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Diff for /OpenXM_contrib/pari-2.2/src/test/32/Attic/compat between version 1.1 and 1.2

version 1.1, 2001/10/02 11:17:12 version 1.2, 2002/09/11 07:27:09
Line 71  x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
Line 71  x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
 ? nfpol=x^5-5*x^3+5*x+25  ? nfpol=x^5-5*x^3+5*x+25
 x^5 - 5*x^3 + 5*x + 25  x^5 - 5*x^3 + 5*x + 25
 ? nf=initalg(nfpol)  ? nf=initalg(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  27946671612683, -2.4285174907194186068992069565359418364, 0.7194669112891317
 269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119  8943997506477288225728, -2.5558200350691694950646071159426779970; 1, -0.1383
 211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I,  8372073406036365047976417441696635 - 0.4918163765776864349975328551474152510
  3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331  7*I, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940822
 539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319  19556466856*I, -0.072312766896812300380582649294307897098 + 2.19808037538462
 06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196  76641195195160383234877*I, -0.98796319352507039803950539735452837196 + 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, -1.0891151457205048250249527946671612683, -2.428517490719418606899
 77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515  2069565359418364, 0.71946691128913178943997506477288225728, -2.5558200350691
 382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8  694950646071159426779970; 1.4142135623730950488016887242096980785, -0.195704
 976972027301414394898806541072047941, 6.408909349142616853840753758109052071  13467375904264179382543977540672, 2.7785222450164664309920925654093065576, -
 2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441  0.10226569567819614506098907018896260032, -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, 4.02152936 E-87, 10.0000000000000000000000  12816401036, 3.0174557027049114270734649132936867272, -3.8416814583731999185
 00000000000000, -5.0000000000000000000000000000000000000, 7.0000000000000000  306312841432940660], 0, [5, 2, 0, -1, -2; 2, -2, -5, -10, 20; 0, -5, 10, -10
 000000000000000000000; 4.02152936 E-87, 19.488486013650707197449403270536023  , 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 0, 200, 110, 177; 0, 345
 970, 8.04305873 E-86, 19.488486013650707197449403270536023970, 4.15045922467  , 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5175, 0
 06085588902013976045703227; 10.000000000000000000000000000000000000, 8.04305  , -10350, -15525; 5175, 13800, -8625, -1725, 27600; 0, -8625, 37950, -17250,
 873 E-86, 85.960217420851846480305133936577594605, -36.034268291482979838267   0; -10350, -1725, -17250, -24150, -15525; -15525, 27600, 0, -15525, -3450],
 056239752434596, 53.576130452511107888183080361946556763; -5.000000000000000   [595125, [238050, -296700, 91425, 1725, 0]~]], [-2.428517490719418606899206
 0000000000000000000000, 19.488486013650707197449403270536023970, -36.0342682  9565359418364, 1.9647119211288133163138753392090569931 + 0.80971492418897895
 91482979838267056239752434596, 60.916248374441986300937507618575151517, -18.  128294082219556466856*I, -0.75045317576910401286427186094108607489 + 1.31014
 470101750219179344070032346246890434; 7.000000000000000000000000000000000000  62685358123283560773619310445915*I], [1, 1/15*x^4 - 2/3*x^2 + 1/3*x + 4/3, x
 0, 4.1504592246706085588902013976045703227, 53.57613045251110788818308036194  , 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 -
 6556763, -18.470101750219179344070032346246890434, 37.9701528928423673408973  2/3], [1, 0, 3, 1, 10; 0, 0, -2, 1, -5; 0, 1, 0, 3, -5; 0, 0, 1, 1, 10; 0, 0
 84258599214282], [5, 0, 10, -5, 7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; -5,  , 0, 3, 0], [1, 0, 0, 0, 0, 0, -1, -1, -2, 4, 0, -1, 3, -1, 1, 0, -2, -1, -3
  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, -51  -1, -1, -1, 3, 0, 1, 1, 3, -3; 0, 0, 1, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, -2
 75, 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, -8625   1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, -1; 0, 0, 0, 0, 1, 0, -1, -1, -1, 1, 0, -1
 0], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.4285174907194186068992  , 0, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1]]
 069565359418364, 1.9647119211288133163138753392090569931 + 0.809714924188978  
 95128294082219556466857*I, -0.75045317576910401286427186094108607489 + 1.310  
 1462685358123283560773619310445915*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]]  
 ? ba=algtobasis(nf,mod(x^3+5,nfpol))  ? ba=algtobasis(nf,mod(x^3+5,nfpol))
 [6, 0, 1, 3, 0]~  [6, 1, 3, 1, 3]~
 ? anell(acurve,100)  ? anell(acurve,100)
 [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1  [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 1
 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,  0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2,
Line 212  mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
Line 202  mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25)
 ? move(0,0,0);box(0,500,500)  ? move(0,0,0);box(0,500,500)
 ? setrand(1);buchimag(1-10^7,1,1)  ? setrand(1);buchimag(1-10^7,1,1)
   ***   Warning: not a fundamental discriminant in quadclassunit.    ***   Warning: not a fundamental discriminant in quadclassunit.
 [2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 1, 0.99984980  [2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 1, 1.00257481
 75377600233]  6299307750]
 ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)  ? setrand(1);bnf=buchinitfu(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-47*I, -2.01097980249891575621226  48550268542821846861610071436900868, -1.36845553 E-48, 0.5005798036324558738
 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590  2620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254
 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376  0123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.14
 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I  15926535897932384626433832795028842*I, -0.3432876442770270943898878667334192
 , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983  1876 + 3.1415926535897932384626433832795028842*I, 2.133629400974756470719099
 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538  7873636390948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745
 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653  732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790
 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0  3417566977293763292119206302198760, -1.2897619530652735025030086072395031017
 .E-47*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264  , -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.50057980363
 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795  245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.72
 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424  41634548149836441438434283070556826, 0.3432876442770270943898878667334192187
 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061  6, -2.1336294009747564707190997873636390948, -0.0661783018827457321853684923
 2 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.14159265358979323  23164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [1
 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926  1, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1,
 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +   [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17
 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342  , [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389  1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.06637297521077796359
 88786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.14  59310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.06637
 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334  29752107779635959310246705326058; 1, 7.0663729752107779635959310246705326058
 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1  ], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]],
 ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~   [-7.0663729752107779635959310246705326058, 8.066372975210777963595931024670
 , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1  5326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [
 ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1,  [3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.88144225126545793
  1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7,  64, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.7903417566977293763292119
  8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310  206302198761, -1.7903417566977293763292119206302198760]]], 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], 153], [mat(1),  
 [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846  
 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071  
 795864769252867665590057684*I]]], 0]  
 ? buchcertify(bnf)  ? buchcertify(bnf)
 1  1
 ? buchfu(bnf)  ? buchfu(bnf)
 [[x + 7], 153]  [[x + 7], 155]
 ? setrand(1);buchinitforcefu(x^2-x-100000)  ? setrand(1);buchinitforcefu(x^2-x-100000)
 [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 - 7.12167580 E-66*I], [-41.8112  4*I; 129.82045011403975460991182396195022419], [-41.811264589129943393339502
 64589129943393339502258694361489 + 0.E-66*I, 9.23990041479022898163762604388  258694361489 + 6.2831853071795864769252867665590057684*I, 9.2399004147902289
 40931575 + 3.1415926535897932384626433832795028842*I, -11.874609881075406725  816376260438840931575 + 3.1415926535897932384626433832795028842*I, -11.87460
 097315997431161032 + 9.4247779607693797153879301498385086526*I, 389.46135034  9881075406725097315997431161032 + 3.1415926535897932384626433832795028842*I,
 211926382973547188585067257 + 12.566370614359172953850573533118011536*I, -44   0.E-67, -51.051165003920172374977128302578454646 + 3.1415926535897932384626
 0.51251534603943620471260018842912722 + 0.E-65*I, -324.551125285099386524779  433832795028842*I, -64.910225057019877304955911980975112095 + 3.141592653589
 55990487556047 + 6.2831853071795864769252867665590057684*I, 229.704245520024  7932384626433832795028842*I, -29.936654708054536668242186261263200456 + 3.14
 97255158146166263724792 + 3.1415926535897932384626433832795028842*I, -785.66  15926535897932384626433832795028842*I, -47.668319071568233997332918482707687
 045186253421572025117972275598325 + 6.2831853071795864769252867665590057684*  878 + 6.2831853071795864769252867665590057684*I, 3.8762936464778825067484824
 I, -554.35531386699327377220656215544062014 + 6.2831853071795864769252867665  790355076166, -6.7377511782956880607802359510546381087 + 3.14159265358979323
 590057684*I, -47.668319071568233997332918482707687879 + 9.424777960769379715  84626433832795028842*I, -35.073513410834255332559266307639723380 + 3.1415926
