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Diff for /OpenXM_contrib/pari-2.2/src/test/64/Attic/nfields between version 1.1 and 1.2

version 1.1, 2001/10/02 11:17:13 version 1.2, 2002/09/11 07:27:12
Line 17  x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 5466035
Line 17  x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 5466035
 ? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8));  ? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8));
 ? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8));  ? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8));
 ? nf=nfinit(nfpol)  ? nf=nfinit(nfpol)
 [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920  [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -1.08911514572050482502495
 69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929  27946671612684, -2.4285174907194186068992069565359418364, 0.7194669112891317
 269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119  8943997506477288225733, -2.5558200350691694950646071159426779971; 1, -0.1383
 211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I,  8372073406036365047976417441696637 - 0.4918163765776864349975328551474152510
  3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331  7*I, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940822
 539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319  19556466857*I, -0.072312766896812300380582649294307897121 + 2.19808037538462
 06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196  76641195195160383234877*I, -0.98796319352507039803950539735452837194 + 1.570
 23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 +  1452385894131769052374806001981108*I; 1, 1.682941293594312776162956161507997
  1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610  6005 + 2.0500351226010726172974286983598602163*I, -0.75045317576910401286427
 81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887  186094108607489 + 1.3101462685358123283560773619310445915*I, -0.787420688747
 04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982  75359433940488309213323154 + 2.1336633893126618034168454610457936017*I, 1.26
 34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I]  58732110596551455718089553258673705 - 2.716479010374315056657802803578983483
 , [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262  4*I], [1, -1.0891151457205048250249527946671612684, -2.428517490719418606899
 77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515  2069565359418364, 0.71946691128913178943997506477288225733, -2.5558200350691
 382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8  694950646071159426779971; 1.4142135623730950488016887242096980785, -0.195704
 976972027301414394898806541072047941, 6.408909349142616853840753758109052071  13467375904264179382543977540673, 2.7785222450164664309920925654093065576, -
 2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441  0.10226569567819614506098907018896260035, -1.3971909474085893198147151262541
 22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929  540506; 0, -0.69553338995335755797766403996841143190, 1.14510982744395651299
 269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875  26149974389115722, 3.1085550780550843138423672171643499921, 2.22052069130868
 724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 -  72788181483285734827868; 1.4142135623730950488016887242096980785, 2.38003840
 1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400  20787979181834702019470475018, -1.0613010590986270398182318786558994412, -1.
 435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104  1135810173202366904448352912286604470, 1.79021506332534372536778891648110361
 7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231  60; 0, 2.8991874737236275652408825679737171586, 1.85282662165584876344468105
 7837223883352537186677084*I], [5, 0.E-77, 10.0000000000000000000000000000000  12816401036, 3.0174557027049114270734649132936867272, -3.8416814583731999185
 00000, -5.0000000000000000000000000000000000000, 7.0000000000000000000000000  306312841432940661], 0, [5, 2, 0, -1, -2; 2, -2, -5, -10, 20; 0, -5, 10, -10
 000000000000; 0.E-77, 19.488486013650707197449403270536023970, 2.07268045322  , 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 0, 200, 110, 177; 0, 345
 2666710 E-76, 19.488486013650707197449403270536023970, 4.1504592246706085588  , 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5175, 0
 902013976045703227; 10.000000000000000000000000000000000000, 2.0726804532226  , -10350, -15525; 5175, 13800, -8625, -1725, 27600; 0, -8625, 37950, -17250,
 66710 E-76, 85.960217420851846480305133936577594605, -36.0342682914829798382   0; -10350, -1725, -17250, -24150, -15525; -15525, 27600, 0, -15525, -3450],
 67056239752434596, 53.576130452511107888183080361946556763; -5.0000000000000   [595125, [238050, -296700, 91425, 1725, 0]~]], [-2.428517490719418606899206
 000000000000000000000000, 19.488486013650707197449403270536023970, -36.03426  9565359418364, 1.9647119211288133163138753392090569931 + 0.80971492418897895
 8291482979838267056239752434596, 60.916248374441986300937507618575151517, -1  128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.31014
 8.470101750219179344070032346246890434; 7.0000000000000000000000000000000000  62685358123283560773619310445915*I], [1, 1/15*x^4 - 2/3*x^2 + 1/3*x + 4/3, x
 000, 4.1504592246706085588902013976045703227, 53.576130452511107888183080361  , 2/15*x^4 - 1/3*x^2 + 2/3*x - 1/3, -1/15*x^4 + 1/3*x^3 + 1/3*x^2 - 4/3*x -
 946556763, -18.470101750219179344070032346246890434, 37.97015289284236734089  2/3], [1, 0, 3, 1, 10; 0, 0, -2, 1, -5; 0, 1, 0, 3, -5; 0, 0, 1, 1, 10; 0, 0
 7384258599214282], [5, 0, 10, -5, 7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; -  , 0, 3, 0], [1, 0, 0, 0, 0, 0, -1, -1, -2, 4, 0, -1, 3, -1, 1, 0, -2, -1, -3
 5, 10, -55, 45, -39; 7, -5, 20, -39, 9], [345, 0, 340, 167, 150; 0, 345, 110  , -1, 0, 4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, -1, -1, 1, 0, -1, -2, -1, 1, 0,
 , 220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [132825, -18975, -  -1, -1, -1, 3, 0, 1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, -2
 5175, 27600, 17250; -18975, 34500, 41400, 3450, -43125; -5175, 41400, -41400  , 0, 1, 0, -1, -1, 0, -1, -2, -1, -1; 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1,
 , -15525, 51750; 27600, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -86   1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1; 0, 0, 0, 0, 1, 0, -1, -1, -1, 1, 0, -1
 250], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.42851749071941860689  , 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1]]
 92069565359418364, 1.9647119211288133163138753392090569931 + 0.8097149241889  
 7895128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.3  
 101462685358123283560773619310445915*I], [1, x, x^2, 1/3*x^3 - 1/3*x^2 - 1/3  
 , 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,  
 1, 1, -5; 0, 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, 1, -2, -1, 0  
 , 1, -5, -5, -3, 0, -2, -5, 1, -4, 0, -1, -3, -4, -3; 0, 1, 0, 0, 0, 1, 0, 0  
 , -2, 0, 0, 0, -5, 0, -5, 0, -2, 0, -5, 0, 0, 0, -5, 0, -4; 0, 0, 1, 0, 0, 0  
 , 1, 1, -2, 1, 1, 1, -5, 3, -3, 0, -2, 3, -5, 1, 0, 1, -3, 1, -2; 0, 0, 0, 1  
 , 0, 0, 0, 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, 0, 5, 0, 0, 0, 15, -5, 10, 0, 5, -5, 10, -2, 1, 0, 10, -2, 7]]  
 ? nf1=nfinit(nfpol,2)  ? nf1=nfinit(nfpol,2)
 [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145  [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59  7205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.71
 741050929194782733001765987770358483, 0.158944197453903762065494816710718942  946691128913178943997506477288225733, 2.555820035069169495064607115942677997
 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753  1; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021  85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0  7895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.1
 .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357  980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312  7194 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035  9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I  10401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.78
 , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013  742068874775359433940488309213323154 - 2.13366338931266180341684546104579360
 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544  17*I, -1.2658732110596551455718089553258673705 + 2.7164790103743150566578028
 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -  035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948  94186068992069565359418364, -0.71946691128913178943997506477288225733, 2.555
 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594  8200350691694950646071159426779971; 1.4142135623730950488016887242096980785,
 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211   -0.19570413467375904264179382543977540674, -2.77852224501646643099209256540
 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.  93065576, 0.10226569567819614506098907018896260035, 1.3971909474085893198147
 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274  151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539  9565129926149974389115722, 3.1085550780550843138423672171643499922, 2.220520
 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732  6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15  3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
 894419745390376206549481671071894289, -0.10730191731399545071859505671520521  12, 1.1135810173202366904448352912286604470, -1.7902150633253437253677889164
 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468  811036160; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000  4446810512816401036, -3.0174557027049114270734649132936867272, 3.84168145837
 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.  31999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10,
 000000000000000000000000000000000000, -44.0000000000000000000000000000000000   -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3
 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712  45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51
 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999  75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250
 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000  , 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126  [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527
 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8  946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864
 42564718082452641322500190813370023; -17.00000000000000000000000000000000000  3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350  1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x
 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018   - 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2], [
 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841  1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0,
 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003   1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1
 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,  , 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1
 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1  , -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1
 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,  , 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
  311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -  1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1
 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700  , 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]]
 , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897  
 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,  
  0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504  
 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359  
 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1,  
  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,  
 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0,  
  0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,  
 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14;  
  0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,  
 -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -  
 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3  
 , 4, -4, 1, 2, 1, -4, -21]]  
 ? nfinit(nfpol,3)  ? nfinit(nfpol,3)
 [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514  [[x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.08911514
 57205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.5  57205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.7
 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894  1946691128913178943997506477288225733, 2.55582003506916949506460711594267799
 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975  71; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602  285514741525107*I, -1.9647119211288133163138753392090569931 + 0.809714924188
 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +  97895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.
 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835  1980803753846276641195195160383234877*I, 0.987963193525070398039505397354528
 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431  37194 + 1.5701452385894131769052374806001981108*I; 1, 1.68294129359431277616
 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703  29561615079976005 + 2.0500351226010726172974286983598602163*I, 0.75045317576
 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*  910401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.7
 I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301  8742068874775359433940488309213323154 - 2.1336633893126618034168454610457936
 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354  017*I, -1.2658732110596551455718089553258673705 + 2.716479010374315056657802
