             GP/PARI CALCULATOR Version 1.35.01
                     (Sparc version)

    Authors: C. Batut, D. Bernardi, H. Cohen and M. Olivier

Type \d, \c, \t, or ?command for help, \q to exit, # for timing

\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=20
   precision = 20 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)
? \\ A
? abs(-0.01)
%4 = 0.010000000000000000000
? acos(0.5)
%5 = 1.0471975511965977461
? acosh(3)
%6 = 1.7627471740390860504
? acurve=initell([0, 0, 1, -1, 0])
%7 = [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.83756543528332303544, 0.26959443640544455826, -1.1071598716887675937]~, 2.9934586462319596298, 2.4513893819867900608*i, -0.47131927795681147588, -1.4354565186686843187*i, 7.3381327407895767390]
? 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 = 1.4567910310469068691
? 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
? anell(acurve, 100)
%15 = [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)
%16 = 66
? apell2(acurve,10007)
%17 = 66
? apol=x^3+5*x+1
%18 = x^3 + 5*x + 1
? apprpadic(apol,1+O(7^8))
%19 = [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))
%20 = [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)
%21 = 3.1415926535897932384
? 3 * asin(sqrt(3)/2)
%22 = 3.1415926535897932384
? asinh(0.5)
%23 = 0.48121182505960344749
? assmat(x^5-12*x^3+0.0005)
%24 = [0, 0, 0, 0, -0.00050000000000000000000; 1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 0, 12; 0, 0, 0, 1, 0]
? 3 * atan(sqrt(3))
%25 = 3.1415926535897932384
? atanh(0.5)
%26 = 0.54930614433405484569
? \\ B
? base(x^3+4*x+5)
%27 = [1, x, 1/7*x^2 - 1/7*x - 2/7]
? bernreal(12)
%28 = -0.25311355311355311355
? bernvec(6)
%29 = [1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
? bezout(123456789,987654321)
%30 = [-8, 1, 9]
? bigomega(12345678987654321)
%31 = 8
? bin(1.1,5)
%32 = -0.0045457500000000000000
? binary(65537)
%33 = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
? bittest(10^100,100)
%34 = 1
? boundcf(pi,5)
%35 = [3, 7, 15, 1, 292]
? boundfact(40!+1,100000)
%36 = [41, 1; 59, 1; 277, 1; 1217669507565553887239873369513188900554127, 1]
? \\ C
? ceil(-2.5)
%37 = -2
? cf(pi)
%38 = [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]
? cf2([1,3,5,7,9],(e-1)/(e+1))
%39 = [1, -3/2*e - 3/2]
? changevar(x + y, [z, t])
%40 = y + z
? char([1, 2; 3, 4], z)
%41 = z^2 - 5*z - 2
? char(mod(x^2+x+1,x^3+5*x+1),z)
%42 = z^3 + 7*z^2 + 16*z - 19
? char2([1, 2; 3, 4], z)
%43 = z^2 - 5*z - 2
? acurve = chell(acurve, [-1, 1, 2, 3])
%44 = [-4, -1, -7, -12, -12, 12, 4, 1, -1, 48, -216, 37, 110592/37, [-0.16243456471667696455, -0.73040556359455544173, -2.1071598716887675937]~, -2.9934586462319596298, -2.4513893819867900608*i, 0.47131927795681147588, 1.4354565186686843187*i, 7.3381327407895767390]
? chinese(mod(7, 15), mod(13, 21))
%45 = mod(97, 105)
? apoint = chptell(apoint, [-1, 1, 2, 3])
%46 = [1, 3]
? isoncurve(acurve, apoint)
%47 = 1
? classno(-12391)
%48 = 63
? classno(1345)
%49 = 6
? classno2(-12391)
%50 = 63
? classno2(1345)
%51 = 6
? coeff(sin(x),7)
%52 = -1/5040
? compo(1+o(7^4), 3)
%53 = 1
? compose(qfi(2, 1, 3), qfi(2, 1, 3))
%54 = qfi(2, -1, 3)
? concat([1, 2], [3, 4])
%55 = [1, 2, 3, 4]
? conj(1+i)
%56 = 1 - i
? %_
%57 = 1 + i
? content([123, 456, 789, 234])
%58 = 3
? convol(sin(x), x * cos(x))
%59 = 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)
%60 = 0.54030230586813971740
? cosh(1)
%61 = 1.5430806348152437784
? cvtoi(1.7)
%62 = 1
? \\ D
? denom(12345/54321)
%63 = 18107
? deriv((x + y)^5, y)
%64 = 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
? ((x+y)^5)'
%65 = 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])
%66 = -30
? det2([1, 2, 3; 1, 5, 6; 9, 8, 7])
%67 = -30
? detr([1, 2, 3; 1, 5, 6; 9, 8, 7])
%68 = -30
? dilog(0.5)
%69 = 0.58224052646501250590
? disc(x^3+4*x+5)
%70 = -931
? discf(x^3+4*x+5)
%71 = -19
? divisors(8!)
