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PolynomialTraits_d provides two different views on the multivariate polynomial.
Many functors consider the polynomial as a univariate polynomial in one variable. By default this is the outermost variable xd-1. However, in general it is possible to select a certain variable.
| static const int | d; | The dimension and the number of variables respectively. |
| PolynomialTraits_d::Polynomial_d | |
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Type representing R[x0, … ,xd-1].
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| PolynomialTraits_d::Coefficient_type | |
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Type representing R[x0, … ,xd-2].
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| PolynomialTraits_d::Innermost_coefficient_type | |
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Type representing the base ring R.
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| PolynomialTraits_d::Coefficient_const_iterator | |
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Const iterator used to iterate through all coefficients of the polynomial.
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| PolynomialTraits_d::Innermost_coefficient_const_iterator | |
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Const iterator used to iterate through all innermost coefficients of the polynomial.
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| template <typename T, int d> | |
| PolynomialTraits_d:: struct Rebind | |
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This nested template class has to define a type Other which is a model
of the concept PolynomialTraits_d, where d is the number of
variables and T the Innermost_coefficient_type.
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In case a functor is not provided it is set to CGAL::Null_functor.
| PolynomialTraits_d::Construct_polynomial | |
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A model of PolynomialTraits_d::ConstructPolynomial.
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| PolynomialTraits_d::Get_coefficient | |
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A model of PolynomialTraits_d::GetCoefficient.
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| PolynomialTraits_d::Get_innermost_coefficient | |
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A model of PolynomialTraits_d::GetInnermostCoefficient.
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| PolynomialTraits_d::Construct_coefficient_const_iterator_range | |
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A model of
PolynomialTraits_d::ConstructCoefficientConstIteratorRange.
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| PolynomialTraits_d::Construct_innermost_coefficient_const_iterator_range | |
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A model of
PolynomialTraits_d::ConstructInnermostCoefficientConstIteratorRange.
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| PolynomialTraits_d::Swap | |
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A model of PolynomialTraits_d::Swap.
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| PolynomialTraits_d::Move | |
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A model of PolynomialTraits_d::Move.
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| PolynomialTraits_d::Degree | |
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A model of PolynomialTraits_d::Degree.
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| PolynomialTraits_d::Total_degree | |
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A model of PolynomialTraits_d::TotalDegree.
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| PolynomialTraits_d::Degree_vector | |
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A model of PolynomialTraits_d::DegreeVector.
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| PolynomialTraits_d::Leading_coefficient | |
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A model of PolynomialTraits_d::LeadingCoefficient.
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| PolynomialTraits_d::Innermost_leading_coefficient | |
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A model of PolynomialTraits_d::InnermostLeadingCoefficient.
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| PolynomialTraits_d::Canonicalize | |
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A model of PolynomialTraits_d::Canonicalize.
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| PolynomialTraits_d::Differentiate | |
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A model of PolynomialTraits_d::Differentiate.
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| PolynomialTraits_d::Evaluate | |
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A model of PolynomialTraits_d::Evaluate.
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| PolynomialTraits_d::Evaluate_homogeneous | |
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A model of PolynomialTraits_d::EvaluateHomogeneous.
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| PolynomialTraits_d::Substitute | |
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A model of PolynomialTraits_d::Substitute.
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| PolynomialTraits_d::Substitute_homogeneous | |
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A model of PolynomialTraits_d::SubstituteHomogeneous.
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| PolynomialTraits_d::Is_zero_at | |
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A model of PolynomialTraits_d::IsZeroAt.
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| PolynomialTraits_d::Is_zero_at_homogeneous | |
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A model of PolynomialTraits_d::IsZeroAtHomogeneous.
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| PolynomialTraits_d::Sign_at | |
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A model of PolynomialTraits_d::SignAt. In case Innermost_coefficient_type is not RealEmbeddable this is CGAL::Null_functor.
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| PolynomialTraits_d::Sign_at_homogeneous | |
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A model of PolynomialTraits_d::SignAtHomogeneous. In case Innermost_coefficient_type is not RealEmbeddable this is CGAL::Null_functor.