 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,  8035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.4285174907
 -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294  194186068992069565359418364, -0.71946691128913178943997506477288225733, 2.55
 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459  58200350691694950646071159426779971; 1.4142135623730950488016887242096980785
 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821  , -0.19570413467375904264179382543977540674, -2.7785222450164664309920925654
 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2  093065576, 0.10226569567819614506098907018896260035, 1.397190947408589319814
 .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927  7151262541540506; 0, 0.69553338995335755797766403996841143190, 1.14510982744
 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753  39565129926149974389115722, 3.1085550780550843138423672171643499922, 2.22052
 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573  06913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2
 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1  .3800384020787979181834702019470475018, 1.0613010590986270398182318786558994
 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052  412, 1.1135810173202366904448352912286604470, -1.790215063325343725367788916
 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346  4811036160; 0, 2.8991874737236275652408825679737171587, -1.85282662165584876
 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000  34446810512816401036, -3.0174557027049114270734649132936867272, 3.8416814583
 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17  731999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10
 .000000000000000000000000000000000000, -44.000000000000000000000000000000000  , -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0,
 000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471  345, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5
 283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499  175, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -1725
 932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000  0, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
 00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912   [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.089115145720504825024952
 62388960975827806174040462368, 143.93295090847353519436673793501057176, -55.  7946671612684, -0.13838372073406036365047976417441696637 + 0.491816376577686
 842564718082452641322500190813370023; -17.0000000000000000000000000000000000  43499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.05003
 00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935  51226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*
 01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201  x - 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2],
 80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084  [1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0
 1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400  , 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -
 38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,  1, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -
  2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -  1, -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0,
 101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215  1, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
 , 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125,   1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -
 -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670  1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]], Mod(-1/2*x^4 + 3/2*x^3 - 5/2*x^2 - 2
 0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89  *x + 1, x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]
 700, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725  
 , 0]~]], [-1.0891151457205048250249527946671612684, -0.138383720734060363650  
 47976417441696637 + 0.49181637657768643499753285514741525107*I, 1.6829412935  
 943127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1  
 , 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,  
  0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0  
 , 0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,  
  0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14  
 ; 0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,  
  -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9,  
 -19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1,  
 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^  
 5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)]  
 ? nfinit(nfpol,4)  ? nfinit(nfpol,4)
 [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145  [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145
 7205048250249527946671612684, 1.1861718006377964594796293860483989860, -0.59  7205048250249527946671612684, 2.4285174907194186068992069565359418364, -0.71
 741050929194782733001765987770358483, 0.158944197453903762065494816710718942  946691128913178943997506477288225733, 2.555820035069169495064607115942677997
 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753  1; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021  85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0  7895128294082219556466856*I, 0.072312766896812300380582649294307897121 + 2.1
 .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357  980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312  7194 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035  9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I  10401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.78
 , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013  742068874775359433940488309213323154 - 2.13366338931266180341684546104579360
 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544  17*I, -1.2658732110596551455718089553258673705 + 2.7164790103743150566578028
 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -  035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948  94186068992069565359418364, -0.71946691128913178943997506477288225733, 2.555
 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594  8200350691694950646071159426779971; 1.4142135623730950488016887242096980785,
 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211   -0.19570413467375904264179382543977540674, -2.77852224501646643099209256540
 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.  93065576, 0.10226569567819614506098907018896260035, 1.3971909474085893198147
 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274  151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539  9565129926149974389115722, 3.1085550780550843138423672171643499922, 2.220520
 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732  6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15  3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
 894419745390376206549481671071894289, -0.10730191731399545071859505671520521  12, 1.1135810173202366904448352912286604470, -1.7902150633253437253677889164
 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468  811036160; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000  4446810512816401036, -3.0174557027049114270734649132936867272, 3.84168145837
 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.  31999185306312841432940661], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10,
 000000000000000000000000000000000000, -44.0000000000000000000000000000000000   -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3
 00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712  45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51
 83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999  75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250
 32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000  , 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450],
 0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126  [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527
 2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8  946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864
 42564718082452641322500190813370023; -17.00000000000000000000000000000000000  3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035
 0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350  1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*x
 1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018   - 1, 1/2*x^4 - x^3 + x^2 + 9/2*x + 1, 1/2*x^4 - x^3 + 2*x^2 + 7/2*x + 2], [
 0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841  1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0,
 447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003   1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1
 8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5,  , 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -1
 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1  , -1, 3, 0, -1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 2, 0, 1
 01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215,  , 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2,
  311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, -  1, 0, -1, 0, 0, 0, 0, -2, 0, 1; 0, 0, 0, 0, 1, 0, 1, -1, -1, 1, 0, -1, 0, -1
 296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700  , 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]]
 , -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -897  
 00, -315675, -87975, 89700, -55200], [595125, [-167325, -82800, 79350, 1725,  
  0]~]], [-1.0891151457205048250249527946671612684, -0.1383837207340603636504  
 7976417441696637 + 0.49181637657768643499753285514741525107*I, 1.68294129359  
 43127761629561615079976005 + 2.0500351226010726172974286983598602163*I], [1,  
  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,  
 0, -1, -1; 0, 0, 1, -1, 0; 0, 0, 0, 2, 0; 0, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0,  
  0, 0, 0, -1, 0, 0, 0, -1, -2, 0, 0, -1, -2, -2, 0, -1, -2, -2, 5; 0, 1, 0,  
 0, 0, 1, 0, -1, -1, -1, 0, -1, -1, -2, 2, 0, -1, -2, -1, 7, 0, -1, 2, 7, 14;  
  0, 0, 1, 0, 0, 0, 1, -1, 0, -2, 1, -1, 0, -3, -3, 0, 0, -3, -4, -1, 0, -2,  
 -3, -1, 15; 0, 0, 0, 1, 0, 0, 0, 2, 1, -3, 0, 2, 0, -2, -13, 1, 1, -2, -9, -  
 19, 0, -3, -13, -19, 7; 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 3, 1, 0, 1, 3  
 , 4, -4, 1, 2, 1, -4, -21]]  
 ? nf3=nfinit(x^6+108);  ? nf3=nfinit(x^6+108);
 ? nf4=nfinit(x^3-10*x+8)  ? nf4=nfinit(x^3-10*x+8)
 [x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -3.50466435358804770515010852590433205  [x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -0.36332823793268357037416860931988791
 79, 6.1413361156553641347759399165844441383; 1, 0.86464088669540302583112842  960, -3.1413361156553641347759399165844441383; 1, -1.76155718183189058754537
 266613688800, 0.37380193147270638662350044992137561317; 1, 2.640023466892644  11274124874988, 2.6261980685272936133764995500786243868; 1, 3.12488541976457
 6793189801032381951699, 3.4848619528719294786005596334941802484], [1, 1, 1;  41579195397367323754183, -0.48486195287192947860055963349418024846], [1, -0.
 -3.5046643535880477051501085259043320579, 0.86464088669540302583112842266613  36332823793268357037416860931988791960, -3.141336115655364134775939916584444
 688800, 2.6400234668926446793189801032381951699; 6.1413361156553641347759399  1383; 1, -1.7615571818318905875453711274124874988, 2.62619806852729361337649
 165844441383, 0.37380193147270638662350044992137561317, 3.484861952871929478  95500786243868; 1, 3.1248854197645741579195397367323754183, -0.4848619528719
 6005596334941802484], [3, -3.454467422037777850 E-77, 10.0000000000000000000  2947860055963349418024846], 0, [3, 1, -1; 1, 13, -5; -1, -5, 17], [284, 76,
 00000000000000000; -3.454467422037777850 E-77, 20.00000000000000000000000000  46; 0, 2, 0; 0, 0, 1], [196, -12, 8; -12, 50, 14; 8, 14, 38], [568, [120, 21
 0000000000, -12.000000000000000000000000000000000000; 10.0000000000000000000  0, 2]~]], [-3.5046643535880477051501085259043320579, 0.864640886695403025831
 00000000000000000, -12.000000000000000000000000000000000000, 50.000000000000  12842266613688800, 2.6400234668926446793189801032381951699], [1, 1/2*x^2 + x
 000000000000000000000000], [3, 0, 10; 0, 20, -12; 10, -12, 50], [284, 168, 2   - 3, -1/2*x^2 + 3], [1, 0, 6; 0, 1, 0; 0, 1, -2], [1, 0, 0, 0, 4, -2, 0, -2
 35; 0, 2, 0; 0, 0, 1], [856, -120, -200; -120, 50, 36; -200, 36, 60], [568,  , 6; 0, 1, 0, 1, 2, 0, 0, 0, -2; 0, 0, 1, 0, 1, -1, 1, -1, -1]]
 [-216, 90, 8]~]], [-3.5046643535880477051501085259043320579, 0.8646408866954  
 0302583112842266613688800, 2.6400234668926446793189801032381951699], [1, x,  
 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  
 , 1, 0, 5, 0, 5, -2; 0, 0, 1, 0, 2, 0, 1, 0, 5]]  
 ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];  ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];
 ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])  ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
 [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060  [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060
 61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468  61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468
 08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672  08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065
 2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1.  2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701
 2897619530652735025030086072395031017 + 0.E-57*I, -2.01097980249891575621226  48550268542821846861610071436900868, 0.E-57, 0.50057980363245587382620331339
 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590  071677436 + 3.1415926535897932384626433832795028842*I, 1.0888562540123011578
 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376  605958199158508674, 1.7241634548149836441438434283070556826 + 3.141592653589
 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I  7932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.1
 , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983  415926535897932384626433832795028842*I, 2.1336294009747564707190997873636390
 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538  948 + 3.1415926535897932384626433832795028842*I, 0.0661783018827457321853684
 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653  92323164193433 + 3.1415926535897932384626433832795028842*I; -1.7903417566977
 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0  293763292119206302198760, -1.2897619530652735025030086072395031017, -0.70148
 .E-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264  550268542821846861610071436900868, 0.E-57, -0.500579803632455873826203313390
 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795  71677436, -1.0888562540123011578605958199158508674, -1.724163454814983644143
 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424  8434283070556826, 0.34328764427702709438988786673341921876, -2.1336294009747
 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061  564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
 2 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.14159265358979323  [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926  [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [2
 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +  , 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [-
 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342  2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [x
 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389  ^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
 88786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.14  1, 7.0663729752107779635959310246705326058], [1, -8.066372975210777963595931
 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334  0246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, 1
 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1  15], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.06637297521077
 ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~  79635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - 1
 , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1  ], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.7
 ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1,  124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + 7
  1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7,  ], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.79
  8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310  03417566977293763292119206302198760]]], 0]
 246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.0663729  
 752107779635959310246705326058, 8.0663729752107779635959310246705326058], [2  
 , 1.0000000000000000000000000000000000000; 1.0000000000000000000000000000000  
 000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114;  
  0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.066372975210777963595931024  
 6705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],  
 [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.7124653051843439746  
 808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),  
 [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846  
 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071  
 795864769252867665590057684*I]]], 0]  
 ? setrand(1);bnfinit(x^2-x-100000,1)  ? setrand(1);bnfinit(x^2-x-100000,1)
 [Mat(5), Mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129.  [Mat(5), Mat([3, 2, 1, 2, 0, 3, 0, 2, 2, 3, 1, 4, 3, 2, 2, 3, 3, 0]), [-129.
 82045011403975460991182396195022419 - 6.283185307179586476925286766559005768  82045011403975460991182396195022419 + 6.283185307179586476925286766559005768
 4*I; 129.82045011403975460991182396195022419 - 12.56637061435917295385057353  4*I; 129.82045011403975460991182396195022419], [-41.811264589129943393339502
 3118011536*I], [-41.811264589129943393339502258694361489 + 8.121413879410077  258694361489 + 6.2831853071795864769252867665590057684*I, 9.2399004147902289
 514 E-115*I, 9.2399004147902289816376260438840931575 + 3.1415926535897932384  816376260438840931575 + 3.1415926535897932384626433832795028842*I, -11.87460
 626433832795028842*I, -11.874609881075406725097315997431161032 + 9.424777960  9881075406725097315997431161032 + 3.1415926535897932384626433832795028842*I,
 7693797153879301498385086526*I, 389.46135034211926382973547188585067257 + 12   0.E-115, -51.051165003920172374977128302578454646 + 3.141592653589793238462
 .566370614359172953850573533118011536*I, -440.512515346039436204712600188429  6433832795028842*I, -64.910225057019877304955911980975112095 + 3.14159265358
 12722 + 0.E-113*I, -324.55112528509938652477955990487556047 + 6.283185307179  97932384626433832795028842*I, -29.936654708054536668242186261263200456 + 3.1
 5864769252867665590057684*I, 229.70424552002497255158146166263724792 + 3.141  415926535897932384626433832795028842*I, -47.66831907156823399733291848270768
 5926535897932384626433832795028842*I, -785.660451862534215720251179722755983  7878 + 6.2831853071795864769252867665590057684*I, 3.876293646477882506748482
 25 + 6.2831853071795864769252867665590057684*I, -554.35531386699327377220656  4790355076166, -6.7377511782956880607802359510546381087 + 3.1415926535897932
 215544062014 + 6.2831853071795864769252867665590057684*I, -47.66831907156823  384626433832795028842*I, -35.073513410834255332559266307639723380 + 3.141592
 3997332918482707687879 + 9.4247779607693797153879301498385086526*I, 177.4887  6535897932384626433832795028842*I, 33.130781426597481571750300827582717074 +
 6918560798860724474244465791207 + 6.497131103528062011 E-114*I, -875.6123693   2.030353469852519378 E-115*I, 54.878404098312329644822020875673145627 + 4.0
 7168080069763246690606885226 + 2.598852441411224804 E-113*I, 54.878404098312  60706939705038757 E-115*I, -14.980188104648613073630759189293219180 + 3.1415
 329644822020875673145627 + 9.4247779607693797153879301498385086526*I, -404.4  926535897932384626433832795028842*I, -26.83107648448133031970874306940114230
 4153844676787690336623107514389175 + 0.E-113*I, 232.809823743598178900114904  8 + 3.1415926535897932384626433832795028842*I, -19.7067490665160655124889078
 85449930607 + 6.2831853071795864769252867665590057684*I, -668.80899963671483  34878146944 + 3.1415926535897932384626433832795028842*I, -22.104515522613877
 856204802764462926790 + 9.4247779607693797153879301498385086526*I, 367.35683  880850594423816214544 + 3.1415926535897932384626433832795028842*I, -45.68755
 481950538594888487746203445802 + 12.566370614359172953850573533118011536*I,  8235607825900087984737729869105 + 6.2831853071795864769252867665590057684*I,
 -1214.0716092619656173892944003952818868 + 9.4247779607693797153879301498385   47.668319071568233997332918482707687879 + 8.121413879410077514 E-115*I; 41.
 086526*I, -125.94415646756187210316334148291471657 + 6.283185307179586476925  811264589129943393339502258694361489, -9.23990041479022898163762604388409315
 2867665590057684*I; 41.811264589129943393339502258694361489 + 6.283185307179  75, 11.874609881075406725097315997431161032, 0.E-115, 51.0511650039201723749
 5864769252867665590057684*I, -9.2399004147902289816376260438840931575 + 12.5  77128302578454646, 64.910225057019877304955911980975112095, 29.9366547080545
 66370614359172953850573533118011536*I, 11.8746098810754067250973159974311610  36668242186261263200456, 47.668319071568233997332918482707687879, -3.8762936
 32 + 8.121413879410077514 E-115*I, -389.46135034211926382973547188585067257  464778825067484824790355076166, 6.7377511782956880607802359510546381087, 35.
 + 6.2831853071795864769252867665590057684*I, 440.512515346039436204712600188  073513410834255332559266307639723380, -33.1307814265974815717503008275827170
 42912722 + 3.1415926535897932384626433832795028842*I, 324.551125285099386524  74, -54.878404098312329644822020875673145627, 14.980188104648613073630759189
 77955990487556047 + 9.4247779607693797153879301498385086526*I, -229.70424552  293219180, 26.831076484481330319708743069401142309, 19.706749066516065512488
 002497255158146166263724792 + 6.2831853071795864769252867665590057684*I, 785  907834878146944, 22.104515522613877880850594423816214544, 45.687558235607825
 .66045186253421572025117972275598325 + 9.42477796076937971538793014983850865  900087984737729869105, -47.668319071568233997332918482707687878], [[2, [2, 1
 26*I, 554.35531386699327377220656215544062014 + 3.14159265358979323846264338  ]~, 1, 1, [1, 1]~], [5, [5, 1]~, 1, 1, [1, 1]~], [13, [-5, 1]~, 1, 1, [6, 1]
 32795028842*I, 47.668319071568233997332918482707687878 + 3.14159265358979323  ~], [2, [3, 1]~, 1, 1, [0, 1]~], [5, [6, 1]~, 1, 1, [0, 1]~], [7, [4, 1]~, 2
 84626433832795028842*I, -177.48876918560798860724474244465791207 + 6.2831853  , 1, [-3, 1]~], [13, [6, 1]~, 1, 1, [-5, 1]~], [23, [7, 1]~, 1, 1, [-6, 1]~]
 071795864769252867665590057684*I, 875.61236937168080069763246690606885226 +  , [43, [-15, 1]~, 1, 1, [16, 1]~], [17, [20, 1]~, 1, 1, [-2, 1]~], [17, [15,
 6.497131103528062011 E-114*I, -54.878404098312329644822020875673145627 + 9.4   1]~, 1, 1, [3, 1]~], [29, [14, 1]~, 1, 1, [-13, 1]~], [29, [-13, 1]~, 1, 1,
 247779607693797153879301498385086526*I, 404.44153844676787690336623107514389   [14, 1]~], [31, [39, 1]~, 1, 1, [-7, 1]~], [31, [24, 1]~, 1, 1, [8, 1]~], [
 175 + 9.4247779607693797153879301498385086526*I, -232.8098237435981789001149  41, [7, 1]~, 1, 1, [-6, 1]~], [41, [-6, 1]~, 1, 1, [7, 1]~], [43, [16, 1]~,
 0485449930607 + 3.1415926535897932384626433832795028842*I, 668.8089996367148  1, 1, [-15, 1]~], [23, [-6, 1]~, 1, 1, [7, 1]~]], 0, [x^2 - x - 100000, [2,
 3856204802764462926790 + 6.2831853071795864769252867665590057684*I, -367.356  0], 400001, 1, [[1, -316.72816130129840161392089489603747004; 1, 315.7281613
 83481950538594888487746203445803 + 3.1415926535897932384626433832795028842*I  0129840161392089489603747004], [1, -316.72816130129840161392089489603747004;
 , 1214.0716092619656173892944003952818868 + 3.141592653589793238462643383279   1, 315.72816130129840161392089489603747004], 0, [2, -1; -1, 200001], [40000
 5028842*I, 125.94415646756187210316334148291471657 + 6.283185307179586476925  1, 200001; 0, 1], [200001, 1; 1, 2], [400001, [200001, 1]~]], [-315.72816130
 2867665590057684*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2, [2, 1]~, 1, 1, [1, 1]  129840161392089489603747004, 316.72816130129840161392089489603747004], [1, x
 ~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-1, 1]~], [7, [3, 1]~,   - 1], [1, 1; 0, 1], [1, 0, 0, 100000; 0, 1, 1, -1]], [[5, [5], [[2, 0; 0, 1
 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5, 1]~, 1, 1, [-6, 1]~]  ]]], 129.82045011403975460991182396195022419, 0.9876536979069047228, [2, -1]
 , [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [-7, 1  , [379554884019013781006303254896369154068336082609238336*x + 11983616564425
 ]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [-14, 1]~, 1, 1, [13  0789990462835950022871665178127611316131167], 185], [Mat(1), [[0, 0]], [[-41
 , 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~, 1, 1, [7, 1]~], [31,  .811264589129943393339502258694361489 + 6.2831853071795864769252867665590057
  [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1]~], [41, [6, 1]~, 1,  684*I, 41.811264589129943393339502258694361489]]], 0]
 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [15, 1]~, 1, 1, [-16, 1]  
 ~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18], [  
 x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.72816130129840161392089489603  
 747004; 1, 316.72816130129840161392089489603747004], [1, 1; -315.72816130129  
 840161392089489603747004, 316.72816130129840161392089489603747004], [2, 1.00  
 00000000000000000000000000000000000; 1.0000000000000000000000000000000000000  
 , 200001.00000000000000000000000000000000], [2, 1; 1, 200001], [400001, 2000  
 00; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~]], [-315.7281613012984  
 0161392089489603747004, 316.72816130129840161392089489603747004], [1, x], [1  
 , 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.8  
 2045011403975460991182396195022419, 0.9876536979069047239, [2, -1], [3795548  
 84019013781006303254896369154068336082609238336*x + 119836165644250789990462  
 835950022871665178127611316131167], 186], [Mat(1), [[0, 0]], [[-41.811264589  
 129943393339502258694361489 + 8.121413879410077514 E-115*I, 41.8112645891299  
 43393339502258694361489 + 6.2831853071795864769252867665590057684*I]]], 0]  
 ? \p19  ? \p19
    realprecision = 19 significant digits     realprecision = 19 significant digits
 ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)  ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
 [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071  [x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2 - x - 9], [-3.233732695981516672
 82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0,  , -0.07182350902743636344, 4.305556205008953036], [10889, 5698, 8994; 0, 1,
  1], Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 10, 69, 33, 39,  0; 0, 0, 1], Mat(2), Mat([1, 1, 0, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 39, 10,
 57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-4, 3, -1, 2, 3, 11, 1, -  33, 57, 69], [2, [-1, 0, 0]~], [[0, 1, 0]~, [5, 3, 1]~], [-4, -1, 2, 3, 10,
 1, -7; 1, 1, 1, 1, 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]  3, 1, 7, 2; 1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
 ? \p38  ? \p38
    realprecision = 38 significant digits     realprecision = 38 significant digits
 ? bnrinit(bnf,[[5,3;0,1],[1,0]],1)  ? bnrinit(bnf,[[5,4;0,1],[1,0]],1)
 [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106  [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746  061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767  808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1  52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
 .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122  148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659  9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337  8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*  97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
