:
! 1251: [Mod(1, y^3 - y - 1)*x 1]
! 1252:
! 1253: [Mod(1, y^3 - y - 1)*x^2 + Mod(1, y^3 - y - 1) 1]
! 1254:
! 1255: ? aut=nfgaloisconj(nf3)
! 1256: [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
! 1257: , -x]~
! 1258: ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
! 1259: Mod(1/2*x^5 - 9*x^2, x^6 + 108)
! 1260: ? nfhilbert(nf,3,5)
! 1261: -1
! 1262: ? nfhilbert(nf,3,5,idf[1,1])
! 1263: -1
! 1264: ? nfhnf(nf,[a,aid])
! 1265: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
! 1266: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
! 1267: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
! 1268: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1269: 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;
! 1270: 0, 0, 0, 0, 1]]]
! 1271: ? nfhnfmod(nf,[a,aid],da)
! 1272: [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1
! 1273: , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,
! 1274: 0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0
! 1275: , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
! 1276: 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;
! 1277: 0, 0, 0, 0, 1]]]
! 1278: ? nfisideal(bnf[7],[5,1;0,1])
! 1279: 1
! 1280: ? nfisincl(x^2+1,x^4+1)
! 1281: [-x^2, x^2]
! 1282: ? nfisincl(x^2+1,nfinit(x^4+1))
! 1283: [-x^2, x^2]
! 1284: ? nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
! 1285: [x, -x^2 - x + 1, x^2 - 2]
! 1286: ? nfisisom(x^3-2,nfinit(x^3-6*x^2-6*x-30))
! 1287: [-1/25*x^2 + 13/25*x - 2/5]
! 1288: ? nfroots(nf2,x+2)
! 1289: [Mod(-2, y^3 - y - 1)]
! 1290: ? nfrootsof1(nf)
! 1291: [2, [-1, 0, 0, 0, 0]~]
! 1292: ? nfsnf(nf,[as,haid,vaid])
! 1293: [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3
! 1294: 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0;
! 1295: 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
! 1296: ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0,
! 1297: 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
! 1298: ? nfsubfields(nf)
! 1299: [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]]
! 1300: ? polcompositum(x^4-4*x+2,x^3-x-1)
! 1301: [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
! 1302: ^2 - 128*x - 5]
! 1303: ? polcompositum(x^4-4*x+2,x^3-x-1,1)
! 1304: [[x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*
! 1305: x^2 - 128*x - 5, Mod(-279140305176/29063006931199*x^11 + 129916611552/290630
! 1306: 06931199*x^10 + 1272919322296/29063006931199*x^9 - 2813750209005/29063006931
! 1307: 199*x^8 - 2859411937992/29063006931199*x^7 - 414533880536/29063006931199*x^6
! 1308: - 35713977492936/29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 4
! 1309: 9785595543672/29063006931199*x^3 + 9423768373204/29063006931199*x^2 - 427797
! 1310: 76146743/29063006931199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8
! 1311: *x^9 + 12*x^8 + 12*x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), M
! 1312: od(-279140305176/29063006931199*x^11 + 129916611552/29063006931199*x^10 + 12
! 1313: 72919322296/29063006931199*x^9 - 2813750209005/29063006931199*x^8 - 28594119
! 1314: 37992/29063006931199*x^7 - 414533880536/29063006931199*x^6 - 35713977492936/
! 1315: 29063006931199*x^5 - 17432607267590/29063006931199*x^4 + 49785595543672/2906
! 1316: 3006931199*x^3 + 9423768373204/29063006931199*x^2 - 13716769215544/290630069
! 1317: 31199*x + 37962587857138/29063006931199, x^12 - 4*x^10 + 8*x^9 + 12*x^8 + 12
! 1318: *x^7 + 138*x^6 + 132*x^5 - 43*x^4 + 58*x^2 - 128*x - 5), -1]]
! 1319: ? polgalois(x^6-3*x^2-1)
! 1320: [12, 1, 1]
! 1321: ? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
! 1322: [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
! 1323: - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8]
! 1324: ? polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
! 1325:
! 1326: [1 x - 1]
! 1327:
! 1328: [1/115*x^2 - 14/115*x - 327/115 x^2 - 10]
! 1329:
! 1330: [3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]
! 1331:
! 1332: [1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]
! 1333:
! 1334: ? polred(x^4+576,1)
! 1335: [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]
! 1336: ? polred(x^4+576,3)
! 1337:
! 1338: [1 x - 1]
! 1339:
! 1340: [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
! 1341:
! 1342: [-1/24*x^2 x^2 + 1]
! 1343:
! 1344: [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
! 1345:
! 1346: ? polred(p2,0,fa)
! 1347: [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
