* Rational function normalization test suite. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2016 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include "exams.h"
+#include "ginac.h"
+using namespace GiNaC;
+
+#include <iostream>
+using namespace std;
static symbol w("w"), x("x"), y("y"), z("z");
static unsigned check_normal(const ex &e, const ex &d)
{
- ex en = e.normal();
- if (en.compare(d) != 0) {
- clog << "normal form of " << e << " erroneously returned "
- << en << " (should be " << d << ")" << endl;
- return 1;
- }
- return 0;
+ ex en = e.normal();
+ if (!en.is_equal(d)) {
+ clog << "normal form of " << e << " erroneously returned "
+ << en << " (should be " << d << ")" << endl;
+ return 1;
+ }
+ return 0;
+}
+
+static unsigned exam_normal1()
+{
+ unsigned result = 0;
+ ex e, d;
+
+ // Expansion
+ e = pow(x, 2) - (x+1)*(x-1) - 1;
+ d = 0;
+ result += check_normal(e, d);
+
+ // Expansion inside functions
+ e = sin(x*(x+1)-x) + 1;
+ d = sin(pow(x, 2)) + 1;
+ result += check_normal(e, d);
+
+ // Fraction addition
+ e = 2/x + y/3;
+ d = (x*y + 6) / (x*3);
+ result += check_normal(e, d);
+
+ e = pow(x, -1) + x/(x+1);
+ d = (pow(x, 2)+x+1)/(x*(x+1));
+ result += check_normal(e, d);
+
+ return result;
+}
+
+static unsigned exam_normal2()
+{
+ unsigned result = 0;
+ ex e, d;
+
+ // Fraction cancellation
+ e = numeric(1)/2 * z * (2*x + 2*y);
+ d = z * (x + y);
+ result += check_normal(e, d);
+
+ e = numeric(1)/6 * z * (3*x + 3*y) * (2*x + 2*w);
+ d = z * (x + y) * (x + w);
+ result += check_normal(e, d);
+
+ e = (3*x + 3*y) * (w/3 + z/3);
+ d = (x + y) * (w + z);
+ result += check_normal(e, d);
+
+ // Fails stochastically with the new tinfo mechanism, because
+ // sometimes the equivalent answer ... / pow(y - x, 2) is calculated.
+ // TODO: make check for both cases.
+// e = (pow(x, 2) - pow(y, 2)) / pow(x-y, 3);
+// d = (x + y) / pow(x - y, 2);
+// result += check_normal(e, d);
+
+ e = (pow(x, -1) + x) / (pow(x , 2) * 2 + 2);
+ d = pow(x * 2, -1);
+ result += check_normal(e, d);
+
+ // Fails stochastically with the new tinfo mechanism, because
+ // sometimes the equivalent answer ... / pow(y - x, 2) is calculated.
+ // TODO: make check for both cases.
+ // Fraction cancellation with rational coefficients
+// e = (pow(x, 2) - pow(y, 2)) / pow(x/2 - y/2, 3);
+// d = (8 * x + 8 * y) / pow(x - y, 2);
+// result += check_normal(e, d);
+
+ // Fraction cancellation with rational coefficients
+ e = z/5 * (x/7 + y/10) / (x/14 + y/20);
+ d = 2*z/5;
+ result += check_normal(e, d);
+
+ return result;
+}
+
+static unsigned exam_normal3()
+{
+ unsigned result = 0;
+ ex e, d;
+
+ // Distribution of powers
+ e = pow(x/y, 2);
+ d = pow(x, 2) / pow(y, 2);
+ result += check_normal(e, d);
+
+ // Distribution of powers (integer, distribute) and fraction addition
+ e = pow(pow(x, -1) + x, 2);
+ d = pow(pow(x, 2) + 1, 2) / pow(x, 2);
+ result += check_normal(e, d);
+
+ // Distribution of powers (non-integer, don't distribute) and fraction addition
+ e = pow(pow(x, -1) + x, numeric(1)/2);
+ d = pow((pow(x, 2) + 1) / x, numeric(1)/2);
+ result += check_normal(e, d);
+
+ return result;
}