%72 = [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)
%73 = [2, 99]~
? divres(x^7 - 1, x^5 + 1)
%74 = [x^2, -x^2 - 1]~
? divsum(8!,x,x)
%75 = 159120
? \\ E
? eigen([1, 2, 3; 4, 5, 6; 7, 8, 9])
%76 = [-1.2833494518006402718 +  0.E-29*i, 1, 0.28334945180064027179 +  0.E-30*i; -0.14167472590032013589 +  0.E-29*i, -2, 0.64167472590032013589 +  0.E-29*i; 1, 1, 1]
? eint1(2)
%77 = 0.048900510708061119567
? erfc(2)
%78 = 0.0046777349810472658379
? eta(q)
%79 = 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^16)
? euler
%80 = 0.57721566490153286060
? z = y; y = x; eval(z)
%81 = x
? exp(1)
%82 = 2.7182818284590452353
? extract([1,2,3,4,5,6,7,8,9,10], 1000)
%83 = [4, 6, 7, 8, 9, 10]
? \\ F
? fact(10)
%84 = 3628800
? 10!
%85 = 3628800
? lift(lift(factfq(x^3+x^2+x-1,3,t^3+t^2+t-1)))
%86 = [x + (2*t^2 + 2), 1; x + (t^2 + t + 2), 1; x + 2*t, 1]
? factmod(x^11+1, 7)
%87 = [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)
%88 = [661, 1; 537913, 1; 1000357, 1]
? p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
%89 = x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 3853890514072057
? fa=[11699, 6; 2392997, 2; 4987333019653, 2]
%90 = [11699, 6; 2392997, 2; 4987333019653, 2]
? factoredbase(p,fa)
%91 = [1, x, x^2, 1/11699*x^3 + 1847/11699*x^2 - 132/11699*x - 2641/11699, 1/139623738889203638909659*x^4 - 1552451622081122020/139623738889203638909659*x^3 + 418509858130821123141/139623738889203638909659*x^2 - 68109137985075994073134/139623738889203638909659*x - 13185339461968406/58346808996920447]
? factoreddiscf(p,fa)
%92 = 136866601
? \precision=40
   precision = 40 significant digits
? factoredpolred(p,fa)
%93 = [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]~
? \precision=20
   precision = 20 significant digits
? factorpadic(apol,7,8)
%94 = [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)
%95 = [x^2 + x + 1, 1; x - 1, 1; x^12 + x^9 + x^6 + x^3 + 1, 1]
? factpol(x^15-1, 0)
%96 = [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)
%97 = [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)
%98 = 354224848179261915075
? floor(-1/2)
%99 = -1
? floor(-2.5)
%100 = -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
0.25881904510252076234
0.50000000000000000000
0.70710678118654752440
0.86602540378443864676
0.96592582628906828675
1.0000000000000000000
0.96592582628906828675
0.86602540378443864676
0.70710678118654752440
0.50000000000000000000
0.25881904510252076234
3.0292258760486853327 E-28
? frac(-2.7)
%101 = 0.30000000000000000000
? \\ G
? gamh(10)
%102 = 1133278.3889487855673
? gamma(10.5)
%103 = 1133278.3889487855673
? gauss(hilbert(10),[1, 2, 3, 4, 5, 6, 7, 8, 9, 0])
%104 = [9236800, -831303990, 18288515520, -170691240720, 832112321040, -2329894066500, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
? gcd(12345678, 87654321)
%105 = 9
? globalred(acurve)
%106 = [37, [1, -1, 2, 2]]
? \\ H
? hclassno(2000003)
%107 = 357
? hell(acurve, apoint)
%108 = 0.40889126591975072188
? hell2(acurve, apoint)
%109 = 0.40889126591975072188
? hell3(acurve, apoint)
%110 = 0.40889126591975072188
? hermite(1/hilbert(7))
%111 = [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))
