X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_pseries.cpp;h=040c5e58a047d2e1712109467e95ea2493ca6a87;hp=cb65a53361de1ce5fa8edfda060edfab572c1412;hb=7131108e7ed6563e0d004793c5b723a05f191536;hpb=3d9039b1a02aedda5eff2392e9c76df986e94f52 diff --git a/check/exam_pseries.cpp b/check/exam_pseries.cpp index cb65a533..040c5e58 100644 --- a/check/exam_pseries.cpp +++ b/check/exam_pseries.cpp @@ -3,7 +3,7 @@ * Series expansion test (Laurent and Taylor series). */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -27,23 +27,31 @@ static symbol x("x"); static unsigned check_series(const ex &e, const ex &point, const ex &d, int order = 8) { ex es = e.series(x==point, order); - ex ep = ex_to_pseries(es).convert_to_poly(); - if (!(ep - d).is_zero()) { + ex ep = ex_to(es).convert_to_poly(); + if (!(ep - d).expand().is_zero()) { clog << "series expansion of " << e << " at " << point << " erroneously returned " << ep << " (instead of " << d << ")" << endl; - (ep-d).printtree(clog); + clog << tree << (ep-d) << dflt; return 1; } return 0; } // Series expansion -static unsigned exam_series1(void) +static unsigned exam_series1() { + using GiNaC::log; + + symbol a("a"); + symbol b("b"); unsigned result = 0; ex e, d; + e = pow(a+b, x); + d = 1 + Order(pow(x, 1)); + result += check_series(e, 0, d, 1); + e = sin(x); d = x - pow(x, 3) / 6 + pow(x, 5) / 120 - pow(x, 7) / 5040 + Order(pow(x, 8)); result += check_series(e, 0, d); @@ -69,15 +77,15 @@ static unsigned exam_series1(void) result += check_series(e, 1, d); e = pow(x + pow(x, 3), -1); - d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + Order(pow(x, 7)); + d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + pow(x, 7) + Order(pow(x, 8)); result += check_series(e, 0, d); e = pow(pow(x, 2) + pow(x, 4), -1); - d = pow(x, -2) - 1 + pow(x, 2) - pow(x, 4) + Order(pow(x, 6)); + d = pow(x, -2) - 1 + pow(x, 2) - pow(x, 4) + pow(x, 6) + Order(pow(x, 8)); result += check_series(e, 0, d); e = pow(sin(x), -2); - d = pow(x, -2) + numeric(1,3) + pow(x, 2) / 15 + pow(x, 4) * 2/189 + Order(pow(x, 5)); + d = pow(x, -2) + numeric(1,3) + pow(x, 2) / 15 + pow(x, 4) * 2/189 + pow(x, 6) / 675 + Order(pow(x, 8)); result += check_series(e, 0, d); e = sin(x) / cos(x); @@ -85,7 +93,7 @@ static unsigned exam_series1(void) result += check_series(e, 0, d); e = cos(x) / sin(x); - d = pow(x, -1) - x / 3 - pow(x, 3) / 45 - pow(x, 5) * 2/945 + Order(pow(x, 6)); + d = pow(x, -1) - x / 3 - pow(x, 3) / 45 - pow(x, 5) * 2/945 - pow(x, 7) / 4725 + Order(pow(x, 8)); result += check_series(e, 0, d); e = pow(numeric(2), x); @@ -98,24 +106,51 @@ static unsigned exam_series1(void) d = 1 + t + pow(t, 2) / 2 + pow(t, 3) / 6 + pow(t, 4) / 24 + pow(t, 5) / 120 + pow(t, 6) / 720 + pow(t, 7) / 5040 + Order(pow(x, 8)); result += check_series(e, 0, d.expand()); + e = log(x); + d = e; + result += check_series(e, 0, d, 1); + result += check_series(e, 0, d, 2); + + e = pow(x, 8) * pow(pow(x,3)+ pow(x + pow(x,3), 2), -2); + d = pow(x, 4) - 2*pow(x, 5) + Order(pow(x, 6)); + result += check_series(e, 0, d, 6); + + e = cos(x) * pow(sin(x)*(pow(x, 5) + 4 * pow(x, 2)), -3); + d = pow(x, -9) / 64 - 3 * pow(x, -6) / 256 - pow(x, -5) / 960 + 535 * pow(x, -3) / 96768 + + pow(x, -2) / 1280 - pow(x, -1) / 14400 - numeric(283, 129024) - 2143 * x / 5322240 + + Order(pow(x, 2)); + result += check_series(e, 0, d, 2); + + e = sqrt(1+x*x) * sqrt(1+2*x*x); + d = 1 + Order(pow(x, 2)); + result += check_series(e, 0, d, 2); + + e = pow(x, 4) * sin(a) + pow(x, 2); + d = pow(x, 2) + Order(pow(x, 3)); + result += check_series(e, 0, d, 3); + + e = log(a*x + b*x*x*log(x)); + d = log(a*x) + b/a*log(x)*x - pow(b/a, 2)/2*pow(log(x)*x, 2) + Order(pow(x, 3)); + result += check_series(e, 0, d, 3); + return result; } // Series addition -static unsigned exam_series2(void) +static unsigned exam_series2() { unsigned result = 0; ex e, d; e = pow(sin(x), -1).series(x==0, 8) + pow(sin(-x), -1).series(x==0, 12); - d = Order(pow(x, 6)); + d = Order(pow(x, 8)); result += check_series(e, 0, d); return result; } // Series multiplication -static unsigned exam_series3(void) +static unsigned exam_series3() { unsigned result = 0; ex e, d; @@ -127,8 +162,26 @@ static unsigned exam_series3(void) return result; } +// Series exponentiation +static unsigned exam_series4() +{ + unsigned result = 0; + ex e, d; + + e = pow((2*cos(x)).series(x==0, 5), 2).series(x==0, 5); + d = 4 - 4*pow(x, 2) + 4*pow(x, 4)/3 + Order(pow(x, 5)); + result += check_series(e, 0, d); + + e = pow(tgamma(x), 2).series(x==0, 2); + d = pow(x,-2) - 2*Euler/x + (pow(Pi,2)/6+2*pow(Euler,2)) + + x*(-4*pow(Euler, 3)/3 -pow(Pi,2)*Euler/3 - 2*zeta(3)/3) + Order(pow(x, 2)); + result += check_series(e, 0, d); + + return result; +} + // Order term handling -static unsigned exam_series4(void) +static unsigned exam_series5() { unsigned result = 0; ex e, d; @@ -148,7 +201,7 @@ static unsigned exam_series4(void) } // Series expansion of tgamma(-1) -static unsigned exam_series5(void) +static unsigned exam_series6() { ex e = tgamma(2*x); ex d = pow(x+1,-1)*numeric(1,4) + @@ -180,26 +233,25 @@ static unsigned exam_series5(void) } // Series expansion of tan(x==Pi/2) -static unsigned exam_series6(void) +static unsigned exam_series7() { ex e = tan(x*Pi/2); ex d = pow(x-1,-1)/Pi*(-2) + pow(x-1,1)*Pi/6 + pow(x-1,3)*pow(Pi,3)/360 +pow(x-1,5)*pow(Pi,5)/15120 + pow(x-1,7)*pow(Pi,7)/604800 - +Order(pow(x-1,8)); - return check_series(e,1,d,8); + +Order(pow(x-1,9)); + return check_series(e,1,d,9); } // Series expansion of log(sin(x==0)) -static unsigned exam_series7(void) +static unsigned exam_series8() { ex e = log(sin(x)); - ex d = log(x) - pow(x,2)/6 - pow(x,4)/180 - pow(x,6)/2835 - +Order(pow(x,8)); - return check_series(e,0,d,8); + ex d = log(x) - pow(x,2)/6 - pow(x,4)/180 - pow(x,6)/2835 - pow(x,8)/37800 + Order(pow(x,9)); + return check_series(e,0,d,9); } // Series expansion of Li2(sin(x==0)) -static unsigned exam_series8(void) +static unsigned exam_series9() { ex e = Li2(sin(x)); ex d = x + pow(x,2)/4 - pow(x,3)/18 - pow(x,4)/48 @@ -209,8 +261,10 @@ static unsigned exam_series8(void) } // Series expansion of Li2((x==2)^2), caring about branch-cut -static unsigned exam_series9(void) +static unsigned exam_series10() { + using GiNaC::log; + ex e = Li2(pow(x,2)); ex d = Li2(4) + (-log(3) + I*Pi*csgn(I-I*pow(x,2))) * (x-2) + (numeric(-2,3) + log(3)/4 - I*Pi/4*csgn(I-I*pow(x,2))) * pow(x-2,2) @@ -221,8 +275,10 @@ static unsigned exam_series9(void) } // Series expansion of logarithms around branch points -static unsigned exam_series10(void) +static unsigned exam_series11() { + using GiNaC::log; + unsigned result = 0; ex e, d; symbol a("a"); @@ -254,15 +310,17 @@ static unsigned exam_series10(void) result += check_series(e,0,d,5); e = log((1-x)/x); - d = log(1-x) - (x-1) + pow(x-1,2)/2 - pow(x-1,3)/3 + Order(pow(x-1,4)); - result += check_series(e,1,d,4); + d = log(1-x) - (x-1) + pow(x-1,2)/2 - pow(x-1,3)/3 + pow(x-1,4)/4 + Order(pow(x-1,5)); + result += check_series(e,1,d,5); return result; } // Series expansion of other functions around branch points -static unsigned exam_series11(void) +static unsigned exam_series12() { + using GiNaC::log; + unsigned result = 0; ex e, d; @@ -287,7 +345,7 @@ static unsigned exam_series11(void) } -unsigned exam_pseries(void) +unsigned exam_pseries() { unsigned result = 0; @@ -305,6 +363,7 @@ unsigned exam_pseries(void) result += exam_series9(); cout << '.' << flush; result += exam_series10(); cout << '.' << flush; result += exam_series11(); cout << '.' << flush; + result += exam_series12(); cout << '.' << flush; if (!result) { cout << " passed " << endl;