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1992-05-20
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44KB
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1,466 lines
GP/PARI CALCULATOR Version 1.37
(Sparc version)
Copyright 1989,1992 by 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)
? initrect(0,500,500)
? \\ 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
? akell(acurve,1000000007)
%15 = 43800
? anell(acurve, 100)
%16 = [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)
%17 = 66
? apell2(acurve,10007)
%18 = 66
? apol=x^3+5*x+1
%19 = x^3 + 5*x + 1
? apprpadic(apol,1+O(7^8))
%20 = [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))
%21 = [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)
%22 = 3.1415926535897932384
? 3 * asin(sqrt(3)/2)
%23 = 3.1415926535897932384
? asinh(0.5)
%24 = 0.48121182505960344749
? assmat(x^5-12*x^3+0.0005)
%25 =
|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))
%26 = 3.1415926535897932384
? atanh(0.5)
%27 = 0.54930614433405484569
? \\ B
? base(x^3+4*x+5)
%28 = [1, x, 1/7*x^2 - 1/7*x - 2/7]
? bernreal(12)
%29 = -0.25311355311355311355
? bernvec(6)
%30 = [1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730]
? bezout(123456789,987654321)
%31 = [-8, 1, 9]
? bigomega(12345678987654321)
%32 = 8
? bin(1.1,5)
%33 = -0.0045457500000000000000
? binary(65537)
%34 = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
? bittest(10^100,100)
%35 = 1
? boundcf(pi,5)
%36 = [3, 7, 15, 1, 292]
? boundfact(40!+1,100000)
%37 =
|41 1 |
|59 1 |
|277 1 |
|1217669507565553887239873369513188900554127 1 |
? box(0,0,0,500,500)
? \\buchimag(1-10^15,0.8,20)
? \\buchreal(10^15-3,0,0.8,20)
? \\ C
? ceil(-2.5)
%38 = -2
? centerlift(mod(456,555))
%39 = -99
? cf(pi)
%40 = [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],(exp(1)-1)/(exp(1)+1))
%41 = [0, 6, 10, 42, 30]
? changevar(x + y, [z, t])
%42 = y + z
? char([1, 2; 3, 4], z)
%43 = x^2 - 5*x - 2
? char(mod(x^2+x+1,x^3+5*x+1),z)
%44 = z^3 + 7*z^2 + 16*z - 19
? char1([1, 2; 3, 4], z)
%45 = z^2 - 5*z - 2
? char2(mod(1,8191)*[1, 2; 3, 4], z)
%46 = z^2 + mod(8186, 8191)*z + mod(8189, 8191)
? acurve = chell(acurve, [-1, 1, 2, 3])
%47 = [-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))
%48 = mod(97, 105)
? apoint = chptell(apoint, [-1, 1, 2, 3])
%49 = [1, 3]
? isoncurve(acurve, apoint)
%50 = 1
? classno(-12391)
%51 = 63
? classno(1345)
%52 = 6
? classno2(-12391)
%53 = 63
? classno2(1345)
%54 = 6
? coeff(sin(x),7)
%55 = -1/5040
? compo(1+o(7^4), 3)
%56 = 1
? compose(qfi(2, 1, 3), qfi(2, 1, 3))
%57 = qfi(2, -1, 3)
? comprealraw(qfr(5,3,-1,0.),qfr(7,1,-1,0.))
%58 = qfr(35, 43, 13, 0.E-28)
? concat([1, 2], [3, 4])
%59 = [1, 2, 3, 4]
? conj(1+i)
%60 = 1 - i
? %_
%61 = 1 + i
? content([123, 456, 789, 234])
%62 = 3
? convol(sin(x), x * cos(x))
%63 = 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)
%64 = 0.54030230586813971740
? cosh(1)
%65 = 1.5430806348152437784
? move(0,200,150)
? cursor(0)
%66 = [200, 150]
? cvtoi(1.7)
%67 = 1
? cyclo(105)
%68 = 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)
%69 = 18107
? deriv((x + y)^5, y)
%70 = 5*x^4 + 20*y*x^3 + 30*y^2*x^2 + 20*y^3*x + 5*y^4
? ((x+y)^5)'
%71 = 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])
%72 = -30
? det2([1, 2, 3; 1, 5, 6; 9, 8, 7])
%73 = -30
? detr([1, 2, 3; 1, 5, 6; 9, 8, 7])
%74 = -30
? dilog(0.5)
%75 = 0.58224052646501250590
? disc(x^3+4*x+5)
%76 = -931
? discf(x^3+4*x+5)
%77 = -19
? divisors(8!)
