Functions
template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Canonicalize::result_type	CGAL::canonicalize (const Polynomial_d &p)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Compare::result_type	CGAL::compare (const Polynomial_d &p, const Polynomial_d &q)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Degree::result_type	CGAL::degree (const Polynomial_d &p, int i, index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Degree_vector::result_type	CGAL::degree_vector (const Polynomial_d &p)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Differentiate::result_type	CGAL::differentiate (const Polynomial_d &p, index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Evaluate_homogeneous::result_type	CGAL::evaluate_homogeneous (const Polynomial_d &p, Polynomial_traits_d< Polynomial_d >::Coefficient_type u, Polynomial_traits_d< Polynomial_d >::Coefficient_type v)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Evaluate::result_type	CGAL::evaluate (const Polynomial_d &p, Polynomial_traits_d< Polynomial_d >::Coefficient_type x)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Gcd_up_to_constant_factor::result_type	CGAL::gcd_up_to_constant_factor (const Polynomial_d &p, const Polynomial_d &q)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::get_coefficient::result_type	CGAL::get_coefficient (const Polynomial_d &p, int i)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::get_innermost_coefficient::result_type	CGAL::get_innermost_coefficient (const Polynomial_d &p, Exponent_vector ev)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Innermost_leading_coefficient::result_type	CGAL::innermost_leading_coefficient (const Polynomial_d &p)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Integral_division_up_to_constant_factor::result_type	CGAL::integral_division_up_to_constant_factor (const Polynomial_d &p, const Polynomial_d &q)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Invert::result_type	CGAL::invert (const Polynomial_d &p, int index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Is_square_free::result_type	CGAL::is_square_free (const Polynomial_d &p)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d , class InputIterator >
Polynomial_traits_d < Polynomial_d > ::Is_zero_at_homogeneous::result_type	CGAL::is_zero_at_homogeneous (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d , class InputIterator >
Polynomial_traits_d < Polynomial_d > ::Is_zero_at::result_type	CGAL::is_zero_at (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Leading_coefficient::result_type	CGAL::leading_coefficient (const Polynomial_d &p)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Make_square_free::result_type	CGAL::make_square_free (const Polynomial_d &p)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Move::result_type	CGAL::move (const Polynomial_d &p, int i, int j)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Multivariate_content::result_type	CGAL::multivariate_content (const Polynomial_d &p)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Negate::result_type	CGAL::negate (const Polynomial_d &p, int index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<typename Polynomial_d >
int	CGAL::number_of_real_roots (Polynomial_d f)
	computes the number of distinct real roots of $f$ . More...

template<typename InputIterator >
int	CGAL::number_of_real_roots (InputIterator start, InputIterator end)
	computes the number of distinct real roots of $f$ whose principal Sturm-Habicht coefficients are passed by the iterator range. More...

template<class Polynomial_d , class InputIterator >
Polynomial_traits_d < Polynomial_d > ::Permute::result_type	CGAL::permute (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<typename Polynomial_d , typename OutputIterator >
OutputIterator	CGAL::polynomial_subresultants (Polynomial_d p, Polynomial_d q, OutputIterator out)
	computes the polynomial subresultants of $p$ and $q$ , with respect to the outermost variable. More...

template<typename Polynomial_d , typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	CGAL::polynomial_subresultants_with_cofactors (Polynomial_d p, Polynomial_d q, OutputIterator1 sres_out, OutputIterator2 coP_out, OutputIterator3 coQ_out)
	computes the polynomial subresultants of $p$ and $q$ , `sres_out`, with respect to the outermost variable, and the cofactors for $P$ , `coP_out` and $Q$ , `coQ_out`. More...

template<typename Polynomial_d , typename OutputIterator >
OutputIterator	CGAL::principal_sturm_habicht_sequence (typename Polynomial_d f, OutputIterator out)
	computes the principal Sturm-Habicht coefficients of $f$ with respect to the outermost variable. More...

