=================================================================== RCS file: /home/cvs/OpenXM_contrib/pari-2.2/src/test/64/Attic/nfields,v retrieving revision 1.1 retrieving revision 1.2 diff -u -p -r1.1 -r1.2 --- OpenXM_contrib/pari-2.2/src/test/64/Attic/nfields 2001/10/02 11:17:13 1.1 +++ OpenXM_contrib/pari-2.2/src/test/64/Attic/nfields 2002/09/11 07:27:12 1.2 @@ -17,451 +17,350 @@ x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 5466035 ? setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8)); ? setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8)); ? nf=nfinit(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; 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1, 1.682941293594312776162 +9561615079976005 + 2.0500351226010726172974286983598602163*I, 0.750453175769 +10401286427186094108607489 - 1.3101462685358123283560773619310445915*I, 0.78 +742068874775359433940488309213323154 - 2.13366338931266180341684546104579360 +17*I, -1.2658732110596551455718089553258673705 + 2.7164790103743150566578028 +035789834834*I], [1, -1.0891151457205048250249527946671612684, 2.42851749071 +94186068992069565359418364, -0.71946691128913178943997506477288225733, 2.555 +8200350691694950646071159426779971; 1.4142135623730950488016887242096980785, + -0.19570413467375904264179382543977540674, -2.77852224501646643099209256540 +93065576, 0.10226569567819614506098907018896260035, 1.3971909474085893198147 +151262541540506; 0, 0.69553338995335755797766403996841143190, 1.145109827443 +9565129926149974389115722, 3.1085550780550843138423672171643499922, 2.220520 +6913086872788181483285734827868; 1.4142135623730950488016887242096980785, 2. +3800384020787979181834702019470475018, 1.06130105909862703981823187865589944 +12, 1.1135810173202366904448352912286604470, -1.7902150633253437253677889164 +811036160; 0, 2.8991874737236275652408825679737171587, -1.852826621655848763 +4446810512816401036, -3.0174557027049114270734649132936867272, 3.84168145837 +31999185306312841432940661], 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]] ? nf3=nfinit(x^6+108); ? nf4=nfinit(x^3-10*x+8) -[x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -3.50466435358804770515010852590433205 -79, 6.1413361156553641347759399165844441383; 1, 0.86464088669540302583112842 -266613688800, 0.37380193147270638662350044992137561317; 1, 2.640023466892644 -6793189801032381951699, 3.4848619528719294786005596334941802484], [1, 1, 1; --3.5046643535880477051501085259043320579, 0.86464088669540302583112842266613 -688800, 2.6400234668926446793189801032381951699; 6.1413361156553641347759399 -165844441383, 0.37380193147270638662350044992137561317, 3.484861952871929478 -6005596334941802484], [3, -3.454467422037777850 E-77, 10.0000000000000000000 -00000000000000000; -3.454467422037777850 E-77, 20.00000000000000000000000000 -0000000000, -12.000000000000000000000000000000000000; 10.0000000000000000000 -00000000000000000, -12.000000000000000000000000000000000000, 50.000000000000 -000000000000000000000000], [3, 0, 10; 0, 20, -12; 10, -12, 50], [284, 168, 2 -35; 0, 2, 0; 0, 0, 1], [856, -120, -200; -120, 50, 36; -200, 36, 60], [568, -[-216, 90, 8]~]], [-3.5046643535880477051501085259043320579, 0.8646408866954 -0302583112842266613688800, 2.6400234668926446793189801032381951699], [1, x, -1/2*x^2], [1, 0, 0; 0, 1, 0; 0, 0, 2], [1, 0, 0, 0, 0, -4, 0, -4, 0; 0, 1, 0 -, 1, 0, 5, 0, 5, -2; 0, 0, 1, 0, 2, 0, 1, 0, 5]] +[x^3 - 10*x + 8, [3, 0], 568, 2, [[1, -0.36332823793268357037416860931988791 +960, -3.1413361156553641347759399165844441383; 1, -1.76155718183189058754537 +11274124874988, 2.6261980685272936133764995500786243868; 1, 3.12488541976457 +41579195397367323754183, -0.48486195287192947860055963349418024846], [1, -0. +36332823793268357037416860931988791960, -3.141336115655364134775939916584444 +1383; 1, -1.7615571818318905875453711274124874988, 2.62619806852729361337649 +95500786243868; 1, 3.1248854197645741579195397367323754183, -0.4848619528719 +2947860055963349418024846], 0, [3, 1, -1; 1, 13, -5; -1, -5, 17], [284, 76, +46; 0, 2, 0; 0, 0, 1], [196, -12, 8; -12, 50, 14; 8, 14, 38], [568, [120, 21 +0, 2]~]], [-3.5046643535880477051501085259043320579, 0.864640886695403025831 +12842266613688800, 2.6400234668926446793189801032381951699], [1, 1/2*x^2 + x + - 3, -1/2*x^2 + 3], [1, 0, 6; 0, 1, 0; 0, 1, -2], [1, 0, 0, 0, 4, -2, 0, -2 +, 6; 0, 1, 0, 1, 2, 0, 0, 0, -2; 0, 0, 1, 0, 1, -1, 1, -1, -1]] ? setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7]; ? setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2]) [Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.71246530518434397468087951060 -61300699 + 3.1415926535897932384626433832795028842*I; 2.71246530518434397468 -08795106061300699 - 6.2831853071795864769252867665590057684*I], [9.927737672 -2507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1. -2897619530652735025030086072395031017 + 0.E-57*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-56*I, 24.478366048541841504313284087778334822 + 3.14159265358979323846264 -33832795028842*I; -9.9277376722507613003718504524486100858 + 6.2831853071795 -864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.424 -7779607693797153879301498385086526*I, 2.010979802498915756212263409891761061 -2 + 0.E-57*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-57*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], 185], [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, 0.E-57, 0.50057980363245587382620331339 +071677436 + 3.1415926535897932384626433832795028842*I, 1.0888562540123011578 +605958199158508674, 1.7241634548149836441438434283070556826 + 3.141592653589 +7932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3.1 +415926535897932384626433832795028842*I, 2.1336294009747564707190997873636390 +948 + 3.1415926535897932384626433832795028842*I, 0.0661783018827457321853684 +92323164193433 + 3.1415926535897932384626433832795028842*I; -1.7903417566977 +293763292119206302198760, -1.2897619530652735025030086072395031017, -0.70148 +550268542821846861610071436900868, 0.E-57, -0.500579803632455873826203313390 +71677436, -1.0888562540123011578605958199158508674, -1.724163454814983644143 +8434283070556826, 0.34328764427702709438988786673341921876, -2.1336294009747 +564707190997873636390948, -0.066178301882745732185368492323164193433], [[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]~], [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, -8.0663729752107779635959310246705326058; +1, 7.0663729752107779635959310246705326058], [1, -8.066372975210777963595931 +0246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, 1 +15], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.06637297521077 +79635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - 1 +], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2.7 +124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + 7 +], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.79 +03417566977293763292119206302198760]]], 0] ? setrand(1);bnfinit(x^2-x-100000,1) -[Mat(5), Mat([3, 2, 1, 2, 0, 3, 2, 3, 0, 0, 1, 4, 3, 2, 2, 3, 3, 2]), [-129. -82045011403975460991182396195022419 - 6.283185307179586476925286766559005768 -4*I; 129.82045011403975460991182396195022419 - 12.56637061435917295385057353 -3118011536*I], [-41.811264589129943393339502258694361489 + 8.121413879410077 -514 E-115*I, 9.2399004147902289816376260438840931575 + 3.1415926535897932384 -626433832795028842*I, -11.874609881075406725097315997431161032 + 9.424777960 -7693797153879301498385086526*I, 389.46135034211926382973547188585067257 + 12 -.566370614359172953850573533118011536*I, -440.512515346039436204712600188429 -12722 + 0.E-113*I, -324.55112528509938652477955990487556047 + 6.283185307179 -5864769252867665590057684*I, 229.70424552002497255158146166263724792 + 3.141 -5926535897932384626433832795028842*I, -785.660451862534215720251179722755983 -25 + 6.2831853071795864769252867665590057684*I, -554.35531386699327377220656 -215544062014 + 6.2831853071795864769252867665590057684*I, -47.66831907156823 -3997332918482707687879 + 9.4247779607693797153879301498385086526*I, 177.4887 -6918560798860724474244465791207 + 6.497131103528062011 E-114*I, -875.6123693 -7168080069763246690606885226 + 2.598852441411224804 E-113*I, 54.878404098312 -329644822020875673145627 + 9.4247779607693797153879301498385086526*I, -404.4 -4153844676787690336623107514389175 + 0.E-113*I, 232.809823743598178900114904 -85449930607 + 6.2831853071795864769252867665590057684*I, -668.80899963671483 -856204802764462926790 + 9.4247779607693797153879301498385086526*I, 367.35683 -481950538594888487746203445802 + 12.566370614359172953850573533118011536*I, --1214.0716092619656173892944003952818868 + 9.4247779607693797153879301498385 -086526*I, -125.94415646756187210316334148291471657 + 6.283185307179586476925 -2867665590057684*I; 41.811264589129943393339502258694361489 + 6.283185307179 -5864769252867665590057684*I, -9.2399004147902289816376260438840931575 + 12.5 -66370614359172953850573533118011536*I, 11.8746098810754067250973159974311610 -32 + 8.121413879410077514 E-115*I, -389.46135034211926382973547188585067257 -+ 6.2831853071795864769252867665590057684*I, 440.512515346039436204712600188 -42912722 + 3.1415926535897932384626433832795028842*I, 324.551125285099386524 -77955990487556047 + 9.4247779607693797153879301498385086526*I, -229.70424552 -002497255158146166263724792 + 6.2831853071795864769252867665590057684*I, 785 -.66045186253421572025117972275598325 + 9.42477796076937971538793014983850865 -26*I, 554.35531386699327377220656215544062014 + 3.14159265358979323846264338 -32795028842*I, 47.668319071568233997332918482707687878 + 3.14159265358979323 -84626433832795028842*I, -177.48876918560798860724474244465791207 + 6.2831853 -071795864769252867665590057684*I, 875.61236937168080069763246690606885226 + -6.497131103528062011 E-114*I, -54.878404098312329644822020875673145627 + 9.4 -247779607693797153879301498385086526*I, 404.44153844676787690336623107514389 -175 + 9.4247779607693797153879301498385086526*I, -232.8098237435981789001149 -0485449930607 + 3.1415926535897932384626433832795028842*I, 668.8089996367148 -3856204802764462926790 + 6.2831853071795864769252867665590057684*I, -367.356 -83481950538594888487746203445803 + 3.1415926535897932384626433832795028842*I -, 1214.0716092619656173892944003952818868 + 3.141592653589793238462643383279 -5028842*I, 125.94415646756187210316334148291471657 + 6.283185307179586476925 -2867665590057684*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, [-16, 1] -~]]~, [1, 3, 6, 2, 4, 5, 7, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18], [ -x^2 - x - 100000, [2, 0], 400001, 1, [[1, -315.72816130129840161392089489603 -747004; 1, 316.72816130129840161392089489603747004], [1, 1; -315.72816130129 -840161392089489603747004, 316.72816130129840161392089489603747004], [2, 1.00 -00000000000000000000000000000000000; 1.0000000000000000000000000000000000000 -, 200001.00000000000000000000000000000000], [2, 1; 1, 200001], [400001, 2000 -00; 0, 1], [200001, -1; -1, 2], [400001, [200000, 1]~]], [-315.7281613012984 -0161392089489603747004, 316.72816130129840161392089489603747004], [1, x], [1 -, 0; 0, 1], [1, 0, 0, 100000; 0, 1, 1, 1]], [[5, [5], [[2, 1; 0, 1]]], 129.8 -2045011403975460991182396195022419, 0.9876536979069047239, [2, -1], [3795548 -84019013781006303254896369154068336082609238336*x + 119836165644250789990462 -835950022871665178127611316131167], 186], [Mat(1), [[0, 0]], [[-41.811264589 -129943393339502258694361489 + 8.121413879410077514 E-115*I, 41.8112645891299 -43393339502258694361489 + 6.2831853071795864769252867665590057684*I]]], 0] +[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-115, -51.051165003920172374977128302578454646 + 3.141592653589793238462 +6433832795028842*I, -64.910225057019877304955911980975112095 + 3.14159265358 +97932384626433832795028842*I, -29.936654708054536668242186261263200456 + 3.1 +415926535897932384626433832795028842*I, -47.66831907156823399733291848270768 +7878 + 6.2831853071795864769252867665590057684*I, 3.876293646477882506748482 +4790355076166, -6.7377511782956880607802359510546381087 + 3.1415926535897932 +384626433832795028842*I, -35.073513410834255332559266307639723380 + 3.141592 +6535897932384626433832795028842*I, 33.130781426597481571750300827582717074 + + 2.030353469852519378 E-115*I, 54.878404098312329644822020875673145627 + 4.0 +60706939705038757 E-115*I, -14.980188104648613073630759189293219180 + 3.1415 +926535897932384626433832795028842*I, -26.83107648448133031970874306940114230 +8 + 3.1415926535897932384626433832795028842*I, -19.7067490665160655124889078 +34878146944 + 3.1415926535897932384626433832795028842*I, -22.104515522613877 +880850594423816214544 + 3.1415926535897932384626433832795028842*I, -45.68755 +8235607825900087984737729869105 + 6.2831853071795864769252867665590057684*I, + 47.668319071568233997332918482707687879 + 8.121413879410077514 E-115*I; 41. +811264589129943393339502258694361489, -9.23990041479022898163762604388409315 +75, 11.874609881075406725097315997431161032, 0.E-115, 51.0511650039201723749 +77128302578454646, 64.910225057019877304955911980975112095, 29.9366547080545 +36668242186261263200456, 47.668319071568233997332918482707687879, -3.8762936 +464778825067484824790355076166, 6.7377511782956880607802359510546381087, 35. +073513410834255332559266307639723380, -33.1307814265974815717503008275827170 +74, -54.878404098312329644822020875673145627, 14.980188104648613073630759189 +293219180, 26.831076484481330319708743069401142309, 19.706749066516065512488 +907834878146944, 22.104515522613877880850594423816214544, 45.687558235607825 +900087984737729869105, -47.668319071568233997332918482707687878], [[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, -316.72816130129840161392089489603747004; 1, 315.7281613 +0129840161392089489603747004], [1, -316.72816130129840161392089489603747004; + 1, 315.72816130129840161392089489603747004], 0, [2, -1; -1, 200001], [40000 +1, 200001; 0, 1], [200001, 1; 1, 2], [400001, [200001, 1]~]], [-315.72816130 +129840161392089489603747004, 316.72816130129840161392089489603747004], [1, x + - 1], [1, 1; 0, 1], [1, 0, 0, 100000; 0, 1, 1, -1]], [[5, [5], [[2, 0; 0, 1 +]]], 129.82045011403975460991182396195022419, 0.9876536979069047228, [2, -1] +, [379554884019013781006303254896369154068336082609238336*x + 11983616564425 +0789990462835950022871665178127611316131167], 185], [Mat(1), [[0, 0]], [[-41 +.811264589129943393339502258694361489 + 6.2831853071795864769252867665590057 +684*I, 41.811264589129943393339502258694361489]]], 0] ? \p19 realprecision = 19 significant digits ? setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3) -[x^3 - x^2 - 14*x - 1, 3, 10889, [1, x, x^2], [-3.233732695981516673, -0.071 -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]] ? \p38 realprecision = 38 significant digits -? bnrinit(bnf,[[5,3;0,1],[1,0]],1) +? bnrinit(bnf,[[5,4;0,1],[1,0]],1) [[Mat(3), Mat([1, 2, 1, 2, 1, 2, 1, 2, 1]), [-2.7124653051843439746808795106 -061300699 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 -808795106061300699 - 6.2831853071795864769252867665590057684*I], [9.92773767 -22507613003718504524486100858 + 3.1415926535897932384626433832795028842*I, 1 -.2897619530652735025030086072395031017 + 0.E-57*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-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 -433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 -5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 -47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 -12 + 0.E-57*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-57*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], 185], [Mat(1), - [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384 -626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307 -1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1] -, [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1] -~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~] -, Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[ -3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]] -? bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2) +061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 +808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306 +52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70 +148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133 +9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157 +8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358 +97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3. +1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639 +0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368 +492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697 +7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014 +8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339 +071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414 +38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974 +7564707190997873636390948, -0.066178301882745732185368492323164193433], [[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]~], [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, -8.0663729752107779635959310246705326058; + 1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593 +10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, +115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107 +779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - +1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2. +7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + +7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7 +903417566977293763292119206302198760]]], [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]]] +? bnr=bnrclass(bnf,[[5,4;0,1],[1,0]],2) [[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-57*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-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 -433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 -5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 -47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 -12 + 0.E-57*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-57*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], 185], [Mat(1), - [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384 -626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307 -1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[5, 3; 0, 1] -, [1, 0]], [8, [4, 2], [[2, 0]~, [-1, 1]~]], Mat([[5, [-2, 1]~, 1, 1, [1, 1] -~], 1]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2)]~], 1]], [[2], [[-1, 1]~] -, Mat(1)]], [1, 0; 0, 1]], [1], [1, -3, -6; 0, 0, 1; 0, 1, 0], [12, [12], [[ -3, 2; 0, 1]]], [[1/2, 0; 0, 0], [1, -1; 1, 1]]] +061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 +808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306 +52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70 +148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133 +9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157 +8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358 +97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3. +1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639 +0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368 +492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697 +7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014 +8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339 +071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414 +38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974 +7564707190997873636390948, -0.066178301882745732185368492323164193433], [[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]~], [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, -8.0663729752107779635959310246705326058; + 1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593 +10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, +115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107 +779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - +1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2. +7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + +7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7 +903417566977293763292119206302198760]]], [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]]] ? rnfinit(nf2,x^5-x-2) [x^5 - x - 2, [[1, 2], [0, 5]], [[49744, 0, 0; 0, 49744, 0; 0, 0, 49744], [3 109, 0, 0]~], [1, 0, 0; 0, 1, 0; 0, 0, 1], [[[1, 1.2671683045421243172528914 @@ -591,56 +490,53 @@ I, -1.0672071180669977537495893497477340535 - 1.390957 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 1, 0; 0, 0, 1]]], [M od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1), 0, 0, 0; 0, 0, Mod(1 , y^3 - y - 1), 0, 0; 0, 0, 0, Mod(1, y^3 - y - 1), 0; 0, 0, 0, 0, Mod(1, y^ -3 - y - 1)], [], [y^3 - y - 1, [1, 1], -23, 1, [[1, 1.3247179572447460259609 -088544780973407, 1.7548776662466927600495088963585286918; 1, -0.662358978622 -37301298045442723904867036 + 0.56227951206230124389918214490937306149*I, 0.1 -2256116687665361997524555182073565405 - 0.7448617666197442365931704286043923 -6724*I], [1, 2; 1.3247179572447460259609088544780973407, -1.3247179572447460 -259609088544780973407 - 1.1245590241246024877983642898187461229*I; 1.7548776 -662466927600495088963585286918, 0.24512233375330723995049110364147130810 + 1 -.4897235332394884731863408572087847344*I], [3, 0.E-96, 2.0000000000000000000 -000000000000000000; 0.E-96, 3.2646329987400782801485266890755860756, 1.32471 -79572447460259609088544780973407; 2.0000000000000000000000000000000000000, 1 -.3247179572447460259609088544780973407, 4.2192762054875453178332176670757633 -303], [3, 0, 2; 0, 2, 3; 2, 3, 2], [23, 13, 15; 0, 1, 0; 0, 0, 1], [-5, 6, - -4; 6, 2, -9; -4, -9, 6], [23, [7, 10, 1]~]], [1.3247179572447460259609088544 -780973407, -0.66235897862237301298045442723904867036 + 0.5622795120623012438 -9918214490937306149*I], [1, y, y^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, -0, 0, 1, 0, 1, 0; 0, 1, 0, 1, 0, 1, 0, 1, 1; 0, 0, 1, 0, 1, 0, 1, 0, 1]], [x -^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 - + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1, Mod(39516536165538345/8 -3718587879473471*x^14 - 6500512476832995/83718587879473471*x^13 - 1962154720 -46117185/83718587879473471*x^12 + 229902227480108910/83718587879473471*x^11 -+ 237380704030959181/83718587879473471*x^10 - 1064931988160773805/8371858787 -9473471*x^9 - 20657086671714300/83718587879473471*x^8 + 1772885205999206010/ -83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^6 - 48388401 -87320655696/83718587879473471*x^5 + 5180390720553188700/83718587879473471*x^ -4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040221/83718587 -879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920215718580450 -/83718587879473471, x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x -^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1), - -1, [1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13, 1/ -83718587879473471*x^14 - 20528463024680133/83718587879473471*x^13 - 47423929 -48888610/83718587879473471*x^12 - 9983523646123358/83718587879473471*x^11 + -40898955597139011/83718587879473471*x^10 + 29412692423971937/837185878794734 -71*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075066/83718587 -879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 