 3879301498385086526*I, 177.48876918560798860724474244465791207 + 9.49556774  535897932384626433832795028842*I, 33.130781426597481571750300827582717074 +
 E-66*I, -875.61236937168080069763246690606885226 - 3.79822709 E-65*I, 54.878  2.96736492 E-67*I, 54.878404098312329644822020875673145627 + 5.93472984 E-67
 404098312329644822020875673145627 + 9.4247779607693797153879301498385086526*  *I, -14.980188104648613073630759189293219180 + 3.141592653589793238462643383
 I, -404.44153844676787690336623107514389175 - 9.49556774 E-66*I, 232.8098237  2795028842*I, -26.831076484481330319708743069401142308 + 3.14159265358979323
 4359817890011490485449930607 + 6.2831853071795864769252867665590057684*I, -6  84626433832795028842*I, -19.706749066516065512488907834878146944 + 3.1415926
 68.80899963671483856204802764462926790 + 9.424777960769379715387930149838508  535897932384626433832795028842*I, -22.104515522613877880850594423816214544 +
 6526*I, 367.35683481950538594888487746203445802 + 9.49556774 E-66*I, -1214.0   3.1415926535897932384626433832795028842*I, -45.6875582356078259000879847377
 716092619656173892944003952818868 + 9.4247779607693797153879301498385086526*  29869105 + 6.2831853071795864769252867665590057684*I, 47.6683190715682339973
 I, -125.94415646756187210316334148291471657 + 6.2831853071795864769252867665  32918482707687879 + 1.18694596 E-66*I; 41.8112645891299433933395022586943614
 590057684*I; 41.811264589129943393339502258694361489 + 6.2831853071795864769  89, -9.2399004147902289816376260438840931575, 11.874609881075406725097315997
 252867665590057684*I, -9.2399004147902289816376260438840931575 + 0.E-66*I, 1  431161032, 0.E-67, 51.051165003920172374977128302578454646, 64.9102250570198
 1.874609881075406725097315997431161032 + 0.E-66*I, -389.46135034211926382973  77304955911980975112095, 29.936654708054536668242186261263200456, 47.6683190
 547188585067257 + 6.2831853071795864769252867665590057684*I, 440.51251534603  71568233997332918482707687879, -3.8762936464778825067484824790355076166, 6.7
 943620471260018842912722 + 3.1415926535897932384626433832795028842*I, 324.55  377511782956880607802359510546381087, 35.07351341083425533255926630763972338
 112528509938652477955990487556047 + 9.4247779607693797153879301498385086526*  0, -33.130781426597481571750300827582717074, -54.878404098312329644822020875
 I, -229.70424552002497255158146166263724792 + 6.2831853071795864769252867665  673145627, 14.980188104648613073630759189293219180, 26.831076484481330319708
 590057684*I, 785.66045186253421572025117972275598325 + 9.4247779607693797153  743069401142309, 19.706749066516065512488907834878146944, 22.104515522613877
 879301498385086526*I, 554.35531386699327377220656215544062014 + 3.1415926535  880850594423816214544, 45.687558235607825900087984737729869105, -47.66831907
 897932384626433832795028842*I, 47.668319071568233997332918482707687878 + 3.1  1568233997332918482707687878], [[2, [2, 1]~, 1, 1, [1, 1]~], [5, [5, 1]~, 1,
 415926535897932384626433832795028842*I, -177.4887691856079886072447424446579   1, [1, 1]~], [13, [-5, 1]~, 1, 1, [6, 1]~], [2, [3, 1]~, 1, 1, [0, 1]~], [5
 1207 + 6.2831853071795864769252867665590057684*I, 875.6123693716808006976324  , [6, 1]~, 1, 1, [0, 1]~], [7, [4, 1]~, 2, 1, [-3, 1]~], [13, [6, 1]~, 1, 1,
 6690606885226 + 2.84867032 E-65*I, -54.878404098312329644822020875673145627   [-5, 1]~], [23, [7, 1]~, 1, 1, [-6, 1]~], [43, [-15, 1]~, 1, 1, [16, 1]~],
 + 9.4247779607693797153879301498385086526*I, 404.441538446767876903366231075  [17, [20, 1]~, 1, 1, [-2, 1]~], [17, [15, 1]~, 1, 1, [3, 1]~], [29, [14, 1]~
 14389175 + 9.4247779607693797153879301498385086526*I, -232.80982374359817890  , 1, 1, [-13, 1]~], [29, [-13, 1]~, 1, 1, [14, 1]~], [31, [39, 1]~, 1, 1, [-
 011490485449930607 + 3.1415926535897932384626433832795028842*I, 668.80899963  7, 1]~], [31, [24, 1]~, 1, 1, [8, 1]~], [41, [7, 1]~, 1, 1, [-6, 1]~], [41,
 671483856204802764462926790 + 6.2831853071795864769252867665590057684*I, -36  [-6, 1]~, 1, 1, [7, 1]~], [43, [16, 1]~, 1, 1, [-15, 1]~], [23, [-6, 1]~, 1,
 7.35683481950538594888487746203445803 + 3.1415926535897932384626433832795028   1, [7, 1]~]], 0, [x^2 - x - 100000, [2, 0], 400001, 1, [[1, -316.7281613012
 842*I, 1214.0716092619656173892944003952818868 + 3.1415926535897932384626433  9840161392089489603747004; 1, 315.72816130129840161392089489603747004], [1,
 832795028842*I, 125.94415646756187210316334148291471657 + 6.2831853071795864  -316.72816130129840161392089489603747004; 1, 315.728161301298401613920894896
 769252867665590057684*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2, [2, 1]~, 1, 1, [  03747004], 0, [2, -1; -1, 200001], [400001, 200001; 0, 1], [200001, 1; 1, 2]
 1, 1]~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-1, 1]~], [7, [3,  , [400001, [200001, 1]~]], [-315.72816130129840161392089489603747004, 316.72
 1]~, 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5, 1]~, 1, 1, [-6,  816130129840161392089489603747004], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 1000
  1]~], [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [  00; 0, 1, 1, -1]], [[5, [5], [[2, 0; 0, 1]]], 129.82045011403975460991182396
 -7, 1]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [-14, 1]~, 1, 1  195022419, 0.9876536979069047228, [2, -1], [37955488401901378100630325489636
 , [13, 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~, 1, 1, [7, 1]~],  9154068336082609238336*x + 1198361656442507899904628359500228716651781276113
  [31, [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1]~], [41, [6, 1]~  16131167], 24], [mat(1), [[0, 0]], [[-41.81126458912994339333950225869436148
 , 1, 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [15, 1]~, 1, 1, [-1  9 + 6.2831853071795864769252867665590057684*I, 41.81126458912994339333950225
 6, 1]~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 1  8694361489]]], 0]
 8], [x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.728161301298401613920894  
 89603747004; 1, 316.72816130129840161392089489603747004], [1, 1; -315.728161  
 30129840161392089489603747004, 316.72816130129840161392089489603747004], [2,  
  1.0000000000000000000000000000000000000; 1.00000000000000000000000000000000  
 00000, 200001.00000000000000000000000000000000], [2, 1; 1, 200001], [400001,  
  200000; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~]], [-315.72816130  
 129840161392089489603747004, 316.72816130129840161392089489603747004], [1, x  
 ], [1, 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]],  
 129.82045011403975460991182396195022419, 0.9876536979069047239, [2, -1], [37  
 9554884019013781006303254896369154068336082609238336*x + 1198361656442507899  
 90462835950022871665178127611316131167], 26], [mat(1), [[0, 0]], [[-41.81126  
 4589129943393339502258694361489 + 0.E-66*I, 41.81126458912994339333950225869  
 4361489 + 6.2831853071795864769252867665590057684*I]]], 0]  
 ? setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)  ? setrand(1);bnf=buchinitfu(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-47*I, -2.01097980249891575621226  48550268542821846861610071436900868, -1.36845553 E-48, 0.5005798036324558738
 34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590  2620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254
 95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376  0123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.14
 98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I  15926535897932384626433832795028842*I, -0.3432876442770270943898878667334192
 , -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983  1876 + 3.1415926535897932384626433832795028842*I, 2.133629400974756470719099
 85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538  7873636390948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745
 79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653  732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790
 5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0  3417566977293763292119206302198760, -1.2897619530652735025030086072395031017
 .E-47*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264  , -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.50057980363
 33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795  245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.72
 864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424  41634548149836441438434283070556826, 0.3432876442770270943898878667334192187
 7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061  6, -2.1336294009747564707190997873636390948, -0.0661783018827457321853684923
 2 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.14159265358979323  23164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [1
 84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926  1, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1,
 535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +   [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17
 3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342  , [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
 4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389  1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.06637297521077796359
 88786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.14  59310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.06637
 15926535897932384626433832795028842*I, -24.478366048541841504313284087778334  29752107779635959310246705326058; 1, 7.0663729752107779635959310246705326058
 822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1  ], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]],
 ]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~   [-7.0663729752107779635959310246705326058, 8.066372975210777963595931024670
 , 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1  5326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [
 ]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1,  [3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.88144225126545793
  1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7,  64, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.7903417566977293763292119
  8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310  206302198761, -1.7903417566977293763292119206302198760]]], 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], 153], [mat(1),  
 [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.14159265358979323846  
 26433832795028842*I, -9.9277376722507613003718504524486100858 + 6.2831853071  
 795864769252867665590057684*I]]], 0]  
 ? setrand(1);buchreal(10^9-3,0,0.5,0.5)  ? setrand(1);buchreal(10^9-3,0,0.5,0.5)
 [4, [4], [qfr(3, 1, -83333333, 0.E-48)], 2800.625251907016076486370621737074  [4, [4], [qfr(3, 1, -83333333, 0.E-48)], 2800.625251907016076486370621737074
 5514, 0.9990369458964383232]  5514, 0.9849577285369119736]
 ? setrand(1);buchgen(x^4-7,0.2,0.2)  ? setrand(1);buchgen(x^4-7,0.2,0.2)
   
