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// Copyright (c) 2006-2007 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; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// 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.
//
// $URL$
// $Id$
//
//
// Author(s) : Michael Hemmer <hemmer@mpi-inf.mpg.de>
//
// =============================================================================
// TODO:
// - Add Devides functor to CGAL::Algebraic_structure_traits
// - remove this file
/*! \file CGAL/Algebraic_number_traits.h
* \brief Defines traits class CGAL::Algebraic_structure_traits_extended.
*/
#ifndef ALGEBRAIC_STRUCTURE_TRAITS_EXTENDED_H
#define ALGEBRAIC_STRUCTURE_TRAITS_EXTENDED_H
#include <CGAL/basic.h>
#include <CGAL/type_traits.h>
#include <CGAL/Algebraic_structure_traits.h>
namespace CGAL {
template <class NT> class Polynomial;
template <class NT, class ROOT> class Sqrt_extension;
// The algebraic structure traits extended base class
// =========================================================================
template< class Type, class Algebra_type >
class Algebraic_structure_traits_extended_base;
template< class Type, class Algebra_type >
class Sqrt_algebraic_structure_traits_extended;
template< class Type, class Algebra_type >
class Polynomial_algebraic_structure_traits_extended;
template< class Type_ >
class Algebraic_structure_traits_extended;
//! The template specialization that can be used for types that are not any
//! of the number type concepts. The divides functor is set to \c Null_functor.
template< class Type_ >
class Algebraic_structure_traits_extended_base< Type_, CGAL::Null_tag >
: public CGAL::Algebraic_structure_traits< Type_> {
public:
typedef Type_ Type;
typedef CGAL::Null_functor Divides;
};
//! The template specialization that is used if the number type is
//! a model of the \c IntegralDomainWithoutDiv concept.
template< class Type_ >
class Algebraic_structure_traits_extended_base< Type_,
Integral_domain_without_division_tag >
: public Algebraic_structure_traits_extended_base< Type_,
CGAL::Null_tag > {
public:
typedef Type_ Type;
};
//! The template specialization that is used if the number type is
//! a model of the \c IntegralDomain concept.
template< class Type_ >
class Algebraic_structure_traits_extended_base< Type_,
Integral_domain_tag >
: public Algebraic_structure_traits_extended_base< Type_,
Integral_domain_without_division_tag > {
};
//! The template specialization that is used if the number type is
//! a model of the \c UFDomain concept. It is equivalent to the specialization
//! for the \c IntegralDomain concept.
template< class Type_ >
class Algebraic_structure_traits_extended_base< Type_,
Unique_factorization_domain_tag >
: public Algebraic_structure_traits_extended_base< Type_,
Integral_domain_tag > {
public:
typedef Type_ Type;
class Divides {
public:
typedef Type first_argument_type;
typedef Type second_argument_type;
typedef Type& third_argument_type;
typedef bool result_type;
bool operator()( const Type& x,
const Type& y,
Type& q) const {
typedef CGAL::Algebraic_structure_traits<Type> AST;
typename AST::Gcd gcd;
// std::cout<<" UFD gcd computation"<<std::endl;
if(gcd(y,x) == x/unit_part(x)){
q = y/x;
return true;
}
else
return false;
}
};
};
//! The template specialization that is used if the number type is
//! a model of the \c EuclideanRing concept.
template< class Type_ >
class Algebraic_structure_traits_extended_base< Type_,
Euclidean_ring_tag >
: public Algebraic_structure_traits_extended_base< Type_,
Unique_factorization_domain_tag > {
public:
typedef Type_ Type;
class Divides {
public:
typedef Type first_argument_type;
typedef Type second_argument_type;
typedef Type& third_argument_type;
typedef bool result_type;
bool operator()( const Type& x,
const Type& y,
Type& q) const {
typedef CGAL::Algebraic_structure_traits<Type> AST;
typename AST::Div div;
// std::cout<<"euclidean ring "<<std::endl;
q = div(y,x);
if(q*x==y)
return true;
else
return false;
}
};
};
//! The template specialization that is used if the number type is
//! a model of the \c Field concept.
template< class Type_ >
class Algebraic_structure_traits_extended_base< Type_, Field_tag >
: public Algebraic_structure_traits_extended_base< Type_,
Integral_domain_tag > {
public:
typedef Type_ Type;
class Divides {
public:
typedef Type first_argument_type;
typedef Type second_argument_type;
typedef Type& third_argument_type;
typedef bool result_type;
bool operator()( const Type& x,
const Type& y,
Type& q) const {
// std::cout<<" divides field"<<std::endl;
q = y/x;
return true;
}
};
};
//! The template specialization that is used if the number type is a model
//! of the \c FieldWithSqrt concept. It is equivalent to the
//! specialization for the \c Field concept.
