             GP/PARI CALCULATOR Version 1.38
                     (Sparcv8 version)

Copyright 1989,1993 by C. Batut, D. Bernardi, H. Cohen and M. Olivier

Type ? for help

\precision      = 28
\serieslength   = 16
\format         = g0.28
\prompt         = ? 
stacksize = 4000000, prime limit = 500000, buffersize = 30000
? ? \precision=40
   precision = 40 significant digits
? pi
%1 = 3.141592653589793238462643383279502884197
? \precision=28
   precision = 28 significant digits
? o(x^12)
%2 = O(x^12)
? 5/3+o(127^5)
%3 = 44 + 42*127 + 42*127^2  + 42*127^3  + 42*127^4  + O(127^5)
? initrect(0,500,500)
? \\ A
? abs(-0.01)
%4 = 0.009999999999999999999999999999
? acos(0.5)
%5 = 1.047197551196597746154214461
? acosh(3)
%6 = 1.762747174039086050465218649
? acurve=initell([0, 0, 1, -1, 0])
%7 = [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.8375654352833230354448108990, 0.2695944364054445582629379513, -1.107159871688767593707748850]~, 2.993458646231959629832009979, 2.451389381986790060854224831*i, -0.4713192779568114758825938970, -1.435456518668684318723208856*i, 7.338132740789576739070721003]
? apoint=[2, 2]
%8 = [2, 2]
? isoncurve(acurve, apoint)
%9 = 1
? addell(acurve, apoint, apoint)
%10 = [21/25, -56/125]
? adj([1, 2; 3, 4])
%11 = 
[4 -2]

[-3 1]

? agm(1, 2)
%12 = 1.456791031046906869186432383
? agm(1 + o(7^5), 8 + o(7^5))
%13 = 1 + 4*7 + 6*7^2  + 5*7^3  + 2*7^4  + O(7^5)
? algdep(2 * cos(2 * pi / 13), 6)
%14 = x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
? algdep2(2 * cos(2 * pi / 13), 6, 15)
%15 = x^6 + x^5 - 5*x^4 - 4*x^3 + 6*x^2 + 3*x - 1
? akell(acurve,1000000007)
%16 = 43800
? anell(acurve, 100)
%17 = [1, -2, -3, 2, -2, 6, -1, 0, 6, 4, -5, -6, -2, 2, 6, -4, 0, -12, 0, -4, 3, 10, 2, 0, -1, 4, -9, -2, 6, -12, -4, 8, 15, 0, 2, 12, -1, 0, 6, 0, -9, -6, 2, -10, -12, -4, -9, 12, -6, 2, 0, -4, 1, 18, 10, 0, 0, -12, 8, 12, -8, 8, -6, -8, 4, -30, 8, 0, -6, -4, 9, 0, -1, 2, 3, 0, 5, -12, 4, 8, 9, 18, -15, 6, 0, -4, -18, 0, 4, 24, 2, 4, 12, 18, 0, -24, 4, 12, -30, -2]
? apell(acurve,10007)
%18 = 66
? apell2(acurve,10007)
%19 = 66
? apol=x^3+5*x+1
%20 = x^3 + 5*x + 1
? apprpadic(apol,1+O(7^8))
%21 = [1 + 6*7 + 4*7^2  + 4*7^3  + 3*7^4  + 4*7^5  + 6*7^7  + O(7^8)]
? apprpadic(x^3+5*x+1,mod(x*(1+O(7^8)),x^2+x-1))
%22 = [mod((1 + 3*7 + 3*7^2  + 4*7^3  + 4*7^4  + 4*7^5  + 2*7^6  + 3*7^7  + O(7^8))*x + (2*7 + 6*7^2  + 6*7^3  + 3*7^4  + 3*7^5  + 4*7^6  + 5*7^7  + O(7^8)), x^2 + x - 1)]~
? 4 * arg(3+3*i)
%23 = 3.141592653589793238462643383
? 3 * asin(sqrt(3)/2)
%24 = 3.141592653589793238462643383
? asinh(0.5)
%25 = 0.4812118250596034474977589134
? assmat(x^5-12*x^3+0.0005)
%26 = 
[0 0 0 0 -0.0005000000000000000000000000000]

[1 0 0 0 0]

[0 1 0 0 0]

[0 0 1 0 12]

[0 0 0 1 0]

? 3 * atan(sqrt(3))
%27 = 3.141592653589793238462643383
? atanh(0.5)
%28 = 0.5493061443340548456976226184
? \\ B
? base(x^3+4*x+5)
%29 = [1, x, 1/7*x^2 + 6/7*x + 5/7]
? base2(x^3+4*x+5)
%30 = [1, x, 1/7*x^2 - 1/7*x - 2/7]
? bernreal(12)
%31 = -0.2531135531135531135531135530
? bernvec(6)
%32 = [1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
? bestappr(pi,10000)
%33 = 355/113
? bezout(123456789,987654321)
%34 = [-8, 1, 9]
? bigomega(12345678987654321)
%35 = 8
? mcurve=initell([0,0,0,-17,0])
%36 = [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728, [4.123105625617660549821409855,  0.E-28, -4.123105625617660549821409856]~, 1.291308440929007220710556423, 1.291308440929007220710556423*i, -1.216437744079808826647426994, -3.649313232239426479942280983*i, 1.667477489614503330712023029]
? mpoints=[[-1,4],[-4,2]]~
%37 = [[-1, 4], [-4, 2]]~
? mhbi=bilhell(mcurve,mpoints,[9,24])
%38 = [-0.7244857103598018414621580588, 1.307328627832055544492943429]~
? bin(1.1,5)
%39 = -0.004545749999999999999999999998
? binary(65537)
%40 = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
? bittest(10^100,100)
%41 = 1
? boundcf(pi,5)
%42 = [3, 7, 15, 1, 292]
? boundfact(40!+1,100000)
%43 = 
[41 1]

[59 1]

[277 1]

[1217669507565553887239873369513188900554127 1]

? move(0,0,0);box(0,500,500)
? buchimag(1-10^7,1,1,20)
%44 = [2416, [1208, 2], [qfi(277, 55, 9028), qfi(1700, 1249, 1700)], 0.9998498075377599973766543080]
? bnf=buchinit(x^2-x-57,0.2,0.2,10)
%45 = [[3], [2, 1, 1], [2.712465305184343974680879510 + 9.424777960769379715387930151*i; -2.712465305184343974680879510 + 6.283185307179586476925286766*i], [-15.35266828261944924973360947 + 9.424777960769379715387930152*i, -3.213045108816799848507082823 + 3.141592653589793238462643383*i, -10.09741958603262901300000000 E-28 +  0.E-27*i, -12.13962317380264940122652664 + 6.283185307179586476925286768*i; 15.35266828261944924973360947 + 6.283185307179586476925286767*i, 3.213045108816799848507082823 + 9.424777960769379715387930149*i, 1.009741958230733871000000000 E-27 + 1.615587133448570966000000000 E-27*i, 12.13962317380264940122652664 + 9.424777960769379715387930151*i], [[3, [0, 1]~, 1, 1, [1, 2]~], [3, [-1, 1]~, 1, 1, [3, 1]~], [5, [-2, 1]~, 1, 1, [2, 2]~], [5, [1, 1]~, 1, 1, [2, 4]~]]~, [1, 3, 2, 4]~, [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931024; 1, 8.066372975210777963595931024], [1, 1; -7.066372975210777963595931024, 8.066372975210777963595931024], [2, 1.000000000000000000000000000; 1.000000000000000000000000000, 115.0000000000000000000000000], [2, 1; 1, 115], [229, 114; 0, 1]], [-7.066372975210777963595931024, 8.066372975210777963595931024], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 0; 0, 1]]], 2.712465305184343974680879510, 0.8814422512654579359661215771, [2, -1]]]
? bnf=buchinitfu(x^2-x-57,0.2,0.2,10)
%46 = [[3], [2, 1, -2], [-2.712465305184343974680879511 + 3.141592653468251228000000000*i; 2.712465305184343974680879510 - 6.283185307179586476925286766*i], [103.9958051454916856362250889 + 3.141592653589793238462643372*i, 67.31105282597614349319578445 + 9.424777960769379715387930141*i, 3.231174266897141933000000000 E-26 + 12.56637061435917295385057352*i, 241.9099919650390696204244797 + 9.424777960769379715387930122*i; -103.9958051454916856362250889 + 12.56637061435917295385057353*i, -67.31105282597614349319578445 + 9.424777960769379715387930149*i, -3.231174266897141933000000000 E-26 + 1.938704560510814189000000000 E-26*i, -241.9099919650390696204244797 + 3.141592653589793238462643381*i], [[3, [0, 1]~, 1, 1, [1, 2]~], [3, [-1, 1]~, 1, 1, [3, 1]~], [5, [-2, 1]~, 1, 1, [2, 2]~], [5, [1, 1]~, 1, 1, [2, 4]~]]~, [1, 3, 2, 4]~, [x^2 - x - 57, [2, 0], 229, 1, [[1, -7.066372975210777963595931024; 1, 8.066372975210777963595931024], [1, 1; -7.066372975210777963595931024, 8.066372975210777963595931024], [2, 1.000000000000000000000000000; 1.000000000000000000000000000, 115.0000000000000000000000000], [2, 1; 1, 115], [229, 114; 0, 1]], [-7.066372975210777963595931024, 8.066372975210777963595931024], [1, x], [1, 0; 0, 1], [1, 0, 0, 57; 0, 1, 1, 1]], [[3, [3], [[3, 0; 0, 1]]], 2.712465305184343974680879510, 0.8814422512654579359661215772, [2, -1], [x + 7], 87]]
? buchreal(10^9-3,0,0.5,0.5,10)
%47 = [4, [4], [qfr(3, 1, -83333333,  0.E-28)], 2800.625251907016076486370620, 0.9990369458964382866784231790]
? buchgen(x^4-7,0.2,0.2,10)
%48 = 
[x^4 - 7]