%112 = [1, 90281/88200, 915853/700700, 29935956703/21628787180, 73281964333/67022907315, 11440600099/20229949194, 1/7; 1/2, 3/4, 638689/600600, 1808070083/1544913370, 9615740595/10213014448, 947649229/1926661828, 1/8; 2/3, 7/72, 514799/2702700, 6529030447/27808440660, 3435875624/17234461881, 1240595855/11559970968, 1/36; 1/2, 19/15, 154337/20270250, 1472086718/104281652475, 118126024613/8272541702880, 20924759/2477136636, 1/432; 2/5, 29/22, 278052/154337, 9280094859/28822090578490, 663200582666/1250387460538755, 5936095714453/15096495101669520, 24973/203724840; 1/3, 356/275, 19875534/8488535, 16172199/7014433, 816909908099/92992290888714210, 685635669739/62374339874600880, 612859/138885773400; 2/7, 18673/15015, 414752084/154491337, 13649262385/3829880418, 1344823650/481665457, 1620334023/11654712086255264, 28309/293445416880]
? hilb(2/3, 3/4, 5)
%113 = 1
? hilbert(5)
%114 = [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))
%115 = 1
? hvector(10,x,1/x)
%116 = [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
? hyperu(1,1,1)
%117 = 0.59634736232319407434
? \\ I
? i^2
%118 = -1
? idmat(5)
%119 = [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)
%120 = 3
? image([1,3,5;2,4,6;3,5,7])
%121 = [1, 3; 2, 4; 3, 5]
? incgam(2, 1)
%122 = 0.73575888234288464319
? incgam1(2, 1)
%123 = -0.26424111765711535680
? incgam2(2, 1)
%124 = 0.73575888234288464319
? incgam3(2, 1)
%125 = 0.26424111765711535680
? indsort([8, 7, 6, 5])
%126 = [4, 3, 2, 1]
? integ(sin(x), x)
%127 = 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)
? \precision=9
   precision = 9 significant digits
? intgen(x=0,pi,sin(x))
%128 = 1.99999999
? sqr(2*intgen(x=0,4,exp(-x^2)))
%129 = 3.14159267
? 4*intinf(x=1,10000,1/(1+x^2))
%130 = 3.14119264
? intnum(x = -0.999, 0.999, 1/sqrt(1 - x^2))
%131 = 3.05305351
? 2 * intopen(x = 0, 100, sin(x)/x)
%132 = 3.12446099
? isfund(12345)
%133 = 1
? isprime(12345678901234567)
%134 = 0
? ispsp(73!+1)
%135 = 1
? isqrt(10!^2+1)
%136 = 3628800
? issqfree(123456789876543219)
%137 = 0
? issquare(12345678987654321)
%138 = 1
? \\ J
? jacobi(hilbert(6))
%139 = [[1.61889985, 0.242360870, 0.0000125707917, 0.000000108272154, 0.0163215213, 0.000615748250]~, [0.748719219, -0.614544828, 0.0111443277, -0.00124818737, 0.240325368, -0.0622265874; 0.440717503, 0.211082482, -0.179732820, 0.0356065323, -0.697651375, 0.490839195; 0.320696870, 0.365893607, 0.604212397, -0.240678704, -0.231389375, -0.535476875; 0.254311386, 0.394706776, -0.443575072, 0.625460110, 0.132863161, -0.417037727; 0.211530840, 0.388190433, -0.441536214, -0.689807474, 0.362714923, 0.0470339851; 0.181442976, 0.370695907, 0.459114608, 0.271605738, 0.502762865, 0.540681598]]
? jbesselh(1,1)
%140 = 0.240297839
? jell(i)
%141 = 1728.00000 + 0.000000000*i
? \\ K
? kbessel(1 + i, 1)
%142 = 0.325459853 + 0.289428196*i
? kbessel2(1 + i, 1)
%143 = 0.325459853 + 0.289428196*i
? ker(matrix(4,4,x,y,x/y))
%144 = [-1/2, -1/3, -1/4; 1, 0, 0; 0, 1, 0; 0, 0, 1]
? keri(matrix(4,4,x,y,x+y))
%145 = [-1, -2; 2, 3; -1, 0; 0, -1]
? kerr(matrix(4,4,x,y,sin(x+y)))
%146 = [1.00000000, 1.08060461; -1.08060461, -0.167706326; 1, 0; 0, 1]
? f(u)=u+1;
? print(f(5)); kill(f);
6
? f=12
%147 = 12
? kro(5,7)
%148 = -1
? kro(3,18)
%149 = 0
? \\ L
? laplace(x*exp(x*y)/(exp(x)-1))
%150 = 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)
%151 = -105
? length(divisors(1000))