%78 = [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)
%79 = [2, 99]~
? divres(x^7 - 1, x^5 + 1)
%80 = [x^2, -x^2 - 1]~
? divsum(8!,x,x)
%81 = 159120
? \\ draw([0,0,0])
? postdraw([0,0,0])
? \\ E
? eigen([1, 2, 3; 4, 5, 6; 7, 8, 9])
%82 =
|-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)
%83 = 0.048900510708061119567
? erfc(2)
%84 = 0.0046777349810472658379
? eta(q)
%85 = 1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + O(q^16)
? euler
%86 = 0.57721566490153286060
? z = y; y = x; eval(z)
%87 = x
? exp(1)
%88 = 2.7182818284590452353
? extract([1,2,3,4,5,6,7,8,9,10], 1000)
%89 = [4, 6, 7, 8, 9, 10]
? \\ F
? 10!
%90 = 3628800
? fact(10)
%91 = 3628800.0000000000000
? lift(lift(factfq(x^3+x^2+x-1,3,t^3+t^2+t-1)))
%92 =
|x + (2*t^2 + 2) 1 |
|x + (t^2 + t + 2) 1 |
|x + 2*t 1 |
? factmod(x^11+1, 7)
%93 =
|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)
%94 =
|661 1 |
|537913 1 |
|1000357 1 |
? p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
%95 = x^5 + 3021*x^4 - 786303*x^3 - 6826636057*x^2 - 546603588746*x + 3853890514072057
? fa=[11699, 6; 2392997, 2; 4987333019653, 2]
%96 =
|11699 6 |
|2392997 2 |
|4987333019653 2 |
? factoredbase(p,fa)
%97 = [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)
%98 = 136866601
? \precision=40
precision = 40 significant digits
? factoredpolred(p,fa)
%99 = [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)
%100 =
|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=20
precision = 20 significant digits
? lift(factornf(y^3+y^2-2*y-1,x^3+x^2-2*x-1))
%101 =
|x - x 1 |
|x + (-x^2 + 2) 1 |
|x + (x^2 + x - 1) 1 |
? factorpadic(apol,7,8)
%102 =
|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)
%103 =
|x^2 + x + 1 1 |
|x - 1 1 |
|x^12 + x^9 + x^6 + x^3 + 1 1 |
? factpol(x^15-1, 0)
%104 =
|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)
%105 =
|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)
%106 = 354224848179261915075
? floor(-1/2)
%107 = -1
? floor(-2.5)
%108 = -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)
%109 = 0.30000000000000000000
? \\ G
? galois(x^6-3*x^2-1)
%110 = [12, 1, 1]
? galoisconj(x^6+108)
%111 = [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)
%112 = 1133278.3889487855673
? gamma(10.5)
%113 = 1133278.3889487855673
? gauss(hilbert(10),[1, 2, 3, 4, 5, 6, 7, 8, 9, 0])
%114 = [9236800, -831303990, 18288515520, -170691240720, 832112321040, -2329894066500, 3883123564320, -3803844432960, 2020775945760, -449057772020]~
? gcd(12345678, 87654321)
%115 = 9
? globalred(acurve)
%116 = [37, [1, -1, 2, 2]]
? k=4;goto(k%2);label(0);print("even");goto(3);label(1);print("odd");label(3);
even
? \\ H
? hclassno(2000003)
%117 = 357
? hell(acurve, apoint)
%118 = 0.40889126591975072188
? hell2(acurve, apoint)
%119 = 0.40889126591975072188
? hell3(acurve, apoint)
%120 = 0.40889126591975072188
? hermite(1/hilbert(7))
%121 =
|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))
%122 =
|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)
%123 = 1
? hilbert(5)
%124 =
|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))
%125 = 1
? hvector(10,x,1/x)
%126 = [1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
? hyperu(1,1,1)
%127 = 0.59634736232319407434
? \\ I
? i^2
%128 = -1
? idmat(5)
%129 =
|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)
%130 = 3