 [x^4 - 7]  [x^4 - 7]
Line 393  I, -229.70424552002497255158146166263724792 + 6.283185
Line 348  I, -229.70424552002497255158146166263724792 + 6.283185
   
 [[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 415  I, -229.70424552002497255158146166263724792 + 6.283185
Line 370  I, -229.70424552002497255158146166263724792 + 6.283185
   
 [[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]]
   
 [26]  [24]
   
 ? setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1)  ? setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1)
   
Line 438  I, -229.70424552002497255158146166263724792 + 6.283185
Line 393  I, -229.70424552002497255158146166263724792 + 6.283185
   
 [[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 + 1478/343]]  [[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]]
   
 [[4/1029*x^3 + 53/1029*x^2 + 66/343*x + 111/343]]  [[1/343*x^3 - 46/1029*x^2 - 122/343*x - 174/343]]
   
 [151]  [154]
   
 ? buchnarrow(bnf)  ? buchnarrow(bnf)
 [3, [3], [[3, 2; 0, 1]]]  [3, [3], [[3, 0; 0, 1]]]
 ? buchray(bnf,[[5,3;0,1],[1,0]])  ? buchray(bnf,[[5,4;0,1],[1,0]])
 [12, [12], [[3, 2; 0, 1]]]  [12, [12], [[3, 0; 0, 1]]]
 ? bnr=buchrayinitgen(bnf,[[5,3;0,1],[1,0]])  ? bnr=buchrayinitgen(bnf,[[5,4;0,1],[1,0]])
 [[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-47*I, -2.0109798024989157562122  148550268542821846861610071436900868, -1.36845553 E-48, 0.500579803632455873
 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659  82620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.08885625
 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337  40123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.1
 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*  415926535897932384626433832795028842*I, -0.343287644277027094389887866733419
 I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498  21876 + 3.1415926535897932384626433832795028842*I, 2.13362940097475647071909
 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153  97873636390948 + 3.1415926535897932384626433832795028842*I, 0.06617830188274
 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265  5732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.79
 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +  03417566977293763292119206302198760, -1.289761953065273502503008607239503101
 0.E-47*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626  7, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.5005798036
 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179  3245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.7
 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42  241634548149836441438434283070556826, 0.343287644277027094389887866733419218
 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106  76, -2.1336294009747564707190997873636390948, -0.066178301882745732185368492
 12 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.1415926535897932  323164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [
 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592  11, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1
 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +  , [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [1
  3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934  7, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438   1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635
 988786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.1  959310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.0663
 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833  729752107779635959310246705326058; 1, 7.066372975210777963595931024670532605
 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,  8], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]]
 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]  , [-7.0663729752107779635959310246705326058, 8.06637297521077796359593102467
 ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,  05326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3],
 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1  [[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512654579
 , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7  364, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.790341756697729376329211
 , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931  9206302198761, -1.7903417566977293763292119206302198760]]], [0, [mat([[6, 1]
 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372  ~, 1])]]], [[[5, 4; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], mat([[5
 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [  , [-1, 1]~, 1, 1, [2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[mod(0, 2)]~
 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000  ], 1]], [[2], [[0, 1]~], mat(1)]], [1, 0; 0, 1]], [1], mat([1, -3, -6]), [12
 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114  , [12], [[3, 0; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]]
 ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102  ? bnr2=buchrayinitgen(bnf,[[25,14;0,1],[1,1]])
 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], 153], [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]]]  
 ? bnr2=buchrayinitgen(bnf,[[25,13;0,1],[1,1]])  
 [[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-47*I, -2.0109798024989157562122  148550268542821846861610071436900868, -1.36845553 E-48, 0.500579803632455873
 634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659  82620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.08885625
 095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337  40123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.1
 698160660239595315877930058147543 + 9.4247779607693797153879301498385086526*  415926535897932384626433832795028842*I, -0.343287644277027094389887866733419
 I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498  21876 + 3.1415926535897932384626433832795028842*I, 2.13362940097475647071909
 385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153  97873636390948 + 3.1415926535897932384626433832795028842*I, 0.06617830188274
 879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265  5732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.79
 35897932384626433832795028842*I, -14.550628376291080203941433635329724736 +  03417566977293763292119206302198760, -1.289761953065273502503008607239503101
 0.E-47*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626  7, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.5005798036
 433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179  3245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.7
 5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42  241634548149836441438434283070556826, 0.343287644277027094389887866733419218
 47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106  76, -2.1336294009747564707190997873636390948, -0.066178301882745732185368492