[[2, 1]]

[[-87808, 1]]

[[1, x, x^2, x^3]]

[[2, [2], [[2, 0, 0, 1; 0, 2, 0, 1; 0, 0, 2, 1; 0, 0, 0, 1]]]]

[14.22997514540551172239563783]

[0.8994830230765078793037651915]

? buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1,10)
%49 = 
[x^4 + 24*x^2 + 585*x + 1791]

[[0, 2]]

[[18981, 3087]]

[[1, x, 1/3*x^2, 1/1029*x^3 + 33/343*x^2 + 188/343*x + 285/343]]

[[4, [4], [[7, 0, 3, 0; 0, 7, 6, 0; 0, 0, 1, 0; 0, 0, 0, 7]]]]

[3.794126968821658934140827422]

[0.9101078280968849675715943997]

[[6, -10/1029*x^3 + 13/343*x^2 - 165/343*x - 1135/343]]

[[1/147*x^3 + 1/147*x^2 - 8/49*x - 9/49]]

[153]

? bytesize(%)
%50 = 1248
? \\ C
? ceil(-2.5)
%51 = -2
? centerlift(mod(456,555))
%52 = -99
? cf(pi)
%53 = [3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3]
? cf2([1,3,5,7,9],(exp(1)-1)/(exp(1)+1))
%54 = [0, 6, 10, 42, 30]
? changevar(x + y, [z, t])
%55 = y + z
? char([1, 2; 3, 4], z)
%56 = z^2 - 5*z - 2
? char(mod(x^2+x+1,x^3+5*x+1),z)
%57 = z^3 + 7*z^2 + 16*z - 19
? char1([1, 2; 3, 4], z)
%58 = z^2 - 5*z - 2
? char2(mod(1,8191)*[1, 2; 3, 4], z)
%59 = z^2 + mod(8186, 8191)*z + mod(8189, 8191)
? acurve = chell(acurve, [-1, 1, 2, 3])
%60 = [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.1624345647166769645551891009, -0.7304055635945554417370620486, -2.107159871688767593707748850]~, -2.993458646231959629832009979, -2.451389381986790060854224831*i, 0.4713192779568114758825938970, 1.435456518668684318723208856*i, 7.338132740789576739070721003]
? chinese(mod(7, 15), mod(13, 21))
%61 = mod(97, 105)
? apoint = chptell(apoint, [-1, 1, 2, 3])
%62 = [1, 3]
? isoncurve(acurve, apoint)
%63 = 1
? classno(-12391)
%64 = 63
? classno(1345)
%65 = 6
? classno2(-12391)
%66 = 63
? classno2(1345)
%67 = 6
? coeff(sin(x),7)
%68 = -1/5040
? compimag(qfi(2, 1, 3), qfi(2, 1, 3))
%69 = qfi(2, -1, 3)
? compo(1+o(7^4), 3)
%70 = 1
? comprealraw(qfr(5,3,-1,0.),qfr(7,1,-1,0.))
%71 = qfr(35, 43, 13,  0.E-28)
? concat([1, 2], [3, 4])
%72 = [1, 2, 3, 4]
? conj(1+i)
%73 = 1 - i
? %_
%74 = 1 + i
? conjvec(mod(x^2+x+1,x^3-x-1))
%75 = [4.079595623491438786010417750 +  0.E-28*i, 0.4602021882542806069947911246 - 0.1825822545574429926939882836*i, 0.4602021882542806069947911246 + 0.1825822545574429926939882836*i]~
? content([123, 456, 789, 234])
%76 = 3
? convol(sin(x), x * cos(x))
%77 = x + 1/12*x^3 + 1/2880*x^5 + 1/3628800*x^7 + 1/14631321600*x^9 + 1/144850083840000*x^11 + 1/2982752926433280000*x^13 + 1/114000816848279961600000*x^15 + O(x^16)
? cos(1)
%78 = 0.5403023058681397174009366074
? cosh(1)
%79 = 1.543080634815243778477905620
? move(0,200,150)
? cursor(0)
%80 = [200.0000000000000000000000000, 150.0000000000000000000000000]
? cvtoi(1.7)
%81 = 1
? cyclo(105)
%82 = x^48 + x^47 + x^46 - x^43 - x^42 - 2*x^41 - x^40 - x^39 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 - x^28 - x^26 - x^24 - x^22 - x^20 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 - x^9 - x^8 - 2*x^7 - x^6 - x^5 + x^2 + x + 1
? \\ D
? denom(12345/54321)
%83 = 18107
? deplin(mod(1,7)*[2,-1;1,3])
%84 = [mod(6, 7), mod(5, 7)]~
? deriv((x + y)^5, y)
%85 = 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
? ((x+y)^5)'
%86 = 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
? det([1, 2, 3; 1, 5, 6; 9, 8, 7])
%87 = -30
? det2([1, 2, 3; 1, 5, 6; 9, 8, 7])
%88 = -30
? detint([1, 2, 3; 4, 5, 6])
%89 = 3
? detr([1, 2, 3; 1, 5, 6; 9, 8, 7])
%90 = -30
? dilog(0.5)
%91 = 0.5822405264650125059026563196
? disc(x^3+4*x+12)
%92 = -4144
? discf(x^3+4*x+12)
%93 = -1036
? divisors(8!)
%94 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 128, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 384, 420, 448, 480, 504, 560, 576, 630, 640, 672, 720, 840, 896, 960, 1008, 1120, 1152, 1260, 1344, 1440, 1680, 1920, 2016, 2240, 2520, 2688, 2880, 3360, 4032, 4480, 5040, 5760, 6720, 8064, 10080, 13440, 20160, 40320]
? divres(345, 123)
%95 = [2, 99]~
? divres(x^7 - 1, x^5 + 1)
%96 = [x^2, -x^2 - 1]~
? divsum(8!,x,x)
%97 = 159120
? \\ draw([0,0,0])
? postdraw([0,0,0])
? \\ E
? eigen([1, 2, 3; 4, 5, 6; 7, 8, 9])
%98 = 
[-1.283349451800640271797810654 +  0.E-29*i 1 0.2833494518006402717978106547 +  0.E-30*i]

[-0.1416747259003201358989053273 +  0.E-29*i -2 0.6416747259003201358989053273 +  0.E-29*i]

[1 1 1]

? eint1(2)
%99 = 0.04890051070806111956723983478
? erfc(2)
%100 = 0.004677734981047265837930743632
? eta(q)
%101 = 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^16)
? euler
%102 = 0.5772156649015328606065120900
? z = y; y = x; eval(z)
%103 = x
? exp(1)
%104 = 2.718281828459045235360287471
? extract([1,2,3,4,5,6,7,8,9,10], 1000)
%105 = [4, 6, 7, 8, 9, 10]
? \\ F
? 10!
%106 = 3628800
? fact(10)
%107 = 3628800.000000000000000000000
? centerlift(lift(factfq(x^3+x^2+x-1,3,t^3+t^2+t-1)))
%108 = 
[x + (-t^2 - 1) 1]

[x + (t^2 + t - 1) 1]

[x - t 1]

? factmod(x^11+1, 7)
%109 = 
[mod(1, 7)*x + mod(1, 7) 1]

[mod(1, 7)*x^10 + mod(6, 7)*x^9 + mod(1, 7)*x^8 + mod(6, 7)*x^7 + mod(1, 7)*x^6 + mod(6, 7)*x^5 + mod(1, 7)*x^4 + mod(6, 7)*x^3 + mod(1, 7)*x^2 + mod(6, 7)*x + mod(1, 7) 1]

? factor(17!+1)
%110 = 
[661 1]

[537913 1]

[1000357 1]

? p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
%111 = x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 3853890514072057
? fa=[11699, 6; 2392997, 2; 4987333019653, 2]
%112 = 
[11699 6]

[2392997 2]

[4987333019653 2]

? factoredbase(p,fa)
%113 = [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 + 11567/11699*x + 9058/11699, 1/139623738889203638909659*x^4 + 10382221331949448021/139623738889203638909659*x^3 + 22461850804225283988868/139623738889203638909659*x^2 + 69939224074195609591113/139623738889203638909659*x + 31989923030048468/58346808996920447]
? factoreddiscf(p,fa)
%114 = 136866601
? \precision=40
   precision = 40 significant digits
? factoredpolred(p,fa)
%115 = [x - 1, x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1, x^5 - x^4 - 52*x^3 - 197*x^2 - 273*x - 127, x^5 - 2*x^4 - 53*x^3 - 46*x^2 + 508*x + 913, x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1]~
? factoredpolred2(p,fa)
%116 = 
[1 x - 1]

[404377049971/139623738889203638909659*x^4 + 1028343729806593/139623738889203638909659*x^3 - 220760129739668913/139623738889203638909659*x^2 - 1391924543479498840309/139623738889203638909659*x - 21580477171925514/58346808996920447 x^5 - 2*x^4 - 13*x^3 + 37*x^2 - 21*x - 1]

[160329790087/139623738889203638909659*x^4 + 1043812506369034/139623738889203638909659*x^3 + 1517006779298914407/139623738889203638909659*x^2 - 522348888528537141362/139623738889203638909659*x - 677624890046649103/58346808996920447 x^5 - x^4 - 52*x^3 - 197*x^2 - 273*x - 127]

[-649489679500/139623738889203638909659*x^4 - 1004850936416946/139623738889203638909659*x^3 + 1850137668999773331/139623738889203638909659*x^2 + 1162464435118744503168/139623738889203638909659*x - 744221404070129897/58346808996920447 x^5 - 2*x^4 - 53*x^3 - 46*x^2 + 508*x + 913]