20152905879672878/8 -3718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 - 847190574595 -7397/83718587879473471*x^3 - 13395753879413605/83718587879473471*x^2 + 27623 -037732247492/83718587879473471*x + 26306699661480593/83718587879473471], [1, - 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1, 0, 0, 0, 0 -, 0, 0, 0, 0, 0, 0, 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -0, 0, 0, 0, 13395753879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 847 -1905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9591643151927789; -0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0, 0, 0, 0, 0, - 0, 1, 0, 0, 0, 0, 0, 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -0, 0, 0, 0, -41014993230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 50 -17479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412692423971937 -; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011; 0, 0, 0, 0, -0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 -, 0, 0, 1, 0, 4742392948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 20 -528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718587879473471 -]]] +3 - y - 1)], [], [y^3 - y - 1, [1, 1], -23, 1, [[1, 0.7548776662466927600495 +0889635852869189, 1.3247179572447460259609088544780973407; 1, -0.87743883312 +334638002475444817926434594 - 0.74486176661974423659317042860439236723*I, -0 +.66235897862237301298045442723904867036 + 0.56227951206230124389918214490937 +306149*I], [1, 0.75487766624669276004950889635852869189, 1.32471795724474602 +59609088544780973407; 1.4142135623730950488016887242096980785, -1.2408858979 +558593537192653626096055786, -0.93671705072735084703311164961686101696; 0, - +1.0533936124468254335289038498031013275, 0.795183311803032710044767156296587 +54002], 0, [3, -1, 0; -1, 1, 3; 0, 3, 2], [23, 16, 13; 0, 1, 0; 0, 0, 1], [- +7, 2, -3; 2, 6, -9; -3, -9, 2], [23, [10, 7, 1]~]], [1.324717957244746025960 +9088544780973407, -0.66235897862237301298045442723904867036 + 0.562279512062 +30124389918214490937306149*I], [1, y^2 - 1, y], [1, 0, 1; 0, 0, 1; 0, 1, 0], + [1, 0, 0, 0, 0, 1, 0, 1, 1; 0, 1, 0, 1, -1, 0, 0, 0, 1; 0, 0, 1, 0, 1, 0, 1 +, 0, 0]], [x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - 5*x^9 + 45*x^8 + 158* +x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + 25*x + 1, Mod(3951653 +6165538345/83718587879473471*x^14 - 6500512476832995/83718587879473471*x^13 +- 196215472046117185/83718587879473471*x^12 + 229902227480108910/83718587879 +473471*x^11 + 237380704030959181/83718587879473471*x^10 - 106493198816077380 +5/83718587879473471*x^9 - 20657086671714300/83718587879473471*x^8 + 17728852 +05999206010/83718587879473471*x^7 + 5952033217241102348/83718587879473471*x^ +6 - 4838840187320655696/83718587879473471*x^5 + 5180390720553188700/83718587 +879473471*x^4 - 8374015687535120430/83718587879473471*x^3 + 8907744727915040 +221/83718587879473471*x^2 + 4155976664123434381/83718587879473471*x + 318920 +215718580450/83718587879473471, x^15 - 5*x^13 + 5*x^12 + 7*x^11 - 26*x^10 - +5*x^9 + 45*x^8 + 158*x^7 - 98*x^6 + 110*x^5 - 190*x^4 + 189*x^3 + 144*x^2 + +25*x + 1), -1, [1, x, x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^ +12, x^13, 1/83718587879473471*x^14 - 20528463024680133/83718587879473471*x^1 +3 - 4742392948888610/83718587879473471*x^12 - 9983523646123358/8371858787947 +3471*x^11 + 40898955597139011/83718587879473471*x^10 + 29412692423971937/837 +18587879473471*x^9 - 5017479463612351/83718587879473471*x^8 + 41014993230075 +066/83718587879473471*x^7 - 2712810874903165/83718587879473471*x^6 + 2015290 +5879672878/83718587879473471*x^5 + 9591643151927789/83718587879473471*x^4 - +8471905745957397/83718587879473471*x^3 - 13395753879413605/83718587879473471 +*x^2 + 27623037732247492/83718587879473471*x + 26306699661480593/83718587879 +473471], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26306699661480593; 0, 1 +, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27623037732247492; 0, 0, 1, 0, 0, 0, +0, 0, 0, 0, 0, 0, 0, 0, 13395753879413605; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, +0, 0, 0, 8471905745957397; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -959164 +3151927789; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -20152905879672878; 0, + 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2712810874903165; 0, 0, 0, 0, 0, 0, +0, 1, 0, 0, 0, 0, 0, 0, -41014993230075066; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, + 0, 0, 0, 5017479463612351; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -29412 +692423971937; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -40898955597139011; +0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 9983523646123358; 0, 0, 0, 0, 0, 0 +, 0, 0, 0, 0, 0, 0, 1, 0, 4742392948888610; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + 0, 0, 1, 20528463024680133; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83718 +587879473471]]] ? bnfcertify(bnf) 1 ? setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2]) @@ -668,13 +564,13 @@ od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1) [[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]] @@ -690,20 +586,20 @@ od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1) [[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]] -[186] +[185] ? setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1]) @@ -713,80 +609,78 @@ od(1, y^3 - y - 1), 0, 0, 0, 0; 0, Mod(1, y^3 - y - 1) [[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 - 1135/343]] +[[6, 10/1029*x^3 - 13/343*x^2 + 165/343*x + 1478/343]] [[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]] -[182] +[365] ? setrand(1);bnfclgp(17) [1, [], []] ? setrand(1);bnfclgp(-31) [3, [3], [Qfb(2, 1, 4)]] ? setrand(1);bnfclgp(x^4+24*x^2+585*x+1791) -[4, [4], [[7, 5, 1, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]] -? bnrconductor(bnf,[[25,13;0,1],[1,1]]) -[[5, 3; 0, 1], [1, 0]] +[4, [4], [[7, 2, 0, 5; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]] +? bnrconductor(bnf,[[25,14;0,1],[1,1]]) +[[5, 4; 0, 1], [1, 0]] ? bnrconductorofchar(bnr,[2]) -[[5, 3; 0, 1], [0, 0]] -? bnfisprincipal(bnf,[5,1;0,1],0) +[[5, 4; 0, 1], [0, 0]] +? bnfisprincipal(bnf,[5,2;0,1],0) [1]~ -? bnfisprincipal(bnf,[5,1;0,1]) -[[1]~, [-2, -1/3]~, 181] +? bnfisprincipal(bnf,[5,2;0,1]) +[[1]~, [7/3, 1/3]~, 187] ? bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57)) [-4, Mod(1, 2)]~ ? \p19 realprecision = 19 significant digits ? bnfmake(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, 0.3677262014027817705 + 3.141592653589793238*I, 0.00437 -5616572659815402 + 3.141592653589793238*I, -0.8305625946607188639, -1.977791 -147836553953 + 3.141592653589793238*I; 0.6716827432867392935 + 3.14159265358 -9793238*I, 0.5379005671092853266, -0.8333219883742404172 + 3.141592653589793 -238*I, -0.2461086674077943078, 0.E-96, 0.9729063188316092378, -0.87383180430 -71131265, -1.552661549868775853 + 3.141592653589793238*I, 0.5774919091398324 -092 + 3.141592653589793238*I; -1.918029732621558454, 1.452155878475514386, 0 -.2929213507612934444, 0.9387477816548985923, 0.E-96, -1.340632520234391008, -0.8694561877344533111, 2.383224144529494717 + 3.141592653589793238*I, 1.4002 -99238696721544 + 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, [ -19, 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, -3.23 -3732695981516673, 10.45702714905988813; 1, -0.07182350902743636344, 0.005158 -616449014232794; 1, 4.305556205008953036, 18.53781423449109762], [1, 1, 1; - -3.233732695981516673, -0.07182350902743636344, 4.305556205008953036; 10.4570 -2714905988813, 0.005158616449014232794, 18.53781423449109762], [3, 1.0000000 -00000000000, 29.00000000000000000; 1.000000000000000000, 29.0000000000000000 -0, 46.00000000000000000; 29.00000000000000000, 46.00000000000000000, 453.000 -0000000000000], [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, [ -1890, 5190, 1]~]], [-3.233732695981516673, -0.07182350902743636344, 4.305556 -205008953036], [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, 1.00000000000000000 -0, [2, -1], [x, x^2 + 2*x - 4], 1000], [Mat(1), [[0, 0, 0]], [[1.24634698933 -4819161 + 3.141592653589793238*I, 0.6716827432867392935 + 3.1415926535897932 -38*I, -1.918029732621558454]]], [-4, 3, -1, 2, 3, 11, 1, -1, -7; 1, 1, 1, 1, - 0, 2, 1, -4, -2; 0, 0, 0, 0, 0, -1, 0, -1, 0]] +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]] ? \p38 realprecision = 38 significant digits ? bnfnarrow(bnf) -[3, [3], [[3, 2; 0, 1]]] +[3, [3], [[3, 0; 0, 1]]] ? bnfreg(x^2-x-57) 2.7124653051843439746808795106061300699 ? bnfsignunit(bnf) @@ -796,57 +690,46 @@ I; 1.459906329303914334, 3.141948414209350543], [1.246 [1] ? bnfunit(bnf) -[[x + 7], 185] -? bnrclass(bnf,[[5,3;0,1],[1,0]]) -[12, [12], [[3, 2; 0, 1]]] -? bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2) +[[x + 7], 187] +? bnrclass(bnf,[[5,4;0,1],[1,0]]) +[12, [12], [[3, 0; 0, 1]]] +? bnr2=bnrclass(bnf,[[25,14;0,1],[1,1]],2) [[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-57*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-56*I, 24.478366048541841504313284087778334822 + 3.1415926535897932384626 -433832795028842*I; -9.9277376722507613003718504524486100858 + 6.283185307179 -5864769252867665590057684*I, -1.2897619530652735025030086072395031017 + 9.42 -47779607693797153879301498385086526*I, 2.01097980249891575621226340989176106 -12 + 0.E-57*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-57*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], 185], [Mat(1), - [[0, 0]], [[9.9277376722507613003718504524486100858 + 3.1415926535897932384 -626433832795028842*I, -9.9277376722507613003718504524486100858 + 6.283185307 -1795864769252867665590057684*I]]], [0, [Mat([[5, 1]~, 1])]]], [[[25, 13; 0, -1], [1, 1]], [80, [20, 2, 2], [[2, 0]~, [0, -2]~, [2, 2]~]], Mat([[5, [-2, 1 -]~, 1, 1, [1, 1]~], 2]), [[[[4], [[2, 0]~], [[2, 0]~], [[Mod(0, 2), Mod(0, 2 -)]~], 1], [[5], [[6, 0]~], [[6, 0]~], [[Mod(0, 2), Mod(0, 2)]~], Mat([1/5, - -13/5])]], [[2, 2], [[0, -2]~, [2, 2]~], [0, 1; 1, 0]]], [1, -12, 0, 0; 0, 0, - 1, 0; 0, 0, 0, 1]], [1], [1, -3, 0, -6; 0, 0, 1, 0; 0, 0, 0, 1; 0, 1, 0, 0] -, [12, [12], [[3, 2; 0, 1]]], [[1, 9, -18; -1/2, -5, 10], [-2, 0; 0, 10]]] -? bnrclassno(bnf,[[5,3;0,1],[1,0]]) +061300698 + 3.1415926535897932384626433832795028842*I; 2.7124653051843439746 +808795106061300699], [1.7903417566977293763292119206302198761, 1.28976195306 +52735025030086072395031017 + 3.1415926535897932384626433832795028842*I, 0.70 +148550268542821846861610071436900868, 0.E-57, 0.5005798036324558738262033133 +9071677436 + 3.1415926535897932384626433832795028842*I, 1.088856254012301157 +8605958199158508674, 1.7241634548149836441438434283070556826 + 3.14159265358 +97932384626433832795028842*I, -0.34328764427702709438988786673341921876 + 3. +1415926535897932384626433832795028842*I, 2.133629400974756470719099787363639 +0948 + 3.1415926535897932384626433832795028842*I, 0.066178301882745732185368 +492323164193433 + 3.1415926535897932384626433832795028842*I; -1.790341756697 +7293763292119206302198760, -1.2897619530652735025030086072395031017, -0.7014 +8550268542821846861610071436900868, 0.E-57, -0.50057980363245587382620331339 +071677436, -1.0888562540123011578605958199158508674, -1.72416345481498364414 +38434283070556826, 0.34328764427702709438988786673341921876, -2.133629400974 +7564707190997873636390948, -0.066178301882745732185368492323164193433], [[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]~], [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, -8.0663729752107779635959310246705326058; + 1, 7.0663729752107779635959310246705326058], [1, -8.06637297521077796359593 +10246705326058; 1, 