150 lines
6.4 KiB
C
150 lines
6.4 KiB
C
|
// Copyright (c) 2008 Max-Planck-Institute Saarbruecken (Germany)
|
||
|
//
|
||
|
// This file is part of CGAL (www.cgal.org)
|
||
|
//
|
||
|
// $URL: https://github.com/CGAL/cgal/blob/v5.1/Polynomial/include/CGAL/Polynomial/fwd.h $
|
||
|
// $Id: fwd.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
|
||
|
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
|
||
|
//
|
||
|
//
|
||
|
// Author(s) : Michael Hemmer
|
||
|
// ============================================================================
|
||
|
|
||
|
|
||
|
#ifndef CGAL_POLYNOMIAL_FWD_H
|
||
|
#define CGAL_POLYNOMIAL_FWD_H
|
||
|
|
||
|
#include <CGAL/basic.h>
|
||
|
|
||
|
namespace CGAL{
|
||
|
|
||
|
template <class NT> class Polynomial;
|
||
|
|
||
|
namespace internal{
|
||
|
template <class NT> inline Polynomial<NT> gcd_(const Polynomial<NT>&, const Polynomial<NT>&);
|
||
|
template <class NT> inline Polynomial<NT> gcd_(const Polynomial<NT>&, const Polynomial<NT>&, Field_tag);
|
||
|
template <class NT> inline Polynomial<NT> gcd_(const Polynomial<NT>&, const Polynomial<NT>&, Unique_factorization_domain_tag);
|
||
|
|
||
|
|
||
|
template <class NT> inline NT gcd_utcf_(const NT& /*a*/, const NT& /*b*/){return NT(1);}
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_(const Polynomial<NT>&, const Polynomial<NT>&);
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_UFD( Polynomial<NT> , Polynomial<NT>) ;
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_Integral_domain(Polynomial<NT>, Polynomial<NT>);
|
||
|
template <class NT> inline Polynomial<NT> gcd_Euclidean_ring(Polynomial<NT>, Polynomial<NT>);
|
||
|
|
||
|
template <class NT> inline Polynomial<NT> modular_gcd_utcf(const Polynomial<NT>&, const Polynomial<NT>&, Integral_domain_tag);
|
||
|
template <class NT> inline Polynomial<NT> modular_gcd_utcf(const Polynomial<NT>&, const Polynomial<NT>&, Unique_factorization_domain_tag);
|
||
|
|
||
|
// is fraction ?
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_is_fraction_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_true);
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_is_fraction_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_false);
|
||
|
|
||
|
// is type modularizable
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_false, Integral_domain_tag);
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_false, Unique_factorization_domain_tag);
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_false, Euclidean_ring_tag);
|
||
|
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_true, Integral_domain_tag);
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_true, Unique_factorization_domain_tag);
|
||
|
template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_true, Euclidean_ring_tag);
|
||
|
|
||
|
|
||
|
// template <class NT> inline NT content_utcf(const Polynomial<NT>&);
|
||
|
template <class NT> inline NT content_utcf_(const Polynomial<NT>&);
|
||
|
|
||
|
template <class NT, class OutputIterator1, class OutputIterator2>
|
||
|
inline int filtered_square_free_factorize( Polynomial<NT>, OutputIterator1, OutputIterator2);
|
||
|
template <class NT, class OutputIterator1, class OutputIterator2>
|
||
|
inline int filtered_square_free_factorize_utcf( const Polynomial<NT>&, OutputIterator1, OutputIterator2);
|
||
|
|
||
|
template <class Coeff, class OutputIterator1, class OutputIterator2>
|
||
