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CGALi::new_resultant -> CGALi::resultant

This commit is contained in:
Michael Hemmer 2008-07-31 09:35:22 +00:00
parent 9f6a417bc9
commit f494549b0c
3 changed files with 41 additions and 39 deletions
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4
Polynomial/include/CGAL/Polynomial/fwd.h
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@ -119,11 +119,11 @@ template<typename OutputIterator, typename NT> OutputIterator
// eliminates outermost variable // eliminates outermost variable
template <class Coeff> template <class Coeff>
inline Coeff new_resultant( inline Coeff resultant(
const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&); const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&);
// eliminates innermost variable // eliminates innermost variable
template <class Coeff> template <class Coeff>
inline Coeff new_resultant_( inline Coeff resultant_(
const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&); const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&);

68
Polynomial/include/CGAL/Polynomial/resultant.h
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@ -64,51 +64,51 @@ CGAL_BEGIN_NAMESPACE
// In turn CGAL::CGALi::resultant_(F,G) eliminates the innermost variable. // In turn CGAL::CGALi::resultant_(F,G) eliminates the innermost variable.
// Dispatching // Dispatching
// CGAL::CGALi::new_resultant_decompose applies if Coeff is a Fraction // CGAL::CGALi::resultant_decompose applies if Coeff is a Fraction
// CGAL::CGALi::new_resultant_modularize applies if Coeff is Modularizable // CGAL::CGALi::resultant_modularize applies if Coeff is Modularizable
// CGAL::CGALi::new_resultant_interpolate applies for multivairate polynomials // CGAL::CGALi::resultant_interpolate applies for multivairate polynomials
// CGAL::CGALi::new_resultant_univariate selects the proper algorithm for IC // CGAL::CGALi::resultant_univariate selects the proper algorithm for IC
namespace CGALi{ namespace CGALi{
template <class Coeff> template <class Coeff>
inline Coeff new_resultant_interpolate( inline Coeff resultant_interpolate(
const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>& ); const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>& );
template <class Coeff> template <class Coeff>
inline Coeff new_resultant_modularize( inline Coeff resultant_modularize(
const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&,
const CGAL::Polynomial<Coeff>&, CGAL::Tag_true); const CGAL::Polynomial<Coeff>&, CGAL::Tag_true);
template <class Coeff> template <class Coeff>
inline Coeff new_resultant_modularize( inline Coeff resultant_modularize(
const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&,
const CGAL::Polynomial<Coeff>&, CGAL::Tag_false); const CGAL::Polynomial<Coeff>&, CGAL::Tag_false);
template <class Coeff> template <class Coeff>
inline Coeff new_resultant_decompose( inline Coeff resultant_decompose(
const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&,
const CGAL::Polynomial<Coeff>&, CGAL::Tag_true); const CGAL::Polynomial<Coeff>&, CGAL::Tag_true);
template <class Coeff> template <class Coeff>
inline Coeff new_resultant_decompose( inline Coeff resultant_decompose(
const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&,
