=================================================================== RCS file: /home/cvs/OpenXM_contrib/pari-2.2/src/test/32/Attic/compat,v retrieving revision 1.1 retrieving revision 1.2 diff -u -p -r1.1 -r1.2 --- OpenXM_contrib/pari-2.2/src/test/32/Attic/compat 2001/10/02 11:17:12 1.1 +++ OpenXM_contrib/pari-2.2/src/test/32/Attic/compat 2002/09/11 07:27:09 1.2 @@ -71,59 +71,49 @@ 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 x^5 - 5*x^3 + 5*x + 25 ? nf=initalg(nfpol) -[x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.42851749071941860689920 -69565359418364, 5.8976972027301414394898806541072047941, -7.0734526715090929 -269887668671457811020, 3.8085820570096366144649278594400435257; 1, 1.9647119 -211288133163138753392090569931 + 0.80971492418897895128294082219556466857*I, - 3.2044546745713084269203768790545260356 + 3.1817131285400005341145852263331 -539899*I, -0.16163499313031744537610982231988834519 + 1.88804378620070569319 -06454476483475283*I, 2.0660709538372480632698971148801090692 + 2.68989675196 -23140991170523711857387388*I; 1, -0.75045317576910401286427186094108607489 + - 1.3101462685358123283560773619310445915*I, -1.15330327593637914666531720610 -81284327 - 1.9664068558894834311780119356739268309*I, 1.19836132888486390887 -04932558927788962 + 0.64370238076256988899570325671192132449*I, -0.470361982 -34206637050236104460013083212 + 0.083628266711589186119416762685933385421*I] -, [1, 2, 2; -2.4285174907194186068992069565359418364, 3.92942384225762663262 -77506784181139862 - 1.6194298483779579025658816443911293371*I, -1.5009063515 -382080257285437218821721497 - 2.6202925370716246567121547238620891831*I; 5.8 -976972027301414394898806541072047941, 6.408909349142616853840753758109052071 -2 - 6.3634262570800010682291704526663079798*I, -2.30660655187275829333063441 -22162568654 + 3.9328137117789668623560238713478536619*I; -7.0734526715090929 -269887668671457811020, -0.32326998626063489075221964463977669038 - 3.7760875 -724014113863812908952966950567*I, 2.3967226577697278177409865117855577924 - -1.2874047615251397779914065134238426489*I; 3.8085820570096366144649278594400 -435257, 4.1321419076744961265397942297602181385 - 5.379793503924628198234104 -7423714774776*I, -0.94072396468413274100472208920026166424 - 0.1672565334231 -7837223883352537186677084*I], [5, 4.02152936 E-87, 10.0000000000000000000000 -00000000000000, -5.0000000000000000000000000000000000000, 7.0000000000000000 -000000000000000000000; 4.02152936 E-87, 19.488486013650707197449403270536023 -970, 8.04305873 E-86, 19.488486013650707197449403270536023970, 4.15045922467 -06085588902013976045703227; 10.000000000000000000000000000000000000, 8.04305 -873 E-86, 85.960217420851846480305133936577594605, -36.034268291482979838267 -056239752434596, 53.576130452511107888183080361946556763; -5.000000000000000 -0000000000000000000000, 19.488486013650707197449403270536023970, -36.0342682 -91482979838267056239752434596, 60.916248374441986300937507618575151517, -18. -470101750219179344070032346246890434; 7.000000000000000000000000000000000000 -0, 4.1504592246706085588902013976045703227, 53.57613045251110788818308036194 -6556763, -18.470101750219179344070032346246890434, 37.9701528928423673408973 -84258599214282], [5, 0, 10, -5, 7; 0, 10, 0, 10, -5; 10, 0, 30, -55, 20; -5, - 10, -55, 45, -39; 7, -5, 20, -39, 9], [345, 0, 340, 167, 150; 0, 345, 110, -220, 153; 0, 0, 5, 2, 1; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [132825, -18975, -51 -75, 27600, 17250; -18975, 34500, 41400, 3450, -43125; -5175, 41400, -41400, --15525, 51750; 27600, 3450, -15525, -3450, 0; 17250, -43125, 51750, 0, -8625 -0], [595125, [-13800, 117300, 67275, 1725, 0]~]], [-2.4285174907194186068992 -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]] +[x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -1.08911514572050482502495 +27946671612683, -2.4285174907194186068992069565359418364, 0.7194669112891317 +8943997506477288225728, -2.5558200350691694950646071159426779970; 1, -0.1383 +8372073406036365047976417441696635 - 0.4918163765776864349975328551474152510 +7*I, 1.9647119211288133163138753392090569931 + 0.809714924188978951282940822 +19556466856*I, -0.072312766896812300380582649294307897098 + 2.19808037538462 +76641195195160383234877*I, -0.98796319352507039803950539735452837196 + 1.570 +1452385894131769052374806001981108*I; 1, 1.682941293594312776162956161507997 +6005 + 2.0500351226010726172974286983598602163*I, -0.75045317576910401286427 +186094108607489 + 1.3101462685358123283560773619310445915*I, -0.787420688747 +75359433940488309213323154 + 2.1336633893126618034168454610457936017*I, 1.26 +58732110596551455718089553258673705 - 2.716479010374315056657802803578983483 +4*I], [1, -1.0891151457205048250249527946671612683, -2.428517490719418606899 +2069565359418364, 0.71946691128913178943997506477288225728, -2.5558200350691 +694950646071159426779970; 1.4142135623730950488016887242096980785, -0.195704 +13467375904264179382543977540672, 2.7785222450164664309920925654093065576, - +0.10226569567819614506098907018896260032, -1.3971909474085893198147151262541 +540506; 0, -0.69553338995335755797766403996841143190, 1.14510982744395651299 +26149974389115722, 3.1085550780550843138423672171643499921, 2.22052069130868 +72788181483285734827868; 1.4142135623730950488016887242096980785, 2.38003840 +20787979181834702019470475018, -1.0613010590986270398182318786558994412, -1. +1135810173202366904448352912286604470, 1.79021506332534372536778891648110361 +60; 0, 2.8991874737236275652408825679737171586, 1.85282662165584876344468105 +12816401036, 3.0174557027049114270734649132936867272, -3.8416814583731999185 +306312841432940660], 0, [5, 2, 0, -1, -2; 2, -2, -5, -10, 20; 0, -5, 10, -10 +, 5; -1, -10, -10, -17, 1; -2, 20, 5, 1, -8], [345, 0, 200, 110, 177; 0, 345 +, 95, 1, 145; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5175, 0 +, -10350, -15525; 5175, 13800, -8625, -1725, 27600; 0, -8625, 37950, -17250, + 0; -10350, -1725, -17250, -24150, -15525; -15525, 27600, 0, -15525, -3450], + [595125, [238050, -296700, 91425, 1725, 0]~]], [-2.428517490719418606899206 +9565359418364, 1.9647119211288133163138753392090569931 + 0.80971492418897895 +128294082219556466856*I, -0.75045317576910401286427186094108607489 + 1.31014 +62685358123283560773619310445915*I], [1, 1/15*x^4 - 2/3*x^2 + 1/3*x + 4/3, x +, 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 - +2/3], [1, 0, 3, 1, 10; 0, 0, -2, 1, -5; 0, 1, 0, 3, -5; 0, 0, 1, 1, 10; 0, 0 +, 0, 3, 0], [1, 0, 0, 0, 0, 0, -1, -1, -2, 4, 0, -1, 3, -1, 1, 0, -2, -1, -3 +, -1, 0, 4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, -1, -1, 1, 0, -1, -2, -1, 1, 0, +-1, -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, 0, -1, -1, 0, -1, -2, -1, -1; 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, + 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, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0, 0, -1]] ? ba=algtobasis(nf,mod(x^3+5,nfpol)) -[6, 0, 1, 3, 0]~ +[6, 1, 3, 1, 3]~ ? 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 0, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2, @@ -212,162 +202,127 @@ mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25) ? move(0,0,0);box(0,500,500) ? setrand(1);buchimag(1-10^7,1,1) *** Warning: not a fundamental discriminant in quadclassunit. -[2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 1, 0.99984980 -75377600233] +[2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 1, 1.00257481 +6299307750] ? 