[320031469790/139623738889203638909659*x^4 + 525154323698149/139623738889203638909659*x^3 + 68805502220272624/139623738889203638909659*x^2 + 116261976244907072724/139623738889203638909659*x - 265513916545157609/58346808996920447 x^5 - 2*x^4 - 62*x^3 + 85*x^2 + 818*x + 1]

? \precision=28
   precision = 28 significant digits
? factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
%117 = 
[mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t, t^3 + t^2 - 2*t - 1) 1]

[mod(1, t^3 + t^2 - 2*t - 1)*x + mod(-t^2 + 2, t^3 + t^2 - 2*t - 1) 1]

[mod(1, t^3 + t^2 - 2*t - 1)*x + mod(t^2 + t - 1, t^3 + t^2 - 2*t - 1) 1]

? factorpadic(apol,7,8)
%118 = 
[(1 + O(7^8))*x + (6 + 2*7^2  + 2*7^3  + 3*7^4  + 2*7^5  + 6*7^6  + O(7^8)) 1]

[(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2  + 4*7^3  + 3*7^4  + 4*7^5  + 6*7^7  + O(7^8))*x + (6 + 5*7 + 3*7^2  + 6*7^3  + 7^4  + 3*7^5  + 2*7^6  + 5*7^7  + O(7^8)) 1]

? factorpadic2(apol,7,8)
%119 = 
[(1 + O(7^8))*x + (6 + 2*7^2  + 2*7^3  + 3*7^4  + 2*7^5  + 6*7^6  + O(7^8)) 1]

[(1 + O(7^8))*x^2 + (1 + 6*7 + 4*7^2  + 4*7^3  + 3*7^4  + 4*7^5  + 6*7^7  + O(7^8))*x + (6 + 5*7 + 3*7^2  + 6*7^3  + 7^4  + 3*7^5  + 2*7^6  + 5*7^7  + O(7^8)) 1]

? factpol(x^15-1, 3)
%120 = 
[x^2 + x + 1 1]

[x - 1 1]

[x^12 + x^9 + x^6 + x^3 + 1 1]

? factpol(x^15-1, 0)
%121 = 
[x^4 + x^3 + x^2 + x + 1 1]

[x^2 + x + 1 1]

[x - 1 1]

[x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]

? factpol2(x^15-1, 0)
%122 = 
[x - 1 1]

[x^2 + x + 1 1]

[x^4 + x^3 + x^2 + x + 1 1]

[x^8 - x^7 + x^5 - x^4 + x^3 - x + 1 1]

? fibo(100)
%123 = 354224848179261915075
? floor(-1/2)
%124 = -1
? floor(-2.5)
%125 = -3
? for(x=1,5,print(x!))
1
2
6
24
120
? fordiv(10,x,print(x))
1
2
5
10
? forprime(p=1,30,print(p))
2
3
5
7
11
13
17
19
23
29
? forstep(x=0,pi,pi/12,print(sin(x)))
 0.E-28
0.2588190451025207623488988376
0.4999999999999999999999999999
0.7071067811865475244008443620
0.8660254037844386467637231707
0.9659258262890682867497431997
1.000000000000000000000000000
0.9659258262890682867497431997
0.8660254037844386467637231708
0.7071067811865475244008443622
0.5000000000000000000000000001
0.2588190451025207623488988378
3.029225876048685332781037690 E-28
? frac(-2.7)
%126 = 0.3000000000000000000000000000
? \\ G
? galois(x^6-3*x^2-1)
%127 = [12, 1, 1]
? galoisconj(x^6+108)
%128 = [x, -1/12*x^4 + 1/2*x, 1/12*x^4 - 1/2*x, -x, 1/12*x^4 + 1/2*x, -1/12*x^4 - 1/2*x]
? gamh(10)
%129 = 1133278.388948785567334574165
? gamma(10.5)
%130 = 1133278.388948785567334574165
? gauss(hilbert(10),[1, 2, 3, 4, 5, 6, 7, 8, 9, 0])
%131 = [9236800, -831303990, 18288515520, -170691240720, 832112321040, -2329894066500, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
? gcd(12345678, 87654321)
%132 = 9
? getrand()
%133 = 1400602798
? getstack()
%134 = 29076
? \\ gettime() is at the end
? globalred(acurve)
%135 = [37, [1, -1, 2, 2], 1]
? getstack()
%136 = 29196
? k=4;goto(k%2);label(0);print("even");goto(3);label(1);print("odd");label(3);
even
? \\ H
? hclassno(2000003)
%137 = 357
? hell(acurve, apoint)
%138 = 0.4088912659197507218870887980
? hell2(acurve, apoint)
%139 = 0.4088912659197507218870887982
? hermite(1/hilbert(7))
%140 = 
[420 0 0 0 210 168 175]

[0 840 0 0 0 0 504]

[0 0 2520 0 0 0 1260]

[0 0 0 2520 0 0 840]

[0 0 0 0 13860 0 6930]

[0 0 0 0 0 5544 0]

[0 0 0 0 0 0 12012]

? hermitemod(1/hilbert(7),2067909047925770649600000)
%141 = 
[420 0 0 0 210 168 175]

[0 840 0 0 0 0 504]

[0 0 2520 0 0 0 1260]

[0 0 0 2520 0 0 840]

[0 0 0 0 13860 0 6930]

[0 0 0 0 0 5544 0]

[0 0 0 0 0 0 12012]

? hess(hilbert(7))
%142 = 
[1 90281/58800 -1919947/4344340 4858466341/1095033030 -77651417539/8196787326 3386888964/106615355 1/2]

[1/3 43/48 38789/5585580 268214641/109503303 -581330123627/126464718744 4365450643/274153770 1/4]

[0 217/2880 442223/7447440 53953931/292008808 -32242849453/168619624992 1475457901/1827691800 1/80]

[0 0 1604444/264539275 24208141/149362505292 847880210129/47916076768560 -4544407141/103873817300 -29/40920]

[0 0 0 9773092581/35395807550620 -24363634138919/107305824577186620 72118203606917/60481351061158500 55899/3088554700]

[0 0 0 0 67201501179065/8543442888354179988 -9970556426629/740828619992676600 -3229/13661312210]

[0 0 0 0 0 -258198800769/9279048099409000 -13183/38381527800]

? hilb(2/3, 3/4, 5)
%143 = 1
? hilbert(5)
%144 = 
[1 1/2 1/3 1/4 1/5]

[1/2 1/3 1/4 1/5 1/6]

[1/3 1/4 1/5 1/6 1/7]

[1/4 1/5 1/6 1/7 1/8]

[1/5 1/6 1/7 1/8 1/9]