 I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498  1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153  0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265  492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +  7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626  8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179  071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42  38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106  7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932   [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592   [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +  2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
  3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934  -2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438  x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1   1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833  10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,  115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]  779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
 ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,  1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1  7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
 , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7  7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
 , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931  903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[5, 4;
 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372   0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], Mat([[5, [-1, 1]~, 1, 1, [
 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [  2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[0,
 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000  1]~], Mat(1)]], [1, 0; 0, 1]], [1], Mat([1, -3, -6]), [12, [12], [[3, 0; 0,
 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114  1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
 ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102  ? bnr=bnrclass(bnf,[[5,4;0,1],[1,0]],2)
 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],  
  [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974  
 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),  
  [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384  
 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307  
 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1]  
 , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]  
 ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~]  
 , Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[  
 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]  
 ? bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2)  
 [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106  [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746  061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767  808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1  52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
 .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122  148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659  9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337  8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*  97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
 I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498  1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153  0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265  492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +  7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626  8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179  071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42  38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106  7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932   [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592   [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +  2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
  3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934  -2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438  x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1   1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833  10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,  115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]  779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
 ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,  1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1  7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
 , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7  7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
 , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931  903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[5, 4;
 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372   0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], Mat([[5, [-1, 1]~, 1, 1, [
 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [  2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[0,
 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000  1]~], Mat(1)]], [1, 0; 0, 1]], [1], Mat([1, -3, -6]), [12, [12], [[3, 0; 0,
 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114  1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
 ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102  
 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],  
  [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974  
 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),  
  [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384  
 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307  
 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1]  
 , [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1]  
 ~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~]  
 , Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[  
 3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]  
 ? rnfinit(nf2,x^5-x-2)  ? rnfinit(nf2,x^5-x-2)
 [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3  [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3
 109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914  109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914
Line 591  I, -1.0672071180669977537495893497477340535 - 1.390957
Line 490  I, -1.0672071180669977537495893497477340535 - 1.390957
  0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [M   0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [M
 od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1  od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1
 , y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^  , y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^
 3 - y - 1)], [], [y^3 - y - 1, [1, 1], -23, 1, [[1, 1.3247179572447460259609  3 - y - 1)], [], [y^3 - y - 1, [1, 1], -23, 1, [[1, 0.7548776662466927600495
 088544780973407, 1.7548776662466927600495088963585286918; 1, -0.662358978622  0889635852869189, 1.3247179572447460259609088544780973407; 1, -0.87743883312
 37301298045442723904867036 + 0.56227951206230124389918214490937306149*I, 0.1  334638002475444817926434594 - 0.74486176661974423659317042860439236723*I, -0
 2256116687665361997524555182073565405 - 0.7448617666197442365931704286043923  .66235897862237301298045442723904867036 + 0.56227951206230124389918214490937
 6724*I], [1, 2; 1.3247179572447460259609088544780973407, -1.3247179572447460  306149*I], [1, 0.75487766624669276004950889635852869189, 1.32471795724474602
 259609088544780973407 - 1.1245590241246024877983642898187461229*I; 1.7548776  59609088544780973407; 1.4142135623730950488016887242096980785, -1.2408858979
 662466927600495088963585286918, 0.24512233375330723995049110364147130810 + 1  558593537192653626096055786, -0.93671705072735084703311164961686101696; 0, -
 .4897235332394884731863408572087847344*I], [3, 0.E-96, 2.0000000000000000000  1.0533936124468254335289038498031013275, 0.795183311803032710044767156296587
 000000000000000000; 0.E-96, 3.2646329987400782801485266890755860756, 1.32471  54002], 0, [3, -1, 0; -1, 1, 3; 0, 3, 2], [23, 16, 13; 0, 1, 0; 0, 0, 1], [-
 79572447460259609088544780973407; 2.0000000000000000000000000000000000000, 1  7, 2, -3; 2, 6, -9; -3, -9, 2], [23, [10, 7, 1]~]], [1.324717957244746025960
 .3247179572447460259609088544780973407, 4.2192762054875453178332176670757633  9088544780973407, -0.66235897862237301298045442723904867036 + 0.562279512062
 303], [3, 0, 2; 0, 2, 3; 2, 3, 2], [23, 13, 15; 0, 1, 0; 0, 0, 1], [-5, 6, -  30124389918214490937306149*I], [1, y^2 - 1, y], [1, 0, 1; 0, 0, 1; 0, 1, 0],
 4; 6, 2, -9; -4, -9, 6], [23, [7, 10, 1]~]], [1.3247179572447460259609088544   [1, 0, 0, 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, -1, 0, 0, 0, 1; 0, 0, 1, 0, 1, 0, 1
 780973407, -0.66235897862237301298045442723904867036 + 0.5622795120623012438  , 0, 0]], [x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*
 9918214490937306149*I], [1, y, y^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0,  x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1, Mod(3951653
 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  6165538345/83718587879473471*x^14 - 6500512476832995/83718587879473471*x^13
 ^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  - 196215472046117185/83718587879473471*x^12 + 229902227480108910/83718587879
  + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1, Mod(39516536165538345/8  473471*x^11 + 237380704030959181/83718587879473471*x^10 - 106493198816077380
 3718587879473471*x^14 - 6500512476832995/83718587879473471*x^13 - 1962154720  5/83718587879473471*x^9 - 20657086671714300/83718587879473471*x^8 + 17728852
 46117185/83718587879473471*x^12 + 229902227480108910/83718587879473471*x^11  05999206010/83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^
 + 237380704030959181/83718587879473471*x^10 - 1064931988160773805/8371858787  6 - 4838840187320655696/83718587879473471*x^5 + 5180390720553188700/83718587
 9473471*x^9 - 20657086671714300/83718587879473471*x^8 + 1772885205999206010/  879473471*x^4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040
 83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^6 - 48388401  221/83718587879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920
 87320655696/83718587879473471*x^5 + 5180390720553188700/83718587879473471*x^  215718580450/83718587879473471, x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 -
 4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040221/83718587  5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 +
 879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920215718580450  25*x + 1), -1, [1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^
 /83718587879473471, x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x  12, x^13, 1/83718587879473471*x^14 - 20528463024680133/83718587879473471*x^1
 ^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), -  3 - 4742392948888610/83718587879473471*x^12 - 9983523646123358/8371858787947
 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/  3471*x^11 + 40898955597139011/83718587879473471*x^10 + 29412692423971937/837
 83718587879473471*x^14 - 20528463024680133/83718587879473471*x^13 - 47423929  18587879473471*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075
 48888610/83718587879473471*x^12 - 9983523646123358/83718587879473471*x^11 +  066/83718587879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 2015290
 40898955597139011/83718587879473471*x^10 + 29412692423971937/837185878794734  5879672878/83718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 -
 71*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075066/83718587  8471905745957397/83718587879473471*x^3 - 13395753879413605/83718587879473471
 879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 20152905879672878/8  *x^2 + 27623037732247492/83718587879473471*x + 26306699661480593/83718587879
 3718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 - 847190574595  473471], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1
 7397/83718587879473471*x^3 - 13395753879413605/83718587879473471*x^2 + 27623  , 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0,
 037732247492/83718587879473471*x + 26306699661480593/83718587879473471], [1,  0, 0, 0, 0, 0, 0, 0, 0, 13395753879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0  0, 0, 0, 8471905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -959164
 , 0, 0, 0, 0, 0, 0, 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,  3151927789; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0,
 0, 0, 0, 0, 13395753879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 847   0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0,
 1905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789;  0, 1, 0, 0, 0, 0, 0, 0, -41014993230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0,   0, 0, 0, 5017479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412
  0, 1, 0, 0, 0, 0, 0, 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,  692423971937; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011;
 0, 0, 0, 0, -41014993230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 50  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0
 17479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937  , 0, 0, 0, 0, 0, 0, 1, 0, 4742392948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
 ; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011; 0, 0, 0, 0,   0, 0, 1, 20528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718
 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0  587879473471]]]
 , 0, 0, 1, 0, 4742392948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20  
 528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471  
 ]]]  
 ? bnfcertify(bnf)  ? bnfcertify(bnf)
 1  1
 ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])  ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
Line 668  od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1)
Line 564  od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1)
   
