mirror of https://github.com/CGAL/cgal
54 lines
1.6 KiB
TeX
54 lines
1.6 KiB
TeX
\begin{ccRefConcept}{PolynomialTraits_d::SquareFreeFactorize}
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\ccDefinition
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This \ccc{Functor} computes a square-free factorization
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of a \ccc{PolynomialTraits_d::Polynomial_d}.
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A polynomial $p$ is factored into square-free and pairwise coprime non-constant
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factors $g_i$ with multiplicities $m_i$ and a constant factor $a$, such that
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$p = a \cdot g_1m_1 \cdot ... \cdot g_nm_n$.
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The pairs $(g_i,m_i)$ are written into the given output iterator.\\
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This functor is well defined if \ccc{PolynomialTraits_d::Polynomial_d} is a
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\ccc{UniqueFactorizationDomain}.
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\ccRefines
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Assignable\\
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CopyConstructible\\
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DefaultConstructible\\
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%\ccTypes
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\ccOperations
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\ccSetThreeColumns{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}{xxx}{}
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\ccCreationVariable{fo}
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\ccMethod{template<class OutputIterator>
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OutputIterator operator()(PolynomialTraits_d::Polynomial_d p,
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OutputIterator it,
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PolynomialTraits_d::Innermost_coefficient_type& a);}
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{ Computes square-free factorization of $p$.\\
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The \ccc{OutputIterator} must allow the value type
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\ccc{std::pair<PolynomialTraits_d::Polynomial_d,int>}.
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}
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\ccMethod{template<class OutputIterator>
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OutputIterator operator()(PolynomialTraits_d::Polynomial_d p,
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OutputIterator it);}
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{ As the first operator, just not computing the factor $a$. }
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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::SquareFreeFactorizeUpToConstantFactor}\\
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\ccRefIdfierPage{PolynomialTraits_d::MakeSquareFree}\\
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\end{ccRefConcept}
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