 12 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.1415926535897932  323164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [
 384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592  11, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1
 6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 +  , [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [1
  3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934  7, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1,
 24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438   1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635
 988786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.1  959310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.0663
 415926535897932384626433832795028842*I, -24.47836604854184150431328408777833  729752107779635959310246705326058; 1, 7.066372975210777963595931024670532605
 4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0,  8], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]]
 1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]  , [-7.0663729752107779635959310246705326058, 8.06637297521077796359593102467
 ~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2,  05326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3],
 1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1  [[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512654579
 , 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7  364, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.790341756697729376329211
 , 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931  9206302198761, -1.7903417566977293763292119206302198760]]], [0, [mat([[6, 1]
 0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372  ~, 1])]]], [[[25, 14; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [4, 2]~, [-
 9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [  2, -2]~]], mat([[5, [-1, 1]~, 1, 1, [2, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0
 2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000  ]~], [[mod(0, 2), mod(0, 2)]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[mod(0, 2),
 0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114   mod(0, 2)]~], mat([1/5, -14/5])]], [[2, 2], [[4, 2]~, [-2, -2]~], [1, 0; 0,
 ; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102   1]]], [1, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [1], mat([1, -3, -6, 0]), [1
 46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1],  2, [12], [[3, 0; 0, 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  
 6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 153], [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]]]  
 ? bytesize(%)  ? bytesize(%)
 7604  6372
 ? ceil(-2.5)  ? ceil(-2.5)
 -2  -2
 ? centerlift(mod(456,555))  ? centerlift(mod(456,555))
Line 571  z^2 - 5*z - 2
Line 506  z^2 - 5*z - 2
 z^2 + mod(8186, 8191)*z + mod(8189, 8191)  z^2 + mod(8186, 8191)*z + mod(8189, 8191)
 ? acurve=chell(acurve,[-1,1,2,3])  ? acurve=chell(acurve,[-1,1,2,3])
 [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647  [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647
 1667696455518910092496975959, -0.73040556359455544173706204865073999595, -2.  1667696455518910092496975959, -0.73040556359455544173706204865073999594, -2.
 1071598716887675937077488504242902444]~, -2.99345864623195962983200997945250  1071598716887675937077488504242902444]~, -2.99345864623195962983200997945250
 81778, -2.4513893819867900608542248318665252253*I, 0.47131927795681147588259  81778, -2.4513893819867900608542248318665252253*I, 0.47131927795681147588259
 389708033769964, 1.4354565186686843187232088566788165076*I, 7.33813274078957  389708033769964, 1.4354565186686843187232088566788165076*I, 7.33813274078957
Line 619  od(-279140305176/29063006931199*x^11 + 129916611552/29
Line 554  od(-279140305176/29063006931199*x^11 + 129916611552/29
 qfr(35, 43, 13, 0.E-38)  qfr(35, 43, 13, 0.E-38)
 ? concat([1,2],[3,4])  ? concat([1,2],[3,4])
 [1, 2, 3, 4]  [1, 2, 3, 4]
 ? conductor(bnf,[[25,13;0,1],[1,1]])  ? conductor(bnf,[[25,14;0,1],[1,1]])
 [[[5, 3; 0, 1], [1, 0]], [12, [12], [[3, 2; 0, 1]]], mat(12)]  [[[5, 4; 0, 1], [1, 0]], [12, [12], [[3, 0; 0, 1]]], mat(12)]
 ? conductorofchar(bnr,[2])  ? conductorofchar(bnr,[2])
 [[5, 3; 0, 1], [0, 0]]  [[5, 4; 0, 1], [0, 0]]
 ? conj(1+i)  ? conj(1+i)
 1 - I  1 - I
 ? conjvec(mod(x^2+x+1,x^3-x-1))  ? conjvec(mod(x^2+x+1,x^3-x-1))
Line 735  x^48 + x^47 + x^46 - x^43 - x^42 - 2*x^41 - x^40 - x^3
Line 670  x^48 + x^47 + x^46 - x^43 - x^42 - 2*x^41 - x^40 - x^3
 19, 6; 229, 9]], [mat([77, 1]), 18, 18, [19, 6; 229, 9]]], [[[10, 1; 20, 1],  19, 6; 229, 9]], [mat([77, 1]), 18, 18, [19, 6; 229, 9]]], [[[10, 1; 20, 1],
  0, 0, 0], [[10, 1; 21, 1], 0, 0, 0]]]]   0, 0, 0], [[10, 1; 21, 1], 0, 0, 0]]]]
 ? discrayrel(bnr,mat(6))  ? discrayrel(bnr,mat(6))
 [6, 2, [125, 13; 0, 1]]  [6, 2, [125, 14; 0, 1]]
 ? discrayrel(bnr)  ? discrayrel(bnr)
 [12, 1, [1953125, 1160888; 0, 1]]  [12, 1, [1953125, 1160889; 0, 1]]
 ? discrayrelcond(bnr2)  ? discrayrelcond(bnr2)
 0  0
 ? divisors(8!)  ? divisors(8!)
Line 838  x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 5466035
Line 773  x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 5466035
 *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52  *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
 *x^3 - 197*x^2 - 273*x - 127]  *x^3 - 197*x^2 - 273*x - 127]
 ? factoredpolred2(p,fa)  ? factoredpolred2(p,fa)
   [x - 1, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1, x^5 - 2*x^4 - 53*x^3 - 46
 [1 x - 1]  *x^2 + 508*x + 913, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52
   *x^3 - 197*x^2 - 273*x - 127]
 [320031469790/139623738889203638909659*x^4 + 525154323698149/139623738889203  
 638909659*x^3 + 68805502220272624/139623738889203638909659*x^2 + 11626197624  
 4907072724/139623738889203638909659*x - 265513916545157609/58346808996920447  
  x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1]  
   
 [-649489679500/139623738889203638909659*x^4 - 1004850936416946/1396237388892  
 03638909659*x^3 + 1850137668999773331/139623738889203638909659*x^2 + 1162464  
 435118744503168/139623738889203638909659*x - 744221404070129897/583468089969  
 20447 x^5 - 2*x^4 - 53*x^3 - 46*x^2 + 508*x + 913]  
   
 [404377049971/139623738889203638909659*x^4 + 1028343729806593/13962373888920  
 3638909659*x^3 - 220760129739668913/139623738889203638909659*x^2 - 139192454  
 3479498840309/139623738889203638909659*x - 21580477171925514/583468089969204  
 47 x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1]  
   
 [160329790087/139623738889203638909659*x^4 + 1043812506369034/13962373888920  
 3638909659*x^3 + 1517006779298914407/139623738889203638909659*x^2 - 52234888  
 8528537141362/139623738889203638909659*x - 677624890046649103/58346808996920  
 447 x^5 - x^4 - 52*x^3 - 197*x^2 - 273*x - 127]  
   
 ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)  ? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
   