? image([1,3,5;2,4,6;3,5,7])
%131 =
|1 3 |
|2 4 |
|3 5 |
? incgam(2,1)
%132 = 0.73575888234288464319
? incgam1(2,1)
%133 = -0.26424111765711535680
? incgam2(2,1)
%134 = 0.73575888234288464319
? incgam3(2,1)
%135 = 0.26424111765711535680
? incgam4(4,1,6)
%136 = 5.8860710587430771455
? indexrank([1,1,1;1,1,1;1,1,2])
%137 = [[1, 3], [1, 3]]
? indsort([8, 7, 6, 5])
%138 = [4, 3, 2, 1]
? initalg(x^5-5*x^4+8*x^3-4*x^2-1)
%139 = [x^5 - x - 1, [1, 2], 2869, 1, 5.1967707381019243253, [1.1673039782614186842 + 0.E-28*i, -0.76488443360058472603 - 0.35247154603172624931*i, -0.76488443360058472603 + 0.35247154603172624931*i, 0.18123244446987538390 + 1.0839541013177106684*i, 0.18123244446987538390 - 1.0839541013177106684*i]~, [1, x, x^2, x^3, x^4]]
? initell([0,0,0,-1,0])
%140 = [0, 0, 0, -1, 0, 0, -2, 0, -1, 48, 0, 64, 1728, [1.0000000000000000000, 0.E-28, -1.0000000000000000000]~, 2.6220575542921198104, 2.6220575542921198104*i, -0.59907011736779610372, -1.7972103521033883111*i, 6.8751858180203728275]
? initell2([0,0,0,0,-1])
%141 = [0, 0, 0, 0, -1, 0, 0, -4, 0, 0, 864, -432, 0, [1.0000000000000000000, -0.50000000000000000000 + 0.86602540378443864676*i, -0.50000000000000000000 - 0.86602540378443864676*i]~, 2.4286506478875816118, 1.2143253239437908059 + 2.1032731579881813917*i, -0.74683420022218681310 + 0.E-29*i, -0.37341710011109340655 - 1.9403321694223429012*i, 5.1081157178325565351]
? initrect(1,700,700)
? integ(sin(x), x)
%142 = 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])
%143 =
|-1 |
|-1 |
|-1 |
? \precision=9
precision = 9 significant digits
? intgen(x=0,pi,sin(x))
%144 = 1.99999999
? sqr(2*intgen(x=0,4,exp(-x^2)))
%145 = 3.14159267
? 4*intinf(x=1,10000,1/(1+x^2))
%146 = 3.14119264
? intnum(x = -0.999, 0.999, 1/sqrt(1 - x^2))
%147 = 3.05305351
? 2 * intopen(x = 0, 100, sin(x)/x)
%148 = 3.12446099
? \precision=28
precision = 28 significant digits
? inverseimage([1,1;2,3;5,7],[2,2,6]~)
%149 = [4, -2]~
? isfund(12345)
%150 = 1
? isincl(x^2+1,x^4+1)
%151 = [x^2, -x^2]
? isisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
%152 = [x, x^2 - 2, -x^2 - x + 1]
? isprime(12345678901234567)
%153 = 0
? ispsp(73!+1)
%154 = 1
? isqrt(10!^2+1)
%155 = 3628800
? issqfree(123456789876543219)
%156 = 0
? issquare(12345678987654321)
%157 = 1
? \\ J
? jacobi(hilbert(6))
%158 = [[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)
%159 = 0.2402978391234270108958430447
? jell(i)
%160 = 1727.999999999999999999999999 + 0.E-26*i
? \\ K
? kbessel(1 + i, 1)
%161 = 0.3254597718658414108546463973 + 0.2894280370259921276345671592*i
? kbessel2(1 + i, 1)
%162 = 0.3254597718658414108546463973 + 0.2894280370259921276345671592*i
? x
%163 = x
? y
%164 = x
? ker(matrix(4,4,x,y,x/y))
%165 =
|-1/2 -1/3 -1/4 |
|1 0 0 |
|0 1 0 |
|0 0 1 |
? keri(matrix(4,4,x,y,x+y))
%166 =
|1 2 |
|-2 -3 |
|1 0 |
|0 1 |
? kerint(matrix(4,4,x,y,x*y))
%167 =
|-1 -1 -1 |
|-1 0 1 |
|1 -1 1 |
|0 1 -1 |
? kerint1(matrix(4,4,x,y,x*y))
%168 =
|-1 -1 -1 |
|-1 0 1 |
|1 -1 1 |
|0 1 -1 |
? kerint2(matrix(4,6,x,y,2520/(x+y)))
%169 =
|3 1 |
|-30 -15 |
|70 70 |
|0 -140 |
|-126 126 |
|84 -42 |
? kerr(matrix(4,4,x,y,sin(x+y)))
%170 =
|1.000000000000000000000000000 1.080604611736279434801873214 |
|-1.080604611736279434801873214 -0.1677063269057152260048635409 |
|1 0 |
|0 1 |
? f(u)=u+1;
? print(f(5)); kill(f);
6
? f=12
%171 = 12
? killrect(1)
