mirror of https://github.com/CGAL/cgal
42 lines
1.2 KiB
TeX
42 lines
1.2 KiB
TeX
\begin{ccRefConcept}{Polynomial_d}
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\ccDefinition
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A model \ccc{Polynomial_d} possesses a traits class
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\ccc{CGAL::Polynomial_traits_d<Polynomial_d>}, which is a model of
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\ccc{PolynomialTraits_d}. An \ccc{Polynomial_d} represents a multivariate
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polynomial over some basic ring $R$, this type is denoted as the innermost
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coefficient type and is accessible through the traits class
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\ccc{CGAL::Polynomial_traits_d<Polynomial_d>::Innermost_coefficient}.
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\ccRefines
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\ccc{Polynomial_d} and \ccc{Innermost_coefficient} are at least a
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model of \ccc{IntegralDomainWithoutDiv}. \\
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Moreover, the algebraic structure of \ccc{Polynomial} depends on the
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algebraic structure of \ccc{Innermost_coefficient}:
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\begin{tabular}{|l|l|}
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\hline
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\ccc{Innermost_coefficient}&\ccc{Polynomial_d}\\
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\hline
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\ccc{IntegralDomainWithoutDiv}&\ccc{IntegralDomainWithoutDiv}\\
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\ccc{IntegralDomain}&\ccc{IntegralDomain}\\
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\ccc{UFDomain}&\ccc{UFDomain}\\
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\ccc{EuclideanRing}&\ccc{UFDomain}\\
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\ccc{Field}&\ccc{UFDomain}\\
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\hline
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\end{tabular}
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Note:The concept \ccc{Polynomial_1} refines \ccc{EuclideanRing} in case
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\ccc{Innermost_coefficient} is a \ccc{Field}.
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\ccSeeAlso
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\ccRefIdfierPage{AlgebraicStructureTraits}\\
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\ccRefIdfierPage{PolynomialTraits_d}\\
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\ccHasModels
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\end{ccRefConcept} |