 [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t, t^3 + t^2 - 2*t - 1) 1]  [mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t, t^3 + t^2 - 2*t - 1) 1]
Line 938  x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 5466035
Line 853  x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 5466035
 0.25881904510252076234889883762404832834  0.25881904510252076234889883762404832834
 0.49999999999999999999999999999999999999  0.49999999999999999999999999999999999999
 0.70710678118654752440084436210484903928  0.70710678118654752440084436210484903928
 0.86602540378443864676372317075293618346  0.86602540378443864676372317075293618347
 0.96592582628906828674974319972889736763  0.96592582628906828674974319972889736763
 1.0000000000000000000000000000000000000  1.0000000000000000000000000000000000000
 0.96592582628906828674974319972889736764  0.96592582628906828674974319972889736764
Line 973  mod(x^5, x^6 + 108)
Line 888  mod(x^5, x^6 + 108)
 ? gcd(12345678,87654321)  ? gcd(12345678,87654321)
 9  9
 ? getheap()  ? getheap()
 [214, 48646]  [215, 44753]
 ? getrand()  ? getrand()
 1939683225  498199132
 ? getstack()  ? getstack()
 0  0
 ? globalred(acurve)  ? globalred(acurve)
Line 1083  mod(x^5, x^6 + 108)
Line 998  mod(x^5, x^6 + 108)
 -1  -1
 ? nf1=initalgred(nfpol)  ? nf1=initalgred(nfpol)
 [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, 2.4285174907194186068992069565359418363, -0.71
 741050929194782733001765987770358483, 0.158944197453903762065494816710718942  946691128913178943997506477288225737, 2.555820035069169495064607115942677997
 89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753  0; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532
 285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021  85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889
 752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0  7895128294082219556466856*I, 0.072312766896812300380582649294307897128 + 2.1
 .13249517760521973840801462296650806543*I, -0.053650958656997725359297528357  980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283
 602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312  7195 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162
 7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035  9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769
 26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I  10401286427186094108607491 - 1.3101462685358123283560773619310445914*I, 0.78
 , -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013  742068874775359433940488309213323161 - 2.13366338931266180341684546104579360
 48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544  16*I, -1.2658732110596551455718089553258673704 + 2.7164790103743150566578028
 710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, -  035789834835*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071
 0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948  94186068992069565359418363, -0.71946691128913178943997506477288225737, 2.555
 3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594  8200350691694950646071159426779970; 1.4142135623730950488016887242096980785,
 8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211   -0.19570413467375904264179382543977540673, -2.77852224501646643099209256540
 60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2.  93065576, 0.10226569567819614506098907018896260036, 1.3971909474085893198147
 7407052124261919274965153538200060029 - 13.800355044576098954744153925969274  151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443
 603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539  9565129926149974389115722, 3.1085550780550843138423672171643499921, 2.220520
 303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732  6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2.
 72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15  3800384020787979181834702019470475018, 1.06130105909862703981823187865589944
 894419745390376206549481671071894289, -0.10730191731399545071859505671520521  13, 1.1135810173202366904448352912286604471, -1.7902150633253437253677889164
 623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468  811036159; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763
 99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000  4446810512816401034, -3.0174557027049114270734649132936867271, 3.84168145837
 0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17.  31999185306312841432940662], 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]]  
 ? initalgred2(nfpol)  ? initalgred2(nfpol)
 [[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, 2.4285174907194186068992069565359418363, -0.7
 9741050929194782733001765987770358483, 0.15894419745390376206549481671071894  1946691128913178943997506477288225737, 2.55582003506916949506460711594267799
 289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975  70; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753
 3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602  285514741525107*I, -1.9647119211288133163138753392090569931 + 0.809714924188
 1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 +  97895128294082219556466856*I, 0.072312766896812300380582649294307897128 + 2.
 0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835  1980803753846276641195195160383234877*I, 0.987963193525070398039505397354528
 7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431  37195 + 1.5701452385894131769052374806001981108*I; 1, 1.68294129359431277616
 27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703  29561615079976005 + 2.0500351226010726172974286983598602163*I, 0.75045317576
 526062130959637482576769100030014 + 6.9001775222880494773720769629846373016*  910401286427186094108607491 - 1.3101462685358123283560773619310445914*I, 0.7
 I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301  8742068874775359433940488309213323161 - 2.1336633893126618034168454610457936
 348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354  016*I, -1.2658732110596551455718089553258673704 + 2.716479010374315056657802
 4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684,  8035789834835*I], [1, -1.0891151457205048250249527946671612684, 2.4285174907
 -0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294  194186068992069565359418363, -0.71946691128913178943997506477288225737, 2.55
 83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459  58200350691694950646071159426779970; 1.4142135623730950488016887242096980785
 48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821  , -0.19570413467375904264179382543977540673, -2.7785222450164664309920925654
 160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2  093065576, 0.10226569567819614506098907018896260036, 1.397190947408589319814
 .7407052124261919274965153538200060029 - 13.80035504457609895474415392596927  7151262541540506; 0, 0.69553338995335755797766403996841143190, 1.14510982744
 4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753  39565129926149974389115722, 3.1085550780550843138423672171643499921, 2.22052
 9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573  06913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2
 272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1  .3800384020787979181834702019470475018, 1.0613010590986270398182318786558994
 5894419745390376206549481671071894289, -0.1073019173139954507185950567152052  413, 1.1135810173202366904448352912286604471, -1.790215063325343725367788916
 1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346  4811036159; 0, 2.8991874737236275652408825679737171587, -1.85282662165584876
 899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000  34446810512816401034, -3.0174557027049114270734649132936867271, 3.8416814583
 00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17  731999185306312841432940662], 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)]  
 ? vp=primedec(nf,3)[1]  ? vp=primedec(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,idmat(5),vp)  ? idx=idealmul(nf,idmat(5),vp)
   
 [3 1 2 2 2]  [3 2 1 0 1]
   
 [0 1 0 0 0]  [0 1 0 0 0]
   
Line 1208  I, -8.0696202866361678983472946546849540475 + 8.876767
Line 1097  I, -8.0696202866361678983472946546849540475 + 8.876767
   
 ? 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=ideallllred(nf,idx,[1,5,6])  ? idy=ideallllred(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]
   
 ? idealadd(nf,idx,idy)  ? idealadd(nf,idx,idy)
   
Line 1243  I, -8.0696202866361678983472946546849540475 + 8.876767
Line 1132  I, -8.0696202866361678983472946546849540475 + 8.876767
 [0 0 0 0 1]  [0 0 0 0 1]
   
 ? idealaddone(nf,idx,idy)  ? idealaddone(nf,idx,idy)
 [[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~]  [[3, 2, 1, 2, 1]~, [-2, -2, -1, -2, -1]~]
 ? idealaddmultone(nf,[idy,idx])  ? idealaddmultone(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]~
 ? idealapprfact(nf,idealfactor(nf,idy))  ? idealapprfact(nf,idealfactor(nf,idy))
 [-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]~
 ? 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]
   
 ? idealfactor(nf,idz)  ? 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]
   
 ? 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]]]
 ? 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 1293  I, -8.0696202866361678983472946546849540475 + 8.876767
Line 1182  I, -8.0696202866361678983472946546849540475 + 8.876767
   
 ? idt=idealmulred(nf,idx,idx)  ? idt=idealmulred(nf,idx,idx)
   
 [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 1305  I, -8.0696202866361678983472946546849540475 + 8.876767
Line 1194  I, -8.0696202866361678983472946546849540475 + 8.876767
   
 ? 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]
   
 ? idealdivexact(nf,idx2,idx)  ? idealdivexact(nf,idx2,idx)
   
 [3 1 2 2 2]  [3 2 1 0 1]
   
 [0 1 0 0 0]  [0 1 0 0 0]
   
Line 1329  I, -8.0696202866361678983472946546849540475 + 8.876767
Line 1218  I, -8.0696202866361678983472946546849540475 + 8.876767
   
 ? idealhermite(nf,vp)  ? idealhermite(nf,vp)
   
 [3 1 2 2 2]  [3 2 1 0 1]
   
 [0 1 0 0 0]  [0 1 0 0 0]
   