|
inline int square_free_factorize_utcf(const Polynomial<Coeff>&, OutputIterator1, OutputIterator2);
|
||
|
template <class Coeff, class OutputIterator1, class OutputIterator2>
|
||
|
inline int square_free_factorize_utcf_for_regular_polynomial(const Polynomial<Coeff>&, OutputIterator1, OutputIterator2);
|
||
|
|
||
|
template <class Coeff, class OutputIterator1, class OutputIterator2>
|
||
|
inline int square_free_factorize(const Polynomial<Coeff>&, OutputIterator1, OutputIterator2);
|
||
|
template <class Coeff, class OutputIterator1, class OutputIterator2>
|
||
|
inline int square_free_factorize_for_regular_polynomial(const Polynomial<Coeff>&, OutputIterator1, OutputIterator2);
|
||
|
|
||
|
template <class NT> inline bool may_have_multiple_factor( const Polynomial<NT>&);
|
||
|
template <class NT> inline bool may_have_common_factor(const Polynomial<NT>&,const Polynomial<NT>&);
|
||
|
|
||
|
// eliminates outermost variable
|
||
|
template <class Coeff>
|
||
|
inline Coeff resultant(
|
||
|
const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&);
|
||
|
// eliminates innermost variable
|
||
|
template <class Coeff>
|
||
|
inline Coeff resultant_(
|
||
|
const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&);
|
||
|
|
||
|
|
||
|
|
||
|
template< class Coeff >
|
||
|
struct Simple_matrix;
|
||
|
|
||
|
template<class NT>
|
||
|
internal::Simple_matrix<NT> polynomial_subresultant_matrix(
|
||
|
CGAL::Polynomial<NT> f,
|
||
|
CGAL::Polynomial<NT> g,
|
||
|
int d=0);
|
||
|
|
||
|
template <typename Polynomial_traits_d,typename OutputIterator> inline
|
||
|
OutputIterator polynomial_subresultants
|
||
|
(typename Polynomial_traits_d::Polynomial_d A,
|
||
|
typename Polynomial_traits_d::Polynomial_d B,
|
||
|
OutputIterator out);
|
||
|
|
||
|
|
||
|
template <typename Polynomial_traits_d,typename OutputIterator> inline
|
||
|
OutputIterator principal_subresultants
|
||
|
(typename Polynomial_traits_d::Polynomial_d A,
|
||
|
typename Polynomial_traits_d::Polynomial_d B,
|
||
|
OutputIterator out);
|
||
|
|
||
|
template<typename Polynomial_traits_d,
|
||
|
typename OutputIterator1,
|
||
|
typename OutputIterator2,
|
||
|
typename OutputIterator3>
|
||
|
OutputIterator1 polynomial_subresultants_with_cofactors
|
||
|
(typename Polynomial_traits_d::Polynomial_d P,
|
||
|
typename Polynomial_traits_d::Polynomial_d Q,
|
||
|
OutputIterator1 sres_out,
|
||
|
OutputIterator2 coP_out,
|
||
|
OutputIterator3 coQ_out);
|
||
|
|
||
|
|
||
|
template <typename Polynomial_traits_d,typename OutputIterator> inline
|
||
|
OutputIterator
|
||
|
principal_sturm_habicht_sequence
|
||
|
(typename Polynomial_traits_d::Polynomial_d A,
|
||
|
OutputIterator out);
|
||
|
|
||
|
|
||
|
|
||
|
template<typename Polynomial_traits_d,typename OutputIterator> OutputIterator
|
||
|
sturm_habicht_sequence(typename Polynomial_traits_d::Polynomial_d P,
|
||
|
OutputIterator out);
|
||
|
|
||
|
template<typename Polynomial_traits_d,
|
||
|
typename OutputIterator1,
|
||
|
typename OutputIterator2,
|
||
|
typename OutputIterator3>
|
||
|
OutputIterator1
|
||
|
sturm_habicht_sequence_with_cofactors
|
||
|
(typename Polynomial_traits_d::Polynomial_d P,
|
||
|
OutputIterator1 out_stha,
|
||
|
OutputIterator2 out_f,
|
||
|
OutputIterator3 out_fx);
|
||
|
|
||
|
} // namespace internal
|
||
|
|
||
|
|
||
|
} // namespace CGAL
|
||
|
|
||
|
|
||
|
#include <CGAL/Polynomial.h>
|
||
|
|
||
|
#endif
|