template<typename Polynomial_d , typename OutputIterator >
OutputIterator	CGAL::principal_subresultants (Polynomial_d p, Polynomial_d q, OutputIterator out)
	computes the principal subresultants of $p$ and $q$ , with respect to the outermost variable. More...

template<class Polynomial_d >
void	CGAL::pseudo_division (const Polynomial_d &f, const Polynomial_d &g, Polynomial_d &q, Polynomial_d &r, Polynomial_traits_d< Polynomial_d >::Coefficient_type &D)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Pseudo_division_quotient::result_type	CGAL::pseudo_division_quotient (const Polynomial_d &p, const Polynomial_d &q)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Pseudo_division_remainder::result_type	CGAL::pseudo_division_remainder (const Polynomial_d &p, const Polynomial_d &q)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Resultant::result_type	CGAL::resultant (const Polynomial_d &p, const Polynomial_d &q)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Scale_homogeneous::result_type	CGAL::scale_homogeneous (const Polynomial_d &p, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &u, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &v, int index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Scale::result_type	CGAL::scale (const Polynomial_d &p, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &a, int index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Shift::result_type	CGAL::shift (const Polynomial_d &p, int i, int index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d , class InputIterator >
Polynomial_traits_d < Polynomial_d > ::Sign_at_homogeneous::result_type	CGAL::sign_at_homogeneous (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d , class InputIterator >
Polynomial_traits_d < Polynomial_d > ::Sign_at::result_type	CGAL::sign_at (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d , class OutputIterator >
OutputIterator	CGAL::square_free_factorize (const Polynomial_d &p, OutputIterator it, Polynomial_traits_d< Polynomial >::Innermost_coefficient &a)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d , class OutputIterator >
OutputIterator	CGAL::square_free_factorize (const Polynomial_d &p, OutputIterator it)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d , class OutputIterator >
OutputIterator	CGAL::square_free_factorize_up_to_constant_factor (const Polynomial_d &p, OutputIterator it)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<typename Polynomial_d , typename OutputIterator >
OutputIterator	CGAL::sturm_habicht_sequence (Polynomial_d f, OutputIterator out)
	computes the Sturm-Habicht-sequence of $f$ with respect to the outermost variable. More...

template<typename Polynomial_d , typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	CGAL::sturm_habicht_sequence_with_cofactors (Polynomial_d f, OutputIterator1 stha_out, OutputIterator2 cof_out, OutputIterator3 cofx_out)
	computes the Sturm-Habicht sequence of $f$ `stha_out`, with respect to the outermost variable, and the cofactors for $f$ , `cof_out` and $f'$ , `cofx_out`. More...

template<class Polynomial_d , class InputIterator >
CGAL::Coercion_traits < Polynomial_traits_d < Polynomial_d > ::Innermost_coefficient, std::iterator_traits < Input_iterator >::value_type > ::Type	CGAL::substitute_homogeneous (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d , class InputIterator >
CGAL::Coercion_traits < Polynomial_traits_d < Polynomial_d > ::Innermost_coefficient, std::iterator_traits < Input_iterator >::value_type > ::Type	CGAL::substitute (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Swap::result_type	CGAL::swap (const Polynomial_d &p, int i, int j)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Total_degree::result_type	CGAL::total_degree (const Polynomial_d &p)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Translate_homogeneous::result_type	CGAL::translate_homogeneous (const Polynomial_d &p, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &u, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &v, int index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Translate::result_type	CGAL::translate (const Polynomial_d &p, const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &a, int index=Polynomial_traits_d< Polynomial_d >::d-1)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Univariate_content::result_type	CGAL::univariate_content (const Polynomial_d &p)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

template<class Polynomial_d >
Polynomial_traits_d < Polynomial_d > ::Univariate_content_up_to_constant_factor::result_type	CGAL::univariate_content_up_to_constant_factor (const Polynomial_d &p)
	For a given `Polynomial_d`, adapts the according functor in `Polynomial_traits_d<Polynomial_d>`. More...