%152 = 16
? legendre(10)
%153 = 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x^2 - 63/256
? lift(chinese(mod(7,15),mod(4,21)))
%154 = 67
? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
%155 = [-3, -3, 9, -2, 6]
? lll(hilbert(7))
%156 = [1, -4, -7, 4, -12, 1, 5; -42, 161, 288, -147, 462, -28, -202; 420, -1560, -2835, 1344, -4340, 210, 1970; -1680, 6090, 11200, -5040, 16560, -672, -7735; 3150, -11200, -20790, 9000, -29925, 1050, 14294; -2772, 9702, 18144, -7623, 25564, -792, -12432; 924, -3192, -6006, 2464, -8316, 231, 4104]
? lllgram(hilbert(7))
%157 = [0, 0, 0, 0, 0, -1, 0; 0, 0, 0, 0, 1, 23, -3; 1, 0, 1, -1, -10, -166, 46; -6, -1, -7, 9, 36, 534, -234; 13, 4, 16, -26, -60, -852, 522; -12, -5, -15, 30, 47, 660, -528; 4, 2, 5, -12, -14, -198, 198]
? lllrat(hilbert(7))
%158 = [1, -4, -7, 3, -12, 1, 5; -42, 161, 288, -105, 462, -28, -202; 420, -1560, -2835, 924, -4340, 210, 1970; -1680, 6090, 11200, -3360, 16560, -672, -7735; 3150, -11200, -20790, 5850, -29925, 1050, 14294; -2772, 9702, 18144, -4851, 25564, -792, -12432; 924, -3192, -6006, 1540, -8316, 231, 4104]
? \precision=100
   precision = 100 significant digits
? ln(2)
%159 = 0.6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875
? lngamma(10^50*i)
%160 = -157079632679489661923132169163975144209858469968811.9367375388760847494897709411534189519074068479349 + 11412925464970228420089957273421821038005507443143864.09476847610738955343272591658130426497615564164*i
? \precision=2000
   precision = 2000 significant digits
? log(2)
%161 = 0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335011536449795523912047517268157493206515552473413952588295045300709532636664265410423915781495204374043038550080194417064167151864471283996817178454695702627163106454615025720740248163777338963855069526066834113727387372292895649354702576265209885969320196505855476470330679365443254763274495125040606943814710468994650622016772042452452961268794654619316517468139267250410380254625965686914419287160829380317271436778265487756648508567407764845146443994046142260319309673540257444607030809608504748663852313818167675143866747664789088143714198549423151997354880375165861275352916610007105355824987941472950929311389715599820565439287170007218085761025236889213244971389320378439353088774825970171559107088236836275898425891853530243634214367061189236789192372314672321720534016492568727477823445353476481149418642386776774406069562657379600867076257199184734022651462837904883062033061144630073719489002743643965002580936519443041191150608094879306786515887090060520346842973619384128965255653968602219412292420757432175748909770675268711581705113700915894266547859596489065305846025866838294002283300538207400567705304678700184162404418833232798386349001563121889560650553151272199398332030751408426091479001265168243443893572472788205486271552741877243002489794540196187233980860831664811490930667519339312890431641370681397776498176974868903887789991296503619270710889264105230924783917373501229842420499568935992206602204654941510613918788574424557751020683703086661948089641218680779020818158858000168811597305618667619918739520076671921459223672060253959543654165531129517598994005600036651356756905124592682574394648316833262490180382424082423145230614096380570070255138770268178516306902551370323405380214501901537402950994226299577964742713815736380172987394070424217997226696297993931270693