7.0663729752107779635959310246705326058], 0, [2, -1; -1, +115], [229, 115; 0, 1], [115, 1; 1, 2], [229, [115, 1]~]], [-7.0663729752107 +779635959310246705326058, 8.0663729752107779635959310246705326058], [1, x - +1], [1, 1; 0, 1], [1, 0, 0, 57; 0, 1, 1, -1]], [[3, [3], [[3, 0; 0, 1]]], 2. +7124653051843439746808795106061300699, 0.8814422512654579364, [2, -1], [x + +7], 187], [Mat(1), [[0, 0]], [[1.7903417566977293763292119206302198761, -1.7 +903417566977293763292119206302198760]]], [0, [Mat([[6, 1]~, 1])]]], [[[25, 1 +4; 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), M +od(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]), [12, [12], [[3, 0; 0, + 1]]], [[1, -18, 9; -1/2, 10, -5], [-2, 0; 0, -10]]] +? bnrclassno(bnf,[[5,4;0,1],[1,0]]) 12 ? lu=ideallist(bnf,55,3); ? bnrclassnolist(bnf,lu) @@ -862,9 +745,9 @@ I, -20.610866187462450639586440264933189691 + 9.424777 ? bnrdisc(bnr2,,,2) 0 ? bnrdisc(bnr,Mat(6),,1) -[6, 2, [125, 13; 0, 1]] +[6, 2, [125, 14; 0, 1]] ? bnrdisc(bnr,,,1) -[12, 1, [1953125, 1160888; 0, 1]] +[12, 1, [1953125, 1160889; 0, 1]] ? bnrdisc(bnr2,,,3) 0 ? bnrdisclist(bnf,lu) @@ -911,7 +794,7 @@ I, -20.610866187462450639586440264933189691 + 9.424777 18]], [0, 0, 0]]]], [[[10, 1; 20, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [[10, 1; 21, 1], [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]]]]] ? bnrisprincipal(bnr,idealprimedec(bnf,7)[1]) -[[9]~, [-2170/6561, -931/19683]~, 256] +[[9]~, [112595/19683, 13958/19683]~, 256] ? dirzetak(nf4,30) [1, 2, 0, 3, 1, 0, 0, 4, 0, 2, 1, 0, 0, 0, 0, 5, 1, 0, 0, 3, 0, 2, 0, 0, 2, 0, 1, 0, 1, 0] @@ -924,10 +807,10 @@ I, -20.610866187462450639586440264933189691 + 9.424777 [Mod(1, t^3 + t^2 - 2*t - 1)*x + Mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1] ? vp=idealprimedec(nf,3)[1] -[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] +[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] ? idx=idealmul(nf,matid(5),vp) -[3 1 2 2 2] +[3 2 1 0 1] [0 1 0 0 0] @@ -939,31 +822,31 @@ I, -20.610866187462450639586440264933189691 + 9.424777 ? 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=idealred(nf,idx,[1,5,6]) -[5 0 0 2 0] +[5 0 0 0 2] -[0 5 0 0 0] +[0 5 0 0 2] -[0 0 5 2 0] +[0 0 5 0 1] -[0 0 0 1 0] +[0 0 0 5 2] -[0 0 0 0 5] +[0 0 0 0 1] ? idx2=idealmul(nf,idx,idx) -[9 7 5 8 2] +[9 5 7 0 4] [0 1 0 0 0] @@ -975,9 +858,9 @@ I, -20.610866187462450639586440264933189691 + 9.424777 ? idt=idealmul(nf,idx,idx,1) -[2 0 0 0 1] +[2 0 0 0 0] -[0 2 0 0 1] +[0 2 0 0 0] [0 0 2 0 0] @@ -987,36 +870,36 @@ I, -20.610866187462450639586440264933189691 + 9.424777 ? idz=idealintersect(nf,idx,idy) -[15 5 10 12 10] +[15 10 5 0 12] -[0 5 0 0 0] +[0 5 0 0 2] -[0 0 5 2 0] +[0 0 5 0 1] -[0 0 0 1 0] +[0 0 0 5 2] -[0 0 0 0 5] +[0 0 0 0 1] ? aid=[idx,idy,idz,matid(5),idx] -[[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]] ? bid=idealstar(nf2,54,1) [[[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, 1, 0]~], [[1, -27, 0]~], [[]~], 1]], [[[26], [[2, 1, 0]~], [[-25, -26, 0] ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0 ]~, [1, 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]] + 0]]], [[], [], [;]]], [2106, -77, 10556, 0, -4368, 12012, 0, -13104; 0, 0, +0, 1, -2, 0, -6, -6; -27, 1, -136, 0, 56, -156, 0, 168]] ? vaid=[idx,idy,matid(5)] -[[3, 1, 2, 2, 2; 0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1] -, [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=[matid(5),matid(5),matid(5)] @@ -1037,30 +920,30 @@ I, -20.610866187462450639586440264933189691 + 9.424777 [0 0 0 0 1] ? idealaddtoone(nf,idx,idy) -[[3, 0, 2, 1, 0]~, [-2, 0, -2, -1, 0]~] +[[3, 2, 1, 2, 1]~, [-2, -2, -1, -2, -1]~] ? idealaddtoone(nf,[idy,idx]) [[-5, 0, 0, 0, 0]~, [6, 0, 0, 0, 0]~] ? idealappr(nf,idy) -[-2, 0, -2, 4, 0]~ +[-2, -2, -1, -2, -1]~ ? idealappr(nf,idealfactor(nf,idy),1) -[-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]~ ? idealdiv(nf,idy,idt) -[5 5/2 5/2 7/2 0] +[5 0 5/2 0 1] -[0 5/2 0 0 0] +[0 5/2 0 0 1] -[0 0 5/2 1 0] +[0 0 5/2 0 1/2] -[0 0 0 1/2 0] +[0 0 0 5/2 1] -[0 0 0 0 5/2] +[0 0 0 0 1/2] ? idealdiv(nf,idx2,idx,1) -[3 1 2 2 2] +[3 2 1 0 1] [0 1 0 0 0] @@ -1072,15 +955,15 @@ I, -20.610866187462450639586440264933189691 + 9.424777 ? idf=idealfactor(nf,idz) -[[3, [1, 1, 0, 0, 0]~, 1, 1, [1, -1, -1, 0, 0]~] 1] +[[3, [1, 0, 1, 0, 0]~, 1, 1, [1, -1, -1, -1, 0]~] 1] -[[5, [-2, 0, 0, 0, 1]~, 1, 1, [2, 2, 1, 1, 4]~] 1] +[[5, [-1, 0, 0, 0, 1]~, 1, 1, [2, 0, 3, 0, 1]~] 1] -[[5, [0, 0, -1, 0, 1]~, 4, 1, [4, 5, 4, 2, 0]~] 3] +[[5, [2, 0, 0, 0, 1]~, 4, 1, [2, 2, 1, 2, 1]~] 3] ? idealhnf(nf,vp) -[3 1 2 2 2] +[3 2 1 0 1] [0 1 0 0 0] @@ -1092,7 +975,7 @@ I, -20.610866187462450639586440264933189691 + 9.424777 ? idealhnf(nf,vp[2],3) -[3 1 2 2 2] +[3 2 1 0 1] [0 1 0 0 0] @@ -1103,24 +986,24 @@ I, -20.610866187462450639586440264933189691 + 9.424777 [0 0 0 0 1] ? 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]]] ? ideallog(nf2,w,bid) -[1574, 8, 6]~ +[486, 3, 7]~ ? idealmin(nf,idx,[1,2,3]) -[[-1; 0; 0; 1; 0], [2.0885812311199768913287869744681966008 + 3.141592653589 +[[-2; 1; 1; 0; 1], [2.0885812311199768913287869744681966008 + 3.141592653589 7932384626433832795028842*I, 1.5921096812520196555597562531657929785 + 4.244 7196639216499665715751642189271112*I, -0.79031915447583185468082063233076160 -203 + 2.5437460822678889883600220330800078854*I]] +207 + 2.5437460822678889883600220330800078854*I]] ? idealnorm(nf,idt) 16 ? idp=idealpow(nf,idx,7) -[2187 1807 2129 692 1379] +[2187 1436 1807 630 1822] [0 1 0 0 0] @@ -1132,66 +1015,66 @@ I, -20.610866187462450639586440264933189691 + 9.424777 ? idealpow(nf,idx,7,1) -[5 0 0 2 0] +[2 0 0 0 0] -[0 5 0 0 0] +[0 2 0 0 0] -[0 0 5 2 0] +[0 0 2 0 0] -[0 0 0 1 0] +[0 0 0 2 1] -[0 0 0 0 5] +[0 0 0 0 