1 /** @file exam_normalization.cpp
3 * Rational function normalization test suite. */
6 * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
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25 static symbol w("w"), x("x"), y("y"), z("z");
27 static unsigned check_normal(const ex &e, const ex &d)
30 if (!en.is_equal(d)) {
31 clog << "normal form of " << e << " erroneously returned "
32 << en << " (should be " << d << ")" << endl;
38 static unsigned exam_normal1()
44 e = pow(x, 2) - (x+1)*(x-1) - 1;
46 result += check_normal(e, d);
48 // Expansion inside functions
49 e = sin(x*(x+1)-x) + 1;
50 d = sin(pow(x, 2)) + 1;
51 result += check_normal(e, d);
55 d = (x*y + 6) / (x*3);
56 result += check_normal(e, d);
58 e = pow(x, -1) + x/(x+1);
59 d = (pow(x, 2)+x+1)/(x*(x+1));
60 result += check_normal(e, d);
65 static unsigned exam_normal2()
70 // Fraction cancellation
71 e = numeric(1)/2 * z * (2*x + 2*y);
73 result += check_normal(e, d);
75 e = numeric(1)/6 * z * (3*x + 3*y) * (2*x + 2*w);
76 d = z * (x + y) * (x + w);
77 result += check_normal(e, d);
79 e = (3*x + 3*y) * (w/3 + z/3);
80 d = (x + y) * (w + z);
81 result += check_normal(e, d);
83 e = (pow(x, 2) - pow(y, 2)) / pow(x-y, 3);
84 d = (x + y) / pow(x - y, 2);
85 result += check_normal(e, d);
87 e = (pow(x, -1) + x) / (pow(x , 2) * 2 + 2);
89 result += check_normal(e, d);
91 // Fraction cancellation with rational coefficients
92 e = (pow(x, 2) - pow(y, 2)) / pow(x/2 - y/2, 3);
93 d = (8 * x + 8 * y) / pow(x - y, 2);
94 result += check_normal(e, d);
96 // Fraction cancellation with rational coefficients
97 e = z/5 * (x/7 + y/10) / (x/14 + y/20);
99 result += check_normal(e, d);
104 static unsigned exam_normal3()
109 // Distribution of powers
111 d = pow(x, 2) / pow(y, 2);
112 result += check_normal(e, d);
114 // Distribution of powers (integer, distribute) and fraction addition
115 e = pow(pow(x, -1) + x, 2);
116 d = pow(pow(x, 2) + 1, 2) / pow(x, 2);
117 result += check_normal(e, d);
119 // Distribution of powers (non-integer, don't distribute) and fraction addition
120 e = pow(pow(x, -1) + x, numeric(1)/2);
121 d = pow((pow(x, 2) + 1) / x, numeric(1)/2);
122 result += check_normal(e, d);
127 static unsigned exam_normal4()
132 // Replacement of functions with temporary symbols and fraction cancellation
133 e = pow(sin(x), 2) - pow(cos(x), 2);
134 e /= sin(x) + cos(x);
136 result += check_normal(e, d);
138 // Replacement of non-integer powers with temporary symbols
139 e = (pow(numeric(2), numeric(1)/2) * x + x) / x;
140 d = pow(numeric(2), numeric(1)/2) + 1;
141 result += check_normal(e, d);
143 // Replacement of complex numbers with temporary symbols
144 e = (x + y + x*I + y*I) / (x + y);
146 result += check_normal(e, d);
148 e = (pow(x, 2) + pow(y, 2)) / (x + y*I);
150 result += check_normal(e, d);
152 // More complex rational function
153 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);
154 d = (y*2 + z*2) / (x + y*2);
155 result += check_normal(e, d);
160 /* Test content(), integer_content(), primpart(). */
161 static unsigned check_content(const ex & e, const ex & x, const ex & ic, const ex & c, const ex & pp)
165 ex r_ic = e.integer_content();
166 if (!r_ic.is_equal(ic)) {
167 clog << "integer_content(" << e << ") erroneously returned "
168 << r_ic << " instead of " << ic << endl;
172 ex r_c = e.content(x);
173 if (!r_c.is_equal(c)) {
174 clog << "content(" << e << ", " << x << ") erroneously returned "
175 << r_c << " instead of " << c << endl;
179 ex r_pp = e.primpart(x);
180 if (!r_pp.is_equal(pp)) {
181 clog << "primpart(" << e << ", " << x << ") erroneously returned "
182 << r_pp << " instead of " << pp << endl;
186 ex r = r_c*r_pp*e.unit(x);
187 if (!(r - e).expand().is_zero()) {
188 clog << "product of unit, content, and primitive part of " << e << " yielded "
189 << r << " instead of " << e << endl;
196 static unsigned exam_content()
199 symbol x("x"), y("y");
201 result += check_content(ex(-3)/4, x, ex(3)/4, ex(3)/4, 1);
202 result += check_content(-x/4, x, ex(1)/4, ex(1)/4, x);
203 result += check_content(5*x-15, x, 5, 5, x-3);
204 result += check_content(5*x*y-15*y*y, x, 5, 5*y, x-3*y);
205 result += check_content(-15*x/2+ex(25)/3, x, ex(5)/6, ex(5)/6, 9*x-10);
206 result += check_content(-x*y, x, 1, y, x);
211 unsigned exam_normalization()
215 cout << "examining rational function normalization" << flush;
216 clog << "----------rational function normalization:" << endl;
218 result += exam_normal1(); cout << '.' << flush;
219 result += exam_normal2(); cout << '.' << flush;
220 result += exam_normal3(); cout << '.' << flush;
221 result += exam_normal4(); cout << '.' << flush;
222 result += exam_content(); cout << '.' << flush;
225 cout << " passed " << endl;
226 clog << "(no output)" << endl;
228 cout << " failed " << endl;