? logagm(2)
%162 = 0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335011536449795523912047517268157493206515552473413952588295045300709532636664265410423915781495204374043038550080194417064167151864471283996817178454695702627163106454615025720740248163777338963855069526066834113727387372292895649354702576265209885969320196505855476470330679365443254763274495125040606943814710468994650622016772042452452961268794654619316517468139267250410380254625965686914419287160829380317271436778265487756648508567407764845146443994046142260319309673540257444607030809608504748663852313818167675143866747664789088143714198549423151997354880375165861275352916610007105355824987941472950929311389715599820565439287170007218085761025236889213244971389320378439353088774825970171559107088236836275898425891853530243634214367061189236789192372314672321720534016492568727477823445353476481149418642386776774406069562657379600867076257199184734022651462837904883062033061144630073719489002743643965002580936519443041191150608094879306786515887090060520346842973619384128965255653968602219412292420757432175748909770675268711581705113700915894266547859596489065305846025866838294002283300538207400567705304678700184162404418833232798386349001563121889560650553151272199398332030751408426091479001265168243443893572472788205486271552741877243002489794540196187233980860831664811490930667519339312890431641370681397776498176974868903887789991296503619270710889264105230924783917373501229842420499568935992206602204654941510613918788574424557751020683703086661948089641218680779020818158858000168811597305618667619918739520076671921459223672060253959543654165531129517598994005600036651356756905124592682574394648316833262490180382424082423145230614096380570070255138770268178516306902551370323405380214501901537402950994226299577964742713815736380172987394070424217997226696297993931270693
? \precision=9
   precision = 9 significant digits
? bcurve=initell([0,0,0,-3,0])
%163 = [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)
%164 = [6, 2, [1, 1, 1, 0]]
? \\ M
? mat(concat(vector(4,x,x)~,vector(4,x,10+x)~))
%165 = [1; 2; 3; 4; 11; 12; 13; 14]
? matell(initell([0,0,0,-17,0]),[[-1,4],[-4,2]])
%166 = [0.586091548, 0.223848697; 0.223848697, 0.877513001]
? matextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
%167 = [6, 9, 12; 9, 12, 15; 12, 15, 18; 15, 18, 21; 18, 21, 24]
? matinvr(1.*hilbert(7))
%168 = [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]
? matrix(5,5,x,y,gcd(x,y))
%169 = [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]
? max(2,3)
%170 = 3
? min(2,3)
%171 = 2
? minim([2,1;1,2])
%172 = [6, 2]
? mod(-12,7)
%173 = mod(2, 7)
? modp(-12,7)
%174 = mod(2, 7)
? mu(3*5*7*11*13)
%175 = -1
? \\ N
? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
%176 = [2, 2/3, 2/3, 2/3]
? nextprime(100000000000000000000000)
%177 = 100000000000000000000117
? norm(1+i)
%178 = 2
? norm(mod(x+5,x^3+x+1))
%179 = 129
? norml2(vector(10,x,x))
%180 = 385
? numdiv(2^99*3^49)
%181 = 5000
? numer((x+1)/(x-1))
%182 = x + 1
? \\ O
? 1/(1+x)+o(x^20)
%183 = 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!)