Line 1341  I, -8.0696202866361678983472946546849540475 + 8.876767
Line 1230  I, -8.0696202866361678983472946546849540475 + 8.876767
   
 ? idealhermite2(nf,vp[2],3)  ? idealhermite2(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 1355  I, -8.0696202866361678983472946546849540475 + 8.876767
Line 1244  I, -8.0696202866361678983472946546849540475 + 8.876767
 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 1367  I, -8.0696202866361678983472946546849540475 + 8.876767
Line 1256  I, -8.0696202866361678983472946546849540475 + 8.876767
   
 ? idealpowred(nf,idx,7)  ? idealpowred(nf,idx,7)
   
 [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]
   
 ? idealtwoelt(nf,idy)  ? idealtwoelt(nf,idy)
 [5, [2, 0, 2, 1, 0]~]  [5, [2, 2, 1, 2, 1]~]
 ? idealtwoelt2(nf,idy,10)  ? idealtwoelt2(nf,idy,10)
 [-2, 0, -2, -1, 0]~  [-2, -2, -1, -2, -1]~
 ? idealval(nf,idp,vp)  ? idealval(nf,idp,vp)
 7  7
 ? idmat(5)  ? idmat(5)
Line 1473  x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(
Line 1362  x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(
 1  1
 ? isfund(12345)  ? isfund(12345)
 1  1
 ? isideal(bnf[7],[5,1;0,1])  ? isideal(bnf[7],[5,2;0,1])
 1  1
 ? isincl(x^2+1,x^4+1)  ? isincl(x^2+1,x^4+1)
 [-x^2, x^2]  [-x^2, x^2]
Line 1487  x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(
Line 1376  x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(
 [-1/25*x^2 + 13/25*x - 2/5]  [-1/25*x^2 + 13/25*x - 2/5]
 ? isprime(12345678901234567)  ? isprime(12345678901234567)
 0  0
 ? isprincipal(bnf,[5,1;0,1])  ? isprincipal(bnf,[5,2;0,1])
 [1]~  [1]~
 ? isprincipalgen(bnf,[5,1;0,1])  ? isprincipalgen(bnf,[5,2;0,1])
 [[1]~, [-2, -1/3]~, 151]  [[1]~, [7/3, 1/3]~, 155]
 ? isprincipalraygen(bnr,primedec(bnf,7)[1])  ? isprincipalraygen(bnr,primedec(bnf,7)[1])
 [[9]~, [-2170/6561, -931/19683]~, 192]  [[9]~, [112595/19683, 13958/19683]~, 192]
 ? ispsp(73!+1)  ? ispsp(73!+1)
 1  1
 ? isqrt(10!^2+1)  ? isqrt(10!^2+1)
Line 1597  x
Line 1486  x
 [0 1 -1]  [0 1 -1]
   
 ? kerint2(matrix(4,6,x,y,2520/(x+y)))  ? kerint2(matrix(4,6,x,y,2520/(x+y)))
     ***   this function has been suppressed.
 [3 1]  
   
 [-30 -15]  
   
 [70 70]  
   
 [0 -140]  
   
 [-126 126]  
   
 [84 -42]  
   
 ? f(u)=u+1;  ? f(u)=u+1;
 ? print(f(5));kill(f);  ? print(f(5));kill(f);
 6  6
Line 1695  x
Line 1572  x
 [-60 -105 280 252 -486 471 1290]  [-60 -105 280 252 -486 471 1290]
   
 ? lll1(m)  ? lll1(m)
     ***   this function has been suppressed.
 [-420 -420 840 630 -1092 757 2982]  
   
 [-210 -280 630 504 -876 700 2415]  
   
 [-140 -210 504 420 -749 641 2050]  
   
 [-105 -168 420 360 -658 589 1785]  
   
 [-84 -140 360 315 -588 544 1582]  
   
 [-70 -120 315 280 -532 505 1421]  
   
 [-60 -105 280 252 -486 471 1290]  
   
 ? lllgram(m)  ? lllgram(m)
   
 [1 1 27 -27 69 0 141]  [1 1 27 -27 69 0 141]
Line 1727  x
Line 1590  x
 [0 1 3 -17 3 -7 3]  [0 1 3 -17 3 -7 3]
   
 ? lllgram1(m)  ? lllgram1(m)
     ***   this function has been suppressed.
 [1 1 27 -27 69 0 141]  
   
 [0 1 4 -22 34 -24 49]  
   
 [0 1 3 -21 18 -24 23]  
   
 [0 1 3 -20 10 -19 13]  
   
 [0 1 3 -19 6 -14 8]  
   
 [0 1 3 -18 4 -10 5]  
   
 [0 1 3 -17 3 -7 3]  
   
 ? lllgramint(m)  ? lllgramint(m)
   
 [1 1 27 -27 69 0 141]  [1 1 27 -27 69 0 141]
Line 1813  x
Line 1662  x
 ; 1, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1,  ; 1, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1,
  0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]   0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
 ? lllrat(m)  ? lllrat(m)
     ***   this function has been suppressed.
 [-420 -420 840 630 -1092 -83 2982]  
   
 [-210 -280 630 504 -876 70 2415]  
   
 [-140 -210 504 420 -749 137 2050]  
   
 [-105 -168 420 360 -658 169 1785]  
   
 [-84 -140 360 315 -588 184 1582]  
   
 [-70 -120 315 280 -532 190 1421]  
   
 [-60 -105 280 252 -486 191 1290]  
   