Function Documentation

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Canonicalize::result_type CGAL::canonicalize ( const Polynomial_d & p)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Canonicalize.

For more details see the concept PolynomialTraits_d::Canonicalize.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Canonicalize

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/gcd_up_to_constant_factor.cpp.

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Compare::result_type CGAL::compare	(	const Polynomial_d &	p,
		const Polynomial_d &	q
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Compare.

For more details see the concept PolynomialTraits_d::Compare.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Compare

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Degree::result_type CGAL::degree	(	const Polynomial_d &	p,
		int	i,
		index	= `Polynomial_traits_d< Polynomial_d >::d-1`
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Degree.

For more details see the concept PolynomialTraits_d::Degree.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Degree

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/degree.cpp.

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Degree_vector::result_type CGAL::degree_vector ( const Polynomial_d & p)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::DegreeVector.

For more details see the concept PolynomialTraits_d::DegreeVector.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Degree_vector

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/degree.cpp.

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Differentiate::result_type CGAL::differentiate	(	const Polynomial_d &	p,
		index	= `Polynomial_traits_d< Polynomial_d >::d-1`
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Differentiate.

For more details see the concept PolynomialTraits_d::Differentiate.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Differentiate

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Evaluate::result_type CGAL::evaluate	(	const Polynomial_d &	p,
		Polynomial_traits_d< Polynomial_d >::Coefficient_type	x
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Evaluate.

For more details see the concept PolynomialTraits_d::Evaluate.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Evaluate

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/substitute.cpp.

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Evaluate_homogeneous::result_type CGAL::evaluate_homogeneous	(	const Polynomial_d &	p,
		Polynomial_traits_d< Polynomial_d >::Coefficient_type	u,
		Polynomial_traits_d< Polynomial_d >::Coefficient_type	v
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Evaluate_homogeneous.

For more details see the concept PolynomialTraits_d::EvaluateHomogeneous.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::EvaluateHomogeneous

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Gcd_up_to_constant_factor::result_type CGAL::gcd_up_to_constant_factor	(	const Polynomial_d &	p,
		const Polynomial_d &	q
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Gcd_up_to_constant_factor.

For more details see the concept PolynomialTraits_d::GcdUpToConstantFactor.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::GcdUpToConstantFactor

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::get_coefficient::result_type CGAL::get_coefficient	(	const Polynomial_d &	p,
		int	i
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::GetCoefficient.

For more details see the concept PolynomialTraits_d::GetCoefficient.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::GetCoefficient; PolynomialTraits_d::GetInnermostCoefficient

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/coefficient_access.cpp.

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::get_innermost_coefficient::result_type CGAL::get_innermost_coefficient	(	const Polynomial_d &	p,
		Exponent_vector	ev
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::GetInnermostCoefficient.

For more details see the concept PolynomialTraits_d::GetInnermostCoefficient.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::GetCoefficient; PolynomialTraits_d::GetInnermostCoefficient

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Innermost_leading_coefficient::result_type CGAL::innermost_leading_coefficient ( const Polynomial_d & p)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::InnermostLeadingCoefficient.

For more details see the concept PolynomialTraits_d::InnermostLeadingCoefficient.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::InnermostLeadingCoefficient

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Integral_division_up_to_constant_factor::result_type CGAL::integral_division_up_to_constant_factor	(	const Polynomial_d &	p,
		const Polynomial_d &	q
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Integral_division_up_to_constant_factor.

For more details see the concept PolynomialTraits_d::IntegralDivisionUpToConstantFactor.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::IntegralDivisionUpToConstantFactor

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Invert::result_type CGAL::invert	(	const Polynomial_d &	p,
		int	index = `Polynomial_traits_d< Polynomial_d >::d-1`
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Invert.

For more details see the concept PolynomialTraits_d::Invert.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Invert

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Is_square_free::result_type CGAL::is_square_free ( const Polynomial_d & p)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Is_square_free.