? kro(5,7)
%172 = -1
? kro(3,18)
%173 = 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))
%174 = 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)
%175 = -105
? length(divisors(1000))
%176 = 16
? legendre(10)
%177 = 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])
%178 = -1
? lexsort([[1,5],[2,4],[1,5,1],[1,4,2]])
%179 = [[1, 4, 2], [1, 5], [1, 5, 1], [2, 4]]
? lift(chinese(mod(7,15),mod(4,21)))
%180 = 67
? lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
%181 = [-3, -3, 9, -2, 6]
? lindep2([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],40)
%182 = [3, 3, -9, 2, -6]
? line(0,0,900,900,0)
? lines(0,vector(5,k,50*k),vector(5,k,10*k*k))
? m=1/hilbert(7)
%183 =
|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))
%184 =
|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)
%185 =
|-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)
%186 =
|-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)
%187 =
|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)
%188 =
|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)
%189 =
|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)
%190 = [[-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)
%191 =
|-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)
%192 = [[-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)
%193 =
|-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)
%194 = 0.6931471805599453094172321214581765680755001343602552541206800094933936219696947156058633269964186875
? lngamma(10^50*i)
%195 = -157079632679489661923132169163975144209858469968811.9367375388760847494897709411534189519074068479349 + 11412925464970228420089957273421821038005507443143864.09476847610738955343272591658130426497615564164*i
? \precision=2000
precision = 2000 significant digits
? log(2)
%196 = 0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335011536449795523912047517268157493206515552473413952588295045300709532636664265410423915781495204374043038550080194417064167151864471283996817178454695702627163106454615025720740248163777338963855069526066834113727387372292895649354702576265209885969320196505855476470330679365443254763274495125040606943814710468994650622016772042452452961268794654619316517468139267250410380254625965686914419287160829380317271436778265487756648508567407764845146443994046142260319309673540257444607030809608504748663852313818167675143866747664789088143714198549423151997354880375165861275352916610007105355824987941472950929311389715599820565439287170007218085761025236889213244971389320378439353088774825970171559107088236836275898425891853530243634214367061189236789192372314672321720534016492568727477823445353476481149418642386776774406069562657379600867076257199184734022651462837904883062033061144630073719489002743643965002580936519443041191150608094879306786515887090060520346842973619384128965255653968602219412292420757432175748909770675268711581705113700915894266547859596489065305846025866838294002283300538207400567705304678700184162404418833232798386349001563121889560650553151272199398332030751408426091479001265168243443893572472788205486271552741877243002489794540196187233980860831664811490930667519339312890431641370681397776498176974868903887789991296503619270710889264105230924783917373501229842420499568935992206602204654941510613918788574424557751020683703086661948089641218680779020818158858000168811597305618667619918739520076671921459223672060253959543654165531129517598994005600036651356756905124592682574394648316833262490180382424082423145230614096380570070255138770268178516306902551370323405380214501901537402950994226299577964742713815736380172987394070424217997226696297993931270693