 [[400001, 1]]  [[400001, 1]]
   
 [[1, x]]  [[1, x - 1]]
   
 [[5, [5], [[2, 1; 0, 1]]]]  [[5, [5], [[2, 0; 0, 1]]]]
   
 [129.82045011403975460991182396195022419]  [129.82045011403975460991182396195022419]
   
 [0.9876536979069047239]  [0.9876536979069047228]
   
 [[2, -1]]  [[2, -1]]
   
Line 690  od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1)
Line 586  od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1)
   
 [[400001, 1]]  [[400001, 1]]
   
 [[1, x]]  [[1, x - 1]]
   
 [[5, [5], [[2, 1; 0, 1]]]]  [[5, [5], [[2, 0; 0, 1]]]]
   
 [129.82045011403975460991182396195022419]  [129.82045011403975460991182396195022419]
   
 [0.9876536979069047239]  [0.9876536979069047228]
   
 [[2, -1]]  [[2, -1]]
   
 [[379554884019013781006303254896369154068336082609238336*x + 119836165644250  [[379554884019013781006303254896369154068336082609238336*x + 119836165644250
 789990462835950022871665178127611316131167]]  789990462835950022871665178127611316131167]]
   
 [186]  [185]
   
 ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])  ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
   
Line 713  od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1)
Line 609  od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1)
   
 [[18981, 3087]]  [[18981, 3087]]
   
 [[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 - 155/343*x - 58/343]]  [[1, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343, 17/1029*x^3 - 32/1029
   *x^2 + 109/343*x + 2444/343, -11/343*x^3 + 163/1029*x^2 - 373/343*x - 4260/3
   43]]
   
 [[4, [4], [[7, 6, 2, 4; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]  [[4, [4], [[7, 2, 4, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]]
   
 [3.7941269688216589341408274220859400302]  [3.7941269688216589341408274220859400302]
   
 [0.8826018286655581306]  [0.8826018286655581299]
   
 [[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]]  [[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
   
 [[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]  [[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]
   
 [182]  [365]
   
 ? setrand(1);bnfclgp(17)  ? setrand(1);bnfclgp(17)
 [1, [], []]  [1, [], []]
 ? setrand(1);bnfclgp(-31)  ? setrand(1);bnfclgp(-31)
 [3, [3], [Qfb(2, 1, 4)]]  [3, [3], [Qfb(2, 1, 4)]]
 ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791)  ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791)
 [4, [4], [[7, 5, 1, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]  [4, [4], [[7, 2, 0, 5; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]]
 ? bnrconductor(bnf,[[25,13;0,1],[1,1]])  ? bnrconductor(bnf,[[25,14;0,1],[1,1]])
 [[5, 3; 0, 1], [1, 0]]  [[5, 4; 0, 1], [1, 0]]
 ? bnrconductorofchar(bnr,[2])  ? bnrconductorofchar(bnr,[2])
 [[5, 3; 0, 1], [0, 0]]  [[5, 4; 0, 1], [0, 0]]
 ? bnfisprincipal(bnf,[5,1;0,1],0)  ? bnfisprincipal(bnf,[5,2;0,1],0)
 [1]~  [1]~
 ? bnfisprincipal(bnf,[5,1;0,1])  ? bnfisprincipal(bnf,[5,2;0,1])
 [[1]~, [-2, -1/3]~, 181]  [[1]~, [7/3, 1/3]~, 187]
 ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))  ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
 [-4, Mod(1, 2)]~  [-4, Mod(1, 2)]~
 ? \p19  ? \p19
    realprecision = 19 significant digits     realprecision = 19 significant digits
 ? bnfmake(sbnf)  ? bnfmake(sbnf)
 [Mat(2), Mat([0, 1, 1, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535  [Mat(2), Mat([1, 1, 0, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535
 89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389  89793238*I, -4.562279014988837952 + 3.141592653589793238*I; -2.6335434327389
 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*  76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238*
 I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14  I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14
 1592653589793238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400  1592653589793238*I, 0.5404006376129469727 + 3.141592653589793238*I, -0.69263
 6376129469727 + 3.141592653589793238*I, -0.6926391142471042845 + 3.141592653  91142471042844 + 3.141592653589793238*I, -1.990056445584799713 + 3.141592653
 589793238*I, 0.E-96, 0.3677262014027817705 + 3.141592653589793238*I, 0.00437  589793238*I, -0.8305625946607188643 + 3.141592653589793238*I, 0.E-57, 0.0043
 5616572659815402 + 3.141592653589793238*I, -0.8305625946607188639, -1.977791  75616572659815433 + 3.141592653589793238*I, -1.977791147836553953, 0.3677262
 147836553953 + 3.141592653589793238*I; 0.6716827432867392935 + 3.14159265358  014027817708 + 3.141592653589793238*I; 0.6716827432867392938 + 3.14159265358
 9793238*I, 0.5379005671092853266, -0.8333219883742404172 + 3.141592653589793  9793238*I, -0.8333219883742404170 + 3.141592653589793238*I, -0.2461086674077
 238*I, -0.2461086674077943078, 0.E-96, 0.9729063188316092378, -0.87383180430  943076, 0.5379005671092853269, -1.552661549868775853, 0.E-57, -0.87383180430
 71131265, -1.552661549868775853 + 3.141592653589793238*I, 0.5774919091398324  71131263, 0.5774919091398324092, 0.9729063188316092380; -1.91802973262155845
 092 + 3.141592653589793238*I; -1.918029732621558454, 1.452155878475514386, 0  5, 0.2929213507612934444, 0.9387477816548985923, 1.452155878475514386, 2.383
 .2929213507612934444, 0.9387477816548985923, 0.E-96, -1.340632520234391008,  224144529494717, 0.E-57, 0.8694561877344533111, 1.400299238696721544, -1.340
 0.8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.4002  632520234391008], [[3, [-1, 1, 0]~, 1, 1, [1, 1, 1]~], [5, [-1, 1, 0]~, 1, 1
 99238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]~  , [0, 1, 1]~], [5, [2, 1, 0]~, 1, 1, [1, -2, 1]~], [5, [3, 1, 0]~, 1, 1, [2,
 ], [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [   2, 1]~], [13, [19, 1, 0]~, 1, 1, [-2, -6, 1]~], [3, [10, 1, 1]~, 1, 2, [-1,
 5, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [23, [   1, 0]~], [11, [1, 1, 0]~, 1, 1, [-3, -1, 1]~], [19, [-6, 1, 0]~, 1, 1, [6,
 -10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [13, [  6, 1]~], [23, [-10, 1, 0]~, 1, 1, [-7, 10, 1]~]]~, 0, [x^3 - x^2 - 14*x - 1,
 19, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2   [3, 0], 10889, 1, [[1, -3.233732695981516672, 4.690759845041404811; 1, -0.0
 , 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.23  7182350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.23225
 3732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.005158  8029482144592], [1, -3.233732695981516672, 4.690759845041404811; 1, -0.07182
 616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; -  350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.232258029
 3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.4570  482144592], 0, [3, 1, 1; 1, 29, 8; 1, 8, 129], [10889, 5698, 8994; 0, 1, 0;
 2714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.0000000  0, 0, 1], [3677, -121, -21; -121, 386, -23; -21, -23, 86], [10889, [1899, 51
 00000000000, 29.00000000000000000; 1.000000000000000000, 29.0000000000000000  91, 1]~]], [-3.233732695981516672, -0.07182350902743636344, 4.30555620500895
 0, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.000  3036], [1, x, x^2 - x - 9], [1, 0, 9; 0, 1, 1; 0, 0, 1], [1, 0, 0, 0, 9, 1,
 0000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1  0, 1, 44; 0, 1, 0, 1, 1, 5, 0, 5, 1; 0, 0, 1, 0, 1, 0, 1, 0, -4]], [[2, [2],
 , 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, [   [[3, 2, 0; 0, 1, 0; 0, 0, 1]]], 10.34800724602768011, 1.000000000000000000,
 1890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.305556   [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0.E-57, 0.E-57, 0.E-57]], [[
 205008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1,  1.246346989334819161 + 3.141592653589793238*I, 0.6716827432867392938 + 3.141
 0, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2  592653589793238*I, -1.918029732621558455]]], [-4, -1, 2, 3, 10, 3, 1, 7, 2;
 ], [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.00000000000000000  1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
 0, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0, 0, 0]], [[1.24634698933  
 4819161 + 3.141592653589793238*I, 0.6716827432867392935 + 3.1415926535897932  
 38*I, -1.918029732621558454]]], [-4, 3, -1, 2, 3, 11, 1, -1, -7; 1, 1, 1, 1,  
  0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]]  
 ? \p38  ? \p38
    realprecision = 38 significant digits     realprecision = 38 significant digits
 ? bnfnarrow(bnf)  ? bnfnarrow(bnf)
 [3, [3], [[3, 2; 0, 1]]]  [3, [3], [[3, 0; 0, 1]]]
 ? bnfreg(x^2-x-57)  ? bnfreg(x^2-x-57)
 2.7124653051843439746808795106061300699  2.7124653051843439746808795106061300699
 ? bnfsignunit(bnf)  ? bnfsignunit(bnf)
Line 796  I; 1.459906329303914334, 3.141948414209350543], [1.246
Line 690  I; 1.459906329303914334, 3.141948414209350543], [1.246
 [1]  [1]
   
