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/** @file exam_normalization.cpp
*
* Rational function normalization test suite. */
/*
* GiNaC Copyright (C) 1999-2002 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
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* 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
*/
#include "exams.h"
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;
}
static unsigned exam_normal1(void)
{
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(void)
{
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;
}
static unsigned exam_normal3(void)
{
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_normal4(void)
{
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 exam_normalization(void)
{
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;
}
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