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 -61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468 -08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672 -2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1. -2897619530652735025030086072395031017 + 0.E-47*I, -2.01097980249891575621226 -34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590 -95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376 -98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I -, -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983 -85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538 -79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653 -5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0 -.E-47*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264 -33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795 -864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424 -7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061 -2 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.14159265358979323 -84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926 -535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + -3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342 -4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389 -88786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.14 -15926535897932384626433832795028842*I, -24.478366048541841504313284087778334 -822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1 -]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~ -, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1 -]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, - 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, - 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310 -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] +61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468 +08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065 +2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701 +48550268542821846861610071436900868, -1.36845553 E-48, 0.5005798036324558738 +2620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254 +0123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.14 +15926535897932384626433832795028842*I, -0.3432876442770270943898878667334192 +1876 + 3.1415926535897932384626433832795028842*I, 2.133629400974756470719099 +7873636390948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745 +732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790 +3417566977293763292119206302198760, -1.2897619530652735025030086072395031017 +, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.50057980363 +245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.72 +41634548149836441438434283070556826, 0.3432876442770270943898878667334192187 +6, -2.1336294009747564707190997873636390948, -0.0661783018827457321853684923 +23164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [1 +1, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, + [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17 +, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, +1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.06637297521077796359 +59310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.06637 +29752107779635959310246705326058; 1, 7.0663729752107779635959310246705326058 +], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], + [-7.0663729752107779635959310246705326058, 8.066372975210777963595931024670 +5326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [ +[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.88144225126545793 +64, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.7903417566977293763292119 +206302198761, -1.7903417566977293763292119206302198760]]], 0] ? buchcertify(bnf) 1 ? buchfu(bnf) -[[x + 7], 153] +[[x + 7], 155] ? 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. -82045011403975460991182396195022419 - 6.283185307179586476925286766559005768 -4*I; 129.82045011403975460991182396195022419 - 7.12167580 E-66*I], [-41.8112 -64589129943393339502258694361489 + 0.E-66*I, 9.23990041479022898163762604388 -40931575 + 3.1415926535897932384626433832795028842*I, -11.874609881075406725 -097315997431161032 + 9.4247779607693797153879301498385086526*I, 389.46135034 -211926382973547188585067257 + 12.566370614359172953850573533118011536*I, -44 -0.51251534603943620471260018842912722 + 0.E-65*I, -324.551125285099386524779 -55990487556047 + 6.2831853071795864769252867665590057684*I, 229.704245520024 -97255158146166263724792 + 3.1415926535897932384626433832795028842*I, -785.66 -045186253421572025117972275598325 + 6.2831853071795864769252867665590057684* -I, -554.35531386699327377220656215544062014 + 6.2831853071795864769252867665 -590057684*I, -47.668319071568233997332918482707687879 + 9.424777960769379715 -3879301498385086526*I, 177.48876918560798860724474244465791207 + 9.49556774 -E-66*I, -875.61236937168080069763246690606885226 - 3.79822709 E-65*I, 54.878 -404098312329644822020875673145627 + 9.4247779607693797153879301498385086526* -I, -404.44153844676787690336623107514389175 - 9.49556774 E-66*I, 232.8098237 -4359817890011490485449930607 + 6.2831853071795864769252867665590057684*I, -6 -68.80899963671483856204802764462926790 + 9.424777960769379715387930149838508 -6526*I, 367.35683481950538594888487746203445802 + 9.49556774 E-66*I, -1214.0 -716092619656173892944003952818868 + 9.4247779607693797153879301498385086526* -I, -125.94415646756187210316334148291471657 + 6.2831853071795864769252867665 -590057684*I; 41.811264589129943393339502258694361489 + 6.2831853071795864769 -252867665590057684*I, -9.2399004147902289816376260438840931575 + 0.E-66*I, 1 -1.874609881075406725097315997431161032 + 0.E-66*I, -389.46135034211926382973 -547188585067257 + 6.2831853071795864769252867665590057684*I, 440.51251534603 -943620471260018842912722 + 3.1415926535897932384626433832795028842*I, 324.55 -112528509938652477955990487556047 + 9.4247779607693797153879301498385086526* -I, -229.70424552002497255158146166263724792 + 6.2831853071795864769252867665 -590057684*I, 785.66045186253421572025117972275598325 + 9.4247779607693797153 -879301498385086526*I, 554.35531386699327377220656215544062014 + 3.1415926535 -897932384626433832795028842*I, 47.668319071568233997332918482707687878 + 3.1 -415926535897932384626433832795028842*I, -177.4887691856079886072447424446579 -1207 + 6.2831853071795864769252867665590057684*I, 875.6123693716808006976324 -6690606885226 + 2.84867032 E-65*I, -54.878404098312329644822020875673145627 -+ 9.4247779607693797153879301498385086526*I, 404.441538446767876903366231075 -14389175 + 9.4247779607693797153879301498385086526*I, -232.80982374359817890 -011490485449930607 + 3.1415926535897932384626433832795028842*I, 668.80899963 -671483856204802764462926790 + 6.2831853071795864769252867665590057684*I, -36 -7.35683481950538594888487746203445803 + 3.1415926535897932384626433832795028 -842*I, 1214.0716092619656173892944003952818868 + 3.1415926535897932384626433 -832795028842*I, 125.94415646756187210316334148291471657 + 6.2831853071795864 -769252867665590057684*I], [[2, [1, 1]~, 1, 1, [0, 1]~], [2, [2, 1]~, 1, 1, [ -1, 1]~], [5, [4, 1]~, 1, 1, [0, 1]~], [5, [5, 1]~, 1, 1, [-1, 1]~], [7, [3, -1]~, 2, 1, [3, 1]~], [13, [-6, 1]~, 1, 1, [5, 1]~], [13, [5, 1]~, 1, 1, [-6, - 1]~], [17, [14, 1]~, 1, 1, [2, 1]~], [17, [19, 1]~, 1, 1, [-3, 1]~], [23, [ --7, 1]~, 1, 1, [6, 1]~], [23, [6, 1]~, 1, 1, [-7, 1]~], [29, [-14, 1]~, 1, 1 -, [13, 1]~], [29, [13, 1]~, 1, 1, [-14, 1]~], [31, [23, 1]~, 1, 1, [7, 1]~], - [31, [38, 1]~, 1, 1, [-8, 1]~], [41, [-7, 1]~, 1, 1, [6, 1]~], [41, [6, 1]~ -, 1, 1, [-7, 1]~], [43, [-16, 1]~, 1, 1, [15, 1]~], [43, [15, 1]~, 1, 1, [-1 -6, 1]~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 1 -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] +[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 +4*I; 129.82045011403975460991182396195022419], [-41.811264589129943393339502 +258694361489 + 6.2831853071795864769252867665590057684*I, 9.2399004147902289 +816376260438840931575 + 3.1415926535897932384626433832795028842*I, -11.87460 +9881075406725097315997431161032 + 3.1415926535897932384626433832795028842*I, + 0.E-67, -51.051165003920172374977128302578454646 + 3.1415926535897932384626 +433832795028842*I, -64.910225057019877304955911980975112095 + 3.141592653589 +7932384626433832795028842*I, -29.936654708054536668242186261263200456 + 3.14 +15926535897932384626433832795028842*I, -47.668319071568233997332918482707687 +878 + 6.2831853071795864769252867665590057684*I, 3.8762936464778825067484824 +790355076166, -6.7377511782956880607802359510546381087 + 3.14159265358979323 +84626433832795028842*I, -35.073513410834255332559266307639723380 + 3.1415926 +535897932384626433832795028842*I, 33.130781426597481571750300827582717074 + +2.96736492 E-67*I, 54.878404098312329644822020875673145627 + 5.93472984 E-67 +*I, -14.980188104648613073630759189293219180 + 3.141592653589793238462643383 +2795028842*I, -26.831076484481330319708743069401142308 + 3.14159265358979323 +84626433832795028842*I, -19.706749066516065512488907834878146944 + 3.1415926 +535897932384626433832795028842*I, -22.104515522613877880850594423816214544 + + 3.1415926535897932384626433832795028842*I, -45.6875582356078259000879847377 +29869105 + 6.2831853071795864769252867665590057684*I, 47.6683190715682339973 +32918482707687879 + 1.18694596 E-66*I; 41.8112645891299433933395022586943614 +89, -9.2399004147902289816376260438840931575, 11.874609881075406725097315997 +431161032, 0.E-67, 51.051165003920172374977128302578454646, 64.9102250570198 +77304955911980975112095, 29.936654708054536668242186261263200456, 47.6683190 +71568233997332918482707687879, -3.8762936464778825067484824790355076166, 6.7 +377511782956880607802359510546381087, 35.07351341083425533255926630763972338 +0, -33.130781426597481571750300827582717074, -54.878404098312329644822020875 +673145627, 14.980188104648613073630759189293219180, 26.831076484481330319708 +743069401142309, 19.706749066516065512488907834878146944, 22.104515522613877 +880850594423816214544, 45.687558235607825900087984737729869105, -47.66831907 +1568233997332918482707687878], [[2, [2, 1]~, 1, 1, [1, 1]~], [5, [5, 1]~, 1, + 1, [1, 1]~], [13, [-5, 1]~, 1, 1, [6, 1]~], [2, [3, 1]~, 1, 1, [0, 1]~], [5 +, [6, 1]~, 1, 1, [0, 1]~], [7, [4, 1]~, 2, 1, [-3, 1]~], [13, [6, 1]~, 1, 1, + [-5, 1]~], [23, [7, 1]~, 1, 1, [-6, 1]~], [43, [-15, 1]~, 1, 1, [16, 1]~], +[17, [20, 1]~, 1, 1, [-2, 1]~], [17, [15, 1]~, 1, 1, [3, 1]~], [29, [14, 1]~ +, 1, 1, [-13, 1]~], [29, [-13, 1]~, 1, 1, [14, 1]~], [31, [39, 1]~, 1, 1, [- +7, 1]~], [31, [24, 1]~, 1, 1, [8, 1]~], [41, [7, 1]~, 1, 1, [-6, 1]~], [41, +[-6, 1]~, 1, 1, [7, 1]~], [43, [16, 1]~, 1, 1, [-15, 1]~], [23, [-6, 1]~, 1, + 1, [7, 1]~]], 0, [x^2 - x - 100000, [2, 0], 400001, 1, [[1, -316.7281613012 +9840161392089489603747004; 1, 315.72816130129840161392089489603747004], [1, +-316.72816130129840161392089489603747004; 1, 315.728161301298401613920894896 +03747004], 0, [2, -1; -1, 200001], [400001, 200001; 0, 1], [200001, 1; 1, 2] +, [400001, [200001, 1]~]], [-315.72816130129840161392089489603747004, 316.72 +816130129840161392089489603747004], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 1000 +00; 0, 1, 1, -1]], [[5, [5], [[2, 0; 0, 1]]], 129.82045011403975460991182396 +195022419, 0.9876536979069047228, [2, -1], [37955488401901378100630325489636 +9154068336082609238336*x + 1198361656442507899904628359500228716651781276113 +16131167], 24], [mat(1), [[0, 0]], [[-41.81126458912994339333950225869436148 +9 + 6.2831853071795864769252867665590057684*I, 41.81126458912994339333950225 +8694361489]]], 0] ? 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 -61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468 -08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672 -2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1. -2897619530652735025030086072395031017 + 0.E-47*I, -2.01097980249891575621226 -34098917610612 + 3.1415926535897932384626433832795028842*I, 24.4121877466590 -95772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.3376 -98160660239595315877930058147543 + 9.4247779607693797153879301498385086526*I -, -20.610866187462450639586440264933189691 + 9.42477796076937971538793014983 -85086526*I, 29.258282452818196217527894893424939793 + 9.42477796076937971538 -79301498385086526*I, -0.34328764427702709438988786673341921876 + 3.141592653 -5897932384626433832795028842*I, -14.550628376291080203941433635329724736 + 0 -.E-47*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264 -33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795 -864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424 -7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061 -2 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.14159265358979323 -84626433832795028842*I, -30.337698160660239595315877930058147543 + 3.1415926 -535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + -3.1415926535897932384626433832795028842*I, -29.25828245281819621752789489342 -4939793 + 6.2831853071795864769252867665590057684*I, 0.343287644277027094389 -88786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.14 -15926535897932384626433832795028842*I, -24.478366048541841504313284087778334 -822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, 1 -]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~ -, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, 1 -]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1, - 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7, - 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.0663729752107779635959310 -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] +61300698 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468 +08795106061300699], [1.7903417566977293763292119206302198761, 1.289761953065 +2735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.701 +48550268542821846861610071436900868, -1.36845553 E-48, 0.5005798036324558738 +2620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254 +0123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.14 +15926535897932384626433832795028842*I, -0.3432876442770270943898878667334192 +1876 + 3.1415926535897932384626433832795028842*I, 2.133629400974756470719099 +7873636390948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745 +732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790 +3417566977293763292119206302198760, -1.2897619530652735025030086072395031017 +, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.50057980363 +245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.72 +41634548149836441438434283070556826, 0.3432876442770270943898878667334192187 +6, -2.1336294009747564707190997873636390948, -0.0661783018827457321853684923 +23164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [1 +1, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1, + [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [17 +, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, +1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.06637297521077796359 +59310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.06637 +29752107779635959310246705326058; 1, 7.0663729752107779635959310246705326058 +], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], + [-7.0663729752107779635959310246705326058, 8.066372975210777963595931024670 +5326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [ +[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.88144225126545793 +64, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.7903417566977293763292119 +206302198761, -1.7903417566977293763292119206302198760]]], 0] ? setrand(1);buchreal(10^9-3,0,0.5,0.5) [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) [x^4 - 7] @@ -393,13 +348,13 @@ I, -229.70424552002497255158146166263724792 + 6.283185 [[400001, 1]] -[[1, x]] +[[1, x - 1]] -[[5, [5], [[2, 1; 0, 1]]]] +[[5, [5], [[2, 0; 0, 1]]]] [129.82045011403975460991182396195022419] -[0.9876536979069047239] +[0.9876536979069047228] [[2, -1]] @@ -415,20 +370,20 @@ I, -229.70424552002497255158146166263724792 + 6.283185 [[400001, 1]] -[[1, x]] +[[1, x - 1]] -[[5, [5], [[2, 1; 0, 1]]]] +[[5, [5], [[2, 0; 0, 1]]]] [129.82045011403975460991182396195022419] -[0.9876536979069047239] +[0.9876536979069047228] [[2, -1]] [[379554884019013781006303254896369154068336082609238336*x + 119836165644250 789990462835950022871665178127611316131167]] -[26] +[24] ? setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1) @@ -438,118 +393,98 @@ I, -229.70424552002497255158146166263724792 + 6.283185 [[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] -[0.8826018286655581306] +[0.8826018286655581299] [[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) -[3, [3], [[3, 2; 0, 1]]] -? buchray(bnf,[[5,3;0,1],[1,0]]) -[12, [12], [[3, 2; 0, 1]]] -? bnr=buchrayinitgen(bnf,[[5,3;0,1],[1,0]]) +[3, [3], [[3, 0; 0, 1]]] +? buchray(bnf,[[5,4;0,1],[1,0]]) +[12, [12], [[3, 0; 0, 1]]] +? bnr=buchrayinitgen(bnf,[[5,4;0,1],[1,0]]) [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 -061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 -808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767 -22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1 -.2897619530652735025030086072395031017 + 0.E-47*I, -2.0109798024989157562122 -634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659 -095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337 -698160660239595315877930058147543 + 9.4247779607693797153879301498385086526* -I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498 -385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153 -879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265 -35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + -0.E-47*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 -433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 -5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 -47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 -12 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.1415926535897932 -384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592 -6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + - 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934 -24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438 -988786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.1 -415926535897932384626433832795028842*I, -24.47836604854184150431328408777833 -4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, -1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1] -~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, -1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1 -, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7 -, 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931 -0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372 -9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [ -2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000 -0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114 -; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102 -46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], - [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974 -6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 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]]) +061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 +808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306 +52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70 +148550268542821846861610071436900868, -1.36845553 E-48, 0.500579803632455873 +82620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.08885625 +40123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.1 +415926535897932384626433832795028842*I, -0.343287644277027094389887866733419 +21876 + 3.1415926535897932384626433832795028842*I, 2.13362940097475647071909 +97873636390948 + 3.1415926535897932384626433832795028842*I, 0.06617830188274 +5732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.79 +03417566977293763292119206302198760, -1.289761953065273502503008607239503101 +7, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.5005798036 +3245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.7 +241634548149836441438434283070556826, 0.343287644277027094389887866733419218 +76, -2.1336294009747564707190997873636390948, -0.066178301882745732185368492 +323164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [ +11, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1 +, [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [1 +7, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, + 1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635 +959310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.0663 +729752107779635959310246705326058; 1, 7.066372975210777963595931024670532605 +8], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]] +, [-7.0663729752107779635959310246705326058, 8.06637297521077796359593102467 +05326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], +[[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512654579 +364, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.790341756697729376329211 +9206302198761, -1.7903417566977293763292119206302198760]]], [0, [mat([[6, 1] +~, 1])]]], [[[5, 4; 0, 1], [1, 0]], [8, [4, 2], [[2, 0]~, [0, 1]~]], mat([[5 +, [-1, 1]~, 1, 1, [2, 1]~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[mod(0, 2)]~ +], 1]], [[2], [[0, 1]~], mat(1)]], [1, 0; 0, 1]], [1], mat([1, -3, -6]), [12 +, [12], [[3, 0; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]] +? bnr2=buchrayinitgen(bnf,[[25,14;0,1],[1,1]]) [[mat(3), mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 -061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 -808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767 -22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1 -.2897619530652735025030086072395031017 + 0.E-47*I, -2.0109798024989157562122 -634098917610612 + 3.1415926535897932384626433832795028842*I, 24.412187746659 -095772127915595455170629 + 6.2831853071795864769252867665590057684*I, 30.337 -698160660239595315877930058147543 + 9.4247779607693797153879301498385086526* -I, -20.610866187462450639586440264933189691 + 9.4247779607693797153879301498 -385086526*I, 29.258282452818196217527894893424939793 + 9.4247779607693797153 -879301498385086526*I, -0.34328764427702709438988786673341921876 + 3.14159265 -35897932384626433832795028842*I, -14.550628376291080203941433635329724736 + -0.E-47*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 -433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 -5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 -47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 -12 + 0.E-47*I, -24.412187746659095772127915595455170629 + 3.1415926535897932 -384626433832795028842*I, -30.337698160660239595315877930058147543 + 3.141592 -6535897932384626433832795028842*I, 20.610866187462450639586440264933189691 + - 3.1415926535897932384626433832795028842*I, -29.2582824528181962175278948934 -24939793 + 6.2831853071795864769252867665590057684*I, 0.34328764427702709438 -988786673341921876 + 0.E-48*I, 14.550628376291080203941433635329724736 + 3.1 -415926535897932384626433832795028842*I, -24.47836604854184150431328408777833 -4822 + 3.1415926535897932384626433832795028842*I], [[3, [-1, 1]~, 1, 1, [0, -1]~], [3, [0, 1]~, 1, 1, [-1, 1]~], [5, [-2, 1]~, 1, 1, [1, 1]~], [5, [1, 1] -~, 1, 1, [-2, 1]~], [11, [-2, 1]~, 1, 1, [1, 1]~], [11, [1, 1]~, 1, 1, [-2, -1]~], [17, [-3, 1]~, 1, 1, [2, 1]~], [17, [2, 1]~, 1, 1, [-3, 1]~], [19, [-1 -, 1]~, 1, 1, [0, 1]~], [19, [0, 1]~, 1, 1, [-1, 1]~]]~, [1, 3, 5, 2, 4, 6, 7 -, 8, 10, 9], [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931 -0246705326058; 1, 8.0663729752107779635959310246705326058], [1, 1; -7.066372 -9752107779635959310246705326058, 8.0663729752107779635959310246705326058], [ -2, 1.0000000000000000000000000000000000000; 1.000000000000000000000000000000 -0000000, 115.00000000000000000000000000000000000], [2, 1; 1, 115], [229, 114 -; 0, 1], [115, -1; -1, 2], [229, [114, 1]~]], [-7.06637297521077796359593102 -46705326058, 8.0663729752107779635959310246705326058], [1, x], [1, 0; 0, 1], - [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 2; 0, 1]]], 2.712465305184343974 -6808795106061300699, 0.8814422512654579369, [2, -1], [x + 7], 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]]] +061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 +808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306 +52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70 +148550268542821846861610071436900868, -1.36845553 E-48, 0.500579803632455873 +82620331339071677436 + 3.1415926535897932384626433832795028842*I, 1.08885625 +40123011578605958199158508674, 1.7241634548149836441438434283070556826 + 3.1 +415926535897932384626433832795028842*I, -0.343287644277027094389887866733419 +21876 + 3.1415926535897932384626433832795028842*I, 2.13362940097475647071909 +97873636390948 + 3.1415926535897932384626433832795028842*I, 0.06617830188274 +5732185368492323164193433 + 3.1415926535897932384626433832795028842*I; -1.79 +03417566977293763292119206302198760, -1.289761953065273502503008607239503101 +7, -0.70148550268542821846861610071436900868, 1.36845553 E-48, -0.5005798036 +3245587382620331339071677436, -1.0888562540123011578605958199158508674, -1.7 +241634548149836441438434283070556826, 0.343287644277027094389887866733419218 +76, -2.1336294009747564707190997873636390948, -0.066178301882745732185368492 +323164193433], [[3, [0, 1]~, 1, 1, [1, 1]~], [5, [-1, 1]~, 1, 1, [2, 1]~], [ +11, [-1, 1]~, 1, 1, [2, 1]~], [3, [1, 1]~, 1, 1, [0, 1]~], [5, [2, 1]~, 1, 1 +, [-1, 1]~], [11, [2, 1]~, 1, 1, [-1, 1]~], [19, [1, 1]~, 1, 1, [0, 1]~], [1 +7, [3, 1]~, 1, 1, [-2, 1]~], [17, [-2, 1]~, 1, 1, [3, 1]~], [19, [0, 1]~, 1, + 1, [1, 1]~]], 0, [x^2 - x - 57, [2, 0], 229, 1, [[1, -8.0663729752107779635 +959310246705326058; 1, 7.0663729752107779635959310246705326058], [1, -8.0663 +729752107779635959310246705326058; 1, 7.066372975210777963595931024670532605 +8], 0, [2, -1; -1, 115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]] +, [-7.0663729752107779635959310246705326058, 8.06637297521077796359593102467 +05326058], [1, x - 1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], +[[3, 0; 0, 1]]], 2.7124653051843439746808795106061300699, 0.8814422512654579 +364, [2, -1], [x + 7], 155], [mat(1), [[0, 0]], [[1.790341756697729376329211 +9206302198761, -1.7903417566977293763292119206302198760]]], [0, [mat([[6, 1] +~, 1])]]], [[[25, 14; 0, 1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [4, 2]~, [- +2, -2]~]], mat([[5, [-1, 1]~, 1, 1, [2, 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, -14/5])]], [[2, 2], [[4, 2]~, [-2, -2]~], [1, 0; 0, + 1]]], [1, -12, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]], [1], mat([1, -3, -6, 0]), [1 +2, [12], [[3, 0; 0, 1]]], [[1, -18, 9; -1/2, 10, -5], [-2, 0; 0, -10]]] ? bytesize(%) -7604 +6372 ? ceil(-2.5) -2 ? centerlift(mod(456,555)) @@ -571,7 +506,7 @@ z^2 - 5*z - 2 z^2 + mod(8186, 8191)*z + mod(8189, 8191) ? acurve=chell(acurve,[-1,1,2,3]) [-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 81778, -2.4513893819867900608542248318665252253*I, 0.47131927795681147588259 389708033769964, 1.4354565186686843187232088566788165076*I, 7.33813274078957 @@ -619,10 +554,10 @@ od(-279140305176/29063006931199*x^11 + 129916611552/29 qfr(35, 43, 13, 0.E-38) ? concat([1,2],[3,4]) [1, 2, 3, 4] -? conductor(bnf,[[25,13;0,1],[1,1]]) -[[[5, 3; 0, 1], [1, 0]], [12, [12], [[3, 2; 0, 1]]], mat(12)] +? conductor(bnf,[[25,14;0,1],[1,1]]) +[[[5, 4; 0, 1], [1, 0]], [12, [12], [[3, 0; 0, 1]]], mat(12)] ? conductorofchar(bnr,[2]) -[[5, 3; 0, 1], [0, 0]] +[[5, 4; 0, 1], [0, 0]] ? conj(1+i) 1 - I ? conjvec(mod(x^2+x+1,x^3-x-1)) @@ -735,9 +670,9 @@ 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], 0, 0, 0], [[10, 1; 21, 1], 0, 0, 0]]]] ? discrayrel(bnr,mat(6)) -[6, 2, [125, 13; 0, 1]] +[6, 2, [125, 14; 0, 1]] ? discrayrel(bnr) -[12, 1, [1953125, 1160888; 0, 1]] +[12, 1, [1953125, 1160889; 0, 1]] ? discrayrelcond(bnr2) 0 ? divisors(8!) @@ -838,29 +773,9 @@ 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^3 - 197*x^2 - 273*x - 127] ? factoredpolred2(p,fa) - -[1 x - 1] - -[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] - +[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 +*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] ? 