? logagm(2)
%197 = 0.69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641868754200148102057068573368552023575813055703267075163507596193072757082837143519030703862389167347112335011536449795523912047517268157493206515552473413952588295045300709532636664265410423915781495204374043038550080194417064167151864471283996817178454695702627163106454615025720740248163777338963855069526066834113727387372292895649354702576265209885969320196505855476470330679365443254763274495125040606943814710468994650622016772042452452961268794654619316517468139267250410380254625965686914419287160829380317271436778265487756648508567407764845146443994046142260319309673540257444607030809608504748663852313818167675143866747664789088143714198549423151997354880375165861275352916610007105355824987941472950929311389715599820565439287170007218085761025236889213244971389320378439353088774825970171559107088236836275898425891853530243634214367061189236789192372314672321720534016492568727477823445353476481149418642386776774406069562657379600867076257199184734022651462837904883062033061144630073719489002743643965002580936519443041191150608094879306786515887090060520346842973619384128965255653968602219412292420757432175748909770675268711581705113700915894266547859596489065305846025866838294002283300538207400567705304678700184162404418833232798386349001563121889560650553151272199398332030751408426091479001265168243443893572472788205486271552741877243002489794540196187233980860831664811490930667519339312890431641370681397776498176974868903887789991296503619270710889264105230924783917373501229842420499568935992206602204654941510613918788574424557751020683703086661948089641218680779020818158858000168811597305618667619918739520076671921459223672060253959543654165531129517598994005600036651356756905124592682574394648316833262490180382424082423145230614096380570070255138770268178516306902551370323405380214501901537402950994226299577964742713815736380172987394070424217997226696297993931270693
? \precision=9
precision = 9 significant digits
? bcurve=initell([0,0,0,-3,0])
%198 = [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)
%199 = [6, 2, [1, 1, 1, 0]]
? ccurve=initell([0,0,-1,-1,0])
%200 = [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)
%201 = 0.381575407
? lseriesell(ccurve,2,-37,1.2)-l
%202 = 0.000000000814907252
? \\ M
? mat(concat(vector(4,x,x)~,vector(4,x,10+x)~))
%203 =
|1 |
|2 |
|3 |
|4 |
|11 |
|12 |
|13 |
|14 |
? matell(initell([0,0,0,-17,0]),[[-1,4],[-4,2]])
%204 =
|1.17218309 0.447697394 |
|0.447697394 1.75502600 |
? matextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
%205 =
|6 9 12 |
|9 12 15 |
|12 15 18 |
|15 18 21 |
|18 21 24 |
? matinvr(1.*hilbert(7))
%206 =
|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])
%207 = [3, 2]
? matrix(5,5,x,y,gcd(x,y))
%208 =
|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)
%209 =
|1 1 |
|3 2 |
|5 3 |
? matrixqz2([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0])
%210 =
|19 12 2 |
