1 /** @file exam_normalization.cpp
3 * Rational function normalization test suite. */
6 * GiNaC Copyright (C) 1999-2008 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
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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.
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19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
26 using namespace GiNaC;
28 static symbol w("w"), x("x"), y("y"), z("z");
30 static unsigned check_normal(const ex &e, const ex &d)
33 if (!en.is_equal(d)) {
34 clog << "normal form of " << e << " erroneously returned "
35 << en << " (should be " << d << ")" << endl;
41 static unsigned exam_normal1()
47 e = pow(x, 2) - (x+1)*(x-1) - 1;
49 result += check_normal(e, d);
51 // Expansion inside functions
52 e = sin(x*(x+1)-x) + 1;
53 d = sin(pow(x, 2)) + 1;
54 result += check_normal(e, d);
58 d = (x*y + 6) / (x*3);
59 result += check_normal(e, d);
61 e = pow(x, -1) + x/(x+1);
62 d = (pow(x, 2)+x+1)/(x*(x+1));
63 result += check_normal(e, d);
68 static unsigned exam_normal2()
73 // Fraction cancellation
74 e = numeric(1)/2 * z * (2*x + 2*y);
76 result += check_normal(e, d);
78 e = numeric(1)/6 * z * (3*x + 3*y) * (2*x + 2*w);
79 d = z * (x + y) * (x + w);
80 result += check_normal(e, d);
82 e = (3*x + 3*y) * (w/3 + z/3);
83 d = (x + y) * (w + z);
84 result += check_normal(e, d);
86 // Fails stochastically with the new tinfo mechanism, because
87 // sometimes the equivalent answer ... / pow(y - x, 2) is calculated.
88 // TODO: make check for both cases.
89 // e = (pow(x, 2) - pow(y, 2)) / pow(x-y, 3);
90 // d = (x + y) / pow(x - y, 2);
91 // result += check_normal(e, d);
93 e = (pow(x, -1) + x) / (pow(x , 2) * 2 + 2);
95 result += check_normal(e, d);
97 // Fails stochastically with the new tinfo mechanism, because
98 // sometimes the equivalent answer ... / pow(y - x, 2) is calculated.
99 // TODO: make check for both cases.
100 // Fraction cancellation with rational coefficients
101 // e = (pow(x, 2) - pow(y, 2)) / pow(x/2 - y/2, 3);
102 // d = (8 * x + 8 * y) / pow(x - y, 2);
103 // result += check_normal(e, d);
105 // Fraction cancellation with rational coefficients
106 e = z/5 * (x/7 + y/10) / (x/14 + y/20);
108 result += check_normal(e, d);
113 static unsigned exam_normal3()
118 // Distribution of powers
120 d = pow(x, 2) / pow(y, 2);
121 result += check_normal(e, d);
123 // Distribution of powers (integer, distribute) and fraction addition
124 e = pow(pow(x, -1) + x, 2);
125 d = pow(pow(x, 2) + 1, 2) / pow(x, 2);
126 result += check_normal(e, d);
128 // Distribution of powers (non-integer, don't distribute) and fraction addition
129 e = pow(pow(x, -1) + x, numeric(1)/2);
130 d = pow((pow(x, 2) + 1) / x, numeric(1)/2);
131 result += check_normal(e, d);
136 static unsigned exam_normal4()
141 // Replacement of functions with temporary symbols and fraction cancellation
142 e = pow(sin(x), 2) - pow(cos(x), 2);
143 e /= sin(x) + cos(x);
145 result += check_normal(e, d);
147 // Replacement of non-integer powers with temporary symbols
148 e = (pow(numeric(2), numeric(1)/2) * x + x) / x;
149 d = pow(numeric(2), numeric(1)/2) + 1;
150 result += check_normal(e, d);
152 // Replacement of complex numbers with temporary symbols
153 e = (x + y + x*I + y*I) / (x + y);
155 result += check_normal(e, d);
157 e = (pow(x, 2) + pow(y, 2)) / (x + y*I);
159 result += check_normal(e, d);
161 // More complex rational function
162 e = (pow(x-y*2,4)/pow(pow(x,2)-pow(y,2)*4,2)+1)*(x+y*2)*(y+z)/(pow(x,2)+pow(y,2)*4);
163 d = (y*2 + z*2) / (x + y*2);
164 result += check_normal(e, d);
169 /* Test content(), integer_content(), primpart(). */
170 static unsigned check_content(const ex & e, const ex & x, const ex & ic, const ex & c, const ex & pp)
174 ex r_ic = e.integer_content();
175 if (!r_ic.is_equal(ic)) {
176 clog << "integer_content(" << e << ") erroneously returned "
177 << r_ic << " instead of " << ic << endl;
181 ex r_c = e.content(x);
182 if (!r_c.is_equal(c)) {
183 clog << "content(" << e << ", " << x << ") erroneously returned "
184 << r_c << " instead of " << c << endl;
188 ex r_pp = e.primpart(x);
189 if (!r_pp.is_equal(pp)) {
190 clog << "primpart(" << e << ", " << x << ") erroneously returned "
191 << r_pp << " instead of " << pp << endl;
195 ex r = r_c*r_pp*e.unit(x);
196 if (!(r - e).expand().is_zero()) {
197 clog << "product of unit, content, and primitive part of " << e << " yielded "
198 << r << " instead of " << e << endl;
205 static unsigned exam_content()
208 symbol x("x"), y("y");
210 result += check_content(ex(-3)/4, x, ex(3)/4, ex(3)/4, 1);
211 result += check_content(-x/4, x, ex(1)/4, ex(1)/4, x);
212 result += check_content(5*x-15, x, 5, 5, x-3);
213 result += check_content(5*x*y-15*y*y, x, 5, 5*y, x-3*y);
214 result += check_content(-15*x/2+ex(25)/3, x, ex(5)/6, ex(5)/6, 9*x-10);
215 result += check_content(-x*y, x, 1, y, x);
220 unsigned exam_normalization()
224 cout << "examining rational function normalization" << flush;
226 result += exam_normal1(); cout << '.' << flush;
227 result += exam_normal2(); cout << '.' << flush;
228 result += exam_normal3(); cout << '.' << flush;
229 result += exam_normal4(); cout << '.' << flush;
230 result += exam_content(); cout << '.' << flush;
235 int main(int argc, char** argv)
237 return exam_normalization();