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] @@ -938,7 +853,7 @@ x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 5466035 0.25881904510252076234889883762404832834 0.49999999999999999999999999999999999999 0.70710678118654752440084436210484903928 -0.86602540378443864676372317075293618346 +0.86602540378443864676372317075293618347 0.96592582628906828674974319972889736763 1.0000000000000000000000000000000000000 0.96592582628906828674974319972889736764 @@ -973,9 +888,9 @@ mod(x^5, x^6 + 108) ? gcd(12345678,87654321) 9 ? getheap() -[214, 48646] +[215, 44753] ? getrand() -1939683225 +498199132 ? getstack() 0 ? globalred(acurve) @@ -1083,120 +998,94 @@ mod(x^5, x^6 + 108) -1 ? nf1=initalgred(nfpol) [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 -741050929194782733001765987770358483, 0.158944197453903762065494816710718942 -89; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753 -285514741525107*I, -0.22273329410580226599155701611419649154 - 0.13611876021 -752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + 0 -.13249517760521973840801462296650806543*I, -0.053650958656997725359297528357 -602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.682941293594312 -7761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.37035 -26062130959637482576769100030014 + 6.9001775222880494773720769629846373016*I -, -8.0696202866361678983472946546849540475 + 8.87676767859710424508852843013 -48051602*I, -22.025821140069954155673449879997756863 - 8.4306586896999153544 -710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, - -0.27676744146812072730095952834883393274 - 0.9836327531553728699950657102948 -3050214*I, 3.3658825871886255523259123230159952011 - 4.100070245202145234594 -8573967197204327*I; 1.1861718006377964594796293860483989860, -0.445466588211 -60453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2. -7407052124261919274965153538200060029 - 13.800355044576098954744153925969274 -603*I; -0.59741050929194782733001765987770358483, -0.26334891743571637597539 -303075238832018 - 0.26499035521043947681602924593301613087*I, -16.1392405732 -72335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.15 -894419745390376206549481671071894289, -0.10730191731399545071859505671520521 -623 - 0.55245273628338214076276569363136722973*I, -44.0516422801399083113468 -99759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.000000000 -0000000000000000000000000000, -2.0000000000000000000000000000000000000, -17. -000000000000000000000000000000000000, -44.0000000000000000000000000000000000 -00; 2.0000000000000000000000000000000000000, 15.7781094086719980448363574712 -83695361, 22.314643349754061651916553814602769764, 10.0513952578314782754999 -32716306366248, -108.58917507620841447456569092094763671; -2.000000000000000 -0000000000000000000000, 22.314643349754061651916553814602769764, 100.5239126 -2388960975827806174040462368, 143.93295090847353519436673793501057176, -55.8 -42564718082452641322500190813370023; -17.00000000000000000000000000000000000 -0, 10.051395257831478275499932716306366248, 143.9329509084735351943667379350 -1057176, 288.25823756749944693139292174819167135, 205.7984003827766237572018 -0649465932302; -44.000000000000000000000000000000000000, -108.58917507620841 -447456569092094763671, -55.842564718082452641322500190813370023, 205.7984003 -8277662375720180649465932302, 1112.6092277946777707779250962522343036], [5, -2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, -1 -01, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215, - 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, - -296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -296700 -, -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]] +7205048250249527946671612684, 2.4285174907194186068992069565359418363, -0.71 +946691128913178943997506477288225737, 2.555820035069169495064607115942677997 +0; 1, -0.13838372073406036365047976417441696637 + 0.491816376577686434997532 +85514741525107*I, -1.9647119211288133163138753392090569931 + 0.8097149241889 +7895128294082219556466856*I, 0.072312766896812300380582649294307897128 + 2.1 +980803753846276641195195160383234877*I, 0.9879631935250703980395053973545283 +7195 + 1.5701452385894131769052374806001981108*I; 1, 1.682941293594312776162 +9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769 +10401286427186094108607491 - 1.3101462685358123283560773619310445914*I, 0.78 +742068874775359433940488309213323161 - 2.13366338931266180341684546104579360 +16*I, -1.2658732110596551455718089553258673704 + 2.7164790103743150566578028 +035789834835*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071 +94186068992069565359418363, -0.71946691128913178943997506477288225737, 2.555 +8200350691694950646071159426779970; 1.4142135623730950488016887242096980785, + -0.19570413467375904264179382543977540673, -2.77852224501646643099209256540 +93065576, 0.10226569567819614506098907018896260036, 1.3971909474085893198147 +151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443 +9565129926149974389115722, 3.1085550780550843138423672171643499921, 2.220520 +6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2. +3800384020787979181834702019470475018, 1.06130105909862703981823187865589944 +13, 1.1135810173202366904448352912286604471, -1.7902150633253437253677889164 +811036159; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763 +4446810512816401034, -3.0174557027049114270734649132936867271, 3.84168145837 +31999185306312841432940662], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10, + -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, 3 +45, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 51 +75, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -17250 +, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450], +[595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.0891151457205048250249527 +946671612684, -0.13838372073406036365047976417441696637 + 0.4918163765776864 +3499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.050035 +1226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2*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], [ +1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0, + 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, -1 +, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, -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 +, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -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, -1 +, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 1]] ? initalgred2(nfpol) [[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 -9741050929194782733001765987770358483, 0.15894419745390376206549481671071894 -289; 1, -0.13838372073406036365047976417441696637 + 0.4918163765776864349975 -3285514741525107*I, -0.22273329410580226599155701611419649154 - 0.1361187602 -1752805221674918029071012580*I, -0.13167445871785818798769651537619416009 + -0.13249517760521973840801462296650806543*I, -0.05365095865699772535929752835 -7602608116 + 0.27622636814169107038138284681568361486*I; 1, 1.68294129359431 -27761629561615079976005 + 2.0500351226010726172974286983598602163*I, -1.3703 -526062130959637482576769100030014 + 6.9001775222880494773720769629846373016* -I, -8.0696202866361678983472946546849540475 + 8.8767676785971042450885284301 -348051602*I, -22.025821140069954155673449879997756863 - 8.430658689699915354 -4710860185447589664*I], [1, 2, 2; -1.0891151457205048250249527946671612684, --0.27676744146812072730095952834883393274 - 0.983632753155372869995065710294 -83050214*I, 3.3658825871886255523259123230159952011 - 4.10007024520214523459 -48573967197204327*I; 1.1861718006377964594796293860483989860, -0.44546658821 -160453198311403222839298308 + 0.27223752043505610443349836058142025160*I, -2 -.7407052124261919274965153538200060029 - 13.80035504457609895474415392596927 -4603*I; -0.59741050929194782733001765987770358483, -0.2633489174357163759753 -9303075238832018 - 0.26499035521043947681602924593301613087*I, -16.139240573 -272335796694589309369908095 - 17.753535357194208490177056860269610320*I; 0.1 -5894419745390376206549481671071894289, -0.1073019173139954507185950567152052 -1623 - 0.55245273628338214076276569363136722973*I, -44.051642280139908311346 -899759995513726 + 16.861317379399830708942172037089517932*I], [5, 2.00000000 -00000000000000000000000000000, -2.0000000000000000000000000000000000000, -17 -.000000000000000000000000000000000000, -44.000000000000000000000000000000000 -000; 2.0000000000000000000000000000000000000, 15.778109408671998044836357471 -283695361, 22.314643349754061651916553814602769764, 10.051395257831478275499 -932716306366248, -108.58917507620841447456569092094763671; -2.00000000000000 -00000000000000000000000, 22.314643349754061651916553814602769764, 100.523912 -62388960975827806174040462368, 143.93295090847353519436673793501057176, -55. -842564718082452641322500190813370023; -17.0000000000000000000000000000000000 -00, 10.051395257831478275499932716306366248, 143.932950908473535194366737935 -01057176, 288.25823756749944693139292174819167135, 205.798400382776623757201 -80649465932302; -44.000000000000000000000000000000000000, -108.5891750762084 -1447456569092094763671, -55.842564718082452641322500190813370023, 205.798400 -38277662375720180649465932302, 1112.6092277946777707779250962522343036], [5, - 2, -2, -17, -44; 2, -2, -34, -63, -40; -2, -34, -90, -101, 177; -17, -63, - -101, -27, 505; -44, -40, 177, 505, 828], [345, 0, 160, 252, 156; 0, 345, 215 -, 311, 306; 0, 0, 5, 3, 2; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [163875, -388125, --296700, 234600, -89700; -388125, -1593900, -677925, 595125, -315675; -29670 -0, -677925, 17250, 58650, -87975; 234600, 595125, 58650, -100050, 89700; -89 -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)] +57205048250249527946671612684, 2.4285174907194186068992069565359418363, -0.7 +1946691128913178943997506477288225737, 2.55582003506916949506460711594267799 +70; 1, -0.13838372073406036365047976417441696637 + 0.49181637657768643499753 +285514741525107*I, -1.9647119211288133163138753392090569931 + 0.809714924188 +97895128294082219556466856*I, 0.072312766896812300380582649294307897128 + 2. +1980803753846276641195195160383234877*I, 0.987963193525070398039505397354528 +37195 + 1.5701452385894131769052374806001981108*I; 1, 1.68294129359431277616 +29561615079976005 + 2.0500351226010726172974286983598602163*I, 0.75045317576 +910401286427186094108607491 - 1.3101462685358123283560773619310445914*I, 0.7 +8742068874775359433940488309213323161 - 2.1336633893126618034168454610457936 +016*I, -1.2658732110596551455718089553258673704 + 2.716479010374315056657802 +8035789834835*I], [1, -1.0891151457205048250249527946671612684, 2.4285174907 +194186068992069565359418363, -0.71946691128913178943997506477288225737, 2.55 +58200350691694950646071159426779970; 1.4142135623730950488016887242096980785 +, -0.19570413467375904264179382543977540673, -2.7785222450164664309920925654 +093065576, 0.10226569567819614506098907018896260036, 1.397190947408589319814 +7151262541540506; 0, 0.69553338995335755797766403996841143190, 1.14510982744 +39565129926149974389115722, 3.1085550780550843138423672171643499921, 2.22052 +06913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2 +.3800384020787979181834702019470475018, 1.0613010590986270398182318786558994 +413, 1.1135810173202366904448352912286604471, -1.790215063325343725367788916 +4811036159; 0, 2.8991874737236275652408825679737171587, -1.85282662165584876 +34446810512816401034, -3.0174557027049114270734649132936867271, 3.8416814583 +731999185306312841432940662], 0, [5, 2, 0, 1, 2; 2, -2, 5, 10, -20; 0, 5, 10 +, -10, 5; 1, 10, -10, -17, 1; 2, -20, 5, 1, -8], [345, 0, 145, 235, 168; 0, +345, 250, 344, 200; 0, 0, 5, 4, 3; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [108675, 5 +175, 0, 10350, 15525; 5175, 13800, 8625, 1725, -27600; 0, 8625, 37950, -1725 +0, 0; 10350, 1725, -17250, -24150, -15525; 15525, -27600, 0, -15525, -3450], + [595125, [-238050, 296700, 91425, 1725, 0]~]], [-1.089115145720504825024952 +7946671612684, -0.13838372073406036365047976417441696637 + 0.491816376577686 +43499753285514741525107*I, 1.6829412935943127761629561615079976005 + 2.05003 +51226010726172974286983598602163*I], [1, x, 1/2*x^4 - 3/2*x^3 + 5/2*x^2 + 2* +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], +[1, 0, -1, -7, -14; 0, 1, 1, -2, -15; 0, 0, 0, -2, -4; 0, 0, -1, -1, 2; 0, 0 +, 1, 3, 4], [1, 0, 0, 0, 0, 0, -1, 1, 2, -4, 0, 1, 3, -1, 1, 0, 2, -1, -3, - +1, 0, -4, 1, -1, -1; 0, 1, 0, 0, 0, 1, 1, 1, 1, -1, 0, 1, -2, -1, 1, 0, 1, - +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, 0, 1, 1, 0, -1, 2, 1, 1; 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, -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, - +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 +*x + 1, x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2)] ? 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) -[3 1 2 2 2] +[3 2 1 0 1] [0 1 0 0 0] @@ -1208,27 +1097,27 @@ I, -8.0696202866361678983472946546849540475 + 8.876767 ? 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] ? 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) @@ -1243,45 +1132,45 @@ I, -8.0696202866361678983472946546849540475 + 8.876767 [0 0 0 0 1] ? 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]) [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~] ? idealappr(nf,idy) -[-2, 0, -2, 4, 0]~ +[-2, -2, -1, -2, -1]~ ? idealapprfact(nf,idealfactor(nf,idy)) -[-2, 0, -2, 4, 0]~ +[-2, -2, -1, -2, -1]~ ? 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) -[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) -[[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) -[[[1, 0; 0, 1]], [], [[3, 2; 0, 1], [3, 0; 0, 1]], [[2, 0; 0, 2]], [[5, 3; 0 -, 1], [5, 1; 0, 1]], [], [], [], [[9, 5; 0, 1], [3, 0; 0, 3], [9, 3; 0, 1]], - [], [[11, 9; 0, 1], [11, 1; 0, 1]], [[6, 4; 0, 2], [6, 0; 0, 2]], [], [], [ -[15, 8; 0, 1], [15, 3; 0, 1], [15, 11; 0, 1], [15, 6; 0, 1]], [[4, 0; 0, 4]] -, [[17, 14; 0, 1], [17, 2; 0, 1]], [], [[19, 18; 0, 1], [19, 0; 0, 1]], [[10 -, 6; 0, 2], [10, 2; 0, 2]]] +[[[1, 0; 0, 1]], [], [[3, 0; 0, 1], [3, 1; 0, 1]], [[2, 0; 0, 2]], [[5, 4; 0 +, 1], [5, 2; 0, 1]], [], [], [], [[9, 6; 0, 1], [3, 0; 0, 3], [9, 4; 0, 1]], + [], [[11, 10; 0, 1], [11, 2; 0, 1]], [[6, 0; 0, 2], [6, 2; 0, 2]], [], [], +[[15, 9; 0, 1], [15, 4; 0, 1], [15, 12; 0, 1], [15, 7; 0, 1]], [[4, 0; 0, 4] +], [[17, 15; 0, 1], [17, 3; 0, 1]], [], [[19, 0; 0, 1], [19, 1; 0, 1]], [[10 +, 8; 0, 2], [10, 4; 0, 2]]] ? idx2=idealmul(nf,idx,idx) -[9 7 5 8 2] +[9 5 7 0 4] [0 1 0 0 0] @@ -1293,9 +1182,9 @@ I, -8.0696202866361678983472946546849540475 + 8.876767 ? 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] @@ -1305,19 +1194,19 @@ I, -8.0696202866361678983472946546849540475 + 8.876767 ? 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) -[3 1 2 2 2] +[3 2 1 0 1] [0 1 0 0 0] @@ -1329,7 +1218,7 @@ I, -8.0696202866361678983472946546849540475 + 8.876767 ? idealhermite(nf,vp) -[3 1 2 2 2] +[3 2 1 0 1] [0 1 0 0 0] @@ -1341,7 +1230,7 @@ I, -8.0696202866361678983472946546849540475 + 8.876767 ? idealhermite2(nf,vp[2],3) -[3 1 2 2 2] +[3 2 1 0 1] [0 1 0 0 0] @@ -1355,7 +1244,7 @@ I, -8.0696202866361678983472946546849540475 + 8.876767 16 ? idp=idealpow(nf,idx,7) -[2187 1807 2129 692 1379] +[2187 1436 1807 630 1822] [0 1 0 0 0] @@ -1367,20 +1256,20 @@ I, -8.0696202866361678983472946546849540475 + 8.876767 ? 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) -[5, [2, 0, 2, 1, 0]~] +[5, [2, 2, 1, 2, 1]~] ? idealtwoelt2(nf,idy,10) -[-2, 0, -2, -1, 0]~ +[-2, -2, -1, -2, -1]~ ? idealval(nf,idp,vp) 7 ? idmat(5) @@ -1473,7 +1362,7 @@ x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O( 1 ? isfund(12345) 1 -? isideal(bnf[7],[5,1;0,1]) +? isideal(bnf[7],[5,2;0,1]) 1 ? isincl(x^2+1,x^4+1) [-x^2, x^2] @@ -1487,12 +1376,12 @@ x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O( [-1/25*x^2 + 13/25*x - 2/5] ? isprime(12345678901234567) 0 -? isprincipal(bnf,[5,1;0,1]) +? isprincipal(bnf,[5,2;0,1]) [1]~ -? isprincipalgen(bnf,[5,1;0,1]) -[[1]~, [-2, -1/3]~, 151] +? isprincipalgen(bnf,[5,2;0,1]) +[[1]~, [7/3, 1/3]~, 155] ? isprincipalraygen(bnr,primedec(bnf,7)[1]) -[[9]~, [-2170/6561, -931/19683]~, 192] +[[9]~, [112595/19683, 13958/19683]~, 192] ? ispsp(73!