template< class Type_ >
class Algebraic_structure_traits_extended_base< Type_,
Field_with_sqrt_tag>
: public Algebraic_structure_traits_extended_base< Type_,
Field_tag> {
public:
typedef Type_ Type;
};
//! The template specialization that is used if the number type is a model
//! of the \c FieldWithKthRoot concept. It is equivalent to the
//! specialization for the \c Field concept.
template< class Type_ >
class Algebraic_structure_traits_extended_base< Type_,
Field_with_kth_root_tag>
: public Algebraic_structure_traits_extended_base< Type_,
Field_with_sqrt_tag> {
public:
typedef Type_ Type;
};
//! The template specialization that is used if the number type is a model
//! of the \c FieldWithRootOf concept. It is equivalent to the
//! specialization for the \c FieldWithKthRoot concept.
template< class Type_ >
class Algebraic_structure_traits_extended_base< Type_,
Field_with_root_of_tag >
: public Algebraic_structure_traits_extended_base< Type_,
Field_with_kth_root_tag > {
public:
typedef Type_ Type;
};
//! The template specialization that is used for Sqrt_extensions if the COEFF type is a model
//! of the \c IntegralDomain concept.
template< class Type_, class ROOT >
class Sqrt_algebraic_structure_traits_extended< Sqrt_extension< Type_, ROOT >,
CGAL::Integral_domain_tag >
: public Algebraic_structure_traits_extended_base< Sqrt_extension< Type_, ROOT >,
CGAL::Integral_domain_tag >{
public:
typedef Type_ COEFF;
typedef Sqrt_extension< COEFF, ROOT > Type;
private:
typedef typename CGAL::Coercion_traits< ROOT, COEFF >::Cast Root_nt_cast;
public:
class Divides {
public:
typedef Type first_argument_type;
typedef Type second_argument_type;
typedef Type& third_argument_type;
typedef bool result_type;
bool operator()( const Type& x,
const Type& y,
Type& q) const {
typedef CGAL::Algebraic_structure_traits_extended<COEFF> ASTE;
typename ASTE::Divides divides;
// std::cout<<"integral domain for sqrt"<<std::endl;
bool result;
COEFF q1, q2;
if(x.is_extended()){
// std::cout<<" y is extended "<<std::endl;
COEFF denom = x.a0()*x.a0() - x.a1()*x.a1() * Root_nt_cast()(x.root());
if ( denom == COEFF(0) ) {
// this is for the rare case in which root is a square
// and the (pseudo) algebraic conjugate of p becomes zero
result = divides(COEFF(2)*x.a0(),y.a0(),q1);
if(!result) return false;
result = divides(COEFF(2)*x.a1(),y.a1(),q2);
if(!result) return false;
q = Type(q1 + q2);
}else{
q = y;
q *= Type(x.a0(),-x.a1(),x.root());
result = divides(denom,q.a0(),q1);
if(!result) return false;
result = divides(denom,q.a1(),q2);
if(!result) return false;
q = Type( q1, q2, y.root());
}
}else{
// std::cout<<" x is not extended "<<std::endl;
if(y.is_extended()){
result = divides(x.a0(),y.a0(),q1);
if(!result) return false;
result = divides(x.a0(),y.a1(),q2);
if(!result) return false;
q = Type(q1, q2, y.root());
}else{
result = divides(x.a0(),y.a0(),q1);
if(!result) return false;
q = q1;
}
}
if(q*x==y)
return true;
else
return false;
}
};
};
//! The template specialization that is used for Sqrt_extensions if the COEFF type is a model
//! of the \c UFDomain concept.
template< class Type_, class ROOT >
class Sqrt_algebraic_structure_traits_extended< Sqrt_extension< Type_, ROOT >,
CGAL::Unique_factorization_domain_tag >
: public Sqrt_algebraic_structure_traits_extended< Sqrt_extension< Type_, ROOT >,
CGAL::Integral_domain_tag >
{ };
//! The template specialization that is used for Sqrt_extensions if the COEFF type is a model
//! of the \c EuclideanRing concept.
template< class Type_, class ROOT >
class Sqrt_algebraic_structure_traits_extended< Sqrt_extension< Type_, ROOT >,
CGAL::Euclidean_ring_tag >
: public Sqrt_algebraic_structure_traits_extended< Sqrt_extension< Type_, ROOT >,
CGAL::Integral_domain_tag >
{
public:
typedef Type_ COEFF;
typedef Sqrt_extension< COEFF, ROOT > Type;
};
//! The template specialization that is used for polynomials if the number type is a model
//! of the \c IntegralDomain concept.
