1 /** @file exam_misc.cpp
6 * GiNaC Copyright (C) 1999-2007 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
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
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.
18 * You should have received a copy of the GNU General Public License
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;
29 static unsigned exam_expand_subs()
35 for (unsigned i=0; i<VECSIZE; ++i)
38 // prepare aux so it will swallow anything but a1^2:
39 aux = -e + a[0] + a[1];
40 e = expand(subs(expand(pow(e, 2)), a[0] == aux));
42 if (e != pow(a[1],2)) {
43 clog << "Denny Fliegner's quick consistency check erroneously returned "
51 /* A simple modification of Denny Fliegner's three step consistency test:
52 * 1) e = (a0 + a1)^200
54 * 3) substitute a0 by -a1 in e
55 * after which e should return 0 (without expanding). */
56 static unsigned exam_expand_subs2()
59 symbol a("a"), b("b");
62 e = pow(a+b,200).expand();
66 clog << "e = pow(a+b,200).expand(); f = e.subs(a == -b); erroneously returned "
67 << f << " instead of simplifying to 0." << endl;
74 static unsigned exam_expand_power()
77 symbol x("x"), a("a"), b("b");
80 e = pow(x,pow(a+b,2)-pow(a,2)-pow(b,2)-a*b*2).expand();
83 clog << "e = pow(x,pow(a+b,2)-pow(a,2)-pow(b,2)-a*b*2).expand(); erroneously returned "
84 << e << " instead of simplifying to 1." << endl;
91 static unsigned exam_sqrfree()
94 symbol x("x"), y("y");
97 e1 = (1+x)*pow((2+x),2)*pow((3+x),3)*pow((4+x),4);
98 e2 = sqrfree(expand(e1),lst(x));
100 clog << "sqrfree(expand(" << e1 << ")) erroneously returned "
105 e1 = (x+y)*pow((x+2*y),2)*pow((x+3*y),3)*pow((x+4*y),4);
106 e2 = sqrfree(expand(e1));
108 clog << "sqrfree(expand(" << e1 << ")) erroneously returned "
112 e2 = sqrfree(expand(e1),lst(x));
114 clog << "sqrfree(expand(" << e1 << "),[x]) erroneously returned "
118 e2 = sqrfree(expand(e1),lst(y));
120 clog << "sqrfree(expand(" << e1 << "),[y]) erroneously returned "
124 e2 = sqrfree(expand(e1),lst(x,y));
126 clog << "sqrfree(expand(" << e1 << "),[x,y]) erroneously returned "
134 /* Arithmetic Operators should behave just as one expects from built-in types.
135 * When somebody screws up the operators this routine will most probably fail
136 * to compile. Unfortunately we can only test the stuff that is allowed, not
137 * what is forbidden (e.g. e1+e2 = 42) since that must not compile. :-( */
138 static unsigned exam_operator_semantics()
144 // Assignment should not return const ex though it may be obfuscated:
149 if (e1!=i1 || e2!=i2) {
150 clog << "Semantics of ex::operator=() screwed." << endl;
155 if (e1!=i1 || e2!=i2) {
156 clog << "Semantics of ex::operator=() screwed." << endl;
161 if (e1!=i1 || e2!=i2) {
162 clog << "Semantics of ex::operator=() screwed." << endl;
166 // Prefix/postfix increment/decrement behaviour:
171 if (e1!=i1 || e2!=i2) {
172 clog << "Semantics of increment/decrement operators screwed." << endl;
177 if (e1!=i1 || e2!=i2) {
178 clog << "Semantics of increment/decrement operators screwed." << endl;
182 // prefix increment/decrement must return an lvalue (contrary to postfix):
185 --++----e1; ++(++++++++(++++e2));
186 --++----i1; ++(++++++++(++++i2));
187 if (e1!=i1 || e2!=i2) {
188 clog << "Semantics of prefix increment/decrement operators screwed." << endl;
192 // This one has a good chance of detecting problems in self-assignment:
193 // (which incidentally was severely broken from version 0.7.3 to 0.8.2).
194 ex selfprobe = numeric("65536");
195 selfprobe = selfprobe;
196 if (!is_exactly_a<numeric>(selfprobe)) {
197 clog << "ex (of numeric) after self-assignment became " << selfprobe << endl;
204 /* This checks whether subs() works as intended in some special cases. */
205 static unsigned exam_subs()
211 // This used to fail in GiNaC 1.0.5 because it first substituted
212 // x+1 -> (x-1)+1 -> x, and then substituted again x -> x-1, giving
215 e2 = e1.subs(x == x-1);
216 if (!e2.is_equal(x)) {
217 clog << "(x+1).subs(x==x-1) erroneously returned " << e2 << " instead of x" << endl;
222 e2 = e1.subs(sin(wild()) == cos(wild()));
223 if (!e2.is_equal(cos(1+cos(x)))) {
224 clog << "sin(1+sin(x)).subs(sin($1)==cos($1)) erroneously returned " << e2 << " instead of cos(1+cos(x))" << endl;
231 /* Joris van der Hoeven (he of TeXmacs fame) is a funny guy. He has his own
232 * ideas what a symbolic system should do. Let's make sure we won't disappoint
233 * him some day. Incidentally, this seems to always have worked. */
234 static unsigned exam_joris()
239 ex e = expand(pow(x, x-1) * x);
240 if (e != pow(x, x)) {
241 clog << "x^(x-1)*x did not expand to x^x. Please call Joris!" << endl;
248 /* Test Chris Dams' algebraic substitutions. */
249 static unsigned exam_subs_algebraic()
252 symbol x("x"), y("y");
254 ex e = ex(x*x*x*y*y).subs(x*y==2, subs_options::algebraic);
256 clog << "(x^3*y^2).subs(x*y==2,subs_options::algebraic) erroneously returned " << e << endl;
260 e = ex(x*x*x*x*x).subs(x*x==y, subs_options::algebraic);
262 clog << "x^5.subs(x^2==y,subs_options::algebraic) erroneously returned " << e << endl;
267 if (!e.has(x*y, has_options::algebraic))
268 { clog << "(x^2*y).has(x*y, has_options::algebraic) erroneously returned false." << endl;
272 if (e.has(x*y*y, has_options::algebraic))
273 { clog << "(x^2*y).has(x*y*y, has_options::algebraic) erroneously returned true." << endl;
278 if (!e.has(x*x, has_options::algebraic))
279 { clog << "(x^3*y).has(x*x, has_options::algebraic) erroneously returned false." << endl;
283 if (e.has(y*y, has_options::algebraic))
284 { clog << "(x^3*y).has(y*y, has_options::algebraic) erroneously returned true." << endl;
295 cout << "examining miscellaneous other things" << flush;
297 result += exam_expand_subs(); cout << '.' << flush;
298 result += exam_expand_subs2(); cout << '.' << flush;
299 result += exam_expand_power(); cout << '.' << flush;
300 result += exam_sqrfree(); cout << '.' << flush;
301 result += exam_operator_semantics(); cout << '.' << flush;
302 result += exam_subs(); cout << '.' << flush;
303 result += exam_joris(); cout << '.' << flush;
304 result += exam_subs_algebraic(); cout << '.' << flush;
309 int main(int argc, char** argv)