? hilbp(mod(5,7),mod(6, 7))
%145 = 1
? hvector(10,x,1/x)
%146 = [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
? hyperu(1,1,1)
%147 = 0.5963473623231940743410784940
? \\ I
? i^2
%148 = -1
? nfpol=x^5-5*x^3+5*x+25
%149 = x^5 - 5*x^3 + 5*x + 25
? nf=initalg(nfpol)
%150 = [x^5 - 2*x^4 + 3*x^3 + 8*x^2 + 3*x + 2, [1, 2], 595125, 4, [[1, -1.089115145720504825024952794, 1.186171800637796459479629386, -0.5974105092919478273300176598, 0.1589441974539037620654948166; 1, -0.1383837207340603636504797641 - 0.4918163765776864349975328551*i, -0.2227332941058022659915570161 + 0.1361187602175280522167491802*i, -0.1316744587178581879876965153 - 0.1324951776052197384080146229*i, -0.05365095865699772535929752835 - 0.2762263681416910703813828468*i; 1, 1.682941293594312776162956161 - 2.050035122601072617297428698*i, -1.370352606213095963748257676 - 6.900177522288049477372076962*i, -8.069620286636167898347294654 - 8.876767678597104245088528429*i, -22.02582114006995415567344987 + 8.430658689699915354471086016*i], [1, 2, 2; -1.089115145720504825024952794, -0.2767674414681207273009595283 + 0.9836327531553728699950657102*i, 3.365882587188625552325912323 + 4.100070245202145234594857396*i; 1.186171800637796459479629386, -0.4454665882116045319831140322 - 0.2722375204350561044334983605*i, -2.740705212426191927496515353 + 13.80035504457609895474415392*i; -0.5974105092919478273300176598, -0.2633489174357163759753930307 + 0.2649903552104394768160292459*i, -16.13924057327233579669458930 + 17.75353535719420849017705685*i; 0.1589441974539037620654948166, -0.1073019173139954507185950567 + 0.5524527362833821407627656936*i, -44.05164228013990831134689975 - 16.86131737939983070894217203*i], [5, 2.000000000000000000000000000, -1.999999999999999999999999999, -16.99999999999999999999999999, -43.99999999999999999999999999; 2.000000000000000000000000000, 15.77810940867199804483635747, 22.31464334975406165191655381, 10.05139525783147827549993271, -108.5891750762084144745656909; -1.999999999999999999999999999, 22.31464334975406165191655381, 100.5239126238896097582780617, 143.9329509084735351943667379, -55.84256471808245264132250017; -16.99999999999999999999999999, 10.05139525783147827549993271, 143.9329509084735351943667379, 288.2582375674994469313929217, 205.7984003827766237572018064; -43.99999999999999999999999999, -108.5891750762084144745656909, -55.84256471808245264132250017, 205.7984003827766237572018064, 1112.609227794677770777925096], [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]], [-1.089115145720504825024952794, -0.1383837207340603636504797641 - 0.4918163765776864349975328551*i, 1.682941293594312776162956161 - 2.050035122601072617297428698*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]]
? nf1=initalg0(nfpol)
%151 = [x^5 - 5*x^3 + 5*x + 25, [1, 2], 595125, 45, [[1, -2.428517490719418606899206956, 5.897697202730141439489880654, -0.1757554687789514874988862128, 3.808582057009636614464927858; 1, 1.964711921128813316313875339 - 0.8097149241889789512829408221*i, 3.204454674571308426920376879 - 3.181713128540000534114585226*i, 4.042819681440990981544267056 - 5.069756914740706227305230673*i, 2.066070953837248063269897115 - 2.689896751962314099117052371*i; 1, -0.7504531757691040128642718609 - 1.310146268535812328356077361*i, -1.153303275936379146665317206 + 1.966406855889483431178011935*i, 1.045058052948484762205176049 + 1.322704475126913542182308678*i, -0.4703619823420663705023610445 - 0.08362826671158918611941676267*i], [1, 2, 2; -2.428517490719418606899206956, 3.929423842257626632627750678 + 1.619429848377957902565881644*i, -1.500906351538208025728543721 + 2.620292537071624656712154723*i; 5.897697202730141439489880654, 6.408909349142616853840753758 + 6.363426257080001068229170452*i, -2.306606551872758293330634412 - 3.932813711778966862356023871*i; -0.1757554687789514874988862128, 8.085639362881981963088534113 + 10.13951382948141245461046134*i, 2.090116105896969524410352099 - 2.645408950253827084364617357*i; 3.808582057009636614464927858, 4.132141907674496126539794230 + 5.379793503924628198234104742*i, -0.9407239646841327410047220890 + 0.1672565334231783722388335253*i], [5,  0.E-28, 10.00000000000000000000000000, 10.00000000000000000000000000, 7.000000000000000000000000000;  0.E-28, 19.48848601365070719744940326, -4.038967832922935485000000000 E-28, 19.48848601365070719744940327, 4.150459224670608558890201399; 10.00000000000000000000000000, -4.038967832922935485000000000 E-28, 85.96021742085184648030513393, 59.92594912936886664203807769, 53.57613045251110788818308035; 10.00000000000000000000000000, 19.48848601365070719744940327, 59.92594912936886664203807769, 89.80792921232787310470852907, 42.10602870229192854411304801; 7.000000000000000000000000000, 4.150459224670608558890201399, 53.57613045251110788818308035, 42.10602870229192854411304801, 37.97015289284236734089738425], [5, 0, 10, 10, 7; 0, 10, 0, 10, -5; 10, 0, 30, -15, 20; 10, 10, -15, -20, -12; 7, -5, 20, -12, 9], [345, 0, 340, 166, 150; 0, 345, 110, 220, 153; 0, 0, 5, 1, 1; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1]], [-2.428517490719418606899206956, 1.964711921128813316313875339 - 0.8097149241889789512829408221*i, -0.7504531757691040128642718609 - 1.310146268535812328356077361*i], [1, x, x^2, 1/3*x^3 + 2/3*x^2 + 2/3, 1/15*x^4 + 1/3*x^2 + 1/3*x + 1/3], [1, 0, 0, -2, -5; 0, 1, 0, 0, -5; 0, 0, 1, -2, -5; 0, 0, 0, 3, 0; 0, 0, 0, 0, 15], [1, 0, 0, 0, 0, 0, 0, -2, -3, -3, 0, -2, -5, -15, -4, 0, -3, -15, -21, -11, 0, -3, -4, -11, -4; 0, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, -5, -5, -5, 0, -1, -5, -10, -5, 0, 0, -5, -5, -4; 0, 0, 1, 0, 0, 0, 1, -2, -3, -1, 1, -2, -5, -6, -4, 0, -3, -6, -10, -6, 0, -1, -4, -6, -3; 0, 0, 0, 1, 0, 0, 0, 3, 2, 2, 0, 3, 0, 5, 1, 1, 2, 5, 8, 4, 0, 2, 1, 4, 1; 0, 0, 0, 0, 1, 0, 0, 0, 5, 0, 0, 0, 15, 10, 10, 0, 5, 10, 15, 9, 1, 0, 10, 9, 7]]
? initalg2(nfpol)
%152 = 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]
%153 = [3, [-1, 1, 0, 0, 0]~, 1, 1, [2, 2, 3, 2, 1]~]
? idx=idealmul(nf,idmat(5),vp)
%154 = 
[3 2 2 0 2]

[0 1 0 0 0]

[0 0 1 0 0]

[0 0 0 1 0]

[0 0 0 0 1]

? idealinv(nf,idx)
%155 = 
[1 0 0 0 2/3]

[0 1 0 0 2/3]

[0 0 1 0 0]

[0 0 0 1 2/3]

[0 0 0 0 1/3]

? idy=ideallllred(nf,idx,[1,3,5,7,9])
%156 = 
[6 0 3 0 4]

[0 6 3 0 4]

[0 0 3 0 0]

[0 0 0 6 4]

[0 0 0 0 2]

? idealadd(nf,idx,idy)
%157 = 
[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]

? idz=idealintersect(nf,idx,idy)
%158 = 
[6 0 3 0 0]

[0 6 3 0 0]

[0 0 3 0 0]

[0 0 0 6 0]

[0 0 0 0 6]

? idealfactor(nf,idz)
%159 = 
[[2, [3, 3, 3, 2, 2]~, 1, 4, [2, 1, 0, 0, 0]~] 1]

[[3, [-1, 1, 0, 0, 0]~, 1, 1, [2, 2, 3, 2, 1]~] 1]

[[3, [-1, 1, 1, 0, 0]~, 2, 2, [1, 3, 2, 2, 0]~] 2]

? idealmul(nf,idx,idx)
%160 = 
[9 5 2 3 5]

[0 1 0 0 0]

[0 0 1 0 0]

[0 0 0 1 0]

[0 0 0 0 1]

? idt=idealmulred(nf,idx,idx)
%161 = 
[2 0 1 0 0]

[0 2 1 0 0]

[0 0 1 0 0]

[0 0 0 2 0]

[0 0 0 0 2]

? idealdiv(nf,idy,idt)
%162 = 
[3 0 0 0 2]

[0 3 0 0 2]

[0 0 3 0 0]

[0 0 0 3 2]

[0 0 0 0 1]

? idealpow(nf,idx,7)
%163 = 
[2187 1436 245 984 230]

[0 1 0 0 0]

[0 0 1 0 0]

[0 0 0 1 0]

[0 0 0 0 1]

? idealval(nf,%,vp)
%164 = 7
? idealpowred(nf,idx,7)
%165 = 
[2 0 1 0 0]

[0 2 1 0 0]

[0 0 1 0 0]

[0 0 0 2 0]

[0 0 0 0 2]

? idmat(5)
%166 = 
[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]

? if(3 < 2, print("bof"), print("ok"));
ok
? imag(2+3*i)
%167 = 3
? image([1,3,5;2,4,6;3,5,7])
%168 = 
[1 3]

[2 4]

[3 5]

? imager(pi*[1,3,5;2,4,6;3,5,7])
%169 = 
[3.141592653589793238462643383 9.424777960769379715387930149]

[6.283185307179586476925286766 12.56637061435917295385057353]

[9.424777960769379715387930149 15.70796326794896619231321691]

? incgam(2,1)
%170 = 0.7357588823428846431910475403
? incgam1(2,1)
%171 = -0.2642411176571153568089566720
? incgam2(2,1)
%172 = 0.7357588823428846431910475403
? incgam3(2,1)
%173 = 0.2642411176571153568089524596
? incgam4(4,1,6)
%174 = 5.886071058743077145528380322
? indexrank([1,1,1;1,1,1;1,1,2])
%175 = [[1, 3], [1, 3]]
? indsort([8, 7, 6, 5])
%176 = [4, 3, 2, 1]
? initell([0,0,0,-1,0])
%177 = [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [0.9999999999999999999999999999,  0.E-28, -1.000000000000000000000000000]~, 2.622057554292119810464839589, 2.622057554292119810464839589*i, -0.5990701173677961037199612460, -1.797210352103388311159883738*i, 6.875185818020372827490095779]
? initell2([0,0,0,0,-1])
%178 = [0, 0, 0, 0, -1, 0, 0, -4, 0, 0, 864, -432, 0, [1.000000000000000000000000000, -0.5000000000000000000000000000 + 0.8660254037844386467637231707*i, -0.5000000000000000000000000000 - 0.8660254037844386467637231707*i]~, 2.428650647887581611819941689, 1.214325323943790805909970844 + 2.103273157988181391762528618*i, -0.7468342002221868131034708804 +  0.E-29*i, -0.3734171001110934065517354402 - 1.940332169422342901215136268*i, 5.108115717832556535122194506]
? initrect(1,700,700)
? integ(sin(x), x)
%179 = 1/2*x^2 - 1/24*x^4 + 1/720*x^6 - 1/40320*x^8 + 1/3628800*x^10 - 1/479001600*x^12 + 1/87178291200*x^14 - 1/20922789888000*x^16 + O(x^17)
? intersect([1,2;3,4;5,6],[2,3;7,8;8,9])
%180 = 
[-1]

[-1]

[-1]