%184 = 25
? ordell(acurve, 1)
%185 = [8, 3]
? order(mod(33,2^16+1))
%186 = 2048
? ordred(x^3-12*x+45*x-1)
%187 = [x - 1, x^3 + 33*x - 1, x^3 - 363*x - 2663]~
? \\ P
? pascal(8)
%188 = [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]
? pf(-44,3)
%189 = qfi(3, 2, 4)
? phi(257^2)
%190 = 65792
? pi
%191 = 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)])
? pnqn([2,6,10,14,18,22,26])
%192 = [19318376, 741721; 8927353, 342762]
? pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
%193 = [34, 21; 21, 13]
? polint([0,2,3],[0,4,9],5)
%194 = 25
? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
%195 = [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]~
? polredreal(x^4-28*x^3-458*x^2+9156*x-25321)
%196 = [x - 1, x^4 - 8*x^2 + 6, x^2 - 10, x^4 - 32*x^2 + 216]~
? polsym(x^17-1,17)
%197 = [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
? poly(sin(x),x)
%198 = -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)
%199 = 0.508400578
? polylogd(5,0.5)
%200 = 1.03445942
? polylogp(5,0.5)
%201 = 0.949569346
? powell(acurve,10,apoint)
%202 = [-28919032218753260057646013785951999/292736325329248127651484680640160000, 478051489392386968218136375373985436596569736643531551/158385319626308443937475969221994173751192384064000000]
? pprint((x-12*y)/(y+13*x));
(-(11 /14))
? pprint([1,2;3,4])

|1 2 |

|3 4 |


%204 = [1, 2; 3, 4]
? pprint1(x+y);pprint(x+y);
(2 x )(2 x )
? \precision=100
   precision = 100 significant digits
? pi
%206 = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068
? prec(pi,20)
%207 = 3.141592653589793238462643383254089766000000000000000000000000000000000000000000000000000000000000000
? \precision=20
   precision = 20 significant digits
? prime(100)
%208 = 541
? primes(100)
%209 = [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
? print((x-12*y)/(y+13*x));
-11/14
? print([1,2;3,4])
[1, 2; 3, 4]
%211 = [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!)
%213 = 3335784368058308553334783/905932868585678438400000
? prod(1.,k=1,10,1+1/k!)
%214 = 3.6821540356142043935
? pi^2/6*prodeuler(p=2,10000,1-p^-2)
%215 = 1.0000098157493066238
? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
%216 = 0.33333333333333333333
? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
%217 = 0.33333333333333333333
? psi(1)
%218 = -0.57721566490153286060
? \\ Q
? quadgen(-11)
%219 = w
? quadpoly(-11)
%220 = x^2 - x + 3
? \\ R
? rank(matrix(5,5,x,y,x+y))
%221 = 2
? real(5-7*i)
%222 = 5
? recip(3*x^7-5*x^3+6*x-9)
%223 = -9*x^7 + 6*x^6 - 5*x^4 + 3
? redcomp(qfi(3,10,12))
%224 = qfi(3, -2, 4)
? redreal(qfr(3,10,-20,01.5))
%225 = qfr(3, 16, -7, 1.5000000000000000000)
? regula(17)
%226 = 2.0947125472611012942
? kill(y);print(x+y);reorder([x, y]); print(x+y);
x + y
x + y
? resultant(x^3-1,x^3+1)
%228 = 8
? reverse(tan(x))
%229 = 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,-20,01.5))
%230 = qfr(-20, -10, 3, 2.1074451073987839947)
? rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%231 = x^17 - 1
? rootmod(x^16-1,41)
%232 = [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)
%233 = [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)
%234 = [1.0000000000000000000 +  0.E-28*i, -0.80901699437494742410 + 0.58778525229247312916*i, -0.80901699437494742410 - 0.58778525229247312916*i, 0.30901699437494742410 + 0.95105651629515357211*i, 0.30901699437494742410 - 0.95105651629515357211*i]~
? round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%235 = x^17 - 1
? \\ S
? q*series(anell(acurve,100),q)
%236 = 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)
? sigma(100)
%237 = 217
? sigmak(2,100)
%238 = 13671
? sign(-1)
%239 = -1
? sign(0)
%240 = 0
? sign(0.)
