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// Copyright (c) 1997-2000 Max-Planck-Institute Saarbruecken (Germany). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Nef_2/include/CGAL/Nef_polynomial.h $ // $Id: include/CGAL/Nef_polynomial.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Seel #ifndef CGAL_NEF_POLYNOMIAL_H #define CGAL_NEF_POLYNOMIAL_H #include #include #include #undef CGAL_NEF_DEBUG #define CGAL_NEF_DEBUG 3 #include #include #include #include #include namespace CGAL { #define CGAL_int(T) typename First_if_different::Type #define CGAL_double(T) typename First_if_different::Type template class Nef_polynomial : boost::ordered_field_operators1< Nef_polynomial , boost::ordered_field_operators2< Nef_polynomial, int > > , public Nef::Polynomial { typedef typename CGAL::Nef::Polynomial Base; typedef typename Base::size_type size_type; protected: Nef_polynomial(size_type s) : Base(s) {} public: Nef_polynomial() : Base() {} Nef_polynomial(const NT& a0) : Base(a0) {} Nef_polynomial(const NT& a0, const NT& a1) : Base(a0,a1) {} Nef_polynomial(const NT& a0, const NT& a1, const NT& a2) : Base(a0,a1,a2) {} template Nef_polynomial(std::pair poly) : Base(poly) {} Nef_polynomial(CGAL_double(NT) n) : Base(n) {} Nef_polynomial(CGAL_double(NT) n1, CGAL_double(NT) n2) : Base(n1, n2) {} Nef_polynomial(CGAL_int(NT) n) : Base(NT(n)) {} Nef_polynomial(CGAL_int(NT) n1, CGAL_int(NT) n2) : Base(n1,n2) {} Nef_polynomial(const Base& p) : Base(p) {} Base & polynomial() { return static_cast(*this); } const Base & polynomial() const { return static_cast(*this); } static NT& infi_maximal_value() { CGAL_STATIC_THREAD_LOCAL_VARIABLE(NT, R_, 1); return R_; } friend bool operator==(const Nef_polynomial &a, const Nef_polynomial &b) { return a.polynomial() == b.polynomial(); } friend bool operator==(const Nef_polynomial &a, const NT& b) { return a.polynomial() == b; } friend bool operator==(const Nef_polynomial &a, int b) { return a.polynomial() == b; } friend bool operator<(const Nef_polynomial &a, const Nef_polynomial &b) { return a.polynomial() < b.polynomial(); } friend bool operator<(const Nef_polynomial &a, const NT& b) { return a.polynomial() < b; } friend bool operator<(const Nef_polynomial &a, int b) { return a.polynomial() < b; } friend bool operator>(const Nef_polynomial &a, int b) { return a.polynomial() > b; } }; template inline Nef_polynomial operator+(const Nef_polynomial &a) { return a; } template inline Nef_polynomial operator-(const Nef_polynomial &a) { return - a.polynomial(); } #undef CGAL_double #undef CGAL_int // TODO: integral_division to get it an UniqueFactorizationDomain // TODO: div / mod for EuclideanRing template class Algebraic_structure_traits< Nef_polynomial > : public Algebraic_structure_traits_base < Nef_polynomial, CGAL::Integral_domain_without_division_tag> { typedef Algebraic_structure_traits AST_NT; public: typedef Nef_polynomial Type; typedef typename AST_NT::Is_exact Is_exact; typedef Tag_false Is_numerical_sensitive; class Integral_division : public CGAL::cpp98::binary_function< Type, Type, Type > { public: Type operator()( const Type& x, const Type& y ) const { Type result = x / y; CGAL_postcondition_msg(result * y == x, "exact_division failed\n"); return result; } }; class Gcd : public CGAL::cpp98::binary_function< Type, Type, Type > { public: Type operator()( const Type& x, const Type& y ) const { // By definition gcd(0,0) == 0 if( x == Type(0) && y == Type(0) ) return Type(0); return CGAL::Nef::gcd( x, y ); } CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR( Type ) }; }; template class Real_embeddable_traits< Nef_polynomial > : public INTERN_RET::Real_embeddable_traits_base< Nef_polynomial , CGAL::Tag_true > { public: typedef Nef_polynomial Type; class Abs : public CGAL::cpp98::unary_function< Type, Type> { public: Type inline operator()( const Type& x ) const { return (CGAL::Nef::sign( x ) == CGAL::NEGATIVE)? -x : x; } }; class Sgn : public CGAL::cpp98::unary_function< Type, CGAL::Sign > { public: CGAL::Sign inline operator()( const Type& x ) const { return CGAL::Nef::sign( x ); } }; class Compare : public CGAL::cpp98::binary_function< Type, Type, CGAL::Comparison_result > { public: CGAL::Comparison_result inline operator()( const Type& x, const Type& y ) const { return (CGAL::Comparison_result) CGAL::Nef::sign( x - y ); } }; class To_double : public CGAL::cpp98::unary_function< Type, double > { public: double inline operator()( const Type& p ) const { return CGAL::to_double( p.eval_at(Nef_polynomial::infi_maximal_value())); } }; class To_interval : public CGAL::cpp98::unary_function< Type, std::pair< double, double > > { public: std::pair operator()( const Type& p ) const { return CGAL::to_interval(p.eval_at(Nef_polynomial::infi_maximal_value())); } }; }; template inline Nef_polynomial min BOOST_PREVENT_MACRO_SUBSTITUTION (const Nef_polynomial& x,const Nef_polynomial& y){ return (x<=y)?x:y; } template inline Nef_polynomial max BOOST_PREVENT_MACRO_SUBSTITUTION (const Nef_polynomial& x,const Nef_polynomial& y){ return (x>=y)?x:y; } template class Fraction_traits > { public: typedef Nef_polynomial Type; typedef Fraction_traits Base_traits; typedef typename Base_traits::Is_fraction Is_fraction; typedef CGAL::Nef_polynomial Numerator_type; typedef typename Base_traits::Denominator_type Denominator_type; //TODO: typedef Base_traits::Common_factor Common_factor; class Decompose { public: typedef Type first_argument_type; typedef Numerator_type second_argument_type; typedef Denominator_type third_argument_type; void operator () (const first_argument_type& rat, second_argument_type& num, third_argument_type& den) { typename Base_traits::Decompose decompose; third_argument_type num0; third_argument_type num1; third_argument_type den1; third_argument_type den0; decompose(rat[0], num0, den0); if(rat.degree() > 0) { decompose(rat[1], num1, den1); // TODO den = den1/gcd(den0, den1)*den0; den = den1*den0; num = Numerator_type(num0*den1, num1*den0); } else { den = den0; num = Numerator_type(num0); } } }; class Compose { public: typedef Numerator_type first_argument_type; typedef Denominator_type second_argument_type; typedef Type result_type; result_type operator () (const first_argument_type& num, const second_argument_type& den) { typename Base_traits::Compose compose; if(num.degree() == 0) return result_type(compose(num[0],den)); else return result_type(compose(num[0],den), compose(num[1],den)); } }; }; } //namespace CGAL #endif // CGAL_NEF_POLYNOMIAL_H