1 /** @file exam_normalization.cpp
3 * Rational function normalization test suite. */
6 * GiNaC Copyright (C) 1999-2004 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.compare(d) != 0) {
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, 2) + pow(y, 2) - 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, 2) + pow(y, 2) - 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 unsigned exam_normalization()
164 cout << "examining rational function normalization" << flush;
165 clog << "----------rational function normalization:" << endl;
167 result += exam_normal1(); cout << '.' << flush;
168 result += exam_normal2(); cout << '.' << flush;
169 result += exam_normal3(); cout << '.' << flush;
170 result += exam_normal4(); cout << '.' << flush;
173 cout << " passed " << endl;
174 clog << "(no output)" << endl;
176 cout << " failed " << endl;