1 /** @file series_expansion.cpp
3 * Series expansion test (Laurent and Taylor series). */
6 * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23 #include <ginac/ginac.h>
25 #ifndef NO_GINAC_NAMESPACE
26 using namespace GiNaC;
27 #endif // ndef NO_GINAC_NAMESPACE
31 static unsigned check_series(const ex &e, const ex &point, const ex &d, int order = 8)
33 ex es = e.series(x, point, order);
34 ex ep = static_cast<series *>(es.bp)->convert_to_poly();
35 if (!(ep - d).is_zero()) {
36 clog << "series expansion of " << e << " at " << point
37 << " erroneously returned " << ep << " (instead of " << d
39 (ep-d).printtree(clog);
46 static unsigned series1(void)
52 d = x - pow(x, 3) / 6 + pow(x, 5) / 120 - pow(x, 7) / 5040 + Order(pow(x, 8));
53 result += check_series(e, 0, d);
56 d = 1 - pow(x, 2) / 2 + pow(x, 4) / 24 - pow(x, 6) / 720 + Order(pow(x, 8));
57 result += check_series(e, 0, d);
60 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));
61 result += check_series(e, 0, d);
64 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));
65 result += check_series(e, 0, d);
69 result += check_series(e, 0, d);
72 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));
73 result += check_series(e, 1, d);
75 e = pow(x + pow(x, 3), -1);
76 d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + Order(pow(x, 7));
77 result += check_series(e, 0, d);
79 e = pow(pow(x, 2) + pow(x, 4), -1);
80 d = pow(x, -2) - 1 + pow(x, 2) - pow(x, 4) + Order(pow(x, 6));
81 result += check_series(e, 0, d);
84 d = pow(x, -2) + numeric(1,3) + pow(x, 2) / 15 + pow(x, 4) * 2/189 + Order(pow(x, 5));
85 result += check_series(e, 0, d);
88 d = x + pow(x, 3) / 3 + pow(x, 5) * 2/15 + pow(x, 7) * 17/315 + Order(pow(x, 8));
89 result += check_series(e, 0, d);
92 d = pow(x, -1) - x / 3 - pow(x, 3) / 45 - pow(x, 5) * 2/945 + Order(pow(x, 6));
93 result += check_series(e, 0, d);
95 e = pow(numeric(2), x);
96 ex t = log(ex(2)) * x;
97 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));
98 result += check_series(e, 0, d.expand());
102 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));
103 result += check_series(e, 0, d.expand());
109 static unsigned series2(void)
114 e = pow(sin(x), -1).series(x, 0, 8) + pow(sin(-x), -1).series(x, 0, 12);
115 d = Order(pow(x, 6));
116 result += check_series(e, 0, d);
121 // Series multiplication
122 static unsigned series3(void)
127 e = sin(x).series(x, 0, 8) * pow(sin(x), -1).series(x, 0, 12);
128 d = 1 + Order(pow(x, 7));
129 result += check_series(e, 0, d);
134 // Series of special functions
135 static unsigned series4(void)
142 d = pow(x+1,-1)*numeric(1,4) +
143 pow(x+1,0)*(numeric(3,4) -
144 numeric(1,2)*EulerGamma) +
145 pow(x+1,1)*(numeric(7,4) -
146 numeric(3,2)*EulerGamma +
147 numeric(1,2)*pow(EulerGamma,2) +
148 numeric(1,12)*pow(Pi,2)) +
149 pow(x+1,2)*(numeric(15,4) -
150 numeric(7,2)*EulerGamma -
151 numeric(1,3)*pow(EulerGamma,3) +
152 numeric(1,4)*pow(Pi,2) +
153 numeric(3,2)*pow(EulerGamma,2) -
154 numeric(1,6)*pow(Pi,2)*EulerGamma -
155 numeric(2,3)*zeta(3)) +
156 pow(x+1,3)*(numeric(31,4) - pow(EulerGamma,3) -
157 numeric(15,2)*EulerGamma +
158 numeric(1,6)*pow(EulerGamma,4) +
159 numeric(7,2)*pow(EulerGamma,2) +
160 numeric(7,12)*pow(Pi,2) -
161 numeric(1,2)*pow(Pi,2)*EulerGamma -
163 numeric(1,6)*pow(EulerGamma,2)*pow(Pi,2) +
164 numeric(1,40)*pow(Pi,4) +
165 numeric(4,3)*zeta(3)*EulerGamma) +
167 result += check_series(e, -1, d, 4);
171 d = pow(x-1,-1)/Pi*(-2) +
173 pow(x-1,3)*pow(Pi,3)/360 +
174 pow(x-1,5)*pow(Pi,5)/15120 +
175 pow(x-1,7)*pow(Pi,7)/604800 +
177 result += check_series(e,1,d,8);
182 unsigned series_expansion(void)
186 cout << "checking series expansion..." << flush;
187 clog << "---------series expansion:" << endl;
196 clog << "(no output)" << endl;