1 /** @file exam_pseries.cpp
3 * Series expansion test (Laurent and Taylor series). */
6 * GiNaC Copyright (C) 1999-2000 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
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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
27 static unsigned check_series(const ex &e, const ex &point, const ex &d, int order = 8)
29 ex es = e.series(x==point, order);
30 ex ep = ex_to_pseries(es).convert_to_poly();
31 if (!(ep - d).is_zero()) {
32 clog << "series expansion of " << e << " at " << point
33 << " erroneously returned " << ep << " (instead of " << d
35 (ep-d).printtree(clog);
42 static unsigned exam_series1(void)
48 d = x - pow(x, 3) / 6 + pow(x, 5) / 120 - pow(x, 7) / 5040 + Order(pow(x, 8));
49 result += check_series(e, 0, d);
52 d = 1 - pow(x, 2) / 2 + pow(x, 4) / 24 - pow(x, 6) / 720 + Order(pow(x, 8));
53 result += check_series(e, 0, d);
56 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));
57 result += check_series(e, 0, d);
60 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));
61 result += check_series(e, 0, d);
65 result += check_series(e, 0, d);
68 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));
69 result += check_series(e, 1, d);
71 e = pow(x + pow(x, 3), -1);
72 d = pow(x, -1) - x + pow(x, 3) - pow(x, 5) + Order(pow(x, 7));
73 result += check_series(e, 0, d);
75 e = pow(pow(x, 2) + pow(x, 4), -1);
76 d = pow(x, -2) - 1 + pow(x, 2) - pow(x, 4) + Order(pow(x, 6));
77 result += check_series(e, 0, d);
80 d = pow(x, -2) + numeric(1,3) + pow(x, 2) / 15 + pow(x, 4) * 2/189 + Order(pow(x, 5));
81 result += check_series(e, 0, d);
84 d = x + pow(x, 3) / 3 + pow(x, 5) * 2/15 + pow(x, 7) * 17/315 + Order(pow(x, 8));
85 result += check_series(e, 0, d);
88 d = pow(x, -1) - x / 3 - pow(x, 3) / 45 - pow(x, 5) * 2/945 + Order(pow(x, 6));
89 result += check_series(e, 0, d);
91 e = pow(numeric(2), x);
92 ex t = log(ex(2)) * x;
93 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));
94 result += check_series(e, 0, d.expand());
98 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));
99 result += check_series(e, 0, d.expand());
105 static unsigned exam_series2(void)
110 e = pow(sin(x), -1).series(x==0, 8) + pow(sin(-x), -1).series(x==0, 12);
111 d = Order(pow(x, 6));
112 result += check_series(e, 0, d);
117 // Series multiplication
118 static unsigned exam_series3(void)
123 e = sin(x).series(x==0, 8) * pow(sin(x), -1).series(x==0, 12);
124 d = 1 + Order(pow(x, 7));
125 result += check_series(e, 0, d);
130 // Order term handling
131 static unsigned exam_series4(void)
136 e = 1 + x + pow(x, 2) + pow(x, 3);
138 result += check_series(e, 0, d, 0);
140 result += check_series(e, 0, d, 1);
141 d = 1 + x + Order(pow(x, 2));
142 result += check_series(e, 0, d, 2);
143 d = 1 + x + pow(x, 2) + Order(pow(x, 3));
144 result += check_series(e, 0, d, 3);
145 d = 1 + x + pow(x, 2) + pow(x, 3);
146 result += check_series(e, 0, d, 4);
150 // Series of special functions
151 static unsigned exam_series5(void)
158 d = pow(x+1,-1)*numeric(1,4) +
159 pow(x+1,0)*(numeric(3,4) -
160 numeric(1,2)*Euler) +
161 pow(x+1,1)*(numeric(7,4) -
163 numeric(1,2)*pow(Euler,2) +
164 numeric(1,12)*pow(Pi,2)) +
165 pow(x+1,2)*(numeric(15,4) -
167 numeric(1,3)*pow(Euler,3) +
168 numeric(1,4)*pow(Pi,2) +
169 numeric(3,2)*pow(Euler,2) -
170 numeric(1,6)*pow(Pi,2)*Euler -
171 numeric(2,3)*zeta(3)) +
172 pow(x+1,3)*(numeric(31,4) - pow(Euler,3) -
173 numeric(15,2)*Euler +
174 numeric(1,6)*pow(Euler,4) +
175 numeric(7,2)*pow(Euler,2) +
176 numeric(7,12)*pow(Pi,2) -
177 numeric(1,2)*pow(Pi,2)*Euler -
179 numeric(1,6)*pow(Euler,2)*pow(Pi,2) +
180 numeric(1,40)*pow(Pi,4) +
181 numeric(4,3)*zeta(3)*Euler) +
183 result += check_series(e, -1, d, 4);
187 d = pow(x-1,-1)/Pi*(-2) +
189 pow(x-1,3)*pow(Pi,3)/360 +
190 pow(x-1,5)*pow(Pi,5)/15120 +
191 pow(x-1,7)*pow(Pi,7)/604800 +
193 result += check_series(e,1,d,8);
198 unsigned exam_pseries(void)
202 cout << "examining series expansion" << flush;
203 clog << "----------series expansion:" << endl;
205 result += exam_series1(); cout << '.' << flush;
206 result += exam_series2(); cout << '.' << flush;
207 result += exam_series3(); cout << '.' << flush;
208 result += exam_series4(); cout << '.' << flush;
209 result += exam_series5(); cout << '.' << flush;
212 cout << " passed " << endl;
213 clog << "(no output)" << endl;
215 cout << " failed " << endl;