/usr/include/pynac/normal.h is in libpynac-dev 0.6.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 | /** @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) 1999-2008 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 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 = nullptr, ex *cb = nullptr, 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__
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