159 lines
6.7 KiB
C
159 lines
6.7 KiB
C
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// Copyright (c) 2008 Max-Planck-Institute Saarbruecken (Germany)
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//
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// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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//
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//
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// Author(s) : Michael Hemmer
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// ============================================================================
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#ifndef CGAL_POLYNOMIAL_FWD_H
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#define CGAL_POLYNOMIAL_FWD_H
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#include <CGAL/basic.h>
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namespace CGAL{
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template <class NT> class Polynomial;
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namespace internal{
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template <class NT> inline Polynomial<NT> gcd_(const Polynomial<NT>&, const Polynomial<NT>&);
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template <class NT> inline Polynomial<NT> gcd_(const Polynomial<NT>&, const Polynomial<NT>&, Field_tag);
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template <class NT> inline Polynomial<NT> gcd_(const Polynomial<NT>&, const Polynomial<NT>&, Unique_factorization_domain_tag);
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template <class NT> inline NT gcd_utcf_(const NT& /*a*/, const NT& /*b*/){return NT(1);}
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template <class NT> inline Polynomial<NT> gcd_utcf_(const Polynomial<NT>&, const Polynomial<NT>&);
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template <class NT> inline Polynomial<NT> gcd_utcf_UFD( Polynomial<NT> , Polynomial<NT>) ;
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template <class NT> inline Polynomial<NT> gcd_utcf_Integral_domain(Polynomial<NT>, Polynomial<NT>);
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template <class NT> inline Polynomial<NT> gcd_Euclidean_ring(Polynomial<NT>, Polynomial<NT>);
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template <class NT> inline Polynomial<NT> modular_gcd_utcf(const Polynomial<NT>&, const Polynomial<NT>&, Integral_domain_tag);
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template <class NT> inline Polynomial<NT> modular_gcd_utcf(const Polynomial<NT>&, const Polynomial<NT>&, Unique_factorization_domain_tag);
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// is fraction ?
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template <class NT> inline Polynomial<NT> gcd_utcf_is_fraction_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_true);
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template <class NT> inline Polynomial<NT> gcd_utcf_is_fraction_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_false);
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// is type modularizable
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template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_false, Integral_domain_tag);
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template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_false, Unique_factorization_domain_tag);
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template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_false, Euclidean_ring_tag);
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template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_true, Integral_domain_tag);
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template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_true, Unique_factorization_domain_tag);
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template <class NT> inline Polynomial<NT> gcd_utcf_modularizable_algebra_( const Polynomial<NT>&, const Polynomial<NT>&, ::CGAL::Tag_true, Euclidean_ring_tag);
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// template <class NT> inline NT content_utcf(const Polynomial<NT>&);
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template <class NT> inline NT content_utcf_(const Polynomial<NT>&);
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template <class NT, class OutputIterator1, class OutputIterator2>
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inline int filtered_square_free_factorize( Polynomial<NT>, OutputIterator1, OutputIterator2);
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template <class NT, class OutputIterator1, class OutputIterator2>
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inline int filtered_square_free_factorize_utcf( const Polynomial<NT>&, OutputIterator1, OutputIterator2);
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template <class Coeff, class OutputIterator1, class OutputIterator2>
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inline int square_free_factorize_utcf(const Polynomial<Coeff>&, OutputIterator1, OutputIterator2);
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template <class Coeff, class OutputIterator1, class OutputIterator2>
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inline int square_free_factorize_utcf_for_regular_polynomial(const Polynomial<Coeff>&, OutputIterator1, OutputIterator2);
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template <class Coeff, class OutputIterator1, class OutputIterator2>
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inline int square_free_factorize(const Polynomial<Coeff>&, OutputIterator1, OutputIterator2);
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template <class Coeff, class OutputIterator1, class OutputIterator2>
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inline int square_free_factorize_for_regular_polynomial(const Polynomial<Coeff>&, OutputIterator1, OutputIterator2);
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template <class NT> inline bool may_have_multiple_factor( const Polynomial<NT>&);
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template <class NT> inline bool may_have_common_factor(const Polynomial<NT>&,const Polynomial<NT>&);
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// eliminates outermost variable
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template <class Coeff>
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inline Coeff resultant(
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const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&);
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// eliminates innermost variable
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template <class Coeff>
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inline Coeff resultant_(
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const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&);
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template< class Coeff >
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struct Simple_matrix;
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template<class NT>
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internal::Simple_matrix<NT> polynomial_subresultant_matrix(
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CGAL::Polynomial<NT> f,
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CGAL::Polynomial<NT> g,
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int d=0);
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template <typename Polynomial_traits_d,typename OutputIterator> inline
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OutputIterator polynomial_subresultants
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(typename Polynomial_traits_d::Polynomial_d A,
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typename Polynomial_traits_d::Polynomial_d B,
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OutputIterator out);
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template <typename Polynomial_traits_d,typename OutputIterator> inline
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OutputIterator principal_subresultants
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(typename Polynomial_traits_d::Polynomial_d A,
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typename Polynomial_traits_d::Polynomial_d B,
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OutputIterator out);
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template<typename Polynomial_traits_d,
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typename OutputIterator1,
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typename OutputIterator2,
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typename OutputIterator3>
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OutputIterator1 polynomial_subresultants_with_cofactors
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(typename Polynomial_traits_d::Polynomial_d P,
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typename Polynomial_traits_d::Polynomial_d Q,
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OutputIterator1 sres_out,
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OutputIterator2 coP_out,
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OutputIterator3 coQ_out);
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template <typename Polynomial_traits_d,typename OutputIterator> inline
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OutputIterator
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principal_sturm_habicht_sequence
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(typename Polynomial_traits_d::Polynomial_d A,
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OutputIterator out);
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template<typename Polynomial_traits_d,typename OutputIterator> OutputIterator
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sturm_habicht_sequence(typename Polynomial_traits_d::Polynomial_d P,
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OutputIterator out);
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template<typename Polynomial_traits_d,
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typename OutputIterator1,
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typename OutputIterator2,
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typename OutputIterator3>
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OutputIterator1
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sturm_habicht_sequence_with_cofactors
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(typename Polynomial_traits_d::Polynomial_d P,
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OutputIterator1 out_stha,
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OutputIterator2 out_f,
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OutputIterator3 out_fx);
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} // namespace internal
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} // namespace CGAL
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#include <CGAL/Polynomial.h>
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#endif
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