363 lines
14 KiB
C
363 lines
14 KiB
C
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// Copyright (c) 2006-2013 INRIA Nancy-Grand Est (France). All rights reserved.
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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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// See the file LICENSE.LGPL distributed with CGAL.
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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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// Author: Luis Peñaranda <luis.penaranda@gmx.com>
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#ifndef CGAL_RS_ALGEBRAIC_Z_1_H
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#define CGAL_RS_ALGEBRAIC_Z_1_H
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#include "algebraic_1.h"
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namespace CGAL{
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namespace RS_AK1{
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// This class represents an algebraic number storing two polynomials of
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// which it is root: one of them is the given polynomial; the other one is
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// an integer polynomial, which is used to perform the operations such as
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// refinements. Since RS works only with integer polynomials, this
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// architecture permits to convert the input polynomials only once.
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template <class Polynomial_,
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class ZPolynomial_,
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class Bound_,
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class ZRefiner_,
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class ZComparator_,
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class Ptraits_,
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class ZPtraits_>
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class Algebraic_z_1:
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public Algebraic_1<Polynomial_,Bound_,ZRefiner_,ZComparator_,ZPtraits_>,
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boost::totally_ordered<Algebraic_z_1<Polynomial_,
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ZPolynomial_,
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Bound_,
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ZRefiner_,
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ZComparator_,
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Ptraits_,
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ZPtraits_>,
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double>{
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protected:
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typedef Polynomial_ Polynomial;
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typedef ZPolynomial_ ZPolynomial;
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typedef Bound_ Bound;
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typedef ZRefiner_ ZRefiner;
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typedef ZComparator_ ZComparator;
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typedef ZPtraits_ ZPtraits;
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typedef typename ZPtraits::Coefficient_type ZCoefficient;
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typedef typename ZPtraits::Scale ZScale;
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typedef Ptraits_ Ptraits;
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typedef typename Ptraits::Coefficient_type Coefficient;
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typedef typename Ptraits::Scale Scale;
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typedef Algebraic_1<Polynomial,Bound,ZRefiner,ZComparator,ZPtraits>
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Algebraic_base;
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typedef Algebraic_z_1<Polynomial,
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ZPolynomial,
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Bound,
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ZRefiner,
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ZComparator,
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Ptraits,
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ZPtraits>
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Algebraic;
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ZPolynomial zpol;
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public:
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Algebraic_z_1(){};
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Algebraic_z_1(const Polynomial &p,
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const ZPolynomial &zp,
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const Bound &l,
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const Bound &r):Algebraic_base(p,l,r),zpol(zp){
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CGAL_assertion(l<=r);
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}
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Algebraic_z_1(const Algebraic &a):
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Algebraic_base(a.pol,a.left,a.right),zpol(a.zpol){}
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Algebraic_z_1(const Bound &b){
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typedef typename Ptraits::Shift Shift;
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typedef typename ZPtraits::Shift ZShift;
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this->left=b;
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this->right=b;
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Gmpq q(b);
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this->pol=Coefficient(mpq_denref(q.mpq()))*
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Shift()(Polynomial(1),1,0)-
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Coefficient(mpq_numref(q.mpq()));
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zpol=ZCoefficient(mpq_denref(q.mpq()))*
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ZShift()(ZPolynomial(1),1,0)-
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ZCoefficient(mpq_numref(q.mpq()));
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CGAL_assertion(this->left==this->right);
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CGAL_assertion(this->left==b);
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}
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template <class T>
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Algebraic_z_1(const T &t){
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typedef typename Ptraits::Shift Shift;
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typedef typename ZPtraits::Shift ZShift;
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CGAL::Gmpq q(t);
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this->pol=Coefficient(mpq_denref(q.mpq()))*
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Shift()(Polynomial(1),1,0)-
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Coefficient(mpq_numref(q.mpq()));
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zpol=ZCoefficient(mpq_denref(q.mpq()))*
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ZShift()(ZPolynomial(1),1,0)-
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ZCoefficient(mpq_numref(q.mpq()));
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this->left=Bound(t,std::round_toward_neg_infinity);
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this->right=Bound(t,std::round_toward_infinity);
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CGAL_assertion(this->left<=t&&this->right>=t);
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}
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Algebraic_z_1(const CGAL::Gmpq &q){
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typedef typename Ptraits::Shift Shift;
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typedef typename ZPtraits::Shift ZShift;
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this->pol=Coefficient(mpq_denref(q.mpq()))*