1] ? idealprimedec(nf,2) -[[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]~]] ? idealprimedec(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]~]] ? idealprimedec(nf,11) [[11, [11, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]] ? idealprincipal(nf,Mod(x^3+5,nfpol)) [6] -[0] - [1] [3] -[0] +[1] +[3] + ? idealtwoelt(nf,idy) -[5, [2, 0, 2, 1, 0]~] +[5, [2, 2, 1, 2, 1]~] ? idealtwoelt(nf,idy,10) -[-2, 0, -2, -1, 0]~ +[-2, -2, -1, -2, -1]~ ? idealstar(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, 0, 1]~], [[1, 0, -27]~], [[]~], 1]], [[[26], [[2, 2, 1]~], [[-25, 2, -26] ~], [[]~], 1], [[3, 3, 3], [[1, 3, 0]~, [1, 0, 3]~, [4, 0, 0]~], [[1, -24, 0 ]~, [1, 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]] + 0]]], [[], [], [;]]], [468, 469, 0, 0, -85358, 0, 0, -36582; 0, 0, 1, 0, -5 +, -6, 0, -6; 0, 0, 0, 1, -8, 0, -6, -6]] ? idealval(nf,idp,vp) 7 ? ideleprincipal(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, 5.0387659675158716386435353106610489968 + 1.5851 760343512250049897278861965702423*I, 4.2664040272651028743625910797589683173 - - 0.0083630478144368246110910258645462996191*I]] + - 0.0083630478144368246110910258645462996225*I]] ? ba=nfalgtobasis(nf,Mod(x^3+5,nfpol)) -[6, 0, 1, 3, 0]~ +[6, 1, 3, 1, 3]~ ? bb=nfalgtobasis(nf,Mod(x^3+x,nfpol)) -[1, 1, 1, 3, 0]~ +[1, 1, 4, 1, 3]~ ? bc=matalgtobasis(nf,[Mod(x^2+x,nfpol);Mod(x^2+1,nfpol)]) -[[0, 1, 1, 0, 0]~] +[[3, -2, 1, 1, 0]~] -[[1, 0, 1, 0, 0]~] +[[4, -2, 0, 1, 0]~] ? matbasistoalg(nf,bc) @@ -1214,13 +1097,13 @@ Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25) 4/139623738889203638909659*x - 13185339461968406/58346808996920447] ? 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] @@ -1231,51 +1114,51 @@ Mod(x^3 + 5, x^5 - 5*x^3 + 5*x + 25) ? nfdisc(p2,0,fa) 136866601 ? nfeltdiv(nf,ba,bb) -[755/373, -152/373, 159/373, 120/373, -264/373]~ +[584/373, 66/373, -32/373, -105/373, 120/373]~ ? nfeltdiveuc(nf,ba,bb) -[2, 0, 0, 0, -1]~ +[2, 0, 0, 0, 0]~ ? nfeltdivrem(nf,ba,bb) -[[2, 0, 0, 0, -1]~, [-12, -7, 0, 9, 5]~] +[[2, 0, 0, 0, 0]~, [4, -1, -5, -1, -3]~] ? nfeltmod(nf,ba,bb) -[-12, -7, 0, 9, 5]~ +[4, -1, -5, -1, -3]~ ? nfeltmul(nf,ba,bb) -[-25, -50, -30, 15, 90]~ +[50, -15, -35, 60, 15]~ ? nfeltpow(nf,bb,5) -[23455, 156370, 115855, 74190, -294375]~ +[-291920, 136855, 230560, -178520, 74190]~ ? nfeltreduce(nf,ba,idx) [1, 0, 0, 0, 0]~ ? nfeltval(nf,ba,vp) 0 ? nffactor(nf2,x^3+x) -[Mod(1, y^3 - y - 1)*x 1] +[x 1] -[Mod(1, y^3 - y - 1)*x^2 + Mod(1, y^3 - y - 1) 1] +[x^2 + 1 1] ? aut=nfgaloisconj(nf3) -[x, 1/12*x^4 - 1/2*x, -1/12*x^4 - 1/2*x, 1/12*x^4 + 1/2*x, -1/12*x^4 + 1/2*x -, -x]~ +[-x, x, -1/12*x^4 - 1/2*x, -1/12*x^4 + 1/2*x, 1/12*x^4 - 1/2*x, 1/12*x^4 + 1 +/2*x]~ ? nfgaloisapply(nf3,aut[5],Mod(x^5,x^6+108)) -Mod(1/2*x^5 - 9*x^2, x^6 + 108) +Mod(-1/2*x^5 + 9*x^2, x^6 + 108) ? nfhilbert(nf,3,5) -1 ? nfhilbert(nf,3,5,idf[1,1]) -1 ? nfhnf(nf,[a,aid]) -[[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1 -, 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]]] ? nfhnfmod(nf,[a,aid],da) -[[[1, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~, [0, 0, 0, 0, 0]~; [0, 0, 0, 0, 0]~, [1 -, 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]]] -? nfisideal(bnf[7],[5,1;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]]] +? nfisideal(bnf[7],[5,2;0,1]) 1 ? nfisincl(x^2+1,x^4+1) [-x^2, x^2] @@ -1290,11 +1173,11 @@ Mod(1/2*x^5 - 9*x^2, x^6 + 108) ? nfrootsof1(nf) [2, [-1, 0, 0, 0, 0]~] ? nfsnf(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]] ? nfsubfields(nf) [[x^5 - 5*x^3 + 5*x + 25, x], [x, x^5 - 5*x^3 + 5*x + 25]] ? polcompositum(x^4-4*x+2,x^3-x-1) @@ -1368,25 +1251,28 @@ x^5 - 15*x^4 + 88*x^3 - 278*x^2 + 452*x - 289 0, 0]~, [1, 0, 0]~, [4, 0, 0]~; [0, 0, 0]~, [0, 0, 0]~, [0, 0, 0]~, [1, 0, 0]~, [-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 +]~] ? rnfdisc(nf2,p) -[[416134375, 212940625, 388649575; 0, 3125, 550; 0, 0, 25], [-1280, 5, 5]~] +[[416134375, 202396875, 60056800; 0, 3125, 2700; 0, 0, 25], [-1275, 5, 5]~] ? rnfequation(nf2,p) x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1 ? rnfequation(nf2,p,1) @@ -1394,29 +1280,31 @@ 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] ? rnfhnfbasis(bnf2,aa) -[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/5, 2/5, -4/5]~ [11/25, 99/25, -33/25]~ +[[1, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [6/5, 4/5, -2/5]~ [-22/25, -33/25, 99/25]~ ] -[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [2/5, -2/5, 4/5]~ [-8/25, -72/25, 24/25]~] +[[0, 0, 0]~ [1, 0, 0]~ [0, 0, 0]~ [-6/5, -4/5, 2/5]~ [16/25, 24/25, -72/25]~ +] -[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [1/5, -1/5, 2/5]~ [4/25, 36/25, -12/25]~] +[[0, 0, 0]~ [0, 0, 0]~ [1, 0, 0]~ [-3/5, -2/5, 1/5]~ [-8/25, -12/25, 36/25]~ +] -[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/5, -1/5, 2/5]~ [-2/25, -18/25, 6/25]~] +[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-3/5, -2/5, 1/5]~ [4/25, 6/25, -18/25]~] -[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [1/25, 9/25, -3/25]~] +[[0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [0, 0, 0]~ [-2/25, -3/25, 9/25]~] ? rnfisfree(bnf2,aa) 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]~] ? nfz=zetakinit(x^2-2); ? zetak(nfz,-3) 0.091666666666666666666666666666666666666 @@ -1425,15 +1313,15 @@ x^15 - 15*x^11 + 75*x^7 - x^5 - 125*x^3 + 5*x + 1 7938845*I ? setrand(1);quadclassunit(1-10^7,,[1,1]) *** Warning: not a fundamental discriminant in quadclassunit. -[2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 0.99984980 -75377600233] +[2416, [1208, 2], [Qfb(277, 55, 9028), Qfb(1700, 1249, 1700)], 1, 1.00257481 +6299307750] ? setrand(1);quadclassunit(10^9-3,,[0.5,0.5]) [4, [4], [Qfb(3, 1, -83333333, 0.E-57)], 2800.625251907016076486370621737074 -5514, 0.9990369458964383232] +5514, 0.9849577285369119736] ? sizebyte(%) -328 +320 ? getheap -[198, 120613] +[199, 115764] ? print("Total time spent: ",gettime); -Total time spent: 4836 +Total time spent: 3629 ? \q