1 /** @file exam_polygcd.cpp
3 * Some test with polynomial GCD calculations. See also the checks for
4 * rational function normalization in normalization.cpp. */
7 * GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
9 * This program is free software; you can redistribute it and/or modify
10 * it under the terms of the GNU General Public License as published by
11 * the Free Software Foundation; either version 2 of the License, or
12 * (at your option) any later version.
14 * This program is distributed in the hope that it will be useful,
15 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 * GNU General Public License for more details.
19 * You should have received a copy of the GNU General Public License
20 * along with this program; if not, write to the Free Software
21 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
27 using namespace GiNaC;
29 const int MAX_VARIABLES = 3;
31 static symbol x("x"), z("z");
32 static symbol y[MAX_VARIABLES];
35 static unsigned poly_gcd1()
37 for (int v=1; v<=MAX_VARIABLES; v++) {
40 for (int i=0; i<v; i++) {
45 ex f = (e1 + 1) * (e1 + 2);
46 ex g = e2 * (-pow(x, 2) * y[0] * 3 + pow(y[0], 2) - 1);
49 clog << "case 1, gcd(" << f << "," << g << ") = " << r << " (should be 1)" << endl;
56 // Linearly dense quartic inputs with quadratic GCDs
57 static unsigned poly_gcd2()
59 for (int v=1; v<=MAX_VARIABLES; v++) {
62 for (int i=0; i<v; i++) {
67 ex d = pow(e1 + 1, 2);
68 ex f = d * pow(e2 - 2, 2);
69 ex g = d * pow(e1 + 2, 2);
70 ex r = gcd(f.expand(), g.expand());
71 if (!(r - d).expand().is_zero()) {
72 clog << "case 2, gcd(" << f << "," << g << ") = " << r << " (should be " << d << ")" << endl;
79 // Sparse GCD and inputs where degrees are proportional to the number of variables
80 static unsigned poly_gcd3()
82 for (int v=1; v<=MAX_VARIABLES; v++) {
83 ex e1 = pow(x, v + 1);
84 for (int i=0; i<v; i++)
85 e1 += pow(y[i], v + 1);
90 ex r = gcd(f.expand(), g.expand());
91 if (!(r - d).expand().is_zero()) {
92 clog << "case 3, gcd(" << f << "," << g << ") = " << r << " (should be " << d << ")" << endl;
99 // Variation of case 3; major performance degradation with PRS
100 static unsigned poly_gcd3p()
102 for (int v=1; v<=MAX_VARIABLES; v++) {
103 ex e1 = pow(x, v + 1);
105 for (int i=0; i<v; i++) {
106 e1 += pow(y[i], v + 1);
113 ex r = gcd(f.expand(), g.expand());
114 if (!(r - d).expand().is_zero()) {
115 clog << "case 3p, gcd(" << f << "," << g << ") = " << r << " (should be " << d << ")" << endl;
122 // Quadratic non-monic GCD; f and g have other quadratic factors
123 static unsigned poly_gcd4()
125 for (int v=1; v<=MAX_VARIABLES; v++) {
126 ex e1 = pow(x, 2) * pow(y[0], 2);
127 ex e2 = pow(x, 2) - pow(y[0], 2);
129 for (int i=1; i<v; i++) {
137 ex g = d * pow(e3 + 2, 2);
138 ex r = gcd(f.expand(), g.expand());
139 if (!(r - d).expand().is_zero()) {
140 clog << "case 4, gcd(" << f << "," << g << ") = " << r << " (should be " << d << ")" << endl;
147 // Completely dense non-monic quadratic inputs with dense non-monic linear GCDs
148 static unsigned poly_gcd5()
150 for (int v=1; v<=MAX_VARIABLES; v++) {
154 for (int i=0; i<v; i++) {
163 ex r = gcd(f.expand(), g.expand());
164 if (!(r - d).expand().is_zero()) {
165 clog << "case 5, gcd(" << f << "," << g << ") = " << r << " (should be " << d << ")" << endl;
172 // Sparse non-monic quadratic inputs with linear GCDs
173 static unsigned poly_gcd5p()
175 for (int v=1; v<=MAX_VARIABLES; v++) {
177 for (int i=0; i<v; i++)
183 ex r = gcd(f.expand(), g.expand());
184 if (!(r - d).expand().is_zero()) {
185 clog << "case 5p, gcd(" << f << "," << g << ") = " << r << " (should be " << d << ")" << endl;
192 // Trivariate inputs with increasing degrees
193 static unsigned poly_gcd6()
197 for (int j=1; j<=MAX_VARIABLES; j++) {
198 ex d = pow(x, j) * y * (z - 1);
199 ex f = d * (pow(x, j) + pow(y, j + 1) * pow(z, j) + 1);
200 ex g = d * (pow(x, j + 1) + pow(y, j) * pow(z, j + 1) - 7);
201 ex r = gcd(f.expand(), g.expand());
202 if (!(r - d).expand().is_zero()) {
203 clog << "case 6, gcd(" << f << "," << g << ") = " << r << " (should be " << d << ")" << endl;
210 // Trivariate polynomials whose GCD has common factors with its cofactors
211 static unsigned poly_gcd7()
214 ex p = x - y * z + 1;
215 ex q = x - y + z * 3;
217 for (int j=1; j<=MAX_VARIABLES; j++) {
218 for (int k=j+1; k<=4; k++) {
219 ex d = pow(p, j) * pow(q, j);
220 ex f = pow(p, j) * pow(q, k);
221 ex g = pow(p, k) * pow(q, j);
223 if (!(r - d).expand().is_zero() && !(r + d).expand().is_zero()) {
224 clog << "case 7, gcd(" << f << "," << g << ") = " << r << " (should be " << d << ")" << endl;
232 unsigned exam_polygcd()
236 cout << "examining polynomial GCD computation" << flush;
238 result += poly_gcd1(); cout << '.' << flush;
239 result += poly_gcd2(); cout << '.' << flush;
240 result += poly_gcd3(); cout << '.' << flush;
241 result += poly_gcd3p(); cout << '.' << flush; // PRS "worst" case
242 result += poly_gcd4(); cout << '.' << flush;
243 result += poly_gcd5(); cout << '.' << flush;
244 result += poly_gcd5p(); cout << '.' << flush;
245 result += poly_gcd6(); cout << '.' << flush;
246 result += poly_gcd7(); cout << '.' << flush;
251 int main(int argc, char** argv)
253 return exam_polygcd();