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Shift()(Polynomial(1),1,0)-
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Coefficient(mpq_numref(q.mpq()));
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zpol=ZCoefficient(mpq_denref(q.mpq()))*
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ZShift()(ZPolynomial(1),1,0)-
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ZCoefficient(mpq_numref(q.mpq()));
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this->left=Bound();
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this->right=Bound();
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mpfr_t b;
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mpfr_init(b);
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mpfr_set_q(b,q.mpq(),GMP_RNDD);
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mpfr_swap(b,this->left.fr());
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mpfr_set_q(b,q.mpq(),GMP_RNDU);
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mpfr_swap(b,this->right.fr());
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mpfr_clear(b);
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CGAL_assertion(this->left<=q&&this->right>=q);
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}
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~Algebraic_z_1(){}
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ZPolynomial get_zpol()const{return zpol;}
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void set_zpol(const ZPolynomial &p){zpol=p;}
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Algebraic operator-()const{
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return Algebraic(Scale()(this->get_pol(),Coefficient(-1)),
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ZScale()(get_zpol(),ZCoefficient(-1)),
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-this->right,
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-this->left);
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}
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#define CGAL_RS_COMPARE_ALGEBRAIC_Z(_a) \
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(ZComparator()(get_zpol(),this->get_left(),this->get_right(), \
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(_a).get_zpol(),(_a).get_left(),(_a).get_right()))
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Comparison_result compare(Algebraic a)const{
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return CGAL_RS_COMPARE_ALGEBRAIC_Z(a);
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};
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#define CGAL_RS_COMPARE_ALGEBRAIC_Z_TYPE(_t) \
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bool operator<(_t t)const \
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{Algebraic a(t);return CGAL_RS_COMPARE_ALGEBRAIC_Z(a)==CGAL::SMALLER;} \
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bool operator>(_t t)const \
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{Algebraic a(t);return CGAL_RS_COMPARE_ALGEBRAIC_Z(a)==CGAL::LARGER;} \
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bool operator==(_t t)const \
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{Algebraic a(t);return CGAL_RS_COMPARE_ALGEBRAIC_Z(a)==CGAL::EQUAL;}
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bool operator==(Algebraic a)const
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{return CGAL_RS_COMPARE_ALGEBRAIC_Z(a)==CGAL::EQUAL;}
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bool operator!=(Algebraic a)const
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{return CGAL_RS_COMPARE_ALGEBRAIC_Z(a)!=CGAL::EQUAL;}
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bool operator<(Algebraic a)const
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{return CGAL_RS_COMPARE_ALGEBRAIC_Z(a)==CGAL::SMALLER;}
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bool operator<=(Algebraic a)const
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{return CGAL_RS_COMPARE_ALGEBRAIC_Z(a)!=CGAL::LARGER;}
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bool operator>(Algebraic a)const
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{return CGAL_RS_COMPARE_ALGEBRAIC_Z(a)==CGAL::LARGER;}
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bool operator>=(Algebraic a)const
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{return CGAL_RS_COMPARE_ALGEBRAIC_Z(a)!=CGAL::SMALLER;}
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CGAL_RS_COMPARE_ALGEBRAIC_Z_TYPE(double)
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#undef CGAL_RS_COMPARE_ALGEBRAIC_Z_TYPE
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#undef CGAL_RS_COMPARE_ALGEBRAIC_Z
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#ifdef IEEE_DBL_MANT_DIG
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#define CGAL_RS_DBL_PREC IEEE_DBL_MANT_DIG
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#else
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#define CGAL_RS_DBL_PREC 53
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#endif
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double to_double()const{
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typedef Real_embeddable_traits<Bound> RT;
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typedef typename RT::To_double TD;
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ZRefiner()(get_zpol(),
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this->get_left(),
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this->get_right(),
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CGAL_RS_DBL_PREC);
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CGAL_assertion(TD()(this->get_left())==TD()(this->get_right()));
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return TD()(this->get_left());
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}
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std::pair<double,double> to_interval()const{
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typedef Real_embeddable_traits<Bound> RT;
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typedef typename RT::To_interval TI;
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return std::make_pair(TI()(this->get_left()).first,
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TI()(this->get_right()).second);
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}
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#undef CGAL_RS_DBL_PREC
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}; // class Algebraic_z_1
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} // namespace RS_AK1
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// We define Algebraic_z_1 as real-embeddable
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template <class Polynomial_,
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class ZPolynomial_,
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class Bound_,
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class ZRefiner_,
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class ZComparator_,
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class Ptraits_,
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class ZPtraits_>
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class Real_embeddable_traits<RS_AK1::Algebraic_z_1<Polynomial_,
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ZPolynomial_,
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Bound_,
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ZRefiner_,
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ZComparator_,
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Ptraits_,
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ZPtraits_> >:
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public INTERN_RET::Real_embeddable_traits_base<
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RS_AK1::Algebraic_z_1<Polynomial_,
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ZPolynomial_,
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Bound_,
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ZRefiner_,
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ZComparator_,
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Ptraits_,
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ZPtraits_>,
