Polynomial Reference

Michael Hemmer

This package introduces a concept for univariate and multivariate polynomials in \( d\) variables. Though the concept is written for an arbitrary number of variables, the number of variables is considered as fixed for a particular model of this concept.

Introduced in: CGAL 3.3
BibTeX: cgal:h-p-20a
License: LGPL

Classified Reference Pages

Concepts

• Polynomial_d
• PolynomialTraits_d
• PolynomialTraits_d::ConstructPolynomial
• PolynomialTraits_d::GetCoefficient
• PolynomialTraits_d::GetInnermostCoefficient
• PolynomialTraits_d::MonomialRepresentation
• PolynomialTraits_d::ConstructCoefficientConstIteratorRange
• PolynomialTraits_d::ConstructInnermostCoefficientConstIteratorRange
• PolynomialTraits_d::Permute
• PolynomialTraits_d::Swap
• PolynomialTraits_d::Move
• PolynomialTraits_d::Degree
• PolynomialTraits_d::TotalDegree
• PolynomialTraits_d::DegreeVector
• PolynomialTraits_d::LeadingCoefficient
• PolynomialTraits_d::InnermostLeadingCoefficient
• PolynomialTraits_d::Canonicalize
• PolynomialTraits_d::Differentiate
• PolynomialTraits_d::Evaluate
• PolynomialTraits_d::EvaluateHomogeneous
• PolynomialTraits_d::Substitute
• PolynomialTraits_d::SubstituteHomogeneous
• PolynomialTraits_d::IsZeroAt
• PolynomialTraits_d::IsZeroAtHomogeneous
• PolynomialTraits_d::SignAt
• PolynomialTraits_d::SignAtHomogeneous
• PolynomialTraits_d::Compare
• PolynomialTraits_d::UnivariateContent
• PolynomialTraits_d::MultivariateContent
• PolynomialTraits_d::SquareFreeFactorize
• PolynomialTraits_d::MakeSquareFree
• PolynomialTraits_d::IsSquareFree
• PolynomialTraits_d::PseudoDivision
• PolynomialTraits_d::PseudoDivisionQuotient
• PolynomialTraits_d::PseudoDivisionRemainder
• PolynomialTraits_d::GcdUpToConstantFactor
• PolynomialTraits_d::IntegralDivisionUpToConstantFactor
• PolynomialTraits_d::UnivariateContentUpToConstantFactor
• PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor
• PolynomialTraits_d::Shift
• PolynomialTraits_d::Negate
• PolynomialTraits_d::Invert
• PolynomialTraits_d::Translate
• PolynomialTraits_d::TranslateHomogeneous
• PolynomialTraits_d::Scale
• PolynomialTraits_d::ScaleHomogeneous
• PolynomialTraits_d::Resultant
• PolynomialTraits_d::PolynomialSubresultants
• PolynomialTraits_d::PolynomialSubresultantsWithCofactors
• PolynomialTraits_d::PrincipalSubresultants
• PolynomialTraits_d::SturmHabichtSequence
• PolynomialTraits_d::SturmHabichtSequenceWithCofactors
• PolynomialTraits_d::PrincipalSturmHabichtSequence

Classes

• CGAL::Polynomial<Coeff>
• CGAL::Polynomial_traits_d<Polynomial_d>
• CGAL::Exponent_vector
• CGAL::Polynomial_type_generator<T,d>

Functions

• CGAL::get_coefficient()
• CGAL::get_innermost_coefficient()
• CGAL::permute()
• CGAL::swap()
• CGAL::move()
• CGAL::degree()
• CGAL::total_degree()
• CGAL::degree_vector()
• CGAL::leading_coefficient()
• CGAL::innermost_leading_coefficient()
• CGAL::canonicalize()
• CGAL::differentiate()
• CGAL::evaluate()
• CGAL::evaluate_homogeneous()
• CGAL::substitute()
• CGAL::substitute_homogeneous()
• CGAL::is_zero_at()
• CGAL::is_zero_at_homogeneous()
• CGAL::sign_at()
• CGAL::sign_at_homogeneous()
• CGAL::compare()
• CGAL::univariate_content()
• CGAL::multivariate_content()
• CGAL::square_free_factorize()
• CGAL::make_square_free()
• CGAL::pseudo_division()
• CGAL::pseudo_division_quotient()
• CGAL::pseudo_division_remainder()
• CGAL::gcd_up_to_constant_factor()
• CGAL::integral_division_up_to_constant_factor()
• CGAL::univariate_content_up_to_constant_factor()
• CGAL::square_free_factorize_up_to_constant_factor()
• CGAL::shift()
• CGAL::negate()
• CGAL::invert()
• CGAL::translate()
• CGAL::translate_homogeneous()
• CGAL::scale()
• CGAL::scale_homogeneous()
• CGAL::resultant()
• CGAL::polynomial_subresultants()
• CGAL::polynomial_subresultants_with_cofactors()
• CGAL::principal_subresultants()
• CGAL::sturm_habicht_sequence()
• CGAL::sturm_habicht_sequence_with_cofactors()
• CGAL::principal_sturm_habicht_sequence()
• CGAL::number_of_real_roots()

Modules
	Concepts
	Classes
	Functions