 ? bnfunit(bnf)  ? bnfunit(bnf)
 [[x + 7], 185]  [[x + 7], 187]
 ? bnrclass(bnf,[[5,3;0,1],[1,0]])  ? bnrclass(bnf,[[5,4;0,1],[1,0]])
 [12, [12], [[3, 2; 0, 1]]]  [12, [12], [[3, 0; 0, 1]]]
 ? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2)  ? bnr2=bnrclass(bnf,[[25,14;0,1],[1,1]],2)
 [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106  [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106
 061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746  061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746
 808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767  808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306
 22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1  52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70
 .2897619530652735025030086072395031017 + 0.E-57*I, -2.0109798024989157562122  148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133
 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659  9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157
 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337  8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358
 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*  97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.
 I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498  1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639
 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153  0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368
 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265  492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697
 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +  7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014
 0.E-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626  8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339
 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179  071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414
 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42  38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974
 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106  7564707190997873636390948, -0.066178301882745732185368492323164193433], [[3,
 12 + 0.E-57*I, -24.412187746659095772127915595455170629 + 3.1415926535897932   [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [11, [-1, 1]~, 1, 1,
 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592   [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, [-1, 1]~], [11, [
 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +  2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17, [3, 1]~, 1, 1, [
  3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934  -2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, 1, [1, 1]~]], 0, [
 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438  x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635959310246705326058;
 988786673341921876 + 0.E-57*I, 14.550628376291080203941433635329724736 + 3.1   1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593
 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833  10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1,
 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,  115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107
 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]  779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x -
 ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,  1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.
 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1  7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x +
 , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7  7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7
 , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931  903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[25, 1
 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372  4; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [4, 2]~, [-2, -2]~]], Mat([[5,
 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [   [-1, 1]~, 1, 1, [2, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), M
 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000  od(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat(
 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114  [1/5, -14/5])]], [[2, 2], [[4, 2]~, [-2, -2]~], [1, 0; 0, 1]]], [1, -12, 0,
 ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102  0; 0, 0, 1, 0; 0, 0, 0, 1]], [1], Mat([1, -3, -6, 0]), [12, [12], [[3, 0; 0,
 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],   1]]], [[1, -18, 9; -1/2, 10, -5], [-2, 0; 0, -10]]]
  [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974  ? bnrclassno(bnf,[[5,4;0,1],[1,0]])
 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 185], [Mat(1),  
  [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384  
 626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307  
 1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[25, 13; 0,  
 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [0, -2]~, [2, 2]~]], Mat([[5, [-2, 1  
 ]~, 1, 1, [1, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), Mod(0, 2  
 )]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat([1/5, -  
 13/5])]], [[2, 2], [[0, -2]~, [2, 2]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0,  
  1, 0; 0, 0, 0, 1]], [1], [1, -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0]  
 , [12, [12], [[3, 2; 0, 1]]], [[1, 9, -18; -1/2, -5, 10], [-2, 0; 0, 10]]]  
 ? bnrclassno(bnf,[[5,3;0,1],[1,0]])  
 12  12
 ? lu=ideallist(bnf,55,3);  ? lu=ideallist(bnf,55,3);
 ? bnrclassnolist(bnf,lu)  ? bnrclassnolist(bnf,lu)
Line 862  I, -20.610866187462450639586440264933189691 + 9.424777
Line 745  I, -20.610866187462450639586440264933189691 + 9.424777
 ? bnrdisc(bnr2,,,2)  ? bnrdisc(bnr2,,,2)
 0  0
 ? bnrdisc(bnr,Mat(6),,1)  ? bnrdisc(bnr,Mat(6),,1)
 [6, 2, [125, 13; 0, 1]]  [6, 2, [125, 14; 0, 1]]
 ? bnrdisc(bnr,,,1)  ? bnrdisc(bnr,,,1)
 [12, 1, [1953125, 1160888; 0, 1]]  [12, 1, [1953125, 1160889; 0, 1]]
 ? bnrdisc(bnr2,,,3)  ? bnrdisc(bnr2,,,3)
 0  0
 ? bnrdisclist(bnf,lu)  ? bnrdisclist(bnf,lu)
Line 911  I, -20.610866187462450639586440264933189691 + 9.424777
Line 794  I, -20.610866187462450639586440264933189691 + 9.424777
 18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0,  18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0,
 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]]  0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]]
 ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])  ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
 [[9]~, [-2170/6561, -931/19683]~, 256]  [[9]~, [112595/19683, 13958/19683]~, 256]
 ? dirzetak(nf4,30)  ? dirzetak(nf4,30)
 [1, 2, 0, 3, 1, 0, 0, 4, 0, 2, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 0, 2, 0, 0, 2,  [1, 2, 0, 3, 1, 0, 0, 4, 0, 2, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 0, 2, 0, 0, 2,
 0, 1, 0, 1, 0]  0, 1, 0, 1, 0]
Line 924  I, -20.610866187462450639586440264933189691 + 9.424777
Line 807  I, -20.610866187462450639586440264933189691 + 9.424777
 [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]  [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]
   
 ? vp=idealprimedec(nf,3)[1]  ? vp=idealprimedec(nf,3)[1]
 [3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~]  [3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~]
 ? idx=idealmul(nf,matid(5),vp)  ? idx=idealmul(nf,matid(5),vp)
   
 [3 1 2 2 2]  [3 2 1 0 1]
   
 [0 1 0 0 0]  [0 1 0 0 0]
   
Line 939  I, -20.610866187462450639586440264933189691 + 9.424777
Line 822  I, -20.610866187462450639586440264933189691 + 9.424777
   
 ? idealinv(nf,idx)  ? idealinv(nf,idx)
   
 [1 0 2/3 0 0]  [1 0 0 2/3 0]
   
 [0 1 1/3 0 0]  [0 1 0 1/3 0]
   
 [0 0 1/3 0 0]  [0 0 1 1/3 0]
   
 [0 0 0 1 0]  [0 0 0 1/3 0]
   
 [0 0 0 0 1]  [0 0 0 0 1]
   
 ? idy=idealred(nf,idx,[1,5,6])  ? idy=idealred(nf,idx,[1,5,6])
   
 [5 0 0 2 0]  [5 0 0 0 2]
   
 [0 5 0 0 0]  [0 5 0 0 2]
   
 [0 0 5 2 0]  [0 0 5 0 1]
   
 [0 0 0 1 0]  [0 0 0 5 2]
   
 [0 0 0 0 5]  [0 0 0 0 1]
   
 ? idx2=idealmul(nf,idx,idx)  ? idx2=idealmul(nf,idx,idx)
   
 [9 7 5 8 2]  [9 5 7 0 4]
   
 [0 1 0 0 0]  [0 1 0 0 0]
   
Line 975  I, -20.610866187462450639586440264933189691 + 9.424777
Line 858  I, -20.610866187462450639586440264933189691 + 9.424777
   
 ? idt=idealmul(nf,idx,idx,1)  ? idt=idealmul(nf,idx,idx,1)
   
 [2 0 0 0 1]  [2 0 0 0 0]
   
 [0 2 0 0 1]  [0 2 0 0 0]
   
 [0 0 2 0 0]  [0 0 2 0 0]
   
Line 987  I, -20.610866187462450639586440264933189691 + 9.424777
Line 870  I, -20.610866187462450639586440264933189691 + 9.424777
   
 ? idz=idealintersect(nf,idx,idy)  ? idz=idealintersect(nf,idx,idy)
   
 [15 5 10 12 10]  [15 10 5 0 12]
   
 [0 5 0 0 0]  [0 5 0 0 2]
   
 [0 0 5 2 0]  [0 0 5 0 1]
   
 [0 0 0 1 0]  [0 0 0 5 2]
   
 [0 0 0 0 5]  [0 0 0 0 1]
   
 ? aid=[idx,idy,idz,matid(5),idx]  ? aid=[idx,idy,idz,matid(5),idx]
 [[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]  [[3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
 , [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5  , [5, 0, 0, 0, 2; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1
 ], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0,  ], [15, 10, 5, 0, 12; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0,
  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  0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0,
 , 0, 1], [3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0,   0, 1], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0
 0, 0, 1]]  , 0, 1]]
 ? bid=idealstar(nf2,54,1)  ? bid=idealstar(nf2,54,1)
 [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,  [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[  0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]  1, 1, 0]~], [[1, -27, 0]~], [[]~], 1]], [[[26], [[2, 1, 0]~], [[-25, -26, 0]
 ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0  ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
 ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3  ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
 , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,  , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
 [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,  [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
  0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7   0]]], [[], [], [;]]], [2106, -77, 10556, 0, -4368, 12012, 0, -13104; 0, 0,
 , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]  0, 1, -2, 0, -6, -6; -27, 1, -136, 0, 56, -156, 0, 168]]
 ? vaid=[idx,idy,matid(5)]  ? vaid=[idx,idy,matid(5)]
 [[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]  [[3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]
 , [5, 0, 0, 2, 0; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 5  , [5, 0, 0, 0, 2; 0, 5, 0, 0, 2; 0, 0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1
 ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,  ], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0,
 1]]  1]]
 ? haid=[matid(5),matid(5),matid(5)]  ? haid=[matid(5),matid(5),matid(5)]
Line 1037  I, -20.610866187462450639586440264933189691 + 9.424777
Line 920  I, -20.610866187462450639586440264933189691 + 9.424777
 [0 0 0 0 1]  [0 0 0 0 1]
   