-static unsigned exam_normal1(void)
+static unsigned exam_normal4()
{
- unsigned result = 0;
- ex e, d;
-
- // Expansion
- e = pow(x, 2) - (x+1)*(x-1) - 1;
- d = ex(0);
- result += check_normal(e, d);
-
- // Expansion inside functions
- e = sin(x*(x+1)-x) + 1;
- d = sin(pow(x, 2)) + 1;
- result += check_normal(e, d);
-
- // Fraction addition
- e = 2/x + y/3;
- d = (x*y + 6) / (x*3);
- result += check_normal(e, d);
-
- e = pow(x, -1) + x/(x+1);
- d = (pow(x, 2)+x+1)/(x*(x+1));
- result += check_normal(e, d);
-
- return result;
+ unsigned result = 0;
+ ex e, d;
+
+ // Replacement of functions with temporary symbols and fraction cancellation
+ e = pow(sin(x), 2) - pow(cos(x), 2);
+ e /= sin(x) + cos(x);
+ d = sin(x) - cos(x);
+ result += check_normal(e, d);
+
+ // Replacement of non-integer powers with temporary symbols
+ e = (pow(numeric(2), numeric(1)/2) * x + x) / x;
+ d = pow(numeric(2), numeric(1)/2) + 1;
+ result += check_normal(e, d);
+
+ // Replacement of complex numbers with temporary symbols
+ e = (x + y + x*I + y*I) / (x + y);
+ d = 1 + I;
+ result += check_normal(e, d);
+
+ e = (pow(x, 2) + pow(y, 2)) / (x + y*I);
+ d = e;
+ result += check_normal(e, d);
+
+ // More complex rational function
+ 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);
+ d = (y*2 + z*2) / (x + y*2);
+ result += check_normal(e, d);
+
+ // Replacement of nested functions with temporary symbols
+ e = x/(sqrt(sin(z)-1)) + y/(sqrt(sin(z)-1));
+ d = (x + y)/(sqrt(sin(z)-1));
+ result += check_normal(e, d);
+
+ return result;
}
-static unsigned exam_normal2(void)
+/* Test content(), integer_content(), primpart(). */
+static unsigned check_content(const ex & e, const ex & x, const ex & ic, const ex & c, const ex & pp)
{
- unsigned result = 0;
- ex e, d;
-
- // Fraction cancellation
- e = numeric(1)/2 * z * (2*x + 2*y);
- d = z * (x + y);
- result += check_normal(e, d);
-
- e = numeric(1)/6 * z * (3*x + 3*y) * (2*x + 2*w);
- d = z * (x + y) * (x + w);
- result += check_normal(e, d);
-
- e = (3*x + 3*y) * (w/3 + z/3);
- d = (x + y) * (w + z);
- result += check_normal(e, d);
-
- e = (pow(x, 2) - pow(y, 2)) / pow(x-y, 3);
- d = (x + y) / (pow(x, 2) + pow(y, 2) - x * y * 2);
- result += check_normal(e, d);
-
- e = (pow(x, -1) + x) / (pow(x , 2) * 2 + 2);
- d = pow(x * 2, -1);
- result += check_normal(e, d);
-
- // Fraction cancellation with rational coefficients
- e = (pow(x, 2) - pow(y, 2)) / pow(x/2 - y/2, 3);
- d = (8 * x + 8 * y) / (pow(x, 2) + pow(y, 2) - x * y * 2);
- result += check_normal(e, d);
-
- // Fraction cancellation with rational coefficients
- e = z/5 * (x/7 + y/10) / (x/14 + y/20);
- d = 2*z/5;
- result += check_normal(e, d);
-
- return result;
+ unsigned result = 0;
+
+ ex r_ic = e.integer_content();
+ if (!r_ic.is_equal(ic)) {
+ clog << "integer_content(" << e << ") erroneously returned "
+ << r_ic << " instead of " << ic << endl;
+ ++result;
+ }
+
+ ex r_c = e.content(x);
+ if (!r_c.is_equal(c)) {
+ clog << "content(" << e << ", " << x << ") erroneously returned "
+ << r_c << " instead of " << c << endl;
+ ++result;
+ }
+
+ ex r_pp = e.primpart(x);
+ if (!r_pp.is_equal(pp)) {
