\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11.2 - Polynomial
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CGAL Namespace Reference

Namespaces

 cpp11
 
 IO
 
 Scale_space_reconstruction_3
 
 Shape_detection_3
 
 Surface_mesh_parameterization
 

Classes

class  Aff_transformation_2
 
class  Aff_transformation_3
 
class  Identity_transformation
 
class  Reflection
 
class  Rotation
 
class  Scaling
 
class  Translation
 
class  Bbox_2
 
class  Bbox_3
 
class  Cartesian
 
class  Cartesian_converter
 
class  Circle_2
 
class  Circle_3
 
class  Ambient_dimension
 
class  Dimension_tag
 
class  Dynamic_dimension_tag
 
class  Feature_dimension
 
class  Direction_2
 
class  Direction_3
 
class  Exact_predicates_exact_constructions_kernel
 
class  Exact_predicates_exact_constructions_kernel_with_kth_root
 
class  Exact_predicates_exact_constructions_kernel_with_root_of
 
class  Exact_predicates_exact_constructions_kernel_with_sqrt
 
class  Exact_predicates_inexact_constructions_kernel
 
class  Filtered_kernel_adaptor
 
class  Filtered_kernel
 
class  Filtered_predicate
 
class  Homogeneous
 
class  Homogeneous_converter
 
class  Iso_cuboid_3
 
class  Iso_rectangle_2
 
class  Kernel_traits
 
class  Line_2
 
class  Line_3
 
class  Null_vector
 
class  Origin
 
class  Plane_3
 
class  Point_2
 
class  Point_3
 
class  Projection_traits_xy_3
 
class  Projection_traits_xz_3
 
class  Projection_traits_yz_3
 
class  Ray_2
 
class  Ray_3
 
class  Segment_2
 
class  Segment_3
 
class  Simple_cartesian
 
class  Simple_homogeneous
 
class  Sphere_3
 
class  Tetrahedron_3
 
class  Triangle_2
 
class  Triangle_3
 
class  Vector_2
 
class  Vector_3
 
class  Weighted_point_2
 
class  Weighted_point_3
 
struct  Construct_array
 
class  CC_safe_handle
 
class  Compact_container_base
 
class  Compact_container
 
class  Compact_container_traits
 
class  Compact
 
class  Fast
 
class  Concurrent_compact_container_traits
 
class  Concurrent_compact_container
 
class  Default
 
class  Fourtuple
 
class  Cast_function_object
 
class  Compare_to_less
 
class  Creator_1
 
class  Creator_2
 
class  Creator_3
 
class  Creator_4
 
class  Creator_5
 
class  Creator_uniform_2
 
class  Creator_uniform_3
 
class  Creator_uniform_4
 
class  Creator_uniform_5
 
class  Creator_uniform_6
 
class  Creator_uniform_7
 
class  Creator_uniform_8
 
class  Creator_uniform_9
 
class  Creator_uniform_d
 
class  Dereference
 
class  Get_address
 
class  Identity
 
class  Project_facet
 
class  Project_next
 
class  Project_next_opposite
 
class  Project_normal
 
class  Project_opposite_prev
 
class  Project_plane
 
class  Project_point
 
class  Project_prev
 
class  Project_vertex
 
class  In_place_list_base
 
class  In_place_list
 
class  Const_oneset_iterator
 
class  Counting_iterator
 
class  Dispatch_or_drop_output_iterator
 
class  Dispatch_output_iterator
 
class  Emptyset_iterator
 
class  Filter_iterator
 
class  Insert_iterator
 
class  Inverse_index
 
class  Join_input_iterator_1
 
class  Join_input_iterator_2
 
class  Join_input_iterator_3
 
class  N_step_adaptor
 
class  Oneset_iterator
 
class  Random_access_adaptor
 
class  Random_access_value_adaptor
 
class  Iterator_range
 
class  Location_policy
 
class  Multiset
 
class  Object
 
class  Sixtuple
 
class  Spatial_lock_grid_3
 
class  Boolean_tag
 
struct  Null_functor
 
struct  Sequential_tag
 
struct  Parallel_tag
 
class  Null_tag
 
class  Threetuple
 
class  Twotuple
 
class  Uncertain
 
class  Quadruple
 
class  Triple
 
struct  value_type_traits
 
struct  value_type_traits< std::back_insert_iterator< Container > >
 
struct  value_type_traits< std::insert_iterator< Container > >
 
struct  value_type_traits< std::front_insert_iterator< Container > >
 
class  Algebraic_structure_traits
 
class  Euclidean_ring_tag
 
class  Field_tag
 
class  Field_with_kth_root_tag
 
class  Field_with_root_of_tag
 
class  Field_with_sqrt_tag
 
class  Integral_domain_tag
 
class  Integral_domain_without_division_tag
 
class  Unique_factorization_domain_tag
 
class  Coercion_traits
 
class  Fraction_traits
 
class  Real_embeddable_traits
 
class  Circulator_from_container
 
class  Circulator_from_iterator
 
class  Circulator_traits
 
class  Container_from_circulator
 
struct  Circulator_tag
 
struct  Iterator_tag
 
struct  Forward_circulator_tag
 
struct  Bidirectional_circulator_tag
 
struct  Random_access_circulator_tag
 
struct  Circulator_base
 
struct  Forward_circulator_base
 
struct  Bidirectional_circulator_base
 
struct  Random_access_circulator_base
 
class  Forward_circulator_ptrbase
 
class  Bidirectional_circulator_ptrbase
 
class  Random_access_circulator_ptrbase
 
class  Color
 
class  Input_rep
 
class  Output_rep
 
class  Istream_iterator
 
class  Ostream_iterator
 
class  Verbose_ostream
 
class  Modular_traits
 
class  Residue
 
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...
 
class  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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
template<typename Polynomial_d >
int number_of_real_roots (Polynomial_d f)
 computes the number of distinct real roots of \(f\). More...
 
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. More...
 
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>. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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>. More...
 
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. More...
 
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. 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 
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 
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 
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 
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 
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 
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 
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 
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...