? \precision=9
   precision = 9 significant digits
? intgen(x=0,pi,sin(x))
%181 = 1.99999999
? sqr(2*intgen(x=0,4,exp(-x^2)))
%182 = 3.14159267
? 4*intinf(x=1,10000,1/(1+x^2))
%183 = 3.14119264
? intnum(x = -0.999, 0.999, 1/sqrt(1 - x^2))
%184 = 3.05305351
? 2 * intopen(x = 0, 100, sin(x)/x)
%185 = 3.12446099
? \precision=28
   precision = 28 significant digits
? inverseimage([1,1;2,3;5,7],[2,2,6]~)
%186 = [4, -2]~
? isfund(12345)
%187 = 1
? isideal(bnf[7],[5,1;0,1])
%188 = 1
? isincl(x^2+1,x^4+1)
%189 = [x^2, -x^2]
? isisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
%190 = [x, x^2 - 2, -x^2 - x + 1]
? isprime(12345678901234567)
%191 = 0
? isprincipal(bnf,[5,1;0,1])
%192 = [[2]~, [4/9, -1/9]~, 45]
? ispsp(73!+1)
%193 = 1
? isqrt(10!^2+1)
%194 = 3628800
? issqfree(123456789876543219)
%195 = 0
? issquare(12345678987654321)
%196 = 1
? isunit(bnf,mod(3405*x-27466,x^2-x-57))
%197 = [-4, mod(1, 2)]
? \\ J
? jacobi(hilbert(6))
%198 = [[1.618899858924339096970588146, 0.2423608705752095521357284158, 0.00001257075712262519492298239437, 0.0000001082799484565549768538852900, 0.01632152131987582212434507956, 0.0006157483541826576976491993781]~, [0.7487192188790948590028010920, -0.6145448282925867689932001965, 0.01114432093072471053067834095, -0.001248194084082175116939817185, 0.2403253693425233039915422886, -0.06222658815019768177515212657; 0.4407175032435120612716008357, 0.2110824816786704867522767585, -0.1797327572407600375877689803, 0.03560664294428763526612286184, -0.6976513752773701229620833502, 0.4908392097109243629749831600; 0.3206968698222519010635902432, 0.3658936073030261414908655421, 0.6042122067529597300442656657, -0.2406790795884229583773672408, -0.2313893733329038804225136358, -0.5354769216210748659347449113; 0.2543113863404741925178831279, 0.3947067760950175678309463614, -0.4435747162762395455446041165, 0.6254603865492272445775344430, 0.1328631585093355353033383962, -0.4170376922189788684049451526; 0.2115308400789652466421366767, 0.3881904338738864286311144882, -0.4415366410122896622214365491, -0.6898071992938366841980173472, 0.3627149214648714752529945762, 0.04703401893311564970561451458; 0.1814429766487694737221700545, 0.3706959077673628086177550108, 0.4591148168164296028455139429, 0.2716054533663128693001553281, 0.5027628667575153848926056637, 0.5406815631038529388002229385]]
? jbesselh(1,1)
%199 = 0.2402978391234270108958430447
? jell(i)
%200 = 1727.999999999999999999999999 +  0.E-26*i
? \\ K
? kbessel(1 + i, 1)
%201 = 0.3254597718658414108546463973 + 0.2894280370259921276345671592*i
? kbessel2(1 + i, 1)
%202 = 0.3254597718658414108546463973 + 0.2894280370259921276345671592*i
? x
%203 = x
? y
%204 = x
? ker(matrix(4,4,x,y,x/y))
%205 = 
[-1/2 -1/3 -1/4]

[1 0 0]

[0 1 0]

[0 0 1]

? keri(matrix(4,4,x,y,x+y))
%206 = 
[1 2]

[-2 -3]

[1 0]

[0 1]

? kerint(matrix(4,4,x,y,x*y))
%207 = 
[-1 -1 -1]

[-1 0 1]

[1 -1 1]

[0 1 -1]

? kerint1(matrix(4,4,x,y,x*y))
%208 = 
[-1 -1 -1]

[-1 0 1]

[1 -1 1]

[0 1 -1]

? kerint2(matrix(4,6,x,y,2520/(x+y)))
%209 = 
[3 1]

[-30 -15]

[70 70]

[0 -140]

[-126 126]

[84 -42]

? kerr(matrix(4,4,x,y,sin(x+y)))
%210 = 
[1.000000000000000000000000000 1.080604611736279434801873214]

[-1.080604611736279434801873214 -0.1677063269057152260048635409]

[1 0]

[0 1]

? f(u)=u+1;
? print(f(5)); kill(f);
6
? f=12
%211 = 12
? killrect(1)
? kro(5,7)
%212 = -1
? kro(3,18)
%213 = 0
? \\ L
? k=4;goto(k%2);label(0);print("even");goto(3);label(1);print("odd");label(3);
even
? laplace(x*exp(x*y)/(exp(x)-1))
%214 = 1 - 1/2*x + 13/6*x^2 - 3*x^3 + 419/30*x^4 - 30*x^5 + 6259/42*x^6 - 420*x^7 + 22133/10*x^8 - 7560*x^9 + 2775767/66*x^10 - 166320*x^11 + 2655339269/2730*x^12 - 4324320*x^13 + 264873251/10*x^14 + O(x^15)
? lcm(15,-21)
%215 = -105
? length(divisors(1000))
%216 = 16
? legendre(10)
%217 = 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x^2 - 63/256
? lex([1,3],[1,3,5])
%218 = -1
? lexsort([[1,5],[2,4],[1,5,1],[1,4,2]])
%219 = [[1, 4, 2], [1, 5], [1, 5, 1], [2, 4]]
? lift(chinese(mod(7,15),mod(4,21)))
%220 = 67
? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
%221 = [-3, -3, 9, -2, 6]
? lindep2([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
%222 = [-3, -3, 9, -2, 6]
? move(0,0,900);line(0,900,0)
? lines(0,vector(5,k,50*k),vector(5,k,10*k*k))
? m=1/hilbert(7)
%223 = 
[49 -1176 8820 -29400 48510 -38808 12012]

[-1176 37632 -317520 1128960 -1940400 1596672 -504504]

[8820 -317520 2857680 -10584000 18711000 -15717240 5045040]

[-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160]

[48510 -1940400 18711000 -72765000 133402500 -115259760 37837800]

[-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264]

[12012 -504504 5045040 -20180160 37837800 -33297264 11099088]

? mp=concat(m,idmat(7))
%224 = 
[49 -1176 8820 -29400 48510 -38808 12012 1 0 0 0 0 0 0]

[-1176 37632 -317520 1128960 -1940400 1596672 -504504 0 1 0 0 0 0 0]

[8820 -317520 2857680 -10584000 18711000 -15717240 5045040 0 0 1 0 0 0 0]

[-29400 1128960 -10584000 40320000 -72765000 62092800 -20180160 0 0 0 1 0 0 0]

[48510 -1940400 18711000 -72765000 133402500 -115259760 37837800 0 0 0 0 1 0 0]

[-38808 1596672 -15717240 62092800 -115259760 100590336 -33297264 0 0 0 0 0 1 0]

[12012 -504504 5045040 -20180160 37837800 -33297264 11099088 0 0 0 0 0 0 1]

? lll(m)
%225 = 
[-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]

? lll1(m)
%226 = 
[-420 -420 840 630 -1092 757 2982]

[-210 -280 630 504 -876 700 2415]

[-140 -210 504 420 -749 641 2050]

[-105 -168 420 360 -658 589 1785]

[-84 -140 360 315 -588 544 1582]

[-70 -120 315 280 -532 505 1421]

[-60 -105 280 252 -486 471 1290]

? lllgram(m)
%227 = 
[1 1 27 -27 69 0 141]

[0 1 4 -22 35 -42 91]

[0 1 3 -21 19 -42 65]

[0 1 3 -20 11 -36 49]

[0 1 3 -19 7 -30 38]

[0 1 3 -18 5 -25 30]

[0 1 3 -17 4 -21 24]

? lllgram1(m)
%228 = 
[1 1 27 -27 69 0 141]

[0 1 5 -23 35 -42 92]

[0 1 4 -22 19 -42 66]

[0 1 4 -21 11 -36 50]

[0 1 4 -20 7 -30 39]

[0 1 4 -19 5 -25 31]

[0 1 4 -18 4 -21 25]

? lllgramint(m)
%229 = 
[1 1 27 -27 69 0 141]

[0 1 4 -23 34 -24 49]

[0 1 3 -22 18 -24 23]

[0 1 3 -21 10 -19 13]

[0 1 3 -20 6 -14 8]

[0 1 3 -19 4 -10 5]

[0 1 3 -18 3 -7 3]

? lllgramkerim(mp~*mp)
%230 = [[-420, -420, 840, 630, 2982, -1092, 757; -210, -280, 630, 504, 2415, -876, 700; -140, -210, 504, 420, 2050, -749, 641; -105, -168, 420, 360, 1785, -658, 589; -84, -140, 360, 315, 1582, -588, 544; -70, -120, 315, 280, 1421, -532, 505; -60, -105, 280, 252, 1290, -486, 471; 420, 0, 0, 0, -210, 168, 35; 0, 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, -1260; 0, 0, 0, -2520, 0, 0, -840; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 1, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
? lllint(m)
%231 = 
[-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]

? lllkerim(mp)
%232 = [[-420, -420, 840, 630, 2982, -1092, 757; -210, -280, 630, 504, 2415, -876, 700; -140, -210, 504, 420, 2050, -749, 641; -105, -168, 420, 360, 1785, -658, 589; -84, -140, 360, 315, 1582, -588, 544; -70, -120, 315, 280, 1421, -532, 505; -60, -105, 280, 252, 1290, -486, 471; 420, 0, 0, 0, -210, 168, 35; 0, 840, 0, 0, 0, 0, 336; 0, 0, -2520, 0, 0, 0, -1260; 0, 0, 0, -2520, 0, 0, -840; 0, 0, 0, 0, -13860, 0, 6930; 0, 0, 0, 0, 0, 5544, 0; 0, 0, 0, 0, 0, 0, -12012], [0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0; 1, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1]]
? lllrat(m)
%233 = 
[-420 -420 840 630 -1092 -83 2982]

[-210 -280 630 504 -876 70 2415]

