1 /** @file exam_normalization.cpp
3 * Rational function normalization test suite. */
6 * GiNaC Copyright (C) 1999-2018 Johannes Gutenberg University Mainz, Germany
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14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
24 using namespace GiNaC;
29 static symbol w("w"), x("x"), y("y"), z("z");
31 static unsigned check_normal(const ex &e, const ex &d)
34 if (!en.is_equal(d)) {
35 clog << "normal form of " << e << " erroneously returned "
36 << en << " (should be " << d << ")" << endl;
42 static unsigned exam_normal1()
48 e = pow(x, 2) - (x+1)*(x-1) - 1;
50 result += check_normal(e, d);
52 // Expansion inside functions
53 e = sin(x*(x+1)-x) + 1;
54 d = sin(pow(x, 2)) + 1;
55 result += check_normal(e, d);
59 d = (x*y + 6) / (x*3);
60 result += check_normal(e, d);
62 e = pow(x, -1) + x/(x+1);
63 d = (pow(x, 2)+x+1)/(x*(x+1));
64 result += check_normal(e, d);
69 static unsigned exam_normal2()
74 // Fraction cancellation
75 e = numeric(1)/2 * z * (2*x + 2*y);
77 result += check_normal(e, d);
79 e = numeric(1)/6 * z * (3*x + 3*y) * (2*x + 2*w);
80 d = z * (x + y) * (x + w);
81 result += check_normal(e, d);
83 e = (3*x + 3*y) * (w/3 + z/3);
84 d = (x + y) * (w + z);
85 result += check_normal(e, d);
87 // Fails stochastically with the new tinfo mechanism, because
88 // sometimes the equivalent answer ... / pow(y - x, 2) is calculated.
89 // TODO: make check for both cases.
90 // e = (pow(x, 2) - pow(y, 2)) / pow(x-y, 3);
91 // d = (x + y) / pow(x - y, 2);
92 // result += check_normal(e, d);
94 e = (pow(x, -1) + x) / (pow(x , 2) * 2 + 2);
96 result += check_normal(e, d);
98 // Fails stochastically with the new tinfo mechanism, because
99 // sometimes the equivalent answer ... / pow(y - x, 2) is calculated.
100 // TODO: make check for both cases.
101 // Fraction cancellation with rational coefficients
102 // e = (pow(x, 2) - pow(y, 2)) / pow(x/2 - y/2, 3);
103 // d = (8 * x + 8 * y) / pow(x - y, 2);
104 // result += check_normal(e, d);
106 // Fraction cancellation with rational coefficients
107 e = z/5 * (x/7 + y/10) / (x/14 + y/20);
109 result += check_normal(e, d);
114 static unsigned exam_normal3()
119 // Distribution of powers
121 d = pow(x, 2) / pow(y, 2);
122 result += check_normal(e, d);
124 // Distribution of powers (integer, distribute) and fraction addition
125 e = pow(pow(x, -1) + x, 2);
126 d = pow(pow(x, 2) + 1, 2) / pow(x, 2);
127 result += check_normal(e, d);
129 // Distribution of powers (non-integer, don't distribute) and fraction addition
130 e = pow(pow(x, -1) + x, numeric(1)/2);
131 d = pow((pow(x, 2) + 1) / x, numeric(1)/2);
132 result += check_normal(e, d);
137 static unsigned exam_normal4()
142 // Replacement of functions with temporary symbols and fraction cancellation
143 e = pow(sin(x), 2) - pow(cos(x), 2);
144 e /= sin(x) + cos(x);
146 result += check_normal(e, d);
148 // Replacement of non-integer powers with temporary symbols
149 e = (pow(numeric(2), numeric(1)/2) * x + x) / x;
150 d = pow(numeric(2), numeric(1)/2) + 1;
151 result += check_normal(e, d);
153 // Replacement of complex numbers with temporary symbols
154 e = (x + y + x*I + y*I) / (x + y);
156 result += check_normal(e, d);
158 e = (pow(x, 2) + pow(y, 2)) / (x + y*I);
160 result += check_normal(e, d);
162 // More complex rational function
163 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);
164 d = (y*2 + z*2) / (x + y*2);
165 result += check_normal(e, d);
167 // Replacement of nested functions with temporary symbols
168 e = x/(sqrt(sin(z)-1)) + y/(sqrt(sin(z)-1));
169 d = (x + y)/(sqrt(sin(z)-1));
170 result += check_normal(e, d);
175 /* Test content(), integer_content(), primpart(). */
176 static unsigned check_content(const ex & e, const ex & x, const ex & ic, const ex & c, const ex & pp)
180 ex r_ic = e.integer_content();
181 if (!r_ic.is_equal(ic)) {
182 clog << "integer_content(" << e << ") erroneously returned "
183 << r_ic << " instead of " << ic << endl;
187 ex r_c = e.content(x);
188 if (!r_c.is_equal(c)) {
189 clog << "content(" << e << ", " << x << ") erroneously returned "
190 << r_c << " instead of " << c << endl;
194 ex r_pp = e.primpart(x);
195 if (!r_pp.is_equal(pp)) {
196 clog << "primpart(" << e << ", " << x << ") erroneously returned "
197 << r_pp << " instead of " << pp << endl;
201 ex r = r_c*r_pp*e.unit(x);
202 if (!(r - e).expand().is_zero()) {
203 clog << "product of unit, content, and primitive part of " << e << " yielded "
204 << r << " instead of " << e << endl;
211 static unsigned exam_content()
214 symbol x("x"), y("y");
216 result += check_content(ex(-3)/4, x, ex(3)/4, ex(3)/4, 1);
217 result += check_content(-x/4, x, ex(1)/4, ex(1)/4, x);
218 result += check_content(5*x-15, x, 5, 5, x-3);
219 result += check_content(5*x*y-15*y*y, x, 5, 5*y, x-3*y);
220 result += check_content(-15*x/2+ex(25)/3, x, ex(5)/6, ex(5)/6, 9*x-10);
221 result += check_content(-x*y, x, 1, y, x);
226 unsigned exam_normalization()
230 cout << "examining rational function normalization" << flush;
232 result += exam_normal1(); cout << '.' << flush;
233 result += exam_normal2(); cout << '.' << flush;
234 result += exam_normal3(); cout << '.' << flush;
235 result += exam_normal4(); cout << '.' << flush;
236 result += exam_content(); cout << '.' << flush;
241 int main(int argc, char** argv)
243 return exam_normalization();