|0 1 0 |
|0 0 1 |
? matrixqz3([1,3;3,5;5,7])
%211 =
|2 -1 |
|1 0 |
|0 1 |
? max(2,3)
%212 = 3
? min(2,3)
%213 = 2
? minim([2,1;1,2],4,6)
%214 = [6, 2, [0, -1, 1; 1, 1, 0]]
? mod(-12,7)
%215 = mod(2, 7)
? modp(-12,7)
%216 = mod(2, 7)
? mod(10873,49649)^-1
*** impossible inverse modulo: mod(131, 49649)
? modreverse(mod(x^2+1,x^3-x-1))
%217 = mod(x^2 - 3*x + 2, x^3 - 5*x^2 + 8*x - 5)
? move(0,243,583);cursor(0)
%218 = [243, 583]
? mu(3*5*7*11*13)
%219 = -1
? \\ N
? newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
%220 = [2, 2/3, 2/3, 2/3]
? nextprime(100000000000000000000000)
%221 = 100000000000000000000117
? norm(1+i)
%222 = 2
? norm(mod(x+5,x^3+x+1))
%223 = 129
? norml2(vector(10,x,x))
%224 = 385
? nucomp(qfi(2,1,9),qfi(4,3,5),3)
%225 = qfi(2, -1, 9)
? form=qfi(2,1,9);nucomp(form,form,3)
%226 = qfi(4, -3, 5)
? numdiv(2^99*3^49)
%227 = 5000
? numer((x+1)/(x-1))
%228 = x + 1
? nupow(form,111)
%229 = qfi(2, -1, 9)
? \\ O
? 1/(1+x)+o(x^20)
%230 = 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!)
%231 = 25
? ordell(acurve, 1)
%232 = [8, 3]
? order(mod(33,2^16+1))
%233 = 2048
? ordred(x^3-12*x+45*x-1)
%234 = [x - 1, x^3 + 33*x - 1, x^3 - 363*x - 2663]~
? \\ P
? pascal(8)
%235 =
|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 |
? permutation(7,1035)
%236 = [4, 7, 1, 6, 3, 5, 2]
? pf(-44,3)
%237 = qfi(3, 2, 4)
? phi(257^2)
%238 = 65792
? pi
%239 = 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])
%240 =
|19318376 741721 |
|8927353 342762 |
? pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
%241 =
|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))
%242 = [0.999999998 + 0.000000000*i, 3.00000000 + 0.000000000*i]
? polint([0,2,3],[0,4,9],5)
%243 = 25
? polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
%244 = [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)
%245 =
|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)
%246 = [17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17]~
? poly(sin(x),x)
%247 = -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)
%248 = 0.508400578
? polylog(-4,t)
%249 = (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)
%250 = 0.939035495
? polylogdold(5,0.5)
%251 = 1.03445942
? polylogp(5,0.5)
%252 = 0.949569346
? poly([1,2,3,4,5],x)
%253 = x^4 + 2*x^3 + 3*x^2 + 4*x + 5
? polyrev([1,2,3,4,5],x)
%254 = 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,10,apoint)
%255 = [-28919032218753260057646013785951999/292736325329248127651484680640160000, 478051489392386968218136375373985436596569736643531551/158385319626308443937475969221994173751192384064000000]
? powrealraw(qfr(5,3,-1,0.),3)
%256 = qfr(125, 23, 1, 0.000000000)
? pprint((x-12*y)/(y+13*x));
(-(11 /14))
? pprint([1,2;3,4])
|1 2 |
|3 4 |
%258 =
|1 2 |
|3 4 |
? pprint1(x+y);pprint(x+y);
(2 x )(2 x )
? \precision=100
precision = 100 significant digits
? pi
%260 = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068
? prec(pi,20)
%261 = 3.141592653589793238462643383254089766000000000000000000000000000000000000000000000000000000000000000
? \precision=20
precision = 20 significant digits
? prime(100)
%262 = 541
? primes(100)
%263 = [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]
%265 =
|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!)
%267 = 3335784368058308553334783/905932868585678438400000
? prod(1.,k=1,10,1+1/k!)
