* Rational function normalization test suite. */
/*
- * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2021 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
* 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");
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);
+ // 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, 2) + pow(y, 2) - x * y * 2);
- result += check_normal(e, d);
+// 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);
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;
}
return result;
}
+static unsigned exam_exponent_law()
+{
+ unsigned result = 0;
+ ex e, d;
+
+ // simple case
+ e = exp(2*x)-1;
+ e /= exp(x)-1;
+ d = exp(x)+1;
+ result += check_normal(e, d);
+
+ // More involved with powers of two exponents
+ e = exp(15*x)+exp(12*x)+2*exp(10*x)+2*exp(7*x);
+ e /= exp(5*x)+exp(2*x);
+ d = pow(exp(5*x), 2) +2*exp(5*x);
+ result += check_normal(e, d);
+
+ lst bases = {
+ 5*exp(3*x)+7, // Powers of a single exponent
+ 5*exp(3*x)+7*exp(2*x), // Two different factors of a single variable
+ 5*exp(3*x)+7*exp(2*y) // Exponent with different variable
+ };
+
+ for (auto den : bases) {
+ e = pow(den, 3).expand();
+ e /= pow(den, 2).expand();
+ result += check_normal(e, den);
+ }
+
+ // Negative exponents
+ e = (exp(2*x)-exp(-2*x))/(exp(x)-exp(-x));
+ ex en = e.normal();
+ // Either exp(x) or exp(-x) can be viewed as a "symbol" during run-time
+ // thus two different forms of the result are possible
+ ex r1 = (exp(2*x)+1)/exp(x) ;
+ ex r2 = (exp(-2*x)+1)/exp(-x);
+
+ if (!en.is_equal(r1) && !en.is_equal(r2)) {
+ clog << "normal form of " << e << " erroneously returned "
+ << en << " (should be " << r1 << " or " << r2 << ")" << endl;
+ result += 1;
+ }
+
+ return result;
+}
+
+static unsigned exam_power_law()
+{
+ unsigned result = 0;
+ ex e, d;
+
+ lst bases = {x, pow(x, numeric(1,3)), exp(x), sin(x)}; // We run all check for power base of different kinds
+
+ for ( auto b : bases ) {
+
+ // simple case
+ e = 4*b-9;
+ e /= 2*sqrt(b)-3;
+ d = 2*sqrt(b)+3;
+ result += check_normal(e, d);
+
+ // Fractional powers
+ e = 4*pow(b, numeric(2,3))-9;
+ e /= 2*pow(b, numeric(1,3))-3;
+ d = 2*pow(b, numeric(1,3))+3;
+ result += check_normal(e, d);
+
+ // Different powers with the same base
+ e = 4*b-9*sqrt(b);
+ e /= 2*sqrt(b)-3*pow(b, numeric(1,4));
+ d = 2*sqrt(b)+3*pow(b, numeric(1,4));
+ result += check_normal(e, d);
+
+ // Non-numeric powers
+ e = 4*pow(b, 2*y)-9;
+ e /= 2*pow(b, y)-3;
+ d = 2*pow(b, y)+3;
+ result += check_normal(e, d);
+
+ // Non-numeric fractional powers
+ e = 4*pow(b, y)-9;
+ e /= 2*pow(b, y/2)-3;
+ d = 2*pow(b, y/2)+3;
+ result += check_normal(e, d);
+
+ // Different non-numeric powers
+ e = 4*pow(b, 2*y)-9*pow(b, 2*z);
+ e /= 2*pow(b, y)-3*pow(b, z);
+ d = 2*pow(b, y)+3*pow(b, z);
+ result += check_normal(e, d);
+
+ // Different non-numeric fractional powers
+ e = 4*pow(b, y)-9*pow(b, z);
+ e /= 2*pow(b, y/2)-3*pow(b, z/2);
+ d = 2*pow(b, y/2)+3*pow(b, z/2);
+ result += check_normal(e, d);
+
+ // Negative powers
+ e = (b -pow(b,-1));
+ e /= (pow(b, numeric(1,2)) - pow(b, numeric(-1,2)));
+ d = (b+1)*pow(b, numeric(-1,2));
+ result += check_normal(e, d);
+ }
+
+ return result;
+}
+
unsigned exam_normalization()
{
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;
result += exam_content(); cout << '.' << flush;
-
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
+ result += exam_exponent_law(); cout << '.' << flush;
+ result += exam_power_law(); cout << '.' << flush;
return result;
}
+
+int main(int argc, char** argv)
+{
+ return exam_normalization();
+}
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