mirror of https://github.com/CGAL/cgal
50 lines
1.4 KiB
TeX
50 lines
1.4 KiB
TeX
\begin{ccRefConcept}{PolynomialTraits_d::Canonicalize}
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\ccDefinition
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For a given polynomial $p$ this \ccc{AdaptableUnaryFunction} computes the
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unique representative of the set
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\[{\cal P} := \{ q\ |\ \lambda * q = p\ for\ some\ \lambda \in R \},\]
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where $R$ is the base of the polynomial ring.
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In case \ccc{PolynomialTraits::Innermost_coefficient_type} is a model of
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\ccc{Field}, the computed polynomial is the {\em monic} polynomial in
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{$\cal P$}, that is, the innermost leading coefficient equals one.\\
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In case \ccc{PolynomialTraits::Innermost_coefficient_type} is a model
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of \ccc{UniqueFactorizationDomain}, the computed polynomial is the one with
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a multivariate content of one.\\
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For all other cases the notion of uniqueness is up to the concrete model.
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Note that the computed polynomial has the same zero set as the given one.
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\ccRefines
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\ccc{AdaptableUnaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccTypes
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\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
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\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}\ccGlue
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\ccTypedef{typedef PolynomialTraits_d::Polynomial_d argument_type;}{}
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\ccOperations
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\ccCreationVariable{fo}
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\ccMethod{result_type operator()(first_argument_type p);}{
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Returns the canonical representative of $p$.}
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%\ccHasModels
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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} |