/** @file normal.h * * This file defines several functions that work on univariate and * multivariate polynomials and rational functions. * These functions include polynomial quotient and remainder, GCD and LCM * computation, square-free factorization and rational function normalization. */ /* * GiNaC Copyright (C) 1999-2004 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 __GINAC_NORMAL_H__ #define __GINAC_NORMAL_H__ #include "lst.h" namespace GiNaC { 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 ex &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 ex &x, bool check_args = true); // Decompose rational function a(x)=N(x)/D(x) into Q(x)+R(x)/D(x) with degree(R, x) < degree(D, x) extern ex decomp_rational(const ex &a, const ex &x); // Pseudo-remainder of polynomials a(x) and b(x) in Q[x] extern ex prem(const ex &a, const ex &b, const ex &x, bool check_args = true); // Pseudo-remainder of polynomials a(x) and b(x) in Q[x] extern ex sprem(const ex &a, const ex &b, const ex &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 lst &l = lst()); // Square-free partial fraction decomposition of a rational function a(x) extern ex sqrfree_parfrac(const ex & a, const symbol & x); // Collect common factors in sums. extern ex collect_common_factors(const ex & e); // Resultant of two polynomials e1,e2 with respect to symbol s. extern ex resultant(const ex & e1, const ex & e2, const ex & s); } // namespace GiNaC #endif // ndef __GINAC_NORMAL_H__