 ? idealaddtoone(nf,idx,idy)  ? idealaddtoone(nf,idx,idy)
 [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]  [[3, 2, 1, 2, 1]~, [-2, -2, -1, -2, -1]~]
 ? idealaddtoone(nf,[idy,idx])  ? idealaddtoone(nf,[idy,idx])
 [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]  [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~]
 ? idealappr(nf,idy)  ? idealappr(nf,idy)
 [-2, 0, -2, 4, 0]~  [-2, -2, -1, -2, -1]~
 ? idealappr(nf,idealfactor(nf,idy),1)  ? idealappr(nf,idealfactor(nf,idy),1)
 [-2, 0, -2, 4, 0]~  [-2, -2, -1, -2, -1]~
 ? idealcoprime(nf,idx,idx)  ? idealcoprime(nf,idx,idx)
 [-2/3, 2/3, -1/3, 0, 0]~  [1/3, -1/3, -1/3, -1/3, 0]~
 ? idealdiv(nf,idy,idt)  ? idealdiv(nf,idy,idt)
   
 [5 5/2 5/2 7/2 0]  [5 0 5/2 0 1]
   
 [0 5/2 0 0 0]  [0 5/2 0 0 1]
   
 [0 0 5/2 1 0]  [0 0 5/2 0 1/2]
   
 [0 0 0 1/2 0]  [0 0 0 5/2 1]
   
 [0 0 0 0 5/2]  [0 0 0 0 1/2]
   
 ? idealdiv(nf,idx2,idx,1)  ? idealdiv(nf,idx2,idx,1)
   
 [3 1 2 2 2]  [3 2 1 0 1]
   
 [0 1 0 0 0]  [0 1 0 0 0]
   
Line 1072  I, -20.610866187462450639586440264933189691 + 9.424777
Line 955  I, -20.610866187462450639586440264933189691 + 9.424777
   
 ? idf=idealfactor(nf,idz)  ? idf=idealfactor(nf,idz)
   
 [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1]  [[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] 1]
   
 [[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1]  [[5, [-1, 0, 0, 0, 1]~, 1, 1, [2, 0, 3, 0, 1]~] 1]
   
 [[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3]  [[5, [2, 0, 0, 0, 1]~, 4, 1, [2, 2, 1, 2, 1]~] 3]
   
 ? idealhnf(nf,vp)  ? idealhnf(nf,vp)
   
 [3 1 2 2 2]  [3 2 1 0 1]
   
 [0 1 0 0 0]  [0 1 0 0 0]
   
Line 1092  I, -20.610866187462450639586440264933189691 + 9.424777
Line 975  I, -20.610866187462450639586440264933189691 + 9.424777
   
 ? idealhnf(nf,vp[2],3)  ? idealhnf(nf,vp[2],3)
   
 [3 1 2 2 2]  [3 2 1 0 1]
   
 [0 1 0 0 0]  [0 1 0 0 0]
   
Line 1103  I, -20.610866187462450639586440264933189691 + 9.424777
Line 986  I, -20.610866187462450639586440264933189691 + 9.424777
 [0 0 0 0 1]  [0 0 0 0 1]
   
 ? ideallist(bnf,20)  ? ideallist(bnf,20)
 [[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0  [[[1, 0; 0, 1]], [], [[3, 0; 0, 1], [3, 1; 0, 1]], [[2, 0; 0, 2]], [[5, 4; 0
 , 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]],  , 1], [5, 2; 0, 1]], [], [], [], [[9, 6; 0, 1], [3, 0; 0, 3], [9, 4; 0, 1]],
  [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [   [], [[11, 10; 0, 1], [11, 2; 0, 1]], [[6, 0; 0, 2], [6, 2; 0, 2]], [], [],
 [15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]]  [[15, 9; 0, 1], [15, 4; 0, 1], [15, 12; 0, 1], [15, 7; 0, 1]], [[4, 0; 0, 4]
 , [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10  ], [[17, 15; 0, 1], [17, 3; 0, 1]], [], [[19, 0; 0, 1], [19, 1; 0, 1]], [[10
 , 6; 0, 2], [10, 2; 0, 2]]]  , 8; 0, 2], [10, 4; 0, 2]]]
 ? ideallog(nf2,w,bid)  ? ideallog(nf2,w,bid)
 [1574, 8, 6]~  [486, 3, 7]~
 ? idealmin(nf,idx,[1,2,3])  ? idealmin(nf,idx,[1,2,3])
 [[-1; 0; 0; 1; 0], [2.0885812311199768913287869744681966008 + 3.141592653589  [[-2; 1; 1; 0; 1], [2.0885812311199768913287869744681966008 + 3.141592653589
 7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244  7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244
 7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160  7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160
 203 + 2.5437460822678889883600220330800078854*I]]  207 + 2.5437460822678889883600220330800078854*I]]
 ? idealnorm(nf,idt)  ? idealnorm(nf,idt)
 16  16
 ? idp=idealpow(nf,idx,7)  ? idp=idealpow(nf,idx,7)
   
 [2187 1807 2129 692 1379]  [2187 1436 1807 630 1822]
   
 [0 1 0 0 0]  [0 1 0 0 0]
   
Line 1132  I, -20.610866187462450639586440264933189691 + 9.424777
Line 1015  I, -20.610866187462450639586440264933189691 + 9.424777
   
 ? idealpow(nf,idx,7,1)  ? idealpow(nf,idx,7,1)
   
 [5 0 0 2 0]  [2 0 0 0 0]
   
 [0 5 0 0 0]  [0 2 0 0 0]
   
 [0 0 5 2 0]  [0 0 2 0 0]
   
 [0 0 0 1 0]  [0 0 0 2 1]
   
 [0 0 0 0 5]  [0 0 0 0 1]
   
 ? idealprimedec(nf,2)  ? idealprimedec(nf,2)
 [[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1,  [[2, [3, 0, 1, 0, 0]~, 1, 1, [0, 0, 0, 1, 1]~], [2, [12, -4, -2, 11, 3]~, 1,
  4, [1, 1, 0, 0, 0]~]]   4, [1, 0, 1, 0, 0]~]]
 ? idealprimedec(nf,3)  ? idealprimedec(nf,3)
 [[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2,  [[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~], [3, [-1, -1, -1, 0, 0]~,
  2, [1, 2, 3, 1, 0]~]]  2, 2, [0, 2, 2, 1, 0]~]]
 ? idealprimedec(nf,11)  ? idealprimedec(nf,11)
 [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]  [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
 ? idealprincipal(nf,Mod(x^3+5,nfpol))  ? idealprincipal(nf,Mod(x^3+5,nfpol))
   
 [6]  [6]
   
 [0]  
   
 [1]  [1]
   
 [3]  [3]
   
 [0]  [1]
   
   [3]
   
 ? idealtwoelt(nf,idy)  ? idealtwoelt(nf,idy)
 [5, [2, 0, 2, 1, 0]~]  [5, [2, 2, 1, 2, 1]~]
 ? idealtwoelt(nf,idy,10)  ? idealtwoelt(nf,idy,10)
 [-2, 0, -2, -1, 0]~  [-2, -2, -1, -2, -1]~
 ? idealstar(nf2,54)  ? idealstar(nf2,54)
 [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,  [[[54, 0, 0; 0, 54, 0; 0, 0, 54], [0]], [132678, [1638, 9, 9]], [[2, [2, 0,
 0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[  0]~, 1, 3, [1, 0, 0]~], 1; [3, [3, 0, 0]~, 1, 3, [1, 0, 0]~], 3], [[[[7], [[
 0, 1, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 0]  1, 0, 1]~], [[1, 0, -27]~], [[]~], 1]], [[[26], [[2, 2, 1]~], [[-25, 2, -26]
 ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0  ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0
 ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3  ]~, [1, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3
 , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,  , 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,
 [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,  [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,
  0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7   0]]], [[], [], [;]]], [468, 469, 0, 0, -85358, 0, 0, -36582; 0, 0, 1, 0, -5
 , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]  , -6, 0, -6; 0, 0, 0, 1, -8, 0, -6, -6]]
 ? idealval(nf,idp,vp)  ? idealval(nf,idp,vp)
 7  7
 ? ideleprincipal(nf,Mod(x^3+5,nfpol))  ? ideleprincipal(nf,Mod(x^3+5,nfpol))
 [[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897  [[6; 1; 3; 1; 3], [2.2324480827796254080981385584384939684 + 3.1415926535897
 932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851  932384626433832795028841*I, 5.0387659675158716386435353106610489968 + 1.5851
 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173  760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
  - 0.0083630478144368246110910258645462996191*I]]   - 0.0083630478144368246110910258645462996225*I]]
 ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))  ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
 [6, 0, 1, 3, 0]~  [6, 1, 3, 1, 3]~
 ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))  ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
 [1, 1, 1, 3, 0]~  [1, 1, 4, 1, 3]~
 ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])  ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)])
   
 [[0, 1, 1, 0, 0]~]  [[3, -2, 1, 1, 0]~]
   
 [[1, 0, 1, 0, 0]~]  [[4, -2, 0, 1, 0]~]
   
 ? matbasistoalg(nf,bc)  ? matbasistoalg(nf,bc)
   
Line 1214  Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
Line 1097  Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
 4/139623738889203638909659*x - 13185339461968406/58346808996920447]  4/139623738889203638909659*x - 13185339461968406/58346808996920447]
 ? da=nfdetint(nf,[a,aid])  ? da=nfdetint(nf,[a,aid])
   
 [30 5 25 27 10]  [90 70 35 0 65]
   
 [0 5 0 0 0]  [0 5 0 0 0]
   
 [0 0 5 2 0]  [0 0 5 0 0]
   
 [0 0 0 1 0]  [0 0 0 5 0]
   
 [0 0 0 0 5]  [0 0 0 0 5]
   
