X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fseries_expansion.cpp;h=4cd169706d0dd4ca418f5ccdd6c70cd5e68ff9f7;hp=292f5b922751d6a832f2a28168192376d6092643;hb=ff50f412bb89eed2c78adffa0f390341753e8792;hpb=9eab44408b9213d8909b7a9e525f404ad06064dd diff --git a/check/series_expansion.cpp b/check/series_expansion.cpp index 292f5b92..4cd16970 100644 --- a/check/series_expansion.cpp +++ b/check/series_expansion.cpp @@ -3,7 +3,7 @@ * Series expansion test (Laurent and Taylor series). */ /* - * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2000 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 @@ -20,130 +20,203 @@ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ -#include +#include "ginac.h" + +#ifndef NO_NAMESPACE_GINAC using namespace GiNaC; +#endif // ndef NO_NAMESPACE_GINAC static symbol x("x"); -static unsigned check_series(const ex &e, const ex &point, const ex &d) +static unsigned check_series(const ex &e, const ex &point, const ex &d, int order = 8) { - ex es = e.series(x, point, 8); - ex ep = static_cast(es.bp)->convert_to_poly(); - if ((ep - d).compare(exZERO()) != 0) { - clog << "series expansion of " << e << " at " << point + ex es = e.series(x, point, order); + ex ep = ex_to_pseries(es).convert_to_poly(); + if (!(ep - d).is_zero()) { + clog << "series expansion of " << e << " at " << point << " erroneously returned " << ep << " (instead of " << d << ")" << endl; - (ep-d).printtree(clog); - return 1; - } - return 0; + (ep-d).printtree(clog); + return 1; + } + return 0; } // Series expansion static unsigned series1(void) { - unsigned result = 0; - ex e, d; - - 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, exZERO(), d); - - e = cos(x); - d = 1 - pow(x, 2) / 2 + pow(x, 4) / 24 - pow(x, 6) / 720 + Order(pow(x, 8)); - result += check_series(e, exZERO(), d); - - e = exp(x); - d = 1 + x + pow(x, 2) / 2 + pow(x, 3) / 6 + pow(x, 4) / 24 + pow(x, 5) / 120 + pow(x, 6) / 720 + pow(x, 7) / 5040 + Order(pow(x, 8)); - result += check_series(e, exZERO(), d); - - e = pow(1 - x, -1); - d = 1 + x + pow(x, 2) + pow(x, 3) + pow(x, 4) + pow(x, 5) + pow(x, 6) + pow(x, 7) + Order(pow(x, 8)); - result += check_series(e, exZERO(), d); - - e = x + pow(x, -1); - d = x + pow(x, -1); - result += check_series(e, exZERO(), d); - - e = x + pow(x, -1); - d = 2 + pow(x-1, 2) - pow(x-1, 3) + pow(x-1, 4) - pow(x-1, 5) + pow(x-1, 6) - pow(x-1, 7) + Order(pow(x-1, 8)); - result += check_series(e, exONE(), d); - - e = pow(x + pow(x, 3), -1); - d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + Order(pow(x, 7)); - result += check_series(e, exZERO(), 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)); - result += check_series(e, exZERO(), 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)); - result += check_series(e, exZERO(), d); - - e = sin(x) / cos(x); - d = x + pow(x, 3) / 3 + pow(x, 5) * 2/15 + pow(x, 7) * 17/315 + Order(pow(x, 8)); - result += check_series(e, exZERO(), 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)); - result += check_series(e, exZERO(), d); - - e = pow(numeric(2), x); - ex t = log(ex(2)) * x; - 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, exZERO(), d.expand()); - - e = pow(Pi, x); - t = log(Pi) * x; - 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, exZERO(), d.expand()); - - return result; + unsigned result = 0; + ex e, d; + + 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); + + e = cos(x); + d = 1 - pow(x, 2) / 2 + pow(x, 4) / 24 - pow(x, 6) / 720 + Order(pow(x, 8)); + result += check_series(e, 0, d); + + e = exp(x); + d = 1 + x + pow(x, 2) / 2 + pow(x, 3) / 6 + pow(x, 4) / 24 + pow(x, 5) / 120 + pow(x, 6) / 720 + pow(x, 7) / 5040 + Order(pow(x, 8)); + result += check_series(e, 0, d); + + e = pow(1 - x, -1); + d = 1 + x + pow(x, 2) + pow(x, 3) + pow(x, 4) + pow(x, 5) + pow(x, 6) + pow(x, 7) + Order(pow(x, 8)); + result += check_series(e, 0, d); + + e = x + pow(x, -1); + d = x + pow(x, -1); + result += check_series(e, 