+1) 1 ? isqrt(10!^2+1) @@ -1597,19 +1486,7 @@ x [0 1 -1] ? kerint2(matrix(4,6,x,y,2520/(x+y))) - -[3 1] - -[-30 -15] - -[70 70] - -[0 -140] - -[-126 126] - -[84 -42] - + *** this function has been suppressed. ? f(u)=u+1; ? print(f(5));kill(f); 6 @@ -1695,21 +1572,7 @@ x [-60 -105 280 252 -486 471 1290] ? lll1(m) - -[-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] - + *** this function has been suppressed. ? lllgram(m) [1 1 27 -27 69 0 141] @@ -1727,21 +1590,7 @@ x [0 1 3 -17 3 -7 3] ? lllgram1(m) - -[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] - + *** this function has been suppressed. ? lllgramint(m) [1 1 27 -27 69 0 141] @@ -1813,21 +1662,7 @@ 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, 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) - -[-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] - + *** this function has been suppressed. ? \precision=96 realprecision = 96 significant digits ? ln(2) @@ -1913,50 +1748,45 @@ E-19, -1.732050807568877293]~, 1.992332899583490707, 1 ? lseriesell(ccurve,2,-37,1.2)-l -1.08420217 E-19 ? 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 -82350902743636344, 4.305556205008953036], [10889, 5698, 3794; 0, 1, 0; 0, 0, - 1], mat(2), mat([0, 1, 1, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 10, 69, 33, 39, -57], [2, [-1, 0, 0]~], [[0, 1, 0]~, [-4, 2, 1]~], [-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]] +[x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2 - x - 9], [-3.233732695981516672 +, -0.07182350902743636344, 4.305556205008953036], [10889, 5698, 8994; 0, 1, +0; 0, 0, 1], mat(2), mat([1, 1, 0, 1, 1, 0, 1, 1]), [9, 15, 16, 17, 39, 10, +33, 57, 69], [2, [-1, 0, 0]~], [[0, 1, 0]~, [5, 3, 1]~], [-4, -1, 2, 3, 10, +3, 1, 7, 2; 1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]] ? makebigbnf(sbnf) -[mat(2), mat([0, 1, 1, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535 -89793238*I, -4.562279014988837901 + 3.141592653589793238*I; -2.6335434327389 +[mat(2), mat([1, 1, 0, 1, 1, 0, 1, 1]), [1.173637103435061715 + 3.1415926535 +89793238*I, -4.562279014988837952 + 3.141592653589793238*I; -2.6335434327389 76049 + 3.141592653589793238*I, 1.420330600779487357 + 3.141592653589793238* I; 1.459906329303914334, 3.141948414209350543], [1.246346989334819161 + 3.14 -1592653589793238*I, -1.990056445584799713 + 3.141592653589793238*I, 0.540400 -6376129469727 + 3.141592653589793238*I, -0.6926391142471042845 + 3.141592653 -589793238*I, 0.E-96 + 3.141592653589793238*I, 0.3677262014027817705 + 3.1415 -92653589793238*I, 0.004375616572659815402 + 3.141592653589793238*I, -0.83056 -25946607188639, -1.977791147836553953 + 3.141592653589793238*I; 0.6716827432 -867392935 + 3.141592653589793238*I, 0.5379005671092853266, -0.83332198837424 -04172 + 3.141592653589793238*I, -0.2461086674077943078, 0.E-96 + 3.141592653 -589793238*I, 0.9729063188316092378, -0.8738318043071131265, -1.5526615498687 -75853 + 3.141592653589793238*I, 0.5774919091398324092 + 3.141592653589793238 -*I; -1.918029732621558454, 1.452155878475514386, 0.2929213507612934444, 0.93 -87477816548985923, 0.E-96 + 3.141592653589793238*I, -1.340632520234391008, 0 -.8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.40029 -9238696721544 + 3.141592653589793238*I], [[3, [-1, 1, 0]~, 1, 1, [1, 0, 1]~] -, [5, [3, 1, 0]~, 1, 1, [-2, 1, 1]~], [5, [-1, 1, 0]~, 1, 1, [1, 0, 1]~], [5 -, [2, 1, 0]~, 1, 1, [2, 2, 1]~], [3, [1, 0, 1]~, 1, 2, [-1, 1, 0]~], [23, [- -10, 1, 0]~, 1, 1, [7, 9, 1]~], [11, [1, 1, 0]~, 1, 1, [-1, -2, 1]~], [13, [1 -9, 1, 0]~, 1, 1, [2, 6, 1]~], [19, [-6, 1, 0]~, 1, 1, [-3, 5, 1]~]]~, [1, 2, - 3, 4, 5, 6, 7, 8, 9]~, [x^3 - x^2 - 14*x - 1, [3, 0], 10889, 1, [[1, -3.233 -732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.0051586 -16449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; -3 -.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.45702 -714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.00000000 -0000000000, 29.00000000000000000; 1.000000000000000000, 29.00000000000000000 -, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.0000 -000000000000], [3, 1, 29; 1, 29, 46; 29, 46, 453], [10889, 5698, 3794; 0, 1, - 0; 0, 0, 1], [11021, 881, -795; 881, 518, -109; -795, -109, 86], [10889, [1 -890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.3055562 -05008953036], [1, x, x^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 1, 0 -, 1, 1; 0, 1, 0, 1, 0, 14, 0, 14, 15; 0, 0, 1, 0, 1, 1, 1, 1, 15]], [[2, [2] -, [[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]] +1592653589793238*I, 0.5404006376129469727 + 3.141592653589793238*I, -0.69263 +91142471042844 + 3.141592653589793238*I, -1.990056445584799713 + 3.141592653 +589793238*I, -0.8305625946607188643 + 3.141592653589793238*I, 0.E-57, 0.0043 +75616572659815433 + 3.141592653589793238*I, -1.977791147836553953, 0.3677262 +014027817708 + 3.141592653589793238*I; 0.6716827432867392938 + 3.14159265358 +9793238*I, -0.8333219883742404170 + 3.141592653589793238*I, -0.2461086674077 +943076, 0.5379005671092853269, -1.552661549868775853, 0.E-57, -0.87383180430 +71131263, 0.5774919091398324092, 0.9729063188316092380; -1.91802973262155845 +5, 0.2929213507612934444, 0.9387477816548985923, 1.452155878475514386, 2.383 +224144529494717, 0.E-57, 0.8694561877344533111, 1.400299238696721544, -1.340 +632520234391008], [[3, [-1, 1, 0]~, 1, 1, [1, 1, 1]~], [5, [-1, 1, 0]~, 1, 1 +, [0, 1, 1]~], [5, [2, 1, 0]~, 1, 1, [1, -2, 1]~], [5, [3, 1, 0]~, 1, 1, [2, + 2, 1]~], [13, [19, 1, 0]~, 1, 1, [-2, -6, 1]~], [3, [10, 1, 1]~, 1, 2, [-1, + 1, 0]~], [11, [1, 1, 0]~, 1, 1, [-3, -1, 1]~], [19, [-6, 1, 0]~, 1, 1, [6, +6, 1]~], [23, [-10, 1, 0]~, 1, 1, [-7, 10, 1]~]]~, 0, [x^3 - x^2 - 14*x - 1, + [3, 0], 10889, 1, [[1, -3.233732695981516672, 4.690759845041404811; 1, -0.0 +7182350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.23225 +8029482144592], [1, -3.233732695981516672, 4.690759845041404811; 1, -0.07182 +350902743636344, -8.923017874523549402; 1, 4.305556205008953036, 5.232258029 +482144592], 0, [3, 1, 1; 1, 29, 8; 1, 8, 129], [10889, 5698, 8994; 0, 1, 0; +0, 0, 1], [3677, -121, -21; -121, 386, -23; -21, -23, 86], [10889, [1899, 51 +91, 1]~]], [-3.233732695981516672, -0.07182350902743636344, 4.30555620500895 +3036], [1, x, x^2 - x - 9], [1, 0, 9; 0, 1, 1; 0, 0, 1], [1, 0, 0, 0, 9, 1, +0, 1, 44; 0, 1, 0, 1, 1, 5, 0, 5, 1; 0, 0, 1, 0, 1, 0, 1, 0, -4]], [[2, [2], + [[3, 2, 0; 0, 1, 0; 0, 0, 1]]], 10.34800724602768011, 1.000000000000000000, + [2, -1], [x, x^2 + 2*x - 4], 1000], [mat(1), [[0.E-57, 0.E-57, 0.E-57]], [[ +1.246346989334819161 + 3.141592653589793238*I, 0.6716827432867392938 + 3.141 +592653589793238*I, -1.918029732621558455]]], [-4, -1, 2, 3, 10, 3, 1, 7, 2; +1, 1, 1, 1, 5, 0, 1, 2, 1; 0, 0, 0, 0, 1, 0, 0, 0, -1]] ? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~) [1 11] @@ -2081,52 +1911,52 @@ mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5) 5]~ [14, 16, 6, 20, 14]~] ? 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] -, [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 -], [15, 5, 10, 12, 10; 0, 5, 0, 0, 0; 0, 0, 5, 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, 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, 0, 1] +, [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, 10, 5, 0, 12; 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], [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]] ? bb=algtobasis(nf,mod(x^3+x,nfpol)) -[1, 1, 1, 3, 0]~ +[1, 1, 4, 1, 3]~ ? da=nfdetint(nf,[a,aid]) -[30 5 25 27 10] +[90 70 35 0 65] [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] ? 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) -[2, 0, 0, 0, -1]~ +[2, 0, 0, 0, 0]~ ? 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]) -[[[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]~, [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, 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]]] +[[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 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]~], [[10, 4, 5, 6, 7; 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, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, +0; 0, 0, 0, 0, 1]]] ? 