%241 = 0
? signat(hilbert(5)-0.11*idmat(5))
%242 = [2, 3]
? sin(pi/6)
%243 = 0.50000000000000000000
? sinh(1)
%244 = 1.1752011936438014568
? smallbase(x^3+4*x+5)
%245 = [1, x, 1/7*x^2 - 1/7*x - 2/7]
? smalldiscf(x^3+4*x+5)
%246 = -19
? smallfact(100!+1)
%247 = [101, 1; 14303, 1; 149239, 1; 432885273849892962613071800918658949059679308685024481795740765527568493010727023757461397498800981521440877813288657839195622497225621499427628453, 1]
? smallinitell([0,0,0,-17,0])
%248 = [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
? smallpolred(x^4+576)
%249 = [x - 1, x^2 + 1, x^4 - x^2 + 1, x^2 - x + 1]~
? smith(1/hilbert(6))
%250 = [27720, 2520, 2520, 840, 210, 6]
? solve(x=1,4,sin(x))
%251 = 3.1415926535897932384
? sort(vector(17,x,5*x%17))
%252 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
? sqr(1+o(2))
%253 = 1 + O(2^3)
? sqred(hilbert(5))
%254 = [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))
%255 = 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)
%256 = x^5 - 1
? apol=0.3+legendre(10)
%257 = 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x^2 + 0.053906250000000000000
? sturm(apol)
%258 = 4
? sturmpart(apol,0.91,1)
%259 = 1
? subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
%260 = [9, -24]
? subst(sin(x),x,y)
%261 = y - 1/6*y^3 + 1/120*y^5 - 1/5040*y^7 + 1/362880*y^9 - 1/39916800*y^11 + 1/6227020800*y^13 + O(y^15)
? subst(sin(x),x,x+x^2)
%262 = 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 - 14281/3628800*x^12 - 6495059/6227020800*x^13 + 69301/479001600*x^14 + O(x^15)
? sum(0,k=1,10,2^-k)
%263 = 1023/1024
? sum(0.,k=1,10,2^-k)
%264 = 0.99902343750000000000
? \precision=20
   precision = 20 significant digits
? 4*sumalt(n=0,(-1)^n/(2*n+1))
%265 = 3.1415926535897932384
? suminf(n=1,2^-n)
%266 = 1.0000000000000000000
? 6/pi^2*sumpos(n=1,n^-2)
%267 = 1.0000000000000000000
? supplement([1,3;2,4;3,6])
%268 = [1, 3, 0; 2, 4, 0; 3, 6, 1]
? \\ T
? sqr(tan(pi/3))
%269 = 3.0000000000000000000
? tanh(1)
%270 = 0.76159415595576488812
? taylor(y/(x-y),y)
%271 = (O(y^16)*x^15 + y*x^14 + y^2*x^13 + y^3*x^12 + y^4*x^11 + y^5*x^10 + y^6*x^9 + y^7*x^8 + y^8*x^7 + y^9*x^6 + y^10*x^5 + y^11*x^4 + y^12*x^3 + y^13*x^2 + y^14*x + y^15)/x^15
? tchebi(10)
%272 = 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
? teich(7+o(127^12))
%273 = 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}}}}
%274 = (x^3 + 3*y*x^2 + 3*y^2*x + y^3)/(x^2 - 2*y*x + y^2)
? theta(0.5,3)
%275 = 0.080806418251894691300
? thetanullk(0.5,7)
%276 = -804.63037320243369423
? trace(1+i)
%277 = 2
? trace(mod(x+5,x^3+x+1))
%278 = 15
? trans(vector(2,x,x))
%279 = [1, 2]~
? %*%~
%280 = [1, 2; 2, 4]
? trunc(-2.7)
%281 = -2
? trunc(sin(x^2))
%282 = -1/5040*x^14 + 1/120*x^10 - 1/6*x^6 + x^2
? type(mod(x,x^2+1))
%283 = 9
? \\ U
? unit(17)
%284 = 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
%285 = 1
? \\ V
? valuation(6^10000-1,5)
%286 = 5
? vec(sin(x))
%287 = [1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800, 0, 1/6227020800, 0, -1/1307674368000]
? \\ W
? wf(i)
%288 = 1.1892071150027210667 + 2.4994989708065986630 E-30*i
? wf2(i)
%289 = 1.0905077326652576592 +  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)
%290 = -3.7183708611415826976 +  0.E-48*i
? zeta(0.5+14.1347251*i)
%291 = 0.0000000052043097453468479398 - 0.000000032690639869786982176*i
? 
? 