%268 = 3.6821540356142043935
? pi^2/6*prodeuler(p=2,10000,1-p^-2)
%269 = 1.0000098157493066238
? prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
%270 = 0.33333333333333333333
? prodinf1(n=0,-2^-n/(1+2^(-n+1)))
%271 = 0.33333333333333333333
? psi(1)
%272 = -0.57721566490153286060
? \\ Q
? quadgen(-11)
%273 = w
? quadpoly(-11)
%274 = x^2 - x + 3
? \\ R
? smith(matrix(5,5,j,k,random()))
%275 = [226226340965260564453392384, 2147483648, 2147483648, 1, 1]
? rank(matrix(5,5,x,y,x+y))
%276 = 2
? move(0,50,50);rbox(0,100,100)
? print1("give a value for s? ");s=read();print(1/s)
give a value for s? 37.
0.027027027027027027027
%277 = 0.027027027027027027027
? real(5-7*i)
%278 = 5
? recip(3*x^7-5*x^3+6*x-9)
%279 = -9*x^7 + 6*x^6 - 5*x^4 + 3
? redcomp(qfi(3,10,12))
%280 = qfi(3, -2, 4)
? redreal(qfr(3,10,-20,1.5))
%281 = qfr(3, 16, -7, 1.5000000000000000000)
? redrealnod(qfr(3,10,-20,1.5),18)
%282 = qfr(3, 16, -7, 0.00000000000000000000)
? regula(17)
%283 = 2.0947125472611012942
? kill(y);print(x+y);reorder([x, y]); print(x+y);
x + y
x + y
? resultant(x^3-1,x^3+1)
%285 = 8
? resultant2(x^3-1.,x^3+1.)
%286 = 8.0000000000000000000
? reverse(tan(x))
%287 = 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))
%288 = qfr(-20, -10, 3, 2.1074451073987839947)
? rhorealnod(qfr(3,10,-20,1.5),18)
%289 = qfr(-20, -10, 3, 0.00000000000000000000)
? rline(0,200,150)
? cursor(0)
%290 = [200, 150]
? rmove(0,5,5);cursor(0)
%291 = [205, 155]
? rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%292 = x^17 - 1
? rootmod(x^16-1,41)
%293 = [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)
%294 = [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)
%295 = [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]~
? rootslong(x^4-1000000000000000000000)
%296 = [-177827.94100389228012 + 0.E-28*i, 177827.94100389228012 + 0.E-28*i, 6.1098727269992093641 E-151 + 177827.94100389228012*i, 6.1098727269992093641 E-151 - 177827.94100389228012*i]~
? round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%297 = x^17 - 1
? rounderror(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
%298 = -9
? rpoint(0,20,20)
? \\ S
? q*series(anell(acurve,100),q)
%299 = 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)
? shift(1,50)
%300 = 1125899906842624
? shift([3,4,-11,-12],-2)
%301 = [0, 1, -2, -3]
? shiftmul([3,4,-11,-12],-2)
%302 = [3/4, 1, -11/4, -3]
? sigma(100)
%303 = 217
? sigmak(2,100)
%304 = 13671
? sigmak(-3,100)
%305 = 1149823/1000000
? sign(-1)
%306 = -1
? sign(0)
%307 = 0
? sign(0.)
