normal.h

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/*
 *  GiNaC Copyright (C) 1999-2026 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, see <https://www.gnu.org/licenses/>.
 */
 
#ifndef GINAC_NORMAL_H
#define GINAC_NORMAL_H
 
#include "lst.h"
 
namespace GiNaC {
 
struct gcd_options
{
    enum {
        no_heur_gcd = 2,
        no_part_factored = 4,
        use_sr_gcd = 8
 
    };
};
 
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 = nullptr, ex *cb = nullptr,
              bool check_args = true, unsigned options = 0);
 
// 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