template< class Type_ >
class Polynomial_algebraic_structure_traits_extended< CGAL::Polynomial< Type_ >,
Integral_domain_tag >
: public Algebraic_structure_traits_extended_base< CGAL::Polynomial< Type_ >,
CGAL::Integral_domain_tag >{
public:
typedef Type_ NT;
typedef CGAL::Polynomial< NT > Type;
// typedef Unique_factorization_domain_tag Algebraic_category;
class Divides {
public:
typedef Type first_argument_type;
typedef Type second_argument_type;
typedef Type& third_argument_type;
typedef bool result_type;
bool operator()( const Type& p1,
const Type& p2,
Type& q) const {
q=Type(0);
// std::cout<<"new Sqrt POLY"<<std::endl;
typedef CGAL::Algebraic_structure_traits_extended<NT> ASTE;
typename ASTE::Divides divides;
NT q1;
bool result;
int d1 = p1.degree();
int d2 = p2.degree();
if (p2.is_zero()) {
q=Type(0);
return true;
}
if ( d2 < d1 ) {
q = Type(0);
return false;
}
typedef std::vector<NT> Vector;
Vector V_R, V_Q;
V_Q.reserve(d2);
if(d1==0){
for(int i=d2;i>=0;--i){
result=divides(p1[0],p2[i],q1);
if(!result) return false;
V_Q.push_back(q1);
}
V_R.push_back(NT(0));
}
else{
V_R.reserve(d2);
V_R=Vector(p2.begin(),p2.end());
Vector tmp1;
tmp1.reserve(d1);
for(int k=0; k<=d2-d1; ++k){
result=divides(p1[d1],V_R[d2-k],q1);
if(!result) return false;
V_Q.push_back(q1);
for(int j=0;j<d1;++j){
tmp1.push_back(p1[j]*V_Q[k]);
}
V_R[d2-k]=0;
for(int i=d2-d1-k;i<=d2-k-1;++i){
V_R[i]=V_R[i]-tmp1[i-(d2-d1-k)];
}
tmp1.clear();
}
}
q = Type(V_Q.rbegin(),V_Q.rend());
Type r = Type(V_R.begin(),V_R.end());
if(r == Type(0))
return true;
else
return false;
}
};
};
//! The template specialization that is used for polynomials if the COEFF type is a model
//! of the \c UFDomain concept.
template< class Type_ >
class Polynomial_algebraic_structure_traits_extended< CGAL::Polynomial< Type_ >,
CGAL::Unique_factorization_domain_tag >
: public Polynomial_algebraic_structure_traits_extended< CGAL::Polynomial< Type_ >,
CGAL::Integral_domain_tag >
{ };
//! The template specialization that is used for polynomials if the number type is a model
//! of the \c EuclideanRing concept.
template< class Type_ >
class Polynomial_algebraic_structure_traits_extended< CGAL::Polynomial< Type_ >,
Euclidean_ring_tag >
: public Polynomial_algebraic_structure_traits_extended< CGAL::Polynomial< Type_ >,
Integral_domain_tag >{
public:
typedef Type_ NT;
typedef CGAL::Polynomial< Type_ > Type;
// typedef Unique_factorization_domain_tag Algebraic_category;
};
//! The template specialization that is used for polynomials if the number type is a model
//! of the \c Field concept.
template< class Type_ >
class Polynomial_algebraic_structure_traits_extended< CGAL::Polynomial< Type_ >, Field_tag >
: public Polynomial_algebraic_structure_traits_extended< CGAL::Polynomial< Type_ >,
Integral_domain_tag >{
public:
typedef CGAL::Polynomial< Type_ > Type;
// typedef Euclidean_ring_tag Algebraic_category;
class Divides {
public:
typedef Type first_argument_type;
typedef Type second_argument_type;
typedef Type& third_argument_type;
typedef bool result_type;
bool operator()( const Type& p1,
const Type& p2,
Type& q) const {
// std::cout<<"Field POLY"<<std::endl;
if (p2.is_zero()) {
q = Type(0);
return true;
}
Type r;
Type::euclidean_division(p2, p1, q, r);
if(r == Type(0))
return true;
else
return false;
}
};
};
template< class Type_ >
class Algebraic_structure_traits_extended
: public Algebraic_structure_traits_extended_base< Type_,
typename CGAL::Algebraic_structure_traits<Type_>::Algebraic_category > {
};
// The actual algebraic structure extended traits class
template< class Type_, class ROOT >
class Algebraic_structure_traits_extended< Sqrt_extension< Type_, ROOT > >
: public Sqrt_algebraic_structure_traits_extended< Sqrt_extension< Type_, ROOT >,
typename CGAL::Algebraic_structure_traits<Type_>::Algebraic_category > {
};
// The actual algebraic structure extended traits class
template< class Type_ >
class Algebraic_structure_traits_extended< CGAL::Polynomial< Type_ > >
: public Polynomial_algebraic_structure_traits_extended< CGAL::Polynomial< Type_ >,
typename CGAL::Algebraic_structure_traits<Type_>::Algebraic_category > {
};
} //namespace CGAL
#endif // CGAL_ALGEBRAIC_STRUCTURE_TRAITS_EXTENDED_H
// EOF
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