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/** @file genex.cpp
*
* Provides some routines for generating expressions that are later used as
* input in the consistency checks. */
/*
* 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 <cstdlib>
#include "ginac.h"
using namespace std;
using namespace GiNaC;
/* Create a dense univariate random polynomial in x.
* (of the form 9 - 22*a - 17*a^2 + 14*a^3 + 7*a^4 + 7a^5 if degree==5) */
const ex
dense_univariate_poly(const symbol & x, unsigned degree)
{
ex unipoly;
for (unsigned i=0; i<=degree; ++i)
unipoly += numeric((rand()-RAND_MAX/2))*pow(x,i);
return unipoly;
}
/* Create a dense bivariate random polynomial in x1 and x2.
* (of the form 9 + 52*x1 - 27*x1^2 + 84*x2 + 7*x2^2 - 12*x1*x2 if degree==2)
*/
const ex
dense_bivariate_poly(const symbol & x1, const symbol & x2, unsigned degree)
{
ex bipoly;
for (unsigned i1=0; i1<=degree; ++i1)
for (unsigned i2=0; i2<=degree-i1; ++i2)
bipoly += numeric((rand()-RAND_MAX/2))*pow(x1,i1)*pow(x2,i2);
return bipoly;
}
/* Chose a randum symbol or number from the argument list. */
const ex
random_symbol(const symbol & x,
const symbol & y,
const symbol & z,
bool rational = true,
bool complex = false)
{
ex e;
switch (abs(rand()) % 4) {
case 0:
e = x;
break;
case 1:
e = y;
break;
case 2:
e = z;
break;
case 3: {
int c1;
do { c1 = rand()%20 - 10; } while (!c1);
int c2;
do { c2 = rand()%20 - 10; } while (!c2);
if (!rational)
c2 = 1;
e = numeric(c1, c2);
if (complex && !(rand()%5))
e = e*I;
break;
}
}
return e;
}
/* Create a sparse random tree in three symbols. */
const ex
sparse_tree(const symbol & x,
const symbol & y,
const symbol & z,
int level,
bool trig = false, // true includes trigonomatric functions
bool rational = true, // false excludes coefficients in Q
bool complex = false) // true includes complex numbers
{
if (level == 0)
return random_symbol(x,y,z,rational,complex);
switch (abs(rand()) % 10) {
case 0:
case 1:
case 2:
case 3:
return add(sparse_tree(x,y,z,level-1, trig, rational),
sparse_tree(x,y,z,level-1, trig, rational));
case 4:
case 5:
case 6:
return mul(sparse_tree(x,y,z,level-1, trig, rational),
sparse_tree(x,y,z,level-1, trig, rational));
case 7:
case 8: {
ex powbase;
do {
powbase = sparse_tree(x,y,z,level-1, trig, rational);
} while (powbase.is_zero());
return pow(powbase, abs(rand() % 4));
break;
}
case 9:
if (trig) {
switch (abs(rand()) % 4) {
case 0:
return sin(sparse_tree(x,y,z,level-1, trig, rational));
case 1:
return cos(sparse_tree(x,y,z,level-1, trig, rational));
case 2:
return exp(sparse_tree(x,y,z,level-1, trig, rational));
case 3: {
ex logex;
do {
ex logarg;
do {
logarg = sparse_tree(x,y,z,level-1, trig, rational);
} while (logarg.is_zero());
// Keep the evaluator from accidentally plugging an
// unwanted I in the tree:
if (!complex && logarg.info(info_flags::negative))
logarg = -logarg;
logex = log(logarg);
} while (logex.is_zero());
return logex;
break;
}
}
} else
return random_symbol(x,y,z,rational,complex);
}
}
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