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| PolynomialTraits_d::Compare | |
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A model of PolynomialTraits_d::Compare. In case Innermost_coefficient_type is not RealEmbeddable this is CGAL::Null_functor.
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| PolynomialTraits_d::Univariate_content | |
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In case PolynomialTraits_d::Coefficient_type is not a model of
UniqueFactorizationDomain, this is CGAL::Null_functor, otherwise this is
a model of PolynomialTraits_d::UnivariateContent.
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| PolynomialTraits_d::Multivariate_content | |
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In case PolynomialTraits_d::Innermost_coefficient_type is not
a model of UniqueFactorizationDomain, this is CGAL::Null_functor,
otherwise this is a model of
PolynomialTraits_d::MultivariateContent.
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| PolynomialTraits_d::Shift | |
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A model of PolynomialTraits_d::Shift.
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| PolynomialTraits_d::Negate | |
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A model of PolynomialTraits_d::Negate.
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| PolynomialTraits_d::Invert | |
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A model of PolynomialTraits_d::Invert.
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| PolynomialTraits_d::Translate | |
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A model of PolynomialTraits_d::Translate.
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| PolynomialTraits_d::Translate_homogeneous | |
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A model of PolynomialTraits_d::TranslateHomogeneous.
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| PolynomialTraits_d::Scale | |
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A model of PolynomialTraits_d::Scale.
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| PolynomialTraits_d::Scale_homogeneous | |
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A model of PolynomialTraits_d::ScaleHomogeneous.
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| PolynomialTraits_d::Make_square_free | |
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A model of PolynomialTraits_d::MakeSquareFree.
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| PolynomialTraits_d::Square_free_factorize | |
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In case PolynomialTraits::Polynomial_d
is not a model of UniqueFactorizationDomain, this is of type CGAL::Null_functor,
otherwise this is a model of PolynomialTraits_d::SquareFreeFactorize.
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| PolynomialTraits_d::Pseudo_division | |
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A model of PolynomialTraits_d::PseudoDivision.
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| PolynomialTraits_d::Pseudo_division_remainder | |
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A model of PolynomialTraits_d::PseudoDivisionRemainder.
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| PolynomialTraits_d::Pseudo_division_quotient | |
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A model of PolynomialTraits_d::PseudoDivisionQuotient.
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| PolynomialTraits_d::Gcd_up_to_constant_factor | |
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A model of PolynomialTraits_d::GcdUpToConstantFactor.
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| PolynomialTraits_d::Integral_division_up_to_constant_factor | |
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A model of PolynomialTraits_d::IntegralDivisionUpToConstantFactor.
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| PolynomialTraits_d::Content_up_to_constant_factor | |
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A model of PolynomialTraits_d::UnivariateContentUpToConstantFactor.
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| PolynomialTraits_d::Square_free_factorize_up_to_constant_factor | |
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A model of PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor.
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| PolynomialTraits_d::Resultant | |
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A model of PolynomialTraits_d::Resultant.
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| PolynomialTraits_d::Polynomial_subresultants | |
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Either CGAL::Null_functor or a model of PolynomialTraits_d::PolynomialSubresultants.
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| PolynomialTraits_d::Polynomial_subresultants_with_cofactors | |
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Either CGAL::Null_functor or a model of PolynomialTraits_d::PolynomialSubresultants_with_cofactors.
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| PolynomialTraits_d::Principal_subresultants | |
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Either CGAL::Null_functor or a model of PolynomialTraits_d::PrincipalSubresultants.
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| PolynomialTraits_d::Sturm_habicht_sequence | |
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Either CGAL::Null_functor or a model of PolynomialTraits_d::SturmHabichtSequence.
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| PolynomialTraits_d::Sturm_habicht_sequence_with_cofactors | |
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Either CGAL::Null_functor or a model of PolynomialTraits_d::SturmHabichtSequenceWithCofactors.
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| PolynomialTraits_d::Principal_sturm_habicht_sequence | |
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Either CGAL::Null_functor or a model of PolynomialTraits_d::PrincipalSturmHabichtSequence.
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CGAL::Polynomial_traits_d<Polynomial_d>