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CGAL::Tag_true>{
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typedef Polynomial_ P;
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typedef ZPolynomial_ ZP;
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typedef Bound_ B;
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typedef ZRefiner_ R;
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typedef ZComparator_ C;
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typedef Ptraits_ T;
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typedef ZPtraits_ ZT;
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public:
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typedef RS_AK1::Algebraic_z_1<P,ZP,B,R,C,T,ZT> Type;
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typedef CGAL::Tag_true Is_real_embeddable;
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typedef bool Boolean;
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typedef CGAL::Sign Sign;
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typedef CGAL::Comparison_result Comparison_result;
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typedef INTERN_RET::Real_embeddable_traits_base<Type,CGAL::Tag_true>
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Base;
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typedef typename Base::Compare Compare;
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class Sgn:public CGAL::cpp98::unary_function<Type,CGAL::Sign>{
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public:
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CGAL::Sign operator()(const Type &a)const{
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return Compare()(a,Type(0));
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}
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};
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class To_double:public CGAL::cpp98::unary_function<Type,double>{
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public:
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double operator()(const Type &a)const{return a.to_double();}
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};
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class To_interval:
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public CGAL::cpp98::unary_function<Type,std::pair<double,double> >{
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public:
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std::pair<double,double> operator()(const Type &a)const{
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return a.to_interval();
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}
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};
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class Is_zero:public CGAL::cpp98::unary_function<Type,Boolean>{
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public:
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bool operator()(const Type &a)const{
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return Sgn()(a)==CGAL::ZERO;
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}
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};
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class Is_finite:public CGAL::cpp98::unary_function<Type,Boolean>{
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public:
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bool operator()(const Type&)const{return true;}
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};
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class Abs:public CGAL::cpp98::unary_function<Type,Type>{
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public:
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Type operator()(const Type &a)const{
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return Sgn()(a)==CGAL::NEGATIVE?-a:a;
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}
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};
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};
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template <class P,class ZP,class B,class R,class C,class T,class ZT>
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inline
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RS_AK1::Algebraic_z_1<P,ZP,B,R,C,T,ZT> min
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BOOST_PREVENT_MACRO_SUBSTITUTION(RS_AK1::Algebraic_z_1<P,ZP,B,R,C,T,ZT> a,
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RS_AK1::Algebraic_z_1<P,ZP,B,R,C,T,ZT> b){
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return(a<b?a:b);
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}
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template <class P,class ZP,class B,class R,class C,class T,class ZT>
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inline
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RS_AK1::Algebraic_z_1<P,ZP,B,R,C,T,ZT> max
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BOOST_PREVENT_MACRO_SUBSTITUTION(RS_AK1::Algebraic_z_1<P,ZP,B,R,C,T,ZT> a,
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RS_AK1::Algebraic_z_1<P,ZP,B,R,C,T,ZT> b){
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return(a>b?a:b);
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}
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template <class P,class ZP,class B,class R,class C,class T,class ZT>
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inline
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std::ostream& operator<<(std::ostream &o,
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const RS_AK1::Algebraic_z_1<P,ZP,B,R,C,T,ZT> &a){
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return(o<<'['<<a.get_pol()<<','<<
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a.get_zpol()<<','<<
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a.get_left()<<','<<
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a.get_right()<<']');
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}
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template <class P,class ZP,class B,class R,class C,class T,class ZT>
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inline
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std::istream& operator>>(std::istream &i,
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RS_AK1::Algebraic_z_1<P,ZP,B,R,C,T,ZT> &a){
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std::istream::int_type c;
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P pol;
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ZP zpol;
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B lb,rb;
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c=i.get();
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if(c!='['){
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CGAL_error_msg("error reading istream, \'[\' expected");
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return i;
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}
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i>>pol;
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c=i.get();
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if(c!=','){
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CGAL_error_msg("error reading istream, \',\' expected");
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return i;
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}
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i>>zpol;
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c=i.get();
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if(c!=','){
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CGAL_error_msg("error reading istream, \',\' expected");
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return i;
|
||
|
|
}
|
||
|
|
i>>lb;
|
||
|
|
c=i.get();
|
||
|
|
if(c!=','){
|
||
|
|
CGAL_error_msg("error reading istream, \',\' expected");
|
||
|
|
return i;
|
||
|
|
}
|
||
|
|
i>>rb;
|
||
|
|
c=i.get();
|
||
|
|
if(c!=']'){
|
||
|
|
CGAL_error_msg("error reading istream, \']\' expected");
|
||
|
|
return i;
|
||
|
|
}
|
||
|
|
a=RS_AK1::Algebraic_z_1<P,ZP,B,R,C,T,ZT>(pol,zpol,lb,rb);
|
||
|
|
return i;
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace CGAL
|
||
|
|
|
||
|
|
#endif // CGAL_RS_ALGEBRAIC_Z_1_H
|