 ? \precision=96  ? \precision=96
    realprecision = 96 significant digits     realprecision = 96 significant digits
 ? ln(2)  ? ln(2)
Line 1913  E-19, -1.732050807568877293]~, 1.992332899583490707, 1
Line 1748  E-19, -1.732050807568877293]~, 1.992332899583490707, 1
 ? lseriesell(ccurve,2,-37,1.2)-l  ? lseriesell(ccurve,2,-37,1.2)-l
 -1.08420217 E-19  -1.08420217 E-19
 ? sbnf=smallbuchinit(x^3-x^2-14*x-1)  ? sbnf=smallbuchinit(x^3-x^2-14*x-1)
 [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]]
 ? makebigbnf(sbnf)  ? makebigbnf(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 + 3.141592653589793238*I, 0.3677262014027817705 + 3.1415  589793238*I, -0.8305625946607188643 + 3.141592653589793238*I, 0.E-57, 0.0043
 92653589793238*I, 0.004375616572659815402 + 3.141592653589793238*I, -0.83056  75616572659815433 + 3.141592653589793238*I, -1.977791147836553953, 0.3677262
 25946607188639, -1.977791147836553953 + 3.141592653589793238*I; 0.6716827432  014027817708 + 3.141592653589793238*I; 0.6716827432867392938 + 3.14159265358
 867392935 + 3.141592653589793238*I, 0.5379005671092853266, -0.83332198837424  9793238*I, -0.8333219883742404170 + 3.141592653589793238*I, -0.2461086674077
 04172 + 3.141592653589793238*I, -0.2461086674077943078, 0.E-96 + 3.141592653  943076, 0.5379005671092853269, -1.552661549868775853, 0.E-57, -0.87383180430
 589793238*I, 0.9729063188316092378, -0.8738318043071131265, -1.5526615498687  71131263, 0.5774919091398324092, 0.9729063188316092380; -1.91802973262155845
 75853 + 3.141592653589793238*I, 0.5774919091398324092 + 3.141592653589793238  5, 0.2929213507612934444, 0.9387477816548985923, 1.452155878475514386, 2.383
 *I; -1.918029732621558454, 1.452155878475514386, 0.2929213507612934444, 0.93  224144529494717, 0.E-57, 0.8694561877344533111, 1.400299238696721544, -1.340
 87477816548985923, 0.E-96 + 3.141592653589793238*I, -1.340632520234391008, 0  632520234391008], [[3, [-1, 1, 0]~, 1, 1, [1, 1, 1]~], [5, [-1, 1, 0]~, 1, 1
 .8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.40029  , [0, 1, 1]~], [5, [2, 1, 0]~, 1, 1, [1, -2, 1]~], [5, [3, 1, 0]~, 1, 1, [2,
 9238696721544 + 3.141592653589793238*I], [[3, [-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, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [5   1, 0]~], [11, [1, 1, 0]~, 1, 1, [-3, -1, 1]~], [19, [-6, 1, 0]~, 1, 1, [6,
 , [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [23, [-  6, 1]~], [23, [-10, 1, 0]~, 1, 1, [-7, 10, 1]~]]~, 0, [x^3 - x^2 - 14*x - 1,
 10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [13, [1   [3, 0], 10889, 1, [[1, -3.233732695981516672, 4.690759845041404811; 1, -0.0
 9, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2,  7182350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.23225
  3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.233  8029482144592], [1, -3.233732695981516672, 4.690759845041404811; 1, -0.07182
 732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.0051586  350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.232258029
 16449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; -3  482144592], 0, [3, 1, 1; 1, 29, 8; 1, 8, 129], [10889, 5698, 8994; 0, 1, 0;
 .233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.45702  0, 0, 1], [3677, -121, -21; -121, 386, -23; -21, -23, 86], [10889, [1899, 51
 714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.00000000  91, 1]~]], [-3.233732695981516672, -0.07182350902743636344, 4.30555620500895
 0000000000, 29.00000000000000000; 1.000000000000000000, 29.00000000000000000  3036], [1, x, x^2 - x - 9], [1, 0, 9; 0, 1, 1; 0, 0, 1], [1, 0, 0, 0, 9, 1,
 , 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.0000  0, 1, 44; 0, 1, 0, 1, 1, 5, 0, 5, 1; 0, 0, 1, 0, 1, 0, 1, 0, -4]], [[2, [2],
 000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1,   [[3, 2, 0; 0, 1, 0; 0, 0, 1]]], 10.34800724602768011, 1.000000000000000000,
  0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, [1   [2, -1], [x, x^2 + 2*x - 4], 1000], [mat(1), [[0.E-57, 0.E-57, 0.E-57]], [[
 890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.3055562  1.246346989334819161 + 3.141592653589793238*I, 0.6716827432867392938 + 3.141
 05008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0  592653589793238*I, -1.918029732621558455]]], [-4, -1, 2, 3, 10, 3, 1, 7, 2;
 , 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2]  1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]]
 , [[3, 2, 2; 0, 1, 0; 0, 0, 1]]], 10.34800724602767998, 1.000000000000000000  
 , [2, -1], [x, x^2 + 2*x - 4], 1000], [mat(1), [[0, 0, 0]], [[1.246346989334  
 819161 + 3.141592653589793238*I, 0.6716827432867392935 + 3.14159265358979323  
 8*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]]  
 ? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)  ? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)
   
 [1 11]  [1 11]
Line 2081  mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
Line 1911  mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
 5]~ [14, 16, 6, 20, 14]~]  5]~ [14, 16, 6, 20, 14]~]
   
 ? aid=[idx,idy,idz,idmat(5),idx]  ? aid=[idx,idy,idz,idmat(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]]
 ? bb=algtobasis(nf,mod(x^3+x,nfpol))  ? bb=algtobasis(nf,mod(x^3+x,nfpol))
 [1, 1, 1, 3, 0]~  [1, 1, 4, 1, 3]~
 ? 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]
   
 ? nfdiv(nf,ba,bb)  ? nfdiv(nf,ba,bb)
 [755/373, -152/373, 159/373, 120/373, -264/373]~  [584/373, 66/373, -32/373, -105/373, 120/373]~
 ? nfdiveuc(nf,ba,bb)  ? nfdiveuc(nf,ba,bb)
 [2, 0, 0, 0, -1]~  [2, 0, 0, 0, 0]~
 ? nfdivres(nf,ba,bb)  ? nfdivres(nf,ba,bb)
 [[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~]  [[2, 0, 0, 0, 0]~, [4, -1, -5, -1, -3]~]
 ? nfhermite(nf,[a,aid])  ? nfhermite(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]]]
 ? nfhermitemod(nf,[a,aid],da)  ? nfhermitemod(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]]]
 ? nfmod(nf,ba,bb)  ? nfmod(nf,ba,bb)
 [-12, -7, 0, 9, 5]~  [4, -1, -5, -1, -3]~
 ? nfmul(nf,ba,bb)  ? nfmul(nf,ba,bb)
 [-25, -50, -30, 15, 90]~  [50, -15, -35, 60, 15]~
 ? nfpow(nf,bb,5)  ? nfpow(nf,bb,5)
 [23455, 156370, 115855, 74190, -294375]~  [-291920, 136855, 230560, -178520, 74190]~
 ? nfreduce(nf,ba,idx)  ? nfreduce(nf,ba,idx)
 [1, 0, 0, 0, 0]~  [1, 0, 0, 0, 0]~
 ? setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8))  ? setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8))
Line 2138  mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
Line 1968  mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
 [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~]  [[4, 13, 3, 17, 14]~ [14, 16, 11, 5, 4]~ [9, 11, 13, 7, 15]~]
   
 ? vaid=[idx,idy,idmat(5)]  ? vaid=[idx,idy,idmat(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=[idmat(5),idmat(5),idmat(5)]  ? haid=[idmat(5),idmat(5),idmat(5)]
Line 2148  mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
Line 1978  mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 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, 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]]
 ? nfsmith(nf,[as,haid,vaid])  ? nfsmith(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]]
 ? nfval(nf,ba,vp)  ? nfval(nf,ba,vp)
 0  0
 ? norm(1+i)  ? norm(1+i)
Line 2318  x^4 + 2*x^3 + 3*x^2 + 4*x + 5
Line 2148  x^4 + 2*x^3 + 3*x^2 + 4*x + 5
 478051489392386968218136375373985436596569736643531551/158385319626308443937  478051489392386968218136375373985436596569736643531551/158385319626308443937
 475969221994173751192384064000000]  475969221994173751192384064000000]
 ? cmcurve=initell([0,-3/4,0,-2,-1])  ? cmcurve=initell([0,-3/4,0,-2,-1])
 [0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [1.999999999999  [0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [2.000000000000
 999999, -0.6250000000000000000 + 0.3307189138830738238*I, -0.625000000000000  000000, -0.6250000000000000000 + 0.3307189138830738238*I, -0.625000000000000
 0000 - 0.3307189138830738238*I]~, 1.933311705616811546, 0.966655852808405773  0000 - 0.3307189138830738238*I]~, 1.933311705616811546, 0.966655852808405773
 4 + 2.557530989916099474*I, -0.8558486330998558523 - 4.59882981 E-20*I, -0.4  3 + 2.557530989916099474*I, -0.8558486330998558525 - 4.59882981 E-20*I, -0.4
 279243165499279261 - 2.757161217166147204*I, 4.944504600282546729]  279243165499279261 - 2.757161217166147204*I, 4.944504600282546727]
 ? powell(cmcurve,[x,y],quadgen(-7))  ? powell(cmcurve,[x,y],quadgen(-7))
 [((-2 + 3*w)*x^2 + (6 - w))/((-2 - 5*w)*x + (-4 - 2*w)), ((34 - 11*w)*x^3 +  [((-2 + 3*w)*x^2 + (6 - w))/((-2 - 5*w)*x + (-4 - 2*w)), ((34 - 11*w)*x^3 +
 (40 - 28*w)*x^2 + (22 + 23*w)*x)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 + 2  (40 - 28*w)*x^2 + (22 + 23*w)*x)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 + 2
Line 2353  qfr(125, 23, 1, 0.E-18)
Line 2183  qfr(125, 23, 1, 0.E-18)
 ? prime(100)  ? prime(100)
 541  541
 ? primedec(nf,2)  ? primedec(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]~]]
 ? primedec(nf,3)  ? primedec(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]~]]
 ? primedec(nf,11)  ? primedec(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]~]]
 ? primes(100)  ? primes(100)
Line 2398  qfr(125, 23, 1, 0.E-18)
Line 2228  qfr(125, 23, 1, 0.E-18)
   