[-140 -210 504 420 -749 137 2050]

[-105 -168 420 360 -658 169 1785]

[-84 -140 360 315 -588 184 1582]

[-70 -120 315 280 -532 190 1421]

[-60 -105 280 252 -486 191 1290]

? \precision=100
   precision = 100 significant digits
? ln(2)
%234 = 0.6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875
? lngamma(10^50*i)
%235 = -157079632679489661923132169163975144209858469968811.9367375388760847494897709411534189519074068479349 + 11412925464970228420089957273421821038005507443143864.09476847610738955343272591658130426497615564164*i
? \precision=2000
   precision = 2000 significant digits
? log(2)
%236 = 0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335011536449795523912047517268157493206515552473413952588295045300709532636664265410423915781495204374043038550080194417064167151864471283996817178454695702627163106454615025720740248163777338963855069526066834113727387372292895649354702576265209885969320196505855476470330679365443254763274495125040606943814710468994650622016772042452452961268794654619316517468139267250410380254625965686914419287160829380317271436778265487756648508567407764845146443994046142260319309673540257444607030809608504748663852313818167675143866747664789088143714198549423151997354880375165861275352916610007105355824987941472950929311389715599820565439287170007218085761025236889213244971389320378439353088774825970171559107088236836275898425891853530243634214367061189236789192372314672321720534016492568727477823445353476481149418642386776774406069562657379600867076257199184734022651462837904883062033061144630073719489002743643965002580936519443041191150608094879306786515887090060520346842973619384128965255653968602219412292420757432175748909770675268711581705113700915894266547859596489065305846025866838294002283300538207400567705304678700184162404418833232798386349001563121889560650553151272199398332030751408426091479001265168243443893572472788205486271552741877243002489794540196187233980860831664811490930667519339312890431641370681397776498176974868903887789991296503619270710889264105230924783917373501229842420499568935992206602204654941510613918788574424557751020683703086661948089641218680779020818158858000168811597305618667619918739520076671921459223672060253959543654165531129517598994005600036651356756905124592682574394648316833262490180382424082423145230614096380570070255138770268178516306902551370323405380214501901537402950994226299577964742713815736380172987394070424217997226696297993931270693
? logagm(2)
%237 = 0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335011536449795523912047517268157493206515552473413952588295045300709532636664265410423915781495204374043038550080194417064167151864471283996817178454695702627163106454615025720740248163777338963855069526066834113727387372292895649354702576265209885969320196505855476470330679365443254763274495125040606943814710468994650622016772042452452961268794654619316517468139267250410380254625965686914419287160829380317271436778265487756648508567407764845146443994046142260319309673540257444607030809608504748663852313818167675143866747664789088143714198549423151997354880375165861275352916610007105355824987941472950929311389715599820565439287170007218085761025236889213244971389320378439353088774825970171559107088236836275898425891853530243634214367061189236789192372314672321720534016492568727477823445353476481149418642386776774406069562657379600867076257199184734022651462837904883062033061144630073719489002743643965002580936519443041191150608094879306786515887090060520346842973619384128965255653968602219412292420757432175748909770675268711581705113700915894266547859596489065305846025866838294002283300538207400567705304678700184162404418833232798386349001563121889560650553151272199398332030751408426091479001265168243443893572472788205486271552741877243002489794540196187233980860831664811490930667519339312890431641370681397776498176974868903887789991296503619270710889264105230924783917373501229842420499568935992206602204654941510613918788574424557751020683703086661948089641218680779020818158858000168811597305618667619918739520076671921459223672060253959543654165531129517598994005600036651356756905124592682574394648316833262490180382424082423145230614096380570070255138770268178516306902551370323405380214501901537402950994226299577964742713815736380172987394070424217997226696297993931270693
? \precision=9
   precision = 9 significant digits
? bcurve=initell([0,0,0,-3,0])
%238 = [0, 0, 0, -3, 0, 0, -6, 0, -9, 144, 0, 1728, 1728, [1.73205080, 0.000000000, -1.73205080]~, 1.99233289, 1.99233290*i, -0.788420613, -2.36526184*i, 3.96939039]
? localred(bcurve,2)
%239 = [6, 2, [1, 1, 1, 0], 1]
? ccurve=initell([0,0,-1,-1,0])
%240 = [0, 0, -1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.837565435, 0.269594436, -1.10715987]~, 2.99345864, 2.45138937*i, -0.471319277, -1.43545651*i, 7.33813273]
? l=lseriesell(ccurve,2,-37,1)
%241 = 0.381575407
? lseriesell(ccurve,2,-37,1.2)-l
%242 = 0.000000000814907252
? \\ M
? concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)
%243 = 
[1 11]

[2 12]

[3 13]

[4 14]

? matextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
%244 = 
[6 9 12]

[9 12 15]

[12 15 18]

[15 18 21]

[18 21 24]

? ma=mathell(mcurve,mpoints)
%245 = 
[1.17218309 0.447697388]

[0.447697388 1.75502601]

? gauss(ma,mhbi)
%246 = [-0.999999999, 0.999999999]~
? matinvr(1.*hilbert(7))
%247 = 
[49.0948939 -1179.88827 8858.09375 -29549.8554 48787.1582 -39049.1172 12091.6127]

[-1179.84100 37789.1740 -319058.654 1135009.31 -1951583.03 1606397.87 -507714.017]

[8857.34090 -319046.702 2872617.60 -10642705.1 18819493.2 -15811575.0 5076169.07]

[-29546.0926 1134929.50 -10642384.2 40549387.7 -73188844.0 62461274.1 -20301734.5]

[48779.0946 -1951390.55 18818460.5 -73187117.1 134182332. -115937635. 38061436.6]

[-39041.3748 1606200.31 -15810382.0 62458612.6 -115935491. 101177665. -33491014.3]

[12088.8508 -507640.804 5075697.51 -20300550.8 38060165.1 -33490523.9 11162837.3]

? matsize([1,2;3,4;5,6])
%248 = [3, 2]
? matrix(5,5,x,y,gcd(x,y))
%249 = 
[1 1 1 1 1]

[1 2 1 2 1]

[1 1 3 1 1]

[1 2 1 4 1]

[1 1 1 1 5]

? matrixqz([1,3;3,5;5,7],0)
%250 = 
[1 1]

[3 2]

[5 3]

? matrixqz2([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0])
%251 = 
[19 12 2]

[0 1 0]

[0 0 1]

? matrixqz3([1,3;3,5;5,7])
%252 = 
[2 -1]

[1 0]

[0 1]

? max(2,3)
%253 = 3
? min(2,3)
%254 = 2
? minim([2,1;1,2],4,6)
%255 = [6, 2, [0, -1, 1; 1, 1, 0]]
? mod(-12,7)
%256 = mod(2, 7)
? modp(-12,7)
%257 = mod(2, 7)
? mod(10873,49649)^-1
  ***   impossible inverse modulo: mod(131, 49649)
? modreverse(mod(x^2+1,x^3-x-1))
%258 = mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
? move(0,243,583);cursor(0)
%259 = [243.000000, 583.000000]
? mu(3*5*7*11*13)
%260 = -1
? \\ N
? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
%261 = [2, 2/3, 2/3, 2/3]
? nextprime(100000000000000000000000)
%262 = 100000000000000000000117
? norm(1+i)
%263 = 2
? norm(mod(x+5,x^3+x+1))
%264 = 129
? norml2(vector(10,x,x))
%265 = 385
? nucomp(qfi(2,1,9),qfi(4,3,5),3)
%266 = qfi(2, -1, 9)
? form=qfi(2,1,9);nucomp(form,form,3)
%267 = qfi(4, -3, 5)
? numdiv(2^99*3^49)
%268 = 5000
? numer((x+1)/(x-1))
%269 = x + 1
? nupow(form,111)
%270 = qfi(2, -1, 9)
? \\ O
? 1/(1+x)+o(x^20)
%271 = 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 + x^14 - x^15 + x^16 - x^17 + x^18 - x^19 + O(x^20)
? omega(100!)
%272 = 25
? ordell(acurve, 1)
%273 = [8, 3]
? order(mod(33,2^16+1))
%274 = 2048
? tcurve=smallinitell([1,0,1,-19,26])
%275 = [1, 0, 1, -19, 26, 1, -37, 105, -316, 889, -24013, 72900, 702595369/72900]
? orderell(tcurve,[1,2])
%276 = 6
? ordred(x^3-12*x+45*x-1)
%277 = [x - 1, x^3 + 33*x - 1, x^3 - 363*x - 2663]~
? \\ P
? pascal(8)
%278 = 
[1 0 0 0 0 0 0 0 0]

[1 1 0 0 0 0 0 0 0]

[1 2 1 0 0 0 0 0 0]

[1 3 3 1 0 0 0 0 0]

[1 4 6 4 1 0 0 0 0]

[1 5 10 10 5 1 0 0 0]

[1 6 15 20 15 6 1 0 0]

[1 7 21 35 35 21 7 1 0]

[1 8 28 56 70 56 28 8 1]

? perf([2,0,1;0,2,1;1,1,2])
%279 = 6
? permutation(7,1035)
%280 = [4, 7, 1, 6, 3, 5, 2]
? pf(-44,3)
%281 = qfi(3, 2, 4)
? phi(257^2)
%282 = 65792
? pi
%283 = 3.14159265
? plot(x=-5,5,sin(x))

      0.999 xxxx---------------------------------xxxx------------------|
            |   x                               x    xx                |
            |    x                             x       x               |
            |     x                           x                        |
            |      x                         x          x              |
            |       x                                    x             |
            |                               x                          |
            |        x                     x              x            |
            |         x                                    x           |
            |                             x                            |
            -----------x------------------------------------x-----------
            |                            x                             |
            |           x                                    x         |
            |            x              x                     x        |
            |                          x                               |
            |             x                                    x       |
            |              x          x                         x      |
            |                        x                           x     |
            |               x       x                             x    |
            |                xx    x                               x   |
     -0.999 |------------------xxxx---------------------------------xxxx
             -5.000                                                   5.000