%308 = 0
? signat(hilbert(5)-0.11*idmat(5))
%309 = [2, 3]
? simplify(((x+i+1)^2-x^2-2*x*(i+1))^2)
%310 = -4
? sin(pi/6)
%311 = 0.50000000000000000000
? sinh(1)
%312 = 1.1752011936438014568
? size([1.3*10^5,2*i*pi*exp(4*pi)])
%313 = 6
? smallbase(x^3+4*x+5)
%314 = [1, x, 1/7*x^2 - 1/7*x - 2/7]
? smalldiscf(x^3+4*x+5)
%315 = -19
? smallfact(100!+1)
%316 =
|101 1 |
|14303 1 |
|149239 1 |
|432885273849892962613071800918658949059679308685024481795740765527568493010727023757461397498800981521440877813288657839195622497225621499427628453 1 |
? smallinitell([0,0,0,-17,0])
%317 = [0, 0, 0, -17, 0, 0, -34, 0, -289, 816, 0, 314432, 1728]
? smallpolred(x^4+576)
%318 = [x - 1, x^2 - x + 1, x^2 + 1, x^4 - x^2 + 1]~
? smallpolred2(x^4+576)
%319 =
|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))
%320 = [27720, 2520, 2520, 840, 210, 6]
? solve(x=1,4,sin(x))
%321 = 3.1415926535897932384
? sort(vector(17,x,5*x%17))
%322 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
? sqr(1+o(2))
%323 = 1 + O(2^3)
? sqred(hilbert(5))
%324 =
|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))
%325 = 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)
%326 = 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)
%327 = 46189/256*x^10 - 109395/256*x^8 + 45045/128*x^6 - 15015/128*x^4 + 3465/256*x^2 + 0.053906250000000000000
? sturm(apol)
%328 = 4
? sturmpart(apol,0.91,1)
%329 = 1
? subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
%330 = [9, -24]
? subst(sin(x),x,y)
%331 = 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 - 1/1307674368000*y^15 + O(y^16)
? subst(sin(x),x,x+x^2)
%332 = 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 + 26537089/118879488000*x^15 + O(x^16)
? sum(0,k=1,10,2^-k)
%333 = 1023/1024
? sum(0.,k=1,10,2^-k)
%334 = 0.99902343750000000000
? \precision=20
precision = 20 significant digits
? 4*sumalt(n=0,(-1)^n/(2*n+1))
%335 = 3.1415926535897932384
? suminf(n=1,2.^-n)
%336 = 1.0000000000000000000
? 6/pi^2*sumpos(n=1,n^-2)
%337 = 1.0000000000000000000
? supplement([1,3;2,4;3,6])
%338 =
|1 3 0 |
|2 4 0 |
|3 6 1 |
? \\ T
? sqr(tan(pi/3))
%339 = 3.0000000000000000000
? tanh(1)
%340 = 0.76159415595576488812
? taylor(y/(x-y),y)
%341 = (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)
%342 = 512*x^10 - 1280*x^8 + 1120*x^6 - 400*x^4 + 50*x^2 - 1
? tchirnhausen(x^5-x-1)
%343 = x^5 + 65*x^4 + 1352*x^3 + 6890*x^2 - 49884*x - 641933
? teich(7+o(127^12))
%344 = 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}}}}
%345 = (x^3 + 3*y*x^2 + 3*y^2*x + y^3)/(x^2 - 2*y*x + y^2)
? theta(0.5,3)
%346 = 0.080806418251894691300
? thetanullk(0.5,7)
%347 = -804.63037320243369423
? trace(1+i)
%348 = 2
? trace(mod(x+5,x^3+x+1))
%349 = 15
? trans(vector(2,x,x))
%350 = [1, 2]~
? %*%~
%351 =
|1 2 |
|2 4 |
? trunc(-2.7)
%352 = -2
? trunc(sin(x^2))
%353 = -1/5040*x^14 + 1/120*x^10 - 1/6*x^6 + x^2
? type(mod(x,x^2+1))
%354 = 9
? \\ U
? unit(17)
%355 = 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
%356 = 1
? \\ V
? valuation(6^10000-1,5)
%357 = 5
? vec(sin(x))
%358 = [1, 0, -1/6, 0, 1/120, 0, -1/5040, 0, 1/362880, 0, -1/39916800, 0, 1/6227020800, 0, -1/1307674368000]
? vecsort([[1,8],[2,5],[3,6],[4,1]],2)
%359 = [[4, 1], [2, 5], [3, 6], [1, 8]]
? \\ W
? wf(i)
%360 = 1.1892071150027210667 + 2.4994989708065986630 E-30*i
? wf2(i)
%361 = 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)
%362 = 0.72491221490962306779 + 0.E-48*i
? zeta(3)
%363 = 1.2020569031595942854
? zeta(0.5+14.1347251*i)
%364 = 0.0000000052043097453468479398 - 0.000000032690639869786982176*i
?
?
