mirror of https://github.com/CGAL/cgal
103 lines
4.0 KiB
TeX
103 lines
4.0 KiB
TeX
\begin{ccRefConcept}{PolynomialToolBox_d}
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\ccDefinition
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A model of \ccc{PolynomialToolBox_d} is associated to an type
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\ccc{Polynomial_d}, representing a multivariate polynomial
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\footnote{Univariate polynomials are not excluded by this concept.}.
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The number of variables is denoted as the dimension $d$ of the polynomial,
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it is arbitrary but fixed for a certain model of this concept.
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\ccRefines
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\ccc{PolynomialTraits_d}
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%\ccConstants
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%\ccTypes
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\ccHeading{Functors}
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In case a functor is not provided it is set to \ccc{CGAL::Null_functor}.
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%,e.g., \ccc{Sign_at} if \ccc{Innermost_coefficient_type} is not \ccc{RealEmbeddable}.
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\ccSetTwoColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{}
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\ccNestedType{Univariate_content}{
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In case \ccc{PolynomialTraits_d::Coefficient_type} is {\bf not} a model of
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\ccc{UniqueFactorizationDomain}, this is \ccc{CGAL::Null_type}, otherwise this is
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a model of \ccc{PolynomialTraits_d::UnivariateContent}.}
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%\begin{ccAdvanced}
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\ccNestedType{Multivariate_content}{
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In case \ccc{PolynomialTraits_d::Innermost_coefficient_type} is {\bf not}
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a model of \ccc{UniqueFactorizationDomain}, this is \ccc{CGAL::Null_type},
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otherwise this is a model of
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\ccc{PolynomialTraits_d::MultivariateContent}.}
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%\end{ccAdvanced}
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%Manipulation
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\ccNestedType{Shift}{ A model of \ccc{PolynomialTraits_d::Shift}.}\ccGlue
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\ccNestedType{Negate}{ A model of \ccc{PolynomialTraits_d::Negate}.}\ccGlue
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\ccNestedType{Invert}{ A model of \ccc{PolynomialTraits_d::Invert}.}
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\ccNestedType{Translate}{ A model of \ccc{PolynomialTraits_d::Translate}.}\ccGlue
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\ccNestedType{Translate_homogeneous}
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{ A model of \ccc{PolynomialTraits_d::TranslateHomogeneous}.}
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\ccNestedType{Scale}{ A model of \ccc{PolynomialTraits_d::Scale}.}\ccGlue
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\ccNestedType{Scale_homogeneous}
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{ A model of \ccc{PolynomialTraits_d::ScaleHomogeneous}.}
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%\begin{ccAdvanced}
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%\ccNestedType{Scale_up}{ A model of \ccc{PolynomialTraits_d::ScaleUp, return $p(a*x)$}.}
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%\ccNestedType{Scale_down}{ A model of \ccc{PolynomialTraits_d::ScaleDown, return $b^{degree}*p(x/b)$}.}
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%\end{ccAdvanced}
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%unary operations
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\ccNestedType{Make_square_free}
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{ A model of \ccc{PolynomialTraits_d::MakeSquareFree}.}\ccGlue
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\ccNestedType{Square_free_factorize}
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{ In case \ccc{PolynomialTraits::Polynomial_d}
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is not a model of \ccc{UniqueFactorizationDomain}, this is of type \ccc{CGAL::Null_type},
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otherwise this is a model of \ccc{PolynomialTraits_d::SquareFreeFactorize}.}
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%pseudo division
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\ccNestedType{Pseudo_division }
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{ A model of \ccc{PolynomialTraits_d::Pseudo_division}.}\ccGlue
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\ccNestedType{Pseudo_division_remainder}
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{ A model of \ccc{PolynomialTraits_d::Pseudo_division_remainder}.}\ccGlue
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\ccNestedType{Pseudo_division_quotient }
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{ A model of \ccc{PolynomialTraits_d::Pseudo_division_quotient}.}
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%utcf
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\ccNestedType{Gcd_up_to_constant_factor}
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{ A model of \ccc{PolynomialTraits_d::GcdUpToConstantFactor}.}
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\ccGlue
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\ccNestedType{Integral_division_up_to_constant_factor}
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{ A model of \ccc{PolynomialTraits_d::IntegralDivisionUpToConstantFactor}.}
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\ccGlue
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\ccNestedType{Content_up_to_constant_factor}
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{ A model of \ccc{PolynomialTraits_d::ContentUpToConstantFactor}.}
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\ccGlue
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\ccNestedType{Square_free_factorize_up_to_constant_factor}
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{ A model of \ccc{PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor}.}
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%resultant
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\ccNestedType{Resultant}{ A model of \ccc{PolynomialTraits_d::Resultant}.}
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\ccNestedType{Polynomial_subresultants}
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{ A model of \ccc{PolynomialTraits_d::PolynomialSubresultant}.}
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\ccNestedType{Principal_subresultants}
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{ A model of \ccc{PolynomialTraits_d::PrincipalSubresultant}.}
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\ccNestedType{Sturm_habicht_sequence}
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{ A model of \ccc{PolynomialTraits_d::SturmHabichtSequence}.}
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\ccNestedType{Sturm_habicht_sequence_with_cofactors}
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{ A model of \ccc{PolynomialTraits_d::SturmHabichtSequenceWithCofactors}.}
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\ccNestedType{Principal_sturm_habicht_sequence}
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{ A model of \ccc{PolynomialTraits_d::PrincipalSturmHabichtSequence}.}
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% end ccIgnore
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\ccSeeAlso
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\ccRefIdfierPage{Polynomial_d}\\
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\ccRefIdfierPage{PolynomialTraits_d}\\
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\end{ccRefConcept}
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