/** @file normal.h
*
* Functions for polynomial quotient and remainder, GCD and LCM computation
* and square-free factorization. */
/*
* GiNaC Copyright (C) 1999 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
*/
#ifndef NORMAL_H
#define NORMAL_H
class ex;
class symbol;
// Quotient q(x) of polynomials a(x) and b(x) in Q[x], so that a(x)=b(x)*q(x)+r(x)
extern ex quo(const ex &a, const ex &b, const symbol &x, bool check_args = true);
// Remainder r(x) of polynomials a(x) and b(x) in Q[x], so that a(x)=b(x)*q(x)+r(x)
extern ex rem(const ex &a, const ex &b, const symbol &x, bool check_args = true);
// Pseudo-remainder of polynomials a(x) and b(x) in Z[x]
extern ex prem(const ex &a, const ex &b, const symbol &x, bool check_args = true);
// Exact polynomial division of a(X) by b(X) in Q[X] (quotient returned in q), returns false when exact division fails
extern bool divide(const ex &a, const ex &b, ex &q, bool check_args = true);
// Polynomial GCD in Z[X], cofactors are returned in ca and cb, if desired
extern ex gcd(const ex &a, const ex &b, ex *ca = NULL, ex *cb = NULL, bool check_args = true);
// Polynomial LCM in Z[X]
extern ex lcm(const ex &a, const ex &b, bool check_args = true);
// Square-free factorization of a polynomial a(x)
extern ex sqrfree(const ex &a, const symbol &x);
#endif