const CGAL::Polynomial<Coeff>&, CGAL::Tag_false); const CGAL::Polynomial<Coeff>&, CGAL::Tag_false);
template <class Coeff> template <class Coeff>
inline Coeff new_resultant_( inline Coeff resultant_(
const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&); const CGAL::Polynomial<Coeff>&, const CGAL::Polynomial<Coeff>&);
template <class Coeff> template <class Coeff>
inline Coeff new_resultant_univariate( inline Coeff resultant_univariate(
const CGAL::Polynomial<Coeff>& A, const CGAL::Polynomial<Coeff>& A,
const CGAL::Polynomial<Coeff>& B, CGAL::Integral_domain_without_division_tag){ const CGAL::Polynomial<Coeff>& B, CGAL::Integral_domain_without_division_tag){
return hybrid_bezout_subresultant(A,B,0); return hybrid_bezout_subresultant(A,B,0);
} }
template <class Coeff> template <class Coeff>
inline Coeff new_resultant_univariate( inline Coeff resultant_univariate(
const CGAL::Polynomial<Coeff>& A, const CGAL::Polynomial<Coeff>& A,
const CGAL::Polynomial<Coeff>& B, CGAL::Unique_factorization_domain_tag){ const CGAL::Polynomial<Coeff>& B, CGAL::Unique_factorization_domain_tag){
return prs_resultant_ufd(A,B); return prs_resultant_ufd(A,B);
} }
template <class Coeff> template <class Coeff>
inline Coeff new_resultant_univariate( inline Coeff resultant_univariate(
const CGAL::Polynomial<Coeff>& A, const CGAL::Polynomial<Coeff>& A,
const CGAL::Polynomial<Coeff>& B, CGAL::Field_tag){ const CGAL::Polynomial<Coeff>& B, CGAL::Field_tag){
return prs_resultant_field(A,B); return prs_resultant_field(A,B);
@ -121,19 +121,19 @@ namespace CGALi{
template <class IC> template <class IC>
inline IC inline IC
new_resultant_interpolate( resultant_interpolate(
const CGAL::Polynomial<IC>& F, const CGAL::Polynomial<IC>& F,
const CGAL::Polynomial<IC>& G){ const CGAL::Polynomial<IC>& G){
CGAL_precondition(CGAL::Polynomial_traits_d<CGAL::Polynomial<IC> >::d == 1); CGAL_precondition(CGAL::Polynomial_traits_d<CGAL::Polynomial<IC> >::d == 1);
typedef CGAL::Algebraic_structure_traits<IC> AST_IC; typedef CGAL::Algebraic_structure_traits<IC> AST_IC;
typedef typename AST_IC::Algebraic_category Algebraic_category; typedef typename AST_IC::Algebraic_category Algebraic_category;
return CGALi::new_resultant_univariate(F,G,Algebraic_category()); return CGALi::resultant_univariate(F,G,Algebraic_category());
} }
#if CGAL_RESULTANT_USE_INTERPOLATION #if CGAL_RESULTANT_USE_INTERPOLATION
template <class Coeff_2> template <class Coeff_2>
inline inline
CGAL::Polynomial<Coeff_2> new_resultant_interpolate( CGAL::Polynomial<Coeff_2> resultant_interpolate(
const CGAL::Polynomial<CGAL::Polynomial<Coeff_2> >& F, const CGAL::Polynomial<CGAL::Polynomial<Coeff_2> >& F,
const CGAL::Polynomial<CGAL::Polynomial<Coeff_2> >& G){ const CGAL::Polynomial<CGAL::Polynomial<Coeff_2> >& G){
@ -173,7 +173,7 @@ CGAL::Polynomial<Coeff_2> new_resultant_interpolate(
} }
if(degree_vector(Fat_i) == ev_f && degree_vector(Gat_i) == ev_g){ if(degree_vector(Fat_i) == ev_f && degree_vector(Gat_i) == ev_g){
// timer2.start(); // timer2.start();
Coeff_2 res_at_i = new_resultant_interpolate(Fat_i, Gat_i); Coeff_2 res_at_i = resultant_interpolate(Fat_i, Gat_i);
// timer2.stop(); // timer2.stop();
points.push_back(Point(IC(i),res_at_i)); points.push_back(Point(IC(i),res_at_i));
