+++ /dev/null
-/** @file series_expansion.cpp
- *
- * Series expansion test (Laurent and Taylor series). */
-
-/*
- * 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
- * the Free Software Foundation; either version 2 of the License, or
- * (at your option) any later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
- */
-
-#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, int order = 8)
-{
- 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;
-}
-
-// 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, 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, 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;
-
- 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;
-}
-
-// 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;
-}
-
-// 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();
- result += series4();
- result += series5();
-
- if (!result) {
- cout << " passed ";
- clog << "(no output)" << endl;
- } else {
- cout << " failed ";
- }
- return result;
-}
git://www.ginac.de / ginac.git / blobdiff