3 * Functions for polynomial quotient and remainder, GCD and LCM computation
4 * and square-free factorization. */
7 * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
9 * This program is free software; you can redistribute it and/or modify
10 * it under the terms of the GNU General Public License as published by
11 * the Free Software Foundation; either version 2 of the License, or
12 * (at your option) any later version.
14 * This program is distributed in the hope that it will be useful,
15 * but WITHOUT ANY WARRANTY; without even the implied warranty of
16 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 * GNU General Public License for more details.
19 * You should have received a copy of the GNU General Public License
20 * along with this program; if not, write to the Free Software
21 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
24 #ifndef __GINAC_NORMAL_H__
25 #define __GINAC_NORMAL_H__
32 // Quotient q(x) of polynomials a(x) and b(x) in Q[x], so that a(x)=b(x)*q(x)+r(x)
33 extern ex quo(const ex &a, const ex &b, const symbol &x, bool check_args = true);
35 // Remainder r(x) of polynomials a(x) and b(x) in Q[x], so that a(x)=b(x)*q(x)+r(x)
36 extern ex rem(const ex &a, const ex &b, const symbol &x, bool check_args = true);
38 // Pseudo-remainder of polynomials a(x) and b(x) in Z[x]
39 extern ex prem(const ex &a, const ex &b, const symbol &x, bool check_args = true);
41 // Exact polynomial division of a(X) by b(X) in Q[X] (quotient returned in q), returns false when exact division fails
42 extern bool divide(const ex &a, const ex &b, ex &q, bool check_args = true);
44 // Polynomial GCD in Z[X], cofactors are returned in ca and cb, if desired
45 extern ex gcd(const ex &a, const ex &b, ex *ca = NULL, ex *cb = NULL, bool check_args = true);
47 // Polynomial LCM in Z[X]
48 extern ex lcm(const ex &a, const ex &b, bool check_args = true);
50 // Square-free factorization of a polynomial a(x)
51 extern ex sqrfree(const ex &a, const symbol &x);
55 #endif // ndef __GINAC_NORMAL_H__