} }
@ -194,7 +194,7 @@ CGAL::Polynomial<Coeff_2> new_resultant_interpolate(
assert(degree_vector(Gat_i) <= ev_g); assert(degree_vector(Gat_i) <= ev_g);
if(degree_vector(Fat_i) == ev_f && degree_vector(Gat_i) == ev_g){ if(degree_vector(Fat_i) == ev_f && degree_vector(Gat_i) == ev_g){
Coeff_2 res_at_i = new_resultant_interpolate(Fat_i, Gat_i); Coeff_2 res_at_i = resultant_interpolate(Fat_i, Gat_i);
points.push_back(Point(IC(i), res_at_i)); points.push_back(Point(IC(i), res_at_i));
} }
} }
@ -213,16 +213,16 @@ CGAL::Polynomial<Coeff_2> new_resultant_interpolate(
template <class Coeff> template <class Coeff>
inline inline
Coeff new_resultant_modularize( Coeff resultant_modularize(
const CGAL::Polynomial<Coeff>& F, const CGAL::Polynomial<Coeff>& F,
const CGAL::Polynomial<Coeff>& G, const CGAL::Polynomial<Coeff>& G,
CGAL::Tag_false){ CGAL::Tag_false){
return new_resultant_interpolate(F,G); return resultant_interpolate(F,G);
}; };
template <class Coeff> template <class Coeff>
inline inline
Coeff new_resultant_modularize( Coeff resultant_modularize(
const CGAL::Polynomial<Coeff>& F, const CGAL::Polynomial<Coeff>& F,
const CGAL::Polynomial<Coeff>& G, const CGAL::Polynomial<Coeff>& G,
CGAL::Tag_true){ CGAL::Tag_true){
@ -281,7 +281,7 @@ Coeff new_resultant_modularize(
//timer_resultant.start(); //timer_resultant.start();
n++; n++;
mR = new_resultant_interpolate(mF,mG); mR = resultant_interpolate(mF,mG);
//timer_resultant.stop(); //timer_resultant.stop();
//timer_cr.start(); //timer_cr.start();
if(n == 1){ if(n == 1){
@ -308,30 +308,30 @@ Coeff new_resultant_modularize(
//std::cout << "Time Evaluate : " << timer_evaluate.time() << std::endl; //std::cout << "Time Evaluate : " << timer_evaluate.time() << std::endl;
//std::cout << "Time Resultant : " << timer_resultant.time() << std::endl; //std::cout << "Time Resultant : " << timer_resultant.time() << std::endl;
//std::cout << "Time Chinese R : " << timer_cr.time() << std::endl; //std::cout << "Time Chinese R : " << timer_cr.time() << std::endl;
// CGAL_postcondition(R == new_resultant_interpolate(F,G)); // CGAL_postcondition(R == resultant_interpolate(F,G));
return R; return R;
// return new_resultant_interpolate(F,G); // return resultant_interpolate(F,G);
} }
template <class Coeff> template <class Coeff>
inline inline
Coeff new_resultant_decompose( Coeff resultant_decompose(
const CGAL::Polynomial<Coeff>& F, const CGAL::Polynomial<Coeff>& F,
const CGAL::Polynomial<Coeff>& G, const CGAL::Polynomial<Coeff>& G,
CGAL::Tag_false){ CGAL::Tag_false){
#if CGAL_RESULTANT_USE_MODULAR_ARITHMETIC #if CGAL_RESULTANT_USE_MODULAR_ARITHMETIC
typedef CGAL::Polynomial<Coeff> Polynomial; typedef CGAL::Polynomial<Coeff> Polynomial;
typedef typename Modular_traits<Polynomial>::Is_modularizable Is_modularizable; typedef typename Modular_traits<Polynomial>::Is_modularizable Is_modularizable;
return new_resultant_modularize(F,G,Is_modularizable()); return resultant_modularize(F,G,Is_modularizable());
#else #else
return new_resultant_modularize(F,G,CGAL::Tag_false()); return resultant_modularize(F,G,CGAL::Tag_false());
#endif #endif
} }
template <class Coeff> template <class Coeff>
inline inline
Coeff new_resultant_decompose( Coeff resultant_decompose(
