mirror of https://github.com/CGAL/cgal
50 lines
1.7 KiB
TeX
50 lines
1.7 KiB
TeX
\begin{ccRefConcept}{PolynomialTraits_d::GcdUpToConstantFactor}
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\ccDefinition
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This \ccc{AdaptableBinaryFunction} computes the $gcd$
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{\em up to a constant factor (utcf)} of two polynomials of type
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\ccc{PolynomialTraits_d::Polynomial_d}.
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In case the base ring $R$, \ccc{PolynomialTraits_d::Innermost_coefficient},
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is not a \ccc{UFDomain} or not a \ccc{Field} the polynomial ring
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$R[x_0,\dots,x_{d-1}]$ ,\ccc{PolynomialTraits_d::Polynomial_d}, may not
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possess greatest common divisor. However, since the $R$ is an integral
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domain one can consider its quotient field $Q(R)$ for which gcds of
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polynomials exist. A $gcd\_up_to_constant_factor(f,g)$ is a denominator-free
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constant multiple of $gcd(f,g)$ in $Q(R)[x_0,\dots,x_{d-1}]$.
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{\bf Note:} It may not be a divisor of $f$ and $g$ in $R[x_0,\dots,x_{d-1}]$.
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\ccRefines
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\ccc{AdaptableBinaryFunction}
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\ccTypes
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\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
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\ccCreationVariable{gcd_utcf}
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\ccTypedef{typedef PolynomialTraits_d::Polynomial_d result_type;}{}\ccGlue
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\ccTypedef{typedef PolynomialTraits_d::Polynomial_d first_argument_type;}{}\ccGlue
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\ccTypedef{typedef PolynomialTraits_d::Polynomial_d second_argument_type;}{}
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\ccOperations
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\ccMethod{result_type operator()(first_argument_type f,
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second_argument_type g);}
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{return a denominator-free, constant multiple of $gcd(f,g)$}
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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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\ccRefIdfierPage{PolynomialTraits_d::IntegralDivisionUpToConstantFactor}\\
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\ccRefIdfierPage{PolynomialTraits_d::UnivariateContentUpToConstantFactor}\\
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\ccRefIdfierPage{PolynomialTraits_d::SquareFreeFactorizationUpToConstantFactor}\\
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\end{ccRefConcept} |