mirror of https://github.com/CGAL/cgal
52 lines
1.7 KiB
TeX
52 lines
1.7 KiB
TeX
\begin{ccRefConcept}{PolynomialTraits_d::PseudoDivision}
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\ccDefinition
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This \ccc{AdaptableFunctor} computes the {\em pseudo division}
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of two polynomials $f$ and $g$.
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Given $f$ and $g \neq 0$ this functor computes quotient $q$ and
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remainder $r$ such that $D \cdot f = g \cdot q + r$ and $degree(r) < degree(g)$,
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where $ D = leading\_coefficient(g)^{max(0, degree(f)-degree(g)+1)}$
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This functor is useful if the regular division is not available,
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which is the case if \ccc{PolynomialTraits_d::Coefficient_type} is not a \ccc{Field}.
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Hence in general it is not possible to invert the leading coefficient of $g$.
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Instead $f$ is extended by $D$ allowing integral divisions in the internal
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computation.
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\ccRefines
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\ccc{AdaptableFunctor}\\
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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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\ccCreationVariable{fo}
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\ccTypedef{typedef void result_type;}{}\ccGlue
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\ccOperations
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\ccMethod{result_type operator()(PolynomialTraits_d::Polynomial_d f,
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PolynomialTraits_d::Polynomial_d g,
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PolynomialTraits_d::Polynomial_d & q,
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PolynomialTraits_d::Polynomial_d & r,
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PolynomialTraits_d::Coefficient_type & D);}{
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Computes the pseudo division with respect to the outermost variable
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$x_{d-1}$.
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}
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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::PseudoDivision}\\
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\ccRefIdfierPage{PolynomialTraits_d::PseudoDivisionRemainder}\\
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\ccRefIdfierPage{PolynomialTraits_d::PseudoDivisionQuotient}\\
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\end{ccRefConcept} |