! 1348: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
! 1349: *x^3 - 197*x^2 - 273*x - 127]
! 1350: ? polred(p2,1,fa)
! 1351: [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
! 1352: *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
! 1353: *x^3 - 197*x^2 - 273*x - 127]
! 1354: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
! 1355: x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1
! 1356: ? polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
! 1357: [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 -
! 1358: x^4 + 2*x^3 - 4*x^2 + x - 1)]
! 1359: ? polredord(x^3-12*x+45*x-1)
! 1360: [x - 1, x^3 - 363*x - 2663, x^3 + 33*x - 1]
! 1361: ? polsubcyclo(31,5)
! 1362: x^5 + x^4 - 12*x^3 - 21*x^2 + x + 5
! 1363: ? setrand(1);poltschirnhaus(x^5-x-1)
! 1364: x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289
! 1365: ? aa=rnfpseudobasis(nf2,p)
! 1366: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-2, 0, 0]~, [11, 0, 0]~; [0, 0, 0]~,
! 1367: [1, 0, 0]~, [0, 0, 0]~, [2, 0, 0]~, [-8, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [1,
! 1368: 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
! 1369: 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
! 1370: ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
! 1371: , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25;
! 1372: 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1
! 1373: 280, 5, 5]~]
! 1374: ? rnfbasis(bnf2,aa)
! 1375:
! 1376: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [38/25, -33/25, 11/25]~ [-11, -4, 9]~]
! 1377:
! 1378: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-14/25, 24/25, -8/25]~ [28/5, 2/5, -24/5]
! 1379: ~]
! 1380:
! 1381: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [57/25, -12/25, 4/25]~ [-58/5, -47/5, 44/5
! 1382: ]~]
! 1383:
! 1384: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [9/25, 6/25, -2/25]~ [-4/5, -11/5, 2/5]~]
! 1385:
! 1386: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [8/25, -3/25, 1/25]~ [-9/5, -6/5, 7/5]~]
! 1387:
! 1388: ? rnfdisc(nf2,p)
! 1389: [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
! 1390: ? rnfequation(nf2,p)
! 1391: x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
! 1392: ? rnfequation(nf2,p,1)
! 1393: [x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1, Mod(-x^5 + 5*x, x^15 - 1
! 1394: 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
! 1395: ? rnfhnfbasis(bnf2,aa)
! 1396:
! 1397: [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~
! 1398: ]
! 1399:
! 1400: [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]
! 1401:
! 1402: [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]
! 1403:
! 1404: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~]
! 1405:
! 1406: [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]
! 1407:
! 1408: ? rnfisfree(bnf2,aa)
! 1409: 1
! 1410: ? rnfsteinitz(nf2,aa)
! 1411: [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [38/25, -33/25, 11/25]~, [-27/125, 33/
! 1412: 125, -11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-14/25, 24/25, -8/25]~,
! 1413: [6/125, -24/125, 8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [57/25, -12/2
! 1414: 5, 4/25]~, [-53/125, 12/125, -4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [
! 1415: 9/25, 6/25, -2/25]~, [-11/125, -6/125, 2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0,
! 1416: 0, 0]~, [8/25, -3/25, 1/25]~, [-7/125, 3/125, -1/125]~], [[1, 0, 0; 0, 1, 0;
! 1417: 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,
! 1418: 0; 0, 1, 0; 0, 0, 1], [125, 0, 108; 0, 125, 22; 0, 0, 1]], [416134375, 21294
! 1419: 0625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]
! 1420: ? nfz=zetakinit(x^2-2);
! 1421: ? zetak(nfz,-3)
! 1422: 0.091666666666666666666666666666666666666
! 1423: ? zetak(nfz,1.5+3*I)
! 1424: 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
! 1425: 7938845*I
! 1426: ? setrand(1);quadclassunit(1-10^7,,[1,1])
! 1427: *** Warning: not a fundamental discriminant in quadclassunit.
! 1428: [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99984980
! 1429: 75377600233]
! 1430: ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
! 1431: [4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
! 1432: 5514, 0.9990369458964383232]
! 1433: ? sizebyte(%)
! 1434: 328
! 1435: ? getheap
! 1436: [198, 120613]
! 1437: ? print("Total time spent: ",gettime);
! 1438: Total time spent: 4836
! 1439: ? \q
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