For more details see the concept PolynomialTraits_d::IsSquareFree.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::IsSquareFree

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d , class InputIterator >

Polynomial_traits_d<Polynomial_d>::Is_zero_at::result_type CGAL::is_zero_at	(	const Polynomial_d &	p,
		InputIterator	begin,
		InputIterator	end
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Is_zero_at.

For more details see the concept PolynomialTraits_d::IsZeroAt.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::IsZeroAt

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d , class InputIterator >

Polynomial_traits_d<Polynomial_d>::Is_zero_at_homogeneous::result_type CGAL::is_zero_at_homogeneous	(	const Polynomial_d &	p,
		InputIterator	begin,
		InputIterator	end
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Is_zero_at_homogeneous.

For more details see the concept PolynomialTraits_d::IsZeroAtHomogeneous.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::IsZeroAtHomogeneous

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Leading_coefficient::result_type CGAL::leading_coefficient ( const Polynomial_d & p)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Leading_coefficient.

For more details see the concept PolynomialTraits_d::LeadingCoefficient.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::LeadingCoefficient

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Make_square_free::result_type CGAL::make_square_free ( const Polynomial_d & p)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Make_square_free.

For more details see the concept PolynomialTraits_d::MakeSquareFree.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::MakeSquareFree

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Move::result_type CGAL::move	(	const Polynomial_d &	p,
		int	i,
		int	j
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Move.

For more details see the concept PolynomialTraits_d::Move.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Move

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/swap_move.cpp.

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Multivariate_content::result_type CGAL::multivariate_content ( const Polynomial_d & p)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Multivariate_content.

For more details see the concept PolynomialTraits_d::MultivariateContent.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::MultivariateContent

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Negate::result_type CGAL::negate	(	const Polynomial_d &	p,
		int	index = `Polynomial_traits_d< Polynomial_d >::d-1`
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Negate.

For more details see the concept PolynomialTraits_d::Negate.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Negate

#include <CGAL/polynomial_utils.h>

template<typename Polynomial_d >

int CGAL::number_of_real_roots ( Polynomial_d f)

computes the number of distinct real roots of $f$ .

Given a polynomial $f$ , or a range of values that is interpreted as the principal Sturm-Habicht coefficients of $f$ , the function computes

$m:=\# \{\alpha\in\mathbb{R}\mid f(\alpha)=0\}$

that is, the number of distinct real roots of $f$ .

The coefficient type of the polynomial, or the value type of the iterator range, respectively must be a model of RealEmbeddable. In the second version, it is not required to pass the exact princiapl Sturm-Habicht coefficients to the functions; it is only required that the sign of each element corresponds to the sign of the actual principal Sturm-Habicht coefficient.

Advanced

We explain the internals of this function. For a sequence $I:=(a_0,\ldots,a_n)$ of real numbers with $a_0\neq 0$ , define

$C(I)=\ccSum{i=1}{s}\epsilon_i$

where $s$ is the number of subsequences of $I$ of the form

with $a\neq 0,b\neq 0, k\geq 0$ .

For the $i$ -th subsequence of $I$ , define

$\epsilon_i:=\begin{array}{cc} 0 & \mbox{if $k$ is odd},\\ (-1)^{k/2}\mathrm{sign}(ab) & \mbox{if $k$ is even}. \end{array}$

For $f\in\mathbb{R}[x]$ with $\deg f=n$ , we have:

$C(\mathrm{stha}_n(f),\ldots,\mathrm{stha}_0(f)) = \#\{\alpha\in\R\mid f(\alpha)=0\}$

In other words, the signs of the principal Sturm-Habicht coefficients determine the number of distinct real roots of $f$ .

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::PrincipalSturmHabichtSequence

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/subresultants.cpp.

template<typename InputIterator >

int CGAL::number_of_real_roots	(	InputIterator	start,
		InputIterator	end
	)

computes the number of distinct real roots of $f$ whose principal Sturm-Habicht coefficients are passed by the iterator range.

