SPAR/AIModule/BWTA/vendors/CGAL/CGAL/Polynomial/sturm_habicht_sequence.h File Reference

#include <vector>
#include <algorithm>
#include <CGAL/Polynomial/bezout_matrix.h>
#include <CGAL/Polynomial/subresultants.h>

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Namespaces
namespace	CGALi
Functions
template<typename Polynomial_traits_d , typename OutputIterator >
OutputIterator	CGALi::prs_principal_sturm_habicht_sequence (typename Polynomial_traits_d::Polynomial_d P, OutputIterator out)
	compute the leading coefficients of the Sturm-Habicht sequence of the polynomial P
template<typename Polynomial_traits_d , typename OutputIterator >
OutputIterator	CGALi::bezout_principal_sturm_habicht_sequence (typename Polynomial_traits_d::Polynomial_d P, OutputIterator out)
	compute the leading coefficients of the Sturm-Habicht sequence of the polynomial P
template<typename Polynomial_traits_d , typename OutputIterator1 , typename OutputIterator2 >
void	CGALi::prs_first_two_sturm_habicht_coefficients (typename Polynomial_traits_d::Polynomial_d P, OutputIterator1 pstha, OutputIterator2 copstha)
	compute the principal and coprincipal Sturm-Habicht sequence
template<typename Polynomial_traits_d , typename OutputIterator1 , typename OutputIterator2 >
void	CGALi::bezout_first_two_sturm_habicht_coefficients (typename Polynomial_traits_d::Polynomial_d P, OutputIterator1 pstha, OutputIterator2 copstha)
	compute the principal and coprincipal Sturm-Habicht sequence
template<typename Polynomial_traits_d , typename OutputIterator1 , typename OutputIterator2 >
void	CGALi::first_two_sturm_habicht_coefficients_ (typename Polynomial_traits_d::Polynomial_d A, OutputIterator1 pstha, OutputIterator2 copstha, CGAL::Integral_domain_without_division_tag)
template<typename Polynomial_traits_d , typename OutputIterator1 , typename OutputIterator2 >
void	CGALi::first_two_sturm_habicht_coefficients_ (typename Polynomial_traits_d::Polynomial_d A, OutputIterator1 pstha, OutputIterator2 copstha, CGAL::Integral_domain_tag)
template<typename Polynomial_traits_d , typename OutputIterator1 , typename OutputIterator2 >
void	CGALi::first_two_sturm_habicht_coefficients_ (typename Polynomial_traits_d::Polynomial_d A, OutputIterator1 pstha, OutputIterator2 copstha)
template<typename Polynomial_traits_d , typename OutputIterator >
OutputIterator	CGALi::principal_sturm_habicht_sequence_ (typename Polynomial_traits_d::Polynomial_d A, OutputIterator out, CGAL::Integral_domain_without_division_tag)
template<typename Polynomial_traits_d , typename OutputIterator >
OutputIterator	CGALi::principal_sturm_habicht_sequence_ (typename Polynomial_traits_d::Polynomial_d A, OutputIterator out, CGAL::Integral_domain_tag)
template<typename Polynomial_traits_d , typename OutputIterator >
OutputIterator	CGALi::principal_sturm_habicht_sequence_ (typename Polynomial_traits_d::Polynomial_d A, OutputIterator out)
template<typename Polynomial_traits_d , typename OutputIterator1 , typename OutputIterator2 >
void	CGALi::first_two_sturm_habicht_coefficients (typename Polynomial_traits_d::Polynomial_d A, OutputIterator1 pstha, OutputIterator2 copstha)
	computes the first two coefficients of each polynomial of the Sturm-Habicht sequence.
template<typename Polynomial_traits_d , typename OutputIterator >
OutputIterator	CGALi::principal_sturm_habicht_sequence (typename Polynomial_traits_d::Polynomial_d A, OutputIterator out)
	compute the sequence of principal Sturm-Habicht coefficients
template<typename Polynomial_traits_d , typename OutputIterator >
OutputIterator	CGALi::sturm_habicht_sequence (typename Polynomial_traits_d::Polynomial_d P, OutputIterator out)
	compute the Sturm-Habicht sequence
template<typename Polynomial_traits_d , typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	CGALi::sturm_habicht_sequence_with_cofactors (typename Polynomial_traits_d::Polynomial_d P, OutputIterator1 stha_out, OutputIterator2 cof_out, OutputIterator3 cofx_out)
	compute the Sturm-Habicht sequence with cofactors
template<typename InputIterator >
int	number_of_real_roots (InputIterator start, InputIterator end)
	returns the number of roots of a polynomial with given principal Sturm-Habicht sequence (counted without multiplicity)
template<typename Polynomial_d >
int	number_of_real_roots (Polynomial_d f)
	returns the number of roots of a polynomial

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Function Documentation

template<typename InputIterator >

int number_of_real_roots	(	InputIterator	start,
		InputIterator	end
	)

returns the number of roots of a polynomial with given principal Sturm-Habicht sequence (counted without multiplicity)

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template<typename Polynomial_d >

int number_of_real_roots

(

Polynomial_d

f

)

returns the number of roots of a polynomial

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