const CGAL::Polynomial<Coeff>& F, const CGAL::Polynomial<Coeff>& F,
const CGAL::Polynomial<Coeff>& G, const CGAL::Polynomial<Coeff>& G,
CGAL::Tag_true){ CGAL::Tag_true){
@ -350,7 +350,7 @@ Coeff new_resultant_decompose(
Denominator c = CGAL::ipower(a, G.degree()) * CGAL::ipower(b, F.degree()); Denominator c = CGAL::ipower(a, G.degree()) * CGAL::ipower(b, F.degree());
typedef Algebraic_structure_traits<RES> AST_RES; typedef Algebraic_structure_traits<RES> AST_RES;
typedef typename AST_RES::Algebraic_category Algebraic_category; typedef typename AST_RES::Algebraic_category Algebraic_category;
RES res0 = CGAL::CGALi::new_resultant_(F0, G0); RES res0 = CGAL::CGALi::resultant_(F0, G0);
typename Fraction_traits<Coeff>::Compose comp_frac; typename Fraction_traits<Coeff>::Compose comp_frac;
Coeff res = comp_frac(res0, c); Coeff res = comp_frac(res0, c);
typename Algebraic_structure_traits<Coeff>::Simplify simplify; typename Algebraic_structure_traits<Coeff>::Simplify simplify;
@ -361,15 +361,15 @@ Coeff new_resultant_decompose(
template <class Coeff> template <class Coeff>
inline inline
Coeff new_resultant_( Coeff resultant_(
const CGAL::Polynomial<Coeff>& F, const CGAL::Polynomial<Coeff>& F,
const CGAL::Polynomial<Coeff>& G){ const CGAL::Polynomial<Coeff>& G){
#if CGAL_RESULTANT_USE_DECOMPOSE #if CGAL_RESULTANT_USE_DECOMPOSE
typedef CGAL::Fraction_traits<Polynomial<Coeff > > FT; typedef CGAL::Fraction_traits<Polynomial<Coeff > > FT;
typedef typename FT::Is_fraction Is_fraction; typedef typename FT::Is_fraction Is_fraction;
return new_resultant_decompose(F,G,Is_fraction()); return resultant_decompose(F,G,Is_fraction());
#else #else
return new_resultant_decompose(F,G,CGAL::Tag_false()); return resultant_decompose(F,G,CGAL::Tag_false());
#endif #endif
} }
@ -377,14 +377,14 @@ Coeff new_resultant_(
template <class Coeff> template <class Coeff>
inline inline
Coeff new_resultant( Coeff resultant(
const CGAL::Polynomial<Coeff>& F_, const CGAL::Polynomial<Coeff>& F_,
const CGAL::Polynomial<Coeff>& G_){ const CGAL::Polynomial<Coeff>& G_){
// make the variable to be elimnated the innermost one. // make the variable to be elimnated the innermost one.
typedef CGAL::Polynomial_traits_d<CGAL::Polynomial<Coeff> > PT; typedef CGAL::Polynomial_traits_d<CGAL::Polynomial<Coeff> > PT;
CGAL::Polynomial<Coeff> F = typename PT::Move()(F_, PT::d-1, 0); CGAL::Polynomial<Coeff> F = typename PT::Move()(F_, PT::d-1, 0);
CGAL::Polynomial<Coeff> G = typename PT::Move()(G_, PT::d-1, 0); CGAL::Polynomial<Coeff> G = typename PT::Move()(G_, PT::d-1, 0);
return CGALi::new_resultant_(F,G); return CGALi::resultant_(F,G);
} }
} // namespace CGALi } // namespace CGALi

8
Polynomial/include/CGAL/Polynomial_traits_d.h
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@ -1364,10 +1364,12 @@ public:
const Polynomial_d& p, const Polynomial_d& p,
const Polynomial_d& q, const Polynomial_d& q,
int i = (d-1) ) const { int i = (d-1) ) const {
if(i == (d-1) ) // make i the innermost variabl call CGALi::resultant_
return resultant(p,q); // CGALi::resultant would eliminate the outermost variable.
if(i == 0 )
return CGALi::resultant_(p,q);
else else
return resultant(Move()(p,i),Move()(q,i)); return CGALi::resultant_(Move()(p,i,0),Move()(q,i,0));
} }
}; };