 [6]  [6]
   
 [0]  
   
 [1]  [1]
   
 [3]  [3]
   
 [0]  [1]
   
   [3]
   
 ? principalidele(nf,mod(x^3+5,nfpol))  ? principalidele(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, 5.0387659675158716386435353106610489967 + 1.5851
 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173  760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173
  - 0.0083630478144368246110910258645462996191*I]]   - 0.0083630478144368246110910258645462996226*I]]
 ? print((x-12*y)/(y+13*x));  ? print((x-12*y)/(y+13*x));
 -11/14  -11/14
 ? print([1,2;3,4])  ? print([1,2;3,4])
Line 2422  qfr(125, 23, 1, 0.E-18)
Line 2252  qfr(125, 23, 1, 0.E-18)
 ? prod(1.,k=1,10,1+1/k!)  ? prod(1.,k=1,10,1+1/k!)
 3.6821540356142043935732308433185262945  3.6821540356142043935732308433185262945
 ? pi^2/6*prodeuler(p=2,10000,1-p^-2)  ? pi^2/6*prodeuler(p=2,10000,1-p^-2)
 1.0000098157493066238697591433298145174  1.0000098157493066238697591433298145166
 ? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))  ? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
 0.33333333333333333333333333333333333322  0.33333333333333333333333333333333333313
 ? prodinf1(n=0,-2^-n/(1+2^(-n+1)))  ? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
 0.33333333333333333333333333333333333322  0.33333333333333333333333333333333333313
 ? psi(1)  ? psi(1)
 -0.57721566490153286060651209008240243102  -0.57721566490153286060651209008240243104
 ? quaddisc(-252)  ? quaddisc(-252)
 -7  -7
 ? quadgen(-11)  ? quadgen(-11)
Line 2437  w
Line 2267  w
 x^2 - x + 3  x^2 - x + 3
 ? rank(matrix(5,5,x,y,x+y))  ? rank(matrix(5,5,x,y,x+y))
 2  2
 ? rayclassno(bnf,[[5,3;0,1],[1,0]])  ? rayclassno(bnf,[[5,4;0,1],[1,0]])
 12  12
 ? rayclassnolist(bnf,lu)  ? rayclassnolist(bnf,lu)
 [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []  [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], []
Line 2491  mod(1, y^3 - y - 1)*x^5 + mod(-5, y^3 - y - 1)*x + mod
Line 2321  mod(1, y^3 - y - 1)*x^5 + mod(-5, y^3 - y - 1)*x + mod
  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
   ]~]
   
 ? rnfdiscf(nf2,p)  ? rnfdiscf(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
 ? rnfequation2(nf2,p)  ? rnfequation2(nf2,p)
Line 2517  x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1
Line 2350  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]
 ? rnfhermitebasis(bnf2,aa)  ? rnfhermitebasis(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]~]
 ? rootmod(x^16-1,41)  ? rootmod(x^16-1,41)
 [mod(1, 41), mod(3, 41), mod(9, 41), mod(14, 41), mod(27, 41), mod(32, 41),  [mod(1, 41), mod(3, 41), mod(9, 41), mod(14, 41), mod(27, 41), mod(32, 41),
 mod(38, 41), mod(40, 41)]~  mod(38, 41), mod(40, 41)]~
Line 2663  q^101)
Line 2498  q^101)
   
 [1 x - 1]  [1 x - 1]
   
 [-1/192*x^3 - 1/8*x + 1/2 x^2 - x + 1]  [1/192*x^3 + 1/8*x + 1/2 x^2 - x + 1]
   
 [-1/24*x^2 x^2 + 1]  [-1/24*x^2 x^2 + 1]
   
 [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]  [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1]
   
 ? smith(matrix(5,5,j,k,random()))  ? smith(matrix(5,5,j,k,random()))
 [1442459322553825252071178240, 2147483648, 2147483648, 1, 1]  [239509529380671174817611776, 2147483648, 2147483648, 1, 1]
 ? smith(1/hilbert(6))  ? smith(1/hilbert(6))
 [27720, 2520, 2520, 840, 210, 6]  [27720, 2520, 2520, 840, 210, 6]
 ? smithpol(x*idmat(5)-matrix(5,5,j,k,1))  ? smithpol(x*idmat(5)-matrix(5,5,j,k,1))
Line 2789  x + x^2 - 1/6*x^3 - 1/2*x^4 - 59/120*x^5 - 1/8*x^6 + 4
Line 2624  x + x^2 - 1/6*x^3 - 1/2*x^4 - 59/120*x^5 - 1/8*x^6 + 4
 ? trunc(sin(x^2))  ? trunc(sin(x^2))
 1/120*x^10 - 1/6*x^6 + x^2  1/120*x^10 - 1/6*x^6 + x^2
 ? tschirnhaus(x^5-x-1)  ? tschirnhaus(x^5-x-1)
 x^5 - 18*x^3 - 12*x^2 + 785*x + 457  x^5 + 20*x^4 + 158*x^3 + 616*x^2 + 1185*x + 899
 ? type(mod(x,x^2+1))  ? type(mod(x,x^2+1))
 9  9
 ? unit(17)  ? unit(17)
Line 2831  x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 19
Line 2666  x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 19
 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142  0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142
 7938845*I  7938845*I
 ? zidealstar(nf2,54)  ? zidealstar(nf2,54)
 [132678, [1638, 9, 9], [[-27, 2, -27]~, [1, -24, 0]~, [1, 0, -24]~]]  [132678, [1638, 9, 9], [[-14, -4, 19]~, [1, 0, -24]~, [7, -6, 6]~]]
 ? bid=zidealstarinit(nf2,54)  ? bid=zidealstarinit(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], [[3, 2, 0]~], [[3, 2, 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, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~,   0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~, [1,
 [1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0,  0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0, 0]]
  0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7  ], [[], [], [;]]], [2106, -77, 0, -11102, 2184, 0, 6006, -13104; 0, 0, 1, -3
 , -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 0]]  , 0, -6, 0, 0; -27, 1, 0, 142, -28, 0, -78, 168]]
 ? zideallog(nf2,w,bid)  ? zideallog(nf2,w,bid)
 [1574, 8, 6]~  [1234, 0, 5]~
 ? znstar(3120)  ? znstar(3120)
 [768, [12, 4, 4, 2, 2], [mod(67, 3120), mod(2341, 3120), mod(1847, 3120), mo  [768, [12, 4, 4, 2, 2], [mod(67, 3120), mod(2341, 3120), mod(1847, 3120), mo
 d(391, 3120), mod(2081, 3120)]]  d(391, 3120), mod(2081, 3120)]]
 ? getstack()  ? getstack()
 0  0
 ? getheap()  ? getheap()
 [624, 125785]  [620, 118299]
 ? print("Total time spent: ",gettime());  ? print("Total time spent: ",gettime());
 Total time spent: 5060  Total time spent: 1400
 ? \q  ? \q
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