? \\ ploth(x=-5,5,sin(x))
? \\ ploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
? \\ plothraw(vector(100,k,k),vector(100,k,k*k/100))
? pnqn([2,6,10,14,18,22,26])
%284 = 
[19318376 741721]

[8927353 342762]

? pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
%285 = 
[34 21]

[21 13]

? point(0,225,334)
? points(0,vector(10,k,10*k),vector(10,k,5*k*k))
? pointell(acurve,zell(acurve,apoint))
%286 = [0.999999998 + 0.000000000*i, 3.00000000 + 0.000000000*i]
? polint([0,2,3],[0,4,9],5)
%287 = 25
? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
%288 = [x - 1, x^5 - x^4 + 2*x^3 - 4*x^2 + x - 1, x^5 - x^4 + 4*x^3 - 2*x^2 + x - 1, x^5 + 4*x^3 - 4*x^2 + 8*x - 8, x^5 - x^4 - 6*x^3 + 6*x^2 + 13*x - 5]~
? polred2(x^4-28*x^3-458*x^2+9156*x-25321)
%289 = 
[1 x - 1]

[1/4485*x^3 - 7/1495*x^2 - 1034/4485*x + 7924/4485 x^4 - 8*x^2 + 6]

[1/115*x^2 - 14/115*x - 327/115 x^2 - 10]

[3/1495*x^3 - 63/1495*x^2 - 1607/1495*x + 13307/1495 x^4 - 32*x^2 + 216]

? polsym(x^17-1,17)
%290 = [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
? poly(sin(x),x)
%291 = -1/1307674368000*x^15 + 1/6227020800*x^13 - 1/39916800*x^11 + 1/362880*x^9 - 1/5040*x^7 + 1/120*x^5 - 1/6*x^3 + x
? polylog(5,0.5)
%292 = 0.508400578
? polylog(-4,t)
%293 = (t^4 + 11*t^3 + 11*t^2 + t)/(-t^5 + 5*t^4 - 10*t^3 + 10*t^2 - 5*t + 1)
? polylogd(5,0.5)
%294 = 0.939035495
? polylogdold(5,0.5)
%295 = 1.03445942
? polylogp(5,0.5)
%296 = 0.949569346
? poly([1,2,3,4,5],x)
%297 = x^4 + 2*x^3 + 3*x^2 + 4*x + 5
? polyrev([1,2,3,4,5],x)
%298 = 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1
? \\draw([0,20,20])
? postdraw([0,20,20])
? postploth(x=-5,5,sin(x))
? postploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
? postplothraw(vector(100,k,k),vector(100,k,k*k/100))
? powell(acurve,apoint,10)
%299 = [-28919032218753260057646013785951999/292736325329248127651484680640160000, 478051489392386968218136375373985436596569736643531551/158385319626308443937475969221994173751192384064000000]
? powrealraw(qfr(5,3,-1,0.),3)
%300 = qfr(125, 23, 1, 0.000000000)
? pprint((x-12*y)/(y+13*x));
(-(11 /14))
? pprint([1,2;3,4])

[1 2]

[3 4]

%302 = 
[1 2]

[3 4]

? pprint1(x+y);pprint(x+y);
(2 x )(2 x )
? \precision=100
   precision = 100 significant digits
? pi
%304 = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068
? prec(pi,20)
%305 = 3.141592653589793238462643383254089766000000000000000000000000000000000000000000000000000000000000000
? \precision=28
   precision = 28 significant digits
? prime(100)
%306 = 541
? primedec(nf,2)
%307 = [[2, [3, 5, 4, 2, 3]~, 1, 1, [1, 1, 1, 0, 0]~], [2, [3, 3, 3, 2, 2]~, 1, 4, [2, 1, 0, 0, 0]~]]
? primedec(nf,3)
%308 = [[3, [-1, 1, 0, 0, 0]~, 1, 1, [2, 2, 3, 2, 1]~], [3, [-1, 1, 1, 0, 0]~, 2, 2, [1, 3, 2, 2, 0]~]]
? primedec(nf,11)
%309 = [[11, [0, 0, 0, 0, 0]~, 1, 5, [1, 0, 0, 0, 0]~]]
? primes(100)
%310 = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541]
? forprime(p=2,100,print(p, " ", lift(primroot(p))))
2 1
3 2
5 2
7 3
11 2
13 2
17 3
19 2
23 5
29 2
31 3
37 2
41 6
43 3
47 5
53 2
59 2
61 2
67 2
71 7
73 5
79 3
83 2
89 3
97 5
? principalideal(nf1,mod(x^3+5,nfpol))
%311 = 
[3]

[0]

[-2]

[3]

[0]

? principalidele(nf1,mod(x^3+5,nfpol))
%312 = [[3; 0; -2; 3; 0], [2.232448082779625408098138558 + 3.141592653589793238462643383*i, 5.038765967515871638643535310 - 1.585176034351225004989727886*i, 4.266404027265102874362591079 + 0.008363047814436824611091025828*i]~]
? print((x-12*y)/(y+13*x));
-11/14
? print([1,2;3,4])
[1, 2; 3, 4]
%314 = 
[1 2]

[3 4]

? print1(x+y);print1(" egale ");print(x+y);
2*x egale 2*x
? prod(1,k=1,10,1+1/k!)
%316 = 3335784368058308553334783/905932868585678438400000
? prod(1.,k=1,10,1+1/k!)
%317 = 3.682154035614204393573230842
? pi^2/6*prodeuler(p=2,10000,1-p^-2)
%318 = 1.000009815749306623869759122
? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
%319 = 0.3333333333333333333333333329
? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
%320 = 0.3333333333333333333333333329
? psi(1)
%321 = -0.5772156649015328606065120901
? \\ Q
? \\quaddisc(-252)
? quadgen(-11)
%322 = w
? quadpoly(-11)
%323 = x^2 - x + 3
? \\ R
? smith(matrix(5,5,j,k,random()))
%324 = [111618546516892879129935872, 2147483648, 2147483648, 1, 1]
? rank(matrix(5,5,x,y,x+y))
%325 = 2
? move(0,50,50);rbox(0,50,50)
? print1("give a value for s? ");s=read();print(1/s)
give a value for s? 37.
0.02702702702702702702702702702
%326 = 0.02702702702702702702702702702
? real(5-7*i)
%327 = 5
? recip(3*x^7-5*x^3+6*x-9)
%328 = -9*x^7 + 6*x^6 - 5*x^4 + 3
? redimag(qfi(3,10,12))
%329 = qfi(3, -2, 4)
? redreal(qfr(3,10,-20,1.5))
%330 = qfr(3, 16, -7, 1.500000000000000000000000000)
? redrealnod(qfr(3,10,-20,1.5),18)
%331 = qfr(3, 16, -7, 1.500000000000000000000000000)
? regula(17)
%332 = 2.094712547261101294244822846
? kill(y);print(x+y);reorder([x, y]); print(x+y);
x + y
x + y
? resultant(x^3-1,x^3+1)
%334 = 8
? resultant2(x^3-1.,x^3+1.)
%335 = 8.000000000000000000000000000
? reverse(tan(x))
%336 = x - 1/3*x^3 + 1/5*x^5 - 1/7*x^7 + 1/9*x^9 - 1/11*x^11 + 1/13*x^13 - 1/15*x^15 + O(x^16)
? rhoreal(qfr(3,10,-20,1.5))
%337 = qfr(-20, -10, 3, 2.107445107398783994713588025)
? rhorealnod(qfr(3,10,-20,1.5),18)
%338 = qfr(-20, -10, 3, 1.500000000000000000000000000)
? rline(0,200,150)
? cursor(0)
%339 = [250.0000000000000000000000000, 200.0000000000000000000000000]
? rmove(0,5,5);cursor(0)
%340 = [255.0000000000000000000000000, 205.0000000000000000000000000]
? rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%341 = x^17 - 1
? rootmod(x^16-1,41)
%342 = [mod(1, 41), mod(3, 41), mod(9, 41), mod(14, 41), mod(27, 41), mod(32, 41), mod(38, 41), mod(40, 41)]
? rootpadic(x^4+1,41,6)
%343 = [3 + 22*41 + 27*41^2  + 15*41^3  + 27*41^4  + 33*41^5  + O(41^6), 14 + 20*41 + 25*41^2  + 24*41^3  + 4*41^4  + 18*41^5  + O(41^6), 27 + 20*41 + 15*41^2  + 16*41^3  + 36*41^4  + 22*41^5  + O(41^6), 38 + 18*41 + 13*41^2  + 25*41^3  + 13*41^4  + 7*41^5  + O(41^6)]~
? roots(x^5-1)
%344 = [0.9999999999999999999999999999 +  0.E-28*i, -0.8090169943749474241022934171 + 0.5877852522924731291687059546*i, -0.8090169943749474241022934171 - 0.5877852522924731291687059546*i, 0.3090169943749474241022934171 + 0.9510565162951535721164393333*i, 0.3090169943749474241022934171 - 0.9510565162951535721164393333*i]~
? rootslong(x^4-1000000000000000000000)
%345 = [-177827.9410038922801225421195 +  0.E-28*i, 177827.9410038922801225421195 +  0.E-28*i, 6.109872726999209364103958786 E-151 + 177827.9410038922801225421195*i, 6.109872726999209364103958786 E-151 - 177827.9410038922801225421195*i]~
? round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%346 = x^17 - 1
? rounderror(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%347 = -25
? rpoint(0,20,20)
? \\ S
? initrect(3,600,600);scale(3,-7,7,-2,2);cursor(3)
%348 = [-7.000000000000000000000000000, 2.000000000000000000000000000]
? q*series(anell(acurve,100),q)
%349 = q - 2*q^2 - 3*q^3 + 2*q^4 - 2*q^5 + 6*q^6 - q^7 + 6*q^9 + 4*q^10 - 5*q^11 - 6*q^12 - 2*q^13 + 2*q^14 + 6*q^15 - 4*q^16 - 12*q^18 - 4*q^20 + 3*q^21 + 10*q^22 + 2*q^23 - q^25 + 4*q^26 - 9*q^27 - 2*q^28 + 6*q^29 - 12*q^30 - 4*q^31 + 8*q^32 + 15*q^33 + 2*q^35 + 12*q^36 - q^37 + 6*q^39 - 9*q^41 - 6*q^42 + 2*q^43 - 10*q^44 - 12*q^45 - 4*q^46 - 9*q^47 + 12*q^48 - 6*q^49 + 2*q^50 - 4*q^52 + q^53 + 18*q^54 + 10*q^55 - 12*q^58 + 8*q^59 + 12*q^60 - 8*q^61 + 8*q^62 - 6*q^63 - 8*q^64 + 4*q^65 - 30*q^66 + 8*q^67 - 6*q^69 - 4*q^70 + 9*q^71 - q^73 + 2*q^74 + 3*q^75 + 5*q^77 - 12*q^78 + 4*q^79 + 8*q^80 + 9*q^81 + 18*q^82 - 15*q^83 + 6*q^84 - 4*q^86 - 18*q^87 + 4*q^89 + 24*q^90 + 2*q^91 + 4*q^92 + 12*q^93 + 18*q^94 - 24*q^96 + 4*q^97 + 12*q^98 - 30*q^99 - 2*q^100 + O(q^101)
? setprecision(28)
%350 = 28
? setrand(10)
%351 = 10
? setserieslength(12)
%352 = 16
? arat=(x^3+x+1)/x^3;settype(arat,14)
%353 = (x^3 + x + 1)/x^3
? shift(1,50)
%354 = 1125899906842624
? shift([3,4,-11,-12],-2)
%355 = [0, 1, -2, -3]
? shiftmul([3,4,-11,-12],-2)
%356 = [3/4, 1, -11/4, -3]
? sigma(100)
%357 = 217
? sigmak(2,100)
%358 = 13671
? sigmak(-3,100)
%359 = 1149823/1000000
? sign(-1)
%360 = -1
? sign(0)
%361 = 0
? sign(0.)
%362 = 0
? signat(hilbert(5)-0.11*idmat(5))
%363 = [2, 3]
? simplefactmod(x^11+1,7)
%364 = 
[1 1]

