3 * This file defines several functions that work on univariate and
4 * multivariate polynomials and rational functions.
5 * These functions include polynomial quotient and remainder, GCD and LCM
6 * computation, square-free factorization and rational function normalization. */
9 * GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
11 * This program is free software; you can redistribute it and/or modify
12 * it under the terms of the GNU General Public License as published by
13 * the Free Software Foundation; either version 2 of the License, or
14 * (at your option) any later version.
16 * This program is distributed in the hope that it will be useful,
17 * but WITHOUT ANY WARRANTY; without even the implied warranty of
18 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 * GNU General Public License for more details.
21 * You should have received a copy of the GNU General Public License
22 * along with this program; if not, write to the Free Software
23 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
26 #ifndef __GINAC_NORMAL_H__
27 #define __GINAC_NORMAL_H__
34 * Flags to control the behaviour of gcd() and friends
40 * Usually GiNaC tries heuristic GCD algorithm before PRS.
41 * Some people don't like this, so here's a flag to disable it.
45 * GiNaC tries to avoid expanding expressions when computing
46 * GCDs. This is a good idea, but some people dislike it.
47 * Hence the flag to disable special handling of partially
48 * factored polynomials. DON'T SET THIS unless you *really*
49 * know what are you doing!
58 // Quotient q(x) of polynomials a(x) and b(x) in Q[x], so that a(x)=b(x)*q(x)+r(x)
59 extern ex quo(const ex &a, const ex &b, const ex &x, bool check_args = true);
61 // Remainder r(x) of polynomials a(x) and b(x) in Q[x], so that a(x)=b(x)*q(x)+r(x)
62 extern ex rem(const ex &a, const ex &b, const ex &x, bool check_args = true);
64 // Decompose rational function a(x)=N(x)/D(x) into Q(x)+R(x)/D(x) with degree(R, x) < degree(D, x)
65 extern ex decomp_rational(const ex &a, const ex &x);
67 // Pseudo-remainder of polynomials a(x) and b(x) in Q[x]
68 extern ex prem(const ex &a, const ex &b, const ex &x, bool check_args = true);
70 // Pseudo-remainder of polynomials a(x) and b(x) in Q[x]
71 extern ex sprem(const ex &a, const ex &b, const ex &x, bool check_args = true);
73 // Exact polynomial division of a(X) by b(X) in Q[X] (quotient returned in q), returns false when exact division fails
74 extern bool divide(const ex &a, const ex &b, ex &q, bool check_args = true);
76 // Polynomial GCD in Z[X], cofactors are returned in ca and cb, if desired
77 extern ex gcd(const ex &a, const ex &b, ex *ca = NULL, ex *cb = NULL,
78 bool check_args = true, unsigned options = 0);
80 // Polynomial LCM in Z[X]
81 extern ex lcm(const ex &a, const ex &b, bool check_args = true);
83 // Square-free factorization of a polynomial a(x)
84 extern ex sqrfree(const ex &a, const lst &l = lst());
86 // Square-free partial fraction decomposition of a rational function a(x)
87 extern ex sqrfree_parfrac(const ex & a, const symbol & x);
89 // Collect common factors in sums.
90 extern ex collect_common_factors(const ex & e);
92 // Resultant of two polynomials e1,e2 with respect to symbol s.
93 extern ex resultant(const ex & e1, const ex & e2, const ex & s);
97 #endif // ndef __GINAC_NORMAL_H__