+ clog << "primpart(" << e << ", " << x << ") erroneously returned "
+ << r_pp << " instead of " << pp << endl;
+ ++result;
+ }
+
+ ex r = r_c*r_pp*e.unit(x);
+ if (!(r - e).expand().is_zero()) {
+ clog << "product of unit, content, and primitive part of " << e << " yielded "
+ << r << " instead of " << e << endl;
+ ++result;
+ }
+
+ return result;
}
-static unsigned exam_normal3(void)
+static unsigned exam_content()
{
- unsigned result = 0;
- ex e, d;
-
- // Distribution of powers
- e = pow(x/y, 2);
- d = pow(x, 2) / pow(y, 2);
- result += check_normal(e, d);
-
- // Distribution of powers (integer, distribute) and fraction addition
- e = pow(pow(x, -1) + x, 2);
- d = pow(pow(x, 2) + 1, 2) / pow(x, 2);
- result += check_normal(e, d);
-
- // Distribution of powers (non-integer, don't distribute) and fraction addition
- e = pow(pow(x, -1) + x, numeric(1)/2);
- d = pow((pow(x, 2) + 1) / x, numeric(1)/2);
- result += check_normal(e, d);
-
- return result;
+ unsigned result = 0;
+ symbol x("x"), y("y");
+
+ result += check_content(ex(-3)/4, x, ex(3)/4, ex(3)/4, 1);
+ result += check_content(-x/4, x, ex(1)/4, ex(1)/4, x);
+ result += check_content(5*x-15, x, 5, 5, x-3);
+ result += check_content(5*x*y-15*y*y, x, 5, 5*y, x-3*y);
+ result += check_content(-15*x/2+ex(25)/3, x, ex(5)/6, ex(5)/6, 9*x-10);
+ result += check_content(-x*y, x, 1, y, x);
+
+ return result;
}
-static unsigned exam_normal4(void)
+unsigned exam_normalization()
{
- unsigned result = 0;
- ex e, d;
-
- // Replacement of functions with temporary symbols and fraction cancellation
- e = pow(sin(x), 2) - pow(cos(x), 2);
- e /= sin(x) + cos(x);
- d = sin(x) - cos(x);
- result += check_normal(e, d);
-
- // Replacement of non-integer powers with temporary symbols
- e = (pow(numeric(2), numeric(1)/2) * x + x) / x;
- d = pow(numeric(2), numeric(1)/2) + 1;
- result += check_normal(e, d);
-
- // Replacement of complex numbers with temporary symbols
- e = (x + y + x*I + y*I) / (x + y);
- d = 1 + I;
- result += check_normal(e, d);
-
- e = (pow(x, 2) + pow(y, 2)) / (x + y*I);
- d = e;
- result += check_normal(e, d);
-
- // More complex rational function
- 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);
- d = (y*2 + z*2) / (x + y*2);
- result += check_normal(e, d);
-
- return result;
+ unsigned result = 0;
+
+ cout << "examining rational function normalization" << flush;
+
+ result += exam_normal1(); cout << '.' << flush;
+ result += exam_normal2(); cout << '.' << flush;
+ result += exam_normal3(); cout << '.' << flush;
+ result += exam_normal4(); cout << '.' << flush;
+ result += exam_content(); cout << '.' << flush;
+
+ return result;
}
-unsigned exam_normalization(void)
+int main(int argc, char** argv)
{
- unsigned result = 0;
-
- cout << "examining rational function normalization" << flush;
- clog << "----------rational function normalization:" << endl;
-
- result += exam_normal1(); cout << '.' << flush;
- result += exam_normal2(); cout << '.' << flush;
- result += exam_normal3(); cout << '.' << flush;
- result += exam_normal4(); cout << '.' << flush;
-
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
-
- return result;
+ return exam_normalization();
}