Line 1231  Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
Line 1114  Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
 ? nfdisc(p2,0,fa)  ? nfdisc(p2,0,fa)
 136866601  136866601
 ? nfeltdiv(nf,ba,bb)  ? nfeltdiv(nf,ba,bb)
 [755/373, -152/373, 159/373, 120/373, -264/373]~  [584/373, 66/373, -32/373, -105/373, 120/373]~
 ? nfeltdiveuc(nf,ba,bb)  ? nfeltdiveuc(nf,ba,bb)
 [2, 0, 0, 0, -1]~  [2, 0, 0, 0, 0]~
 ? nfeltdivrem(nf,ba,bb)  ? nfeltdivrem(nf,ba,bb)
 [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]  [[2, 0, 0, 0, 0]~, [4, -1, -5, -1, -3]~]
 ? nfeltmod(nf,ba,bb)  ? nfeltmod(nf,ba,bb)
 [-12, -7, 0, 9, 5]~  [4, -1, -5, -1, -3]~
 ? nfeltmul(nf,ba,bb)  ? nfeltmul(nf,ba,bb)
 [-25, -50, -30, 15, 90]~  [50, -15, -35, 60, 15]~
 ? nfeltpow(nf,bb,5)  ? nfeltpow(nf,bb,5)
 [23455, 156370, 115855, 74190, -294375]~  [-291920, 136855, 230560, -178520, 74190]~
 ? nfeltreduce(nf,ba,idx)  ? nfeltreduce(nf,ba,idx)
 [1, 0, 0, 0, 0]~  [1, 0, 0, 0, 0]~
 ? nfeltval(nf,ba,vp)  ? nfeltval(nf,ba,vp)
 0  0
 ? nffactor(nf2,x^3+x)  ? nffactor(nf2,x^3+x)
   
 [Mod(1, y^3 - y - 1)*x 1]  [x 1]
   
 [Mod(1, y^3 - y - 1)*x^2 + Mod(1, y^3 - y - 1) 1]  [x^2 + 1 1]
   
 ? aut=nfgaloisconj(nf3)  ? aut=nfgaloisconj(nf3)
 [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  [-x, x, -1/12*x^4 - 1/2*x, -1/12*x^4 + 1/2*x, 1/12*x^4 - 1/2*x, 1/12*x^4 + 1
 , -x]~  /2*x]~
 ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))  ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108))
 Mod(1/2*x^5 - 9*x^2, x^6 + 108)  Mod(-1/2*x^5 + 9*x^2, x^6 + 108)
 ? nfhilbert(nf,3,5)  ? nfhilbert(nf,3,5)
 -1  -1
 ? nfhilbert(nf,3,5,idf[1,1])  ? nfhilbert(nf,3,5,idf[1,1])
 -1  -1
 ? nfhnf(nf,[a,aid])  ? nfhnf(nf,[a,aid])
 [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1  [[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [
 , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,  1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0
  0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0  , 0, 0, 0]~], [[10, 4, 5, 6, 7; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
 , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;   0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0
 0, 0, 0, 0, 1], [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], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1,
  0, 0, 0, 0, 1]]]  0; 0, 0, 0, 0, 1]]]
 ? nfhnfmod(nf,[a,aid],da)  ? nfhnfmod(nf,[a,aid],da)
 [[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1  [[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [
 , 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0,  1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [1, 0
  0, 0, 0]~], [[2, 1, 1, 1, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0  , 0, 0, 0]~], [[10, 4, 5, 6, 7; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;
 , 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0;   0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0
 0, 0, 0, 0, 1], [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], [3, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1,
  0, 0, 0, 0, 1]]]  0; 0, 0, 0, 0, 1]]]
 ? nfisideal(bnf[7],[5,1;0,1])  ? nfisideal(bnf[7],[5,2;0,1])
 1  1
 ? nfisincl(x^2+1,x^4+1)  ? nfisincl(x^2+1,x^4+1)
 [-x^2, x^2]  [-x^2, x^2]
Line 1290  Mod(1/2*x^5 - 9*x^2, x^6 + 108)
Line 1173  Mod(1/2*x^5 - 9*x^2, x^6 + 108)
 ? nfrootsof1(nf)  ? nfrootsof1(nf)
 [2, [-1, 0, 0, 0, 0]~]  [2, [-1, 0, 0, 0, 0]~]
 ? nfsnf(nf,[as,haid,vaid])  ? nfsnf(nf,[as,haid,vaid])
 [[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3  [[2562748315629757085585610, 436545976069778274371140, 123799938628701108220
 910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 2, 0;  1405, 2356446991473627724963350, 801407102592194537169612; 0, 5, 0, 0, 2; 0,
  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   0, 5, 0, 1; 0, 0, 0, 5, 2; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0
 ; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0,  , 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0;
 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]  0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]]
 ? nfsubfields(nf)  ? nfsubfields(nf)
 [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]]  [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]]
 ? polcompositum(x^4-4*x+2,x^3-x-1)  ? polcompositum(x^4-4*x+2,x^3-x-1)
Line 1368  x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289
Line 1251  x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289
  0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,   0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0,
 0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~  0]~, [-2, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~
 ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1  ], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1
 , 0; 0, 0, 1], [1, 0, 3/5; 0, 1, 2/5; 0, 0, 1/5], [1, 0, 8/25; 0, 1, 22/25;  , 0; 0, 0, 1], [1, 0, 2/5; 0, 1, 3/5; 0, 0, 1/5], [1, 0, 22/25; 0, 1, 8/25;
 0, 0, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1  0, 0, 1/25]], [416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1
 280, 5, 5]~]  275, 5, 5]~]
 ? rnfbasis(bnf2,aa)  ? rnfbasis(bnf2,aa)
   
 [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [38/25, -33/25, 11/25]~ [-11, -4, 9]~]  [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-6/25, 66/25, 77/25]~ [-391/25, -699/25,
   197/25]~]
   
 [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-14/25, 24/25, -8/25]~ [28/5, 2/5, -24/5]  [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [18/25, -48/25, -56/25]~ [268/25, 552/25,
 ~]  -206/25]~]
   
 [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [57/25, -12/25, 4/25]~ [-58/5, -47/5, 44/5  [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [41/25, 24/25, 28/25]~ [-194/25, -116/25,
 ]~]  -127/25]~]
   
 [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [9/25, 6/25, -2/25]~ [-4/5, -11/5, 2/5]~]  [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [17/25, -12/25, -14/25]~ [52/25, 178/25, -
   109/25]~]
   
 [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [8/25, -3/25, 1/25]~ [-9/5, -6/5, 7/5]~]  [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [4/25, 6/25, 7/25]~ [-41/25, -49/25, -3/25
   ]~]
   
 ? rnfdisc(nf2,p)  ? rnfdisc(nf2,p)
 [[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]  [[416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
 ? rnfequation(nf2,p)  ? rnfequation(nf2,p)
 x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1  x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
 ? rnfequation(nf2,p,1)  ? rnfequation(nf2,p,1)
Line 1394  x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
Line 1280  x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
 5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]  5*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1), 0]
 ? rnfhnfbasis(bnf2,aa)  ? rnfhnfbasis(bnf2,aa)
   
 [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~  [[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [6/5, 4/5, -2/5]~ [-22/25, -33/25, 99/25]~
 ]  ]
   
 [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~]  [[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-6/5, -4/5, 2/5]~ [16/25, 24/25, -72/25]~
   ]
   
 [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~]  [[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-3/5, -2/5, 1/5]~ [-8/25, -12/25, 36/25]~
   ]
   
 [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~]  [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/5, -2/5, 1/5]~ [4/25, 6/25, -18/25]~]
   
 [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~]  [[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/25, -3/25, 9/25]~]
   
 ? rnfisfree(bnf2,aa)  ? rnfisfree(bnf2,aa)
 1  1
 ? rnfsteinitz(nf2,aa)  ? rnfsteinitz(nf2,aa)
 [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [38/25, -33/25, 11/25]~, [-27/125, 33/  [[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-6/25, 66/25, 77/25]~, [17/125, -66/1
 125, -11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-14/25, 24/25, -8/25]~,  25, -77/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [18/25, -48/25, -56/25]~,
  [6/125, -24/125, 8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [57/25, -12/2   [-26/125, 48/125, 56/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [41/25, 24/
 5, 4/25]~, [-53/125, 12/125, -4/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [  25, 28/25]~, [-37/125, -24/125, -28/125]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]
 9/25, 6/25, -2/25]~, [-11/125, -6/125, 2/125]~; [0, 0, 0]~, [0, 0, 0]~, [0,  ~, [17/25, -12/25, -14/25]~, [-19/125, 12/125, 14/125]~; [0, 0, 0]~, [0, 0,
 0, 0]~, [8/25, -3/25, 1/25]~, [-7/125, 3/125, -1/125]~], [[1, 0, 0; 0, 1, 0;  0]~, [0, 0, 0]~, [4/25, 6/25, 7/25]~, [-3/125, -6/125, -7/125]~], [[1, 0, 0;
  0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0,   0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]
 0; 0, 1, 0; 0, 0, 1], [125, 0, 108; 0, 125, 22; 0, 0, 1]], [416134375, 21294  , [1, 0, 0; 0, 1, 0; 0, 0, 1], [125, 0, 22; 0, 125, 108; 0, 0, 1]], [4161343
 0625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~]  75, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~]
 ? nfz=zetakinit(x^2-2);  ? nfz=zetakinit(x^2-2);
 ? zetak(nfz,-3)  ? zetak(nfz,-3)
 0.091666666666666666666666666666666666666  0.091666666666666666666666666666666666666
Line 1425  x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
Line 1313  x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
 7938845*I  7938845*I
 ? setrand(1);quadclassunit(1-10^7,,[1,1])  ? setrand(1);quadclassunit(1-10^7,,[1,1])
   ***   Warning: not a fundamental discriminant in quadclassunit.    ***   Warning: not a fundamental discriminant in quadclassunit.
 [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99984980  [2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 1.00257481
 75377600233]  6299307750]
 ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])  ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
 [4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074  [4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074
 5514, 0.9990369458964383232]  5514, 0.9849577285369119736]
 ? sizebyte(%)  ? sizebyte(%)
 328  320
 ? getheap  ? getheap
 [198, 120613]  [199, 115764]
 ? print("Total time spent: ",gettime);  ? print("Total time spent: ",gettime);
 Total time spent: 4836  Total time spent: 3629
 ? \q  ? \q
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