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 -, 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, 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]]] +[[[1, 0, 0, 0, 0]~, [-2, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 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]~], [[10, 4, 5, 6, 7; 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, 2, 1, 0, 1; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, +0; 0, 0, 0, 0, 1]]] ? nfmod(nf,ba,bb) -[-12, -7, 0, 9, 5]~ +[4, -1, -5, -1, -3]~ ? nfmul(nf,ba,bb) -[-25, -50, -30, 15, 90]~ +[50, -15, -35, 60, 15]~ ? nfpow(nf,bb,5) -[23455, 156370, 115855, 74190, -294375]~ +[-291920, 136855, 230560, -178520, 74190]~ ? nfreduce(nf,ba,idx) [1, 0, 0, 0, 0]~ ? setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8)) @@ -2138,8 +1968,8 @@ 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]~] ? 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] -, [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 +[[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, 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]] ? haid=[idmat(5),idmat(5),idmat(5)] @@ -2148,11 +1978,11 @@ 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]] ? nfsmith(nf,[as,haid,vaid]) -[[10951073973332888246310, 5442457637639729109215, 2693780223637146570055, 3 -910837124677073032737, 3754666252923836621170; 0, 5, 0, 0, 0; 0, 0, 5, 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, 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]] +[[2562748315629757085585610, 436545976069778274371140, 123799938628701108220 +1405, 2356446991473627724963350, 801407102592194537169612; 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], [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]] ? nfval(nf,ba,vp) 0 ? norm(1+i) @@ -2318,11 +2148,11 @@ x^4 + 2*x^3 + 3*x^2 + 4*x + 5 478051489392386968218136375373985436596569736643531551/158385319626308443937 475969221994173751192384064000000] ? cmcurve=initell([0,-3/4,0,-2,-1]) -[0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [1.999999999999 -999999, -0.6250000000000000000 + 0.3307189138830738238*I, -0.625000000000000 +[0, -3/4, 0, -2, -1, -3, -4, -4, -1, 105, 1323, -343, -3375, [2.000000000000 +000000, -0.6250000000000000000 + 0.3307189138830738238*I, -0.625000000000000 0000 - 0.3307189138830738238*I]~, 1.933311705616811546, 0.966655852808405773 -4 + 2.557530989916099474*I, -0.8558486330998558523 - 4.59882981 E-20*I, -0.4 -279243165499279261 - 2.757161217166147204*I, 4.944504600282546729] +3 + 2.557530989916099474*I, -0.8558486330998558525 - 4.59882981 E-20*I, -0.4 +279243165499279261 - 2.757161217166147204*I, 4.944504600282546727] ? 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 + (40 - 28*w)*x^2 + (22 + 23*w)*x)/((-90 - w)*x^2 + (-136 + 44*w)*x + (-40 + 2 @@ -2353,11 +2183,11 @@ qfr(125, 23, 1, 0.E-18) ? prime(100) 541 ? primedec(nf,2) -[[2, [3, 1, 0, 0, 0]~, 1, 1, [1, 1, 0, 1, 1]~], [2, [-3, -5, -4, 3, 15]~, 1, - 4, [1, 1, 0, 0, 0]~]] +[[2, [3, 0, 1, 0, 0]~, 1, 1, [0, 0, 0, 1, 1]~], [2, [12, -4, -2, 11, 3]~, 1, + 4, [1, 0, 1, 0, 0]~]] ? primedec(nf,3) -[[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~], [3, [-1, 1, -1, 0, 1]~, 2, - 2, [1, 2, 3, 1, 0]~]] +[[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~], [3, [-1, -1, -1, 0, 0]~, +2, 2, [0, 2, 2, 1, 0]~]] ? primedec(nf,11) [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]] ? primes(100) @@ -2398,19 +2228,19 @@ qfr(125, 23, 1, 0.E-18) [6] -[0] - [1] [3] -[0] +[1] +[3] + ? principalidele(nf,mod(x^3+5,nfpol)) -[[6; 0; 1; 3; 0], [2.2324480827796254080981385584384939684 + 3.1415926535897 -932384626433832795028842*I, 5.0387659675158716386435353106610489968 + 1.5851 +[[6; 1; 3; 1; 3], [2.2324480827796254080981385584384939684 + 3.1415926535897 +932384626433832795028841*I, 5.0387659675158716386435353106610489967 + 1.5851 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173 - - 0.0083630478144368246110910258645462996191*I]] + - 0.0083630478144368246110910258645462996226*I]] ? print((x-12*y)/(y+13*x)); -11/14 ? print([1,2;3,4]) @@ -2422,13 +2252,13 @@ qfr(125, 23, 1, 0.E-18) ? prod(1.,k=1,10,1+1/k!) 3.6821540356142043935732308433185262945 ? pi^2/6*prodeuler(p=2,10000,1-p^-2) -1.0000098157493066238697591433298145174 +1.0000098157493066238697591433298145166 ? prodinf(n=0,(1+2^-n)/(1+2^(-n+1))) -0.33333333333333333333333333333333333322 +0.33333333333333333333333333333333333313 ? prodinf1(n=0,-2^-n/(1+2^(-n+1))) -0.33333333333333333333333333333333333322 +0.33333333333333333333333333333333333313 ? psi(1) --0.57721566490153286060651209008240243102 +-0.57721566490153286060651209008240243104 ? quaddisc(-252) -7 ? quadgen(-11) @@ -2437,7 +2267,7 @@ w x^2 - x + 3 ? rank(matrix(5,5,x,y,x+y)) 2 -? rayclassno(bnf,[[5,3;0,1],[1,0]]) +? rayclassno(bnf,[[5,4;0,1],[1,0]]) 12 ? rayclassnolist(bnf,lu) [[3], [], [3, 3], [3], [6, 6], [], [], [], [3, 3, 3], [], [3, 3], [3, 3], [] @@ -2491,25 +2321,28 @@ 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]~, [-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 -, 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, 1/25]], [416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1 -280, 5, 5]~] +, 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, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1 +275, 5, 5]~] ? 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) -[[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) x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1 ? rnfequation2(nf2,p) @@ -2517,29 +2350,31 @@ 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] ? 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) 1 ? rnfsteinitz(nf2,aa) -[[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [38/25, -33/25, 11/25]~, [-27/125, 33/ -125, -11/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [-14/25, 24/25, -8/25]~, - [6/125, -24/125, 8/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [57/25, -12/2 -5, 4/25]~, [-53/125, 12/125, -4/125]~; [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, -0, 0]~, [8/25, -3/25, 1/25]~, [-7/125, 3/125, -1/125]~], [[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, -0; 0, 1, 0; 0, 0, 1], [125, 0, 108; 0, 125, 22; 0, 0, 1]], [416134375, 21294 -0625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~] +[[[1, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [-6/25, 66/25, 77/25]~, [17/125, -66/1 +25, -77/125]~; [0, 0, 0]~, [1, 0, 0]~, [0, 0, 0]~, [18/25, -48/25, -56/25]~, + [-26/125, 48/125, 56/125]~; [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [41/25, 24/ +25, 28/25]~, [-37/125, -24/125, -28/125]~; [0, 0, 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, 0, 0]~, [4/25, 6/25, 7/25]~, [-3/125, -6/125, -7/125]~], [[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, 0; 0, 1, 0; 0, 0, 1], [125, 0, 22; 0, 125, 108; 0, 0, 1]], [4161343 +75, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~] ? rootmod(x^16-1,41) [mod(1, 41), mod(3, 41), mod(9, 41), mod(14, 41), mod(27, 41), mod(32, 41), mod(38, 41), mod(40, 41)]~ @@ -2663,14 +2498,14 @@ q^101) [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] [-1/192*x^3 + 1/48*x^2 + 1/8*x x^4 - x^2 + 1] ? smith(matrix(5,5,j,k,random())) -[1442459322553825252071178240, 2147483648, 2147483648, 1, 1] +[239509529380671174817611776, 2147483648, 2147483648, 1, 1] ? smith(1/hilbert(6)) [27720, 2520, 2520, 840, 210, 6] ? smithpol(x*idmat(5)-matrix(5,5,j,k,1)) @@ -2789,7 +2624,7 @@ x + x^2 - 1/6*x^3 - 1/2*x^4 - 59/120*x^5 - 1/8*x^6 + 4 ? trunc(sin(x^2)) 1/120*x^10 - 1/6*x^6 + x^2 ? 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)) 9 ? unit(17) @@ -2831,26 +2666,26 @@ x^-2 + 1/5*x^2 - 1/28*x^4 + 1/75*x^6 - 3/1540*x^8 + 19 0.88324345992059326405525724366416928890 - 0.2067536250233895222724230899142 7938845*I ? 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) [[[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, 0]~], [[-26, -27, 0]~], [[]~], 1]], [[[26], [[0, 2, 0]~], [[-27, 2, 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 -, 0, 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~, -[1, 0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0, - 0]]], [[], [], [;]]], [468, 469, 0, 0, -48776, 0, 0, -36582; 0, 0, 1, 0, -7 -, -6, 0, -3; 0, 0, 0, 1, -3, 0, -6, 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, 0, -24]~, [-23, 0, 0]~], [[]~, []~, []~], [0, 1/3, 0; 0, 0, 1/3; 1/3, 0, + 0]], [[3, 3, 3], [[1, 9, 0]~, [1, 0, 9]~, [10, 0, 0]~], [[1, -18, 0]~, [1, +0, -18]~, [-17, 0, 0]~], [[]~, []~, []~], [0, 1/9, 0; 0, 0, 1/9; 1/9, 0, 0]] +], [[], [], [;]]], [2106, -77, 0, -11102, 2184, 0, 6006, -13104; 0, 0, 1, -3 +, 0, -6, 0, 0; -27, 1, 0, 142, -28, 0, -78, 168]] ? zideallog(nf2,w,bid) -[1574, 8, 6]~ +[1234, 0, 5]~ ? znstar(3120) [768, [12, 4, 4, 2, 2], [mod(67, 3120), mod(2341, 3120), mod(1847, 3120), mo d(391, 3120), mod(2081, 3120)]] ? getstack() 0 ? getheap() -[624, 125785] +[620, 118299] ? print("Total time spent: ",gettime()); -Total time spent: 5060 +Total time spent: 1400 ? \q