Given a polynomial $f$ , or a range of values that is interpreted as the principal Sturm-Habicht coefficients of $f$ , the function computes

$m:=\# \{\alpha\in\mathbb{R}\mid f(\alpha)=0\}$

that is, the number of distinct real roots of $f$ .

The coefficient type of the polynomial, or the value type of the iterator range, respectively must be a model of RealEmbeddable. In the second version, it is not required to pass the exact princiapl Sturm-Habicht coefficients to the functions; it is only required that the sign of each element corresponds to the sign of the actual principal Sturm-Habicht coefficient.

Advanced

We explain the internals of this function. For a sequence $I:=(a_0,\ldots,a_n)$ of real numbers with $a_0\neq 0$ , define

$C(I)=\ccSum{i=1}{s}\epsilon_i$

where $s$ is the number of subsequences of $I$ of the form

with $a\neq 0,b\neq 0, k\geq 0$ .

For the $i$ -th subsequence of $I$ , define

$\epsilon_i:=\begin{array}{cc} 0 & \mbox{if $k$ is odd},\\ (-1)^{k/2}\mathrm{sign}(ab) & \mbox{if $k$ is even}. \end{array}$

For $f\in\mathbb{R}[x]$ with $\deg f=n$ , we have:

$C(\mathrm{stha}_n(f),\ldots,\mathrm{stha}_0(f)) = \#\{\alpha\in\R\mid f(\alpha)=0\}$

In other words, the signs of the principal Sturm-Habicht coefficients determine the number of distinct real roots of $f$ .

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::PrincipalSturmHabichtSequence

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d , class InputIterator >

Polynomial_traits_d<Polynomial_d>::Permute::result_type CGAL::permute	(	const Polynomial_d &	p,
		InputIterator	begin,
		InputIterator	end
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Permute.

For more details see the concept PolynomialTraits_d::Permute.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Permute

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/swap_move.cpp.

template<typename Polynomial_d , typename OutputIterator >

OutputIterator CGAL::polynomial_subresultants	(	Polynomial_d	p,
		Polynomial_d	q,
		OutputIterator	out
	)

computes the polynomial subresultants of $p$ and $q$ , with respect to the outermost variable.

Each element is of type Polynomial_d.

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

For more details see the concept PolynomialTraits_d::PolynomialSubresultants.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::PolynomialSubresultants

#include <CGAL/polynomial_utils.h>

template<typename Polynomial_d , typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >

OutputIterator1 CGAL::polynomial_subresultants_with_cofactors	(	Polynomial_d	p,
		Polynomial_d	q,
		OutputIterator1	sres_out,
		OutputIterator2	coP_out,
		OutputIterator3	coQ_out
	)

computes the polynomial subresultants of $p$ and $q$ , sres_out, with respect to the outermost variable, and the cofactors for $P$ , coP_out and $Q$ , coQ_out.

The elements of each output range are of type Polynomial_d.

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

For more details see the concept PolynomialTraits_d::PolynomialSubresultantsWithCofactors.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::PolynomialSubresultantsWithCofactors

#include <CGAL/polynomial_utils.h>

template<typename Polynomial_d , typename OutputIterator >

OutputIterator CGAL::principal_sturm_habicht_sequence	(	typename Polynomial_d	f,
		OutputIterator	out
	)

computes the principal Sturm-Habicht coefficients of $f$ with respect to the outermost variable.

Each element is of type Polynomial_traits_d::Coefficient_typeb.

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

For more details see the concept PolynomialTraits_d::PrincipalSturmHabichtSequence.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::PrincipalSturmHabichtSequence

#include <CGAL/polynomial_utils.h>

template<typename Polynomial_d , typename OutputIterator >

OutputIterator CGAL::principal_subresultants	(	Polynomial_d	p,
		Polynomial_d	q,
		OutputIterator	out
	)

computes the principal subresultants of $p$ and $q$ , with respect to the outermost variable.

Each element is of type Polynomial_traits_d::Coefficient_type.

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

For more details see the concept PolynomialTraits_d::PrincipalSubresultants.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::PrincipalSubresultants

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

void CGAL::pseudo_division	(	const Polynomial_d &	f,
		const Polynomial_d &	g,
		Polynomial_d &	q,
		Polynomial_d &	r,
		Polynomial_traits_d< Polynomial_d >::Coefficient_type &	D
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Pseudo_division.

For more details see the concept PolynomialTraits_d::PseudoDivision.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::PseudoDivision

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Pseudo_division_quotient::result_type CGAL::pseudo_division_quotient	(	const Polynomial_d &	p,
		const Polynomial_d &	q
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Pseudo_division_quotient.

For more details see the concept PolynomialTraits_d::PseudoDivisionQuotient.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::PseudoDivisionQuotient

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Pseudo_division_remainder::result_type CGAL::pseudo_division_remainder	(	const Polynomial_d &	p,
		const Polynomial_d &	q
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Pseudo_division_remainder.

For more details see the concept PolynomialTraits_d::PseudoDivisionRemainder.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::PseudoDivisionRemainder

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Resultant::result_type CGAL::resultant	(	const Polynomial_d &	p,
		const Polynomial_d &	q
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Resultant.

For more details see the concept PolynomialTraits_d::Resultant.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Resultant

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/subresultants.cpp.

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Scale::result_type CGAL::scale	(	const Polynomial_d &	p,
		const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &	a,
		int	index = `Polynomial_traits_d< Polynomial_d >::d-1`
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Scale.

For more details see the concept PolynomialTraits_d::Scale.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Scale

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Scale_homogeneous::result_type CGAL::scale_homogeneous	(	const Polynomial_d &	p,
		const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &	u,
		const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &	v,
		int	index = `Polynomial_traits_d< Polynomial_d >::d-1`
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Scale_homogeneous.

For more details see the concept PolynomialTraits_d::ScaleHomogeneous.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::ScaleHomogeneous

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Shift::result_type CGAL::shift	(	const Polynomial_d &	p,
		int	i,
		int	index = `Polynomial_traits_d< Polynomial_d >::d-1`
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Shift.

For more details see the concept PolynomialTraits_d::Shift.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Shift

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/construction.cpp, and Polynomial/gcd_up_to_constant_factor.cpp.

template<class Polynomial_d , class InputIterator >

Polynomial_traits_d<Polynomial_d>::Sign_at::result_type CGAL::sign_at	(	const Polynomial_d &	p,
		InputIterator	begin,
		InputIterator	end
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Sign_at.

For more details see the concept PolynomialTraits_d::SignAt.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::SignAt

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d , class InputIterator >

Polynomial_traits_d<Polynomial_d>::Sign_at_homogeneous::result_type CGAL::sign_at_homogeneous	(	const Polynomial_d &	p,
		InputIterator	begin,
		InputIterator	end
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Sign_at_homogeneous.

For more details see the concept PolynomialTraits_d::SignAtHomogeneous.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::SignAtHomogeneous

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d , class OutputIterator >

OutputIterator CGAL::square_free_factorize	(	const Polynomial_d &	p,
		OutputIterator	it,
		Polynomial_traits_d< Polynomial >::Innermost_coefficient &	a
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Square_free_factorize.

For more details see the concept PolynomialTraits_d::SquareFreeFactorize.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::SquareFreeFactorize

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d , class OutputIterator >

OutputIterator CGAL::square_free_factorize	(	const Polynomial_d &	p,
		OutputIterator	it
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Square_free_factorize.

For more details see the concept PolynomialTraits_d::SquareFreeFactorize.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::SquareFreeFactorize

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d , class OutputIterator >

OutputIterator CGAL::square_free_factorize_up_to_constant_factor	(	const Polynomial_d &	p,
		OutputIterator	it
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Square_free_factorize_up_to_constant_factor.

For more details see the concept PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor

#include <CGAL/polynomial_utils.h>

template<typename Polynomial_d , typename OutputIterator >

OutputIterator CGAL::sturm_habicht_sequence	(	Polynomial_d	f,
		OutputIterator	out
	)

computes the Sturm-Habicht-sequence of $f$ with respect to the outermost variable.

Each element is of type Polynomial_d.

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

For more details see the concept PolynomialTraits_d::SturmHabichtSequence.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::SturmHabichtSequence

#include <CGAL/polynomial_utils.h>

template<typename Polynomial_d , typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >

OutputIterator1 CGAL::sturm_habicht_sequence_with_cofactors	(	Polynomial_d	f,
		OutputIterator1	stha_out,
		OutputIterator2	cof_out,
		OutputIterator3	cofx_out
	)

computes the Sturm-Habicht sequence of $f$ stha_out, with respect to the outermost variable, and the cofactors for $f$ , cof_out and $f'$ , cofx_out.

The elements of each output range are of type Polynomial_d.

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

For more details see the concept PolynomialTraits_d::SturmHabichtSequenceWithCofactors.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::SturmHabichtSequenceWithCofactors

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d , class InputIterator >

CGAL::Coercion_traits<Polynomial_traits_d<Polynomial_d>::Innermost_coefficient,std::iterator_traits<Input_iterator>::value_type>::Type CGAL::substitute	(	const Polynomial_d &	p,
		InputIterator	begin,
		InputIterator	end
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Substitute.

For more details see the concept PolynomialTraits_d::Substitute.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Substitute

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/substitute.cpp.

template<class Polynomial_d , class InputIterator >

CGAL::Coercion_traits<Polynomial_traits_d<Polynomial_d>::Innermost_coefficient,std::iterator_traits<Input_iterator>::value_type>::Type CGAL::substitute_homogeneous	(	const Polynomial_d &	p,
		InputIterator	begin,
		InputIterator	end
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Substitute_homogeneous.

For more details see the concept PolynomialTraits_d::SubstituteHomogeneous.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::SubstituteHomogeneous

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Swap::result_type CGAL::swap	(	const Polynomial_d &	p,
		int	i,
		int	j
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Swap.

For more details see the concept PolynomialTraits_d::Swap.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Swap

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/swap_move.cpp.

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Total_degree::result_type CGAL::total_degree ( const Polynomial_d & p)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Total_degree.

For more details see the concept PolynomialTraits_d::TotalDegree.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::TotalDegree

#include <CGAL/polynomial_utils.h>

Examples:: Polynomial/degree.cpp.

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Translate::result_type CGAL::translate	(	const Polynomial_d &	p,
		const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &	a,
		int	index = `Polynomial_traits_d< Polynomial_d >::d-1`
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Translate.

For more details see the concept PolynomialTraits_d::Translate.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Translate

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Translate_homogeneous::result_type CGAL::translate_homogeneous	(	const Polynomial_d &	p,
		const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &	u,
		const Polynomial_traits_d< Polynomial_d >::Innermost_coefficient_type &	v,
		int	index = `Polynomial_traits_d< Polynomial_d >::d-1`
	)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Translate_homogeneous.

For more details see the concept PolynomialTraits_d::TranslateHomogeneous.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::TranslateHomogeneous

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Univariate_content::result_type CGAL::univariate_content ( const Polynomial_d & p)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::UnivariateContent.

For more details see the concept PolynomialTraits_d::UnivariateContent.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Univariate_Content

#include <CGAL/polynomial_utils.h>

template<class Polynomial_d >

Polynomial_traits_d<Polynomial_d>::Univariate_content_up_to_constant_factor::result_type CGAL::univariate_content_up_to_constant_factor ( const Polynomial_d & p)

For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.

Adapts Polynomial_traits_d::Univariate_content_up_to_constant_factor.

For more details see the concept PolynomialTraits_d::UnivariateContentUpToConstantFactor.

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::UnivariateContentUpToConstantFactor

#include <CGAL/polynomial_utils.h>

Functions

Function Documentation