CGAL Namespace Reference

Classes
class	Exponent_vector
	For a given (multivariate) monomial the vector of its exponents is called the exponent vector. More...
class	Polynomial
	An instance of the data type Polynomial represents a polynomial \( p = a_0 + a_1*x + ...a_i*x^i\) from the ring \( \mathrm{Coeff}[x]\). More...
class	Polynomial_traits_d
	A model of concept PolynomialTraits_d More...
struct	Polynomial_type_generator
	This class template provides a convenient way to obtain the type representing a multivariate polynomial with d variables, where T is the innermost coefficient type. More...

Functions
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Canonicalize::result_type	canonicalize (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Compare::result_type	compare (const Polynomial_d &p, const Polynomial_d &q)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Degree::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Degree_vector::result_type	degree_vector (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Differentiate::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Evaluate_homogeneous::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Evaluate::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Gcd_up_to_constant_factor::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::get_coefficient::result_type	get_coefficient (const Polynomial_d &p, int i)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::get_innermost_coefficient::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Innermost_leading_coefficient::result_type	innermost_leading_coefficient (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Integral_division_up_to_constant_factor::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Invert::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Is_square_free::result_type	is_square_free (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d , class InputIterator >
Polynomial_traits_d< Polynomial_d >::Is_zero_at_homogeneous::result_type	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>.
template<class Polynomial_d , class InputIterator >
Polynomial_traits_d< Polynomial_d >::Is_zero_at::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Leading_coefficient::result_type	leading_coefficient (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Make_square_free::result_type	make_square_free (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Move::result_type	move (const Polynomial_d &p, int i, int j)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Multivariate_content::result_type	multivariate_content (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Negate::result_type	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>.
template<typename Polynomial_d >
int	number_of_real_roots (Polynomial_d f)
	computes the number of distinct real roots of \(f\).
template<typename InputIterator >
int	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.
template<class Polynomial_d , class InputIterator >
Polynomial_traits_d< Polynomial_d >::Permute::result_type	permute (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<typename Polynomial_d , typename OutputIterator >
OutputIterator	polynomial_subresultants (Polynomial_d p, Polynomial_d q, OutputIterator out)
	computes the polynomial subresultants of \( p\) and \( q\), with respect to the outermost variable.
template<typename Polynomial_d , typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	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.
template<typename Polynomial_d , typename OutputIterator >
OutputIterator	principal_sturm_habicht_sequence (typename Polynomial_d f, OutputIterator out)
	computes the principal Sturm-Habicht coefficients of \( f\) with respect to the outermost variable.
template<typename Polynomial_d , typename OutputIterator >
OutputIterator	principal_subresultants (Polynomial_d p, Polynomial_d q, OutputIterator out)
	computes the principal subresultants of \( p\) and \( q\), with respect to the outermost variable.
template<class Polynomial_d >
void	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Pseudo_division_quotient::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Pseudo_division_remainder::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Resultant::result_type	resultant (const Polynomial_d &p, const Polynomial_d &q)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Scale_homogeneous::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Scale::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Shift::result_type	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>.
template<class Polynomial_d , class InputIterator >
Polynomial_traits_d< Polynomial_d >::Sign_at_homogeneous::result_type	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>.
template<class Polynomial_d , class InputIterator >
Polynomial_traits_d< Polynomial_d >::Sign_at::result_type	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>.
template<class Polynomial_d , class OutputIterator >
OutputIterator	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>.
template<class Polynomial_d , class OutputIterator >
OutputIterator	square_free_factorize (const Polynomial_d &p, OutputIterator it)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d , class OutputIterator >
OutputIterator	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>.
template<typename Polynomial_d , typename OutputIterator >
OutputIterator	sturm_habicht_sequence (Polynomial_d f, OutputIterator out)
	computes the Sturm-Habicht-sequence of \( f\) with respect to the outermost variable.
template<typename Polynomial_d , typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	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.
template<class Polynomial_d , class InputIterator >
CGAL::Coercion_traits< Polynomial_traits_d< Polynomial_d >::Innermost_coefficient, std::iterator_traits< Input_iterator >::value_type >::Type	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>.
template<class Polynomial_d , class InputIterator >
CGAL::Coercion_traits< Polynomial_traits_d< Polynomial_d >::Innermost_coefficient, std::iterator_traits< Input_iterator >::value_type >::Type	substitute (const Polynomial_d &p, InputIterator begin, InputIterator end)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Swap::result_type	swap (const Polynomial_d &p, int i, int j)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Total_degree::result_type	total_degree (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Translate_homogeneous::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Translate::result_type	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>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Univariate_content::result_type	univariate_content (const Polynomial_d &p)
	For a given Polynomial_d, adapts the according functor in Polynomial_traits_d<Polynomial_d>.
template<class Polynomial_d >
Polynomial_traits_d< Polynomial_d >::Univariate_content_up_to_constant_factor::result_type	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>.