[10 1]

? simplify(((x+i+1)^2-x^2-2*x*(i+1))^2)
%365 = -4
? sin(pi/6)
%366 = 0.4999999999999999999999999999
? sinh(1)
%367 = 1.175201193643801456882381850
? size([1.3*10^5,2*i*pi*exp(4*pi)])
%368 = 6
? smallbase(x^3+4*x+12)
%369 = [1, x, 1/2*x^2]
? smalldiscf(x^3+4*x+12)
%370 = -1036
? smallfact(100!+1)
%371 = 
[101 1]

[14303 1]

[149239 1]

[432885273849892962613071800918658949059679308685024481795740765527568493010727023757461397498800981521440877813288657839195622497225621499427628453 1]

? smallinitell([0,0,0,-17,0])
%372 = [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
? smallpolred(x^4+576)
%373 = [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]~
? smallpolred2(x^4+576)
%374 = 
[1 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(1/hilbert(6))
%375 = [27720, 2520, 2520, 840, 210, 6]
? solve(x=1,4,sin(x))
%376 = 3.141592653589793238462643383
? sort(vector(17,x,5*x%17))
%377 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
? sqr(1+o(2))
%378 = 1 + O(2^3)
? sqred(hilbert(5))
%379 = 
[1 1/2 1/3 1/4 1/5]

[0 1/12 1 9/10 4/5]

[0 0 1/180 3/2 12/7]

[0 0 0 1/2800 2]

[0 0 0 0 1/44100]

? sqrt(13+o(127^12))
%380 = 34 + 125*127 + 83*127^2  + 107*127^3  + 53*127^4  + 42*127^5  + 22*127^6  + 98*127^7  + 127^8  + 23*127^9  + 122*127^10  + 79*127^11  + O(127^12)
? srgcd(x^10-1,x^15-1)
%381 = x^5 - 1
? move(0,100,100);string(0,pi)
? move(0,200,200);string(0,"(0,0)")
? \\draw([0,10,10])
? postdraw([0,10,10])
? apol=0.3+legendre(10)
%382 = 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x^2 + 0.05390624999999999999999999999
? sturm(apol)
%383 = 4
? sturmpart(apol,0.91,1)
%384 = 1
? subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
%385 = [9, -24]
? subst(sin(x),x,y)
%386 = y - 1/6*y^3 + 1/120*y^5 - 1/5040*y^7 + 1/362880*y^9 - 1/39916800*y^11 + O(y^12)
? subst(sin(x),x,x+x^2)
%387 = x + x^2 - 1/6*x^3 - 1/2*x^4 - 59/120*x^5 - 1/8*x^6 + 419/5040*x^7 + 59/720*x^8 + 13609/362880*x^9 + 19/13440*x^10 - 273241/39916800*x^11 + O(x^12)
? sum(0,k=1,10,2^-k)
%388 = 1023/1024
? sum(0.,k=1,10,2^-k)
%389 = 0.9990234375000000000000000000
? \precision=28
   precision = 28 significant digits
? 4*sumalt(n=0,(-1)^n/(2*n+1))
%390 = 3.141592653589793238462643383
? suminf(n=1,2.^-n)
%391 = 1.000000000000000000000000000
? 6/pi^2*sumpos(n=1,n^-2)
%392 = 0.9999999999999999999999999996
? supplement([1,3;2,4;3,6])
%393 = 
[1 3 0]

[2 4 0]

[3 6 1]

? \\ T
? sqr(tan(pi/3))
%394 = 3.000000000000000000000000000
? tanh(1)
%395 = 0.7615941559557648881194582825
? taniyama(bcurve)
%396 = [x^-2 - x^2 + 3*x^6 - 2*x^10 + O(x^11), -x^-3 + 3*x - 3*x^5 + 8*x^9 + O(x^10)]
? taylor(y/(x-y),y)
%397 = (O(y^12)*x^11 + y*x^10 + y^2*x^9 + y^3*x^8 + y^4*x^7 + y^5*x^6 + y^6*x^5 + y^7*x^4 + y^8*x^3 + y^9*x^2 + y^10*x + y^11)/x^11
? tchebi(10)
%398 = 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
? teich(7+o(127^12))
%399 = 7 + 57*127 + 58*127^2  + 83*127^3  + 52*127^4  + 109*127^5  + 74*127^6  + 16*127^7  + 60*127^8  + 47*127^9  + 65*127^10  + 5*127^11  + O(127^12)
? texprint((x+y)^3/(x-y)^2)
{{x^{3} + {{3}y}x^{2} + {{3}y^{2}}x + {y^{3}}}\over{x^{2} - {{2}y}x + {y^{2}}}}
%400 = (x^3 + 3*y*x^2 + 3*y^2*x + y^3)/(x^2 - 2*y*x + y^2)
? theta(0.5,3)
%401 = 0.08080641825189469129987168321
? thetanullk(0.5,7)
%402 = -804.6303732024336942278373058
? torsell(tcurve)
%403 = [12, [6, 2], [[1, 2], [7/4, -11/8]]]
? trace(1+i)
%404 = 2
? trace(mod(x+5,x^3+x+1))
%405 = 15
? trans(vector(2,x,x))
%406 = [1, 2]~
? %*%~
%407 = 
[1 2]

[2 4]

? trunc(-2.7)
%408 = -2
? trunc(sin(x^2))
%409 = 1/120*x^10 - 1/6*x^6 + x^2
? tschirnhaus(x^5-x-1)
%410 = x^5 + 5*x^4 + 8*x^3 - 40*x^2 - 24*x + 1039
? type(mod(x,x^2+1))
%411 = 9
? \\ U
? unit(17)
%412 = 3 + 2*w
? n=33;until(n==1,print1(n," ");if(n%2,n=3*n+1,n=n/2));print(1)
33 100 50 25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
%413 = 1
? \\ V
? valuation(6^10000-1,5)
%414 = 5
? vec(sin(x))
%415 = [1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800]
? vecmax([-3,7,-2,11])
%416 = 11
? vecmin([-3,7,-2,11])
%417 = -3
? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
%418 = [[2, 5, 8], [3, 6, -6], [4, 8, 6], [1, 8, 5]]
? vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],[2,1])
%419 = [[2, 5, 8], [3, 6, -6], [1, 8, 5], [4, 8, 6]]
? \\ W
? wf(i)
%420 = 1.189207115002721066717499970 + 2.499498970806598663000000000 E-30*i
? wf2(i)
%421 = 1.090507732665257659207010655 +  0.E-28*i
? m=5; while(m<20, print1(m, " ");m=m+1); print()
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 
? \\ Z
? zell(acurve, apoint)
%422 = 0.7249122149096230677887873983 +  0.E-48*i
? zeta(3)
%423 = 1.202056903159594285399738161
? zeta(0.5+14.1347251*i)
%424 = 0.000000005204309745346847939880542938 - 0.00000003269063986978698217656162947*i
? getstack()
%425 = 102288
? gettime()
%426 = 51120
? 
? 