0, d); + + e = x + pow(x, -1); + d = 2 + pow(x-1, 2) - pow(x-1, 3) + pow(x-1, 4) - pow(x-1, 5) + pow(x-1, 6) - pow(x-1, 7) + Order(pow(x-1, 8)); + 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)); + 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)); + 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)); + result += check_series(e, 0, d); + + e = sin(x) / cos(x); + d = x + pow(x, 3) / 3 + pow(x, 5) * 2/15 + pow(x, 7) * 17/315 + Order(pow(x, 8)); + 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)); + result += check_series(e, 0, d); + + e = pow(numeric(2), x); + ex t = log(ex(2)) * x; + 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 = pow(Pi, x); + t = log(Pi) * x; + 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()); + + return result; } // Series addition static unsigned series2(void) { - unsigned result = 0; - ex e, d; - - e = pow(sin(x), -1).series(x, exZERO(), 8) + pow(sin(-x), -1).series(x, exZERO(), 12); - d = Order(pow(x, 6)); - result += check_series(e, exZERO(), d); - - return result; + 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)); + result += check_series(e, 0, d); + + return result; } // Series multiplication static unsigned series3(void) { - unsigned result = 0; - ex e, d; + unsigned result = 0; + ex e, d; + + e = sin(x).series(x, 0, 8) * pow(sin(x), -1).series(x, 0, 12); + d = 1 + Order(pow(x, 7)); + result += check_series(e, 0, d); + + return result; +} - e = sin(x).series(x, exZERO(), 8) * pow(sin(x), -1).series(x, exZERO(), 12); - d = 1 + Order(pow(x, 7)); - result += check_series(e, exZERO(), d); +// Order term handling +static unsigned series4(void) +{ + unsigned result = 0; + ex e, d; + + e = 1 + x + pow(x, 2) + pow(x, 3); + d = Order(1); + result += check_series(e, 0, d, 0); + d = 1 + Order(x); + result += check_series(e, 0, d, 1); + d = 1 + x + Order(pow(x, 2)); + result += check_series(e, 0, d, 2); + d = 1 + x + pow(x, 2) + Order(pow(x, 3)); + result += check_series(e, 0, d, 3); + d = 1 + x + pow(x, 2) + pow(x, 3); + result += check_series(e, 0, d, 4); + return result; +} - return result; +// Series of special functions +static unsigned series5(void) +{ + unsigned result = 0; + ex e, d; + + // gamma(-1): + e = gamma(2*x); + d = pow(x+1,-1)*numeric(1,4) + + pow(x+1,0)*(numeric(3,4) - + numeric(1,2)*EulerGamma) + + pow(x+1,1)*(numeric(7,4) - + numeric(3,2)*EulerGamma + + numeric(1,2)*pow(EulerGamma,2) + + numeric(1,12)*pow(Pi,2)) + + pow(x+1,2)*(numeric(15,4) - + numeric(7,2)*EulerGamma - + numeric(1,3)*pow(EulerGamma,3) + + numeric(1,4)*pow(Pi,2) + + numeric(3,2)*pow(EulerGamma,2) - + numeric(1,6)*pow(Pi,2)*EulerGamma - + numeric(2,3)*zeta(3)) + + pow(x+1,3)*(numeric(31,4) - pow(EulerGamma,3) - + numeric(15,2)*EulerGamma + + numeric(1,6)*pow(EulerGamma,4) + + numeric(7,2)*pow(EulerGamma,2) + + numeric(7,12)*pow(Pi,2) - + numeric(1,2)*pow(Pi,2)*EulerGamma - + numeric(2)*zeta(3) + + numeric(1,6)*pow(EulerGamma,2)*pow(Pi,2) + + numeric(1,40)*pow(Pi,4) + + numeric(4,3)*zeta(3)*EulerGamma) + + Order(pow(x+1,4)); + result += check_series(e, -1, d, 4); + + // tan(Pi/2) + e = tan(x*Pi/2); + 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)); + result += check_series(e,1,d,8); + + return result; } unsigned series_expansion(void) { - unsigned result = 0; - - cout << "checking series expansion..." << flush; - clog << "---------series expansion:" << endl; - - result += series1(); - result += series2(); - result += series3(); - - if (!result) { - cout << " passed "; - clog << "(no output)" << endl; - } else { - cout << " failed "; - } - return result; + unsigned result = 0; + + cout << "checking series expansion..." << flush; + clog << "---------series expansion:" << endl; + + result += series1(); + result += series2(); + result += series3(); + result += series4(); + result += series5(); + + if (!result) { + cout << " passed "; + clog << "(no output)" << endl; + } else { + cout << " failed "; + } + return result; }