234 lines
6.4 KiB
C++
Executable File
234 lines
6.4 KiB
C++
Executable File
// Copyright (c) 2008 Max-Planck-Institute Saarbruecken (Germany).
|
|
// All rights reserved.
|
|
//
|
|
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
|
// modify it under the terms of the GNU Lesser General Public License as
|
|
// published by the Free Software Foundation; either version 3 of the License,
|
|
// or (at your option) any later version.
|
|
//
|
|
// Licensees holding a valid commercial license may use this file in
|
|
// accordance with the commercial license agreement provided with the software.
|
|
//
|
|
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
|
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
|
//
|
|
// $URL$
|
|
// $Id$
|
|
// SPDX-License-Identifier: LGPL-3.0+
|
|
//
|
|
//
|
|
// Author(s) : Michael Hemmer <hemmer@informatik.uni-mainz.de>
|
|
|
|
#ifndef CGAL_POLYNOMIAL_GCD_IMPLEMENTATIONS_H
|
|
#define CGAL_POLYNOMIAL_GCD_IMPLEMENTATIONS_H
|
|
|
|
|
|
#include <CGAL/basic.h>
|
|
#include <CGAL/Polynomial.h>
|
|
#include <CGAL/Real_timer.h>
|
|
#include <CGAL/polynomial_utils.h>
|
|
#include <CGAL/Polynomial/hgdelta_update.h>
|
|
#include <CGAL/Polynomial/polynomial_gcd.h>
|
|
|
|
|
|
namespace CGAL {
|
|
namespace internal {
|
|
|
|
template <class NT>
|
|
inline
|
|
Polynomial<NT> gcd_utcf_UFD(
|
|
Polynomial<NT> p1, Polynomial<NT> p2
|
|
) {
|
|
// implemented using the subresultant algorithm for gcd computation
|
|
// see [Cohen, 1993], algorithm 3.3.1
|
|
// handle trivial cases
|
|
if (p1.is_zero()){
|
|
if (p2.is_zero()) return Polynomial<NT>(NT(1));
|
|
else {
|
|
return CGAL::canonicalize(p2);
|
|
}
|
|
}
|
|
if (p2.is_zero()){
|
|
return CGAL::canonicalize(p1);
|
|
}
|
|
if (p2.degree() > p1.degree()) {
|
|
Polynomial<NT> p3 = p1; p1 = p2; p2 = p3;
|
|
}
|
|
|
|
// compute gcd of content
|
|
NT p1c = p1.content(), p2c = p2.content();
|
|
NT gcdcont = CGAL::gcd(p1c,p2c);
|
|
|
|
// compute gcd of primitive parts
|
|
p1 /= p1c; p2 /= p2c;
|
|
|
|
NT dummy;
|
|
Polynomial<NT> q, r;
|
|
|
|
NT g = NT(1), h = NT(1);
|
|
for (;;) {
|
|
Polynomial<NT>::pseudo_division(p1, p2, q, r, dummy);
|
|
if (r.is_zero()) { break; }
|
|
|
|
if (r.degree() == 0) {
|
|
return CGAL::canonicalize(Polynomial<NT>(gcdcont));
|
|
}
|
|
int delta = p1.degree() - p2.degree();
|
|
p1 = p2;
|
|
p2 = r / (g * ipower(h, delta));
|
|
g = p1.lcoeff();
|
|
// h = h^(1-delta) * g^delta
|
|
CGAL::internal::hgdelta_update(h, g, delta);
|
|
}
|
|
|
|
p2 /= p2.content() * p2.unit_part();
|
|
|
|
// combine both parts to proper gcd
|
|
p2 *= gcdcont;
|
|
|
|
return CGAL::canonicalize(p2);
|
|
}
|
|
|
|
template <class NT>
|
|
inline
|
|
Polynomial<NT> gcd_Euclidean_ring(
|
|
Polynomial<NT> p1, Polynomial<NT> p2
|
|
) {
|
|
// std::cout<<" gcd_Field"<<std::endl;
|
|
// handle trivial cases
|
|
if (p1.is_zero()){
|
|
if (p2.is_zero()) return Polynomial<NT>(NT(1));
|
|
else return p2 / p2.unit_part();
|
|
}
|
|
if (p2.is_zero())
|
|
return p1 / p1.unit_part();
|
|
if (p2.degree() > p1.degree()) {
|
|
Polynomial<NT> p3 = p1; p1 = p2; p2 = p3;
|
|
}
|
|
|
|
Polynomial<NT> q, r;
|
|
while (!p2.is_zero()) {
|
|
Polynomial<NT>::euclidean_division(p1, p2, q, r);
|
|
p1 = p2; p2 = r;
|
|
}
|
|
p1 /= p1.lcoeff();
|
|
p1.simplify_coefficients();
|
|
return p1;
|
|
}
|
|
|
|
template <class NT>
|
|
inline
|
|
NT content_utcf_(const Polynomial<NT>& p)
|
|
{
|
|
typename Algebraic_structure_traits<NT>::Integral_division idiv;
|
|
typename Algebraic_structure_traits<NT>::Unit_part upart;
|
|
typedef typename Polynomial<NT>::const_iterator const_iterator;
|
|
|
|
const_iterator it = p.begin(), ite = p.end();
|
|
while (*it == NT(0)) it++;
|
|
NT cont = idiv(*it, upart(*it));
|
|
for( ; it != ite; it++) {
|
|
if (cont == NT(1)) break;
|
|
if (*it != NT(0)) cont = internal::gcd_utcf_(cont, *it);
|
|
}
|
|
|
|
return cont;
|
|
}
|
|
|
|
|
|
template <class NT>
|
|
inline
|
|
Polynomial<NT> gcd_utcf_Integral_domain( Polynomial<NT> p1, Polynomial<NT> p2){
|
|
// std::cout<<" gcd_utcf_Integral_domain"<<std::endl;
|
|
typedef Polynomial<NT> POLY;
|
|
|
|
// handle trivial cases
|
|
if (p1.is_zero()){
|
|
if (p2.is_zero()){
|
|
return Polynomial<NT>(NT(1));
|
|
}else{
|
|
return CGAL::canonicalize(p2);
|
|
}
|
|
}
|
|
if (p2.is_zero()){
|
|
return CGAL::canonicalize(p1);
|
|
}
|
|
|
|
if (p2.degree() > p1.degree()) {
|
|
Polynomial<NT> p3 = p1; p1 = p2; p2 = p3;
|
|
}
|
|
|
|
// remove redundant scalar factors
|
|
p1=CGAL::canonicalize(p1);
|
|
p2=CGAL::canonicalize(p2);
|
|
|
|
// compute content of p1 and p2
|
|
NT p1c = internal::content_utcf_(p1);
|
|
NT p2c = internal::content_utcf_(p2);
|
|
|
|
|
|
// compute gcd of content
|
|
NT gcdcont = internal::gcd_utcf_(p1c, p2c);
|
|
|
|
// compute gcd of primitive parts
|
|
p1 = integral_division_up_to_constant_factor(p1, POLY(p1c));
|
|
p2 = integral_division_up_to_constant_factor(p2, POLY(p2c));
|
|
|
|
|
|
Polynomial<NT> q, r;
|
|
|
|
// TODO measure preformance of both methodes with respect to
|
|
// univariat polynomials on Integeres
|
|
// univariat polynomials on Sqrt_extension<Integer,Integer>
|
|
// multivariat polynomials
|
|
// May write specializations for different cases
|
|
#if 0
|
|
// implemented using the subresultant algorithm for gcd computation
|
|
// with respect to constant scalar factors
|
|
// see [Cohen, 1993], algorithm 3.3.1
|
|
NT g = NT(1), h = NT(1), dummy;
|
|
for (;;) {
|
|
Polynomial<NT>::pseudo_division(p1, p2, q, r, dummy);
|
|
if (r.is_zero()) { break; }
|
|
if (r.degree() == 0) { return Polynomial<NT>(gcdcont); }
|
|
int delta = p1.degree() - p2.degree();
|
|
p1 = p2;
|
|
p2 = r / (g * ipower(h, delta));
|
|
g = p1.lcoeff();
|
|
// h = h^(1-delta) * g^delta
|
|
CGAL::internal::hgdelta_update(h, g, delta);
|
|
}
|
|
#else
|
|
// implentaion using just the 'naive' methode
|
|
// but performed much better as the one by Cohen
|
|
// (for univariat polynomials with Sqrt_extension coeffs )
|
|
NT dummy;
|
|
for (;;) {
|
|
Polynomial<NT>::pseudo_division(p1, p2, q, r, dummy);
|
|
if (r.is_zero()) { break; }
|
|
if (r.degree() == 0) { return Polynomial<NT>(gcdcont); }
|
|
p1 = p2;
|
|
p2 = r ;
|
|
p2=CGAL::canonicalize(p2);
|
|
}
|
|
#endif
|
|
|
|
p2 = integral_division_up_to_constant_factor(p2, POLY(content_utcf_(p2)));
|
|
|
|
// combine both parts to proper gcd
|
|
p2 *= gcdcont;
|
|
|
|
Polynomial<NT> result;
|
|
|
|
// make poly unique
|
|
result = CGAL::canonicalize(p2);
|
|
return result;
|
|
}
|
|
|
|
|
|
} // namespace internal
|
|
|
|
} // namespace CGAL
|
|
|
|
#endif //CGAL_POLYNOMIAL_GCD_IMPLEMENTATIONS_H
|