mirror of https://github.com/CGAL/cgal
60 lines
2.3 KiB
TeX
60 lines
2.3 KiB
TeX
\begin{ccRefConcept}{PolynomialTraits_d::SturmHabichtSequenceWithCofactors}
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\textbf{Note:} This functor is optional!
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\ccDefinition
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Computes the Sturm-Habicht polynomials of a polynomial $f$ of degree $n$,
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as defined in the documentation of \ccc{PolynomialTraits_d::SturmHabichtSequence}.
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Moreover, for $\mathrm{Stha}_i(f)$, polynomials $u_i$ and $v_i$
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with $\deg u_i\leq n-i-2$ and $\deg v_i\leq n-i-1$ are computed
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such that $\mathrm{Sres}_i(p,q)=u_i f + v_i f'$. $u_i$ and $v_i$ are called
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the \emph{cofactors} of $\mathrm{Stha}_i(f)$.
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The result is written in three output ranges, each of length $\min\{n,m\}+1$,
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starting with the $0$-th Sturm-Habicht polynomial $\mathrm{Stha_0(f)}$
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and the corresponding cofactors.
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\ccRefines
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\ccc{AdaptableBinaryFunction}\\
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\ccc{CopyConstructible}\\
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\ccc{DefaultConstructible}\\
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\ccCreationVariable{fo}
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\ccOperations
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\ccMethod{template<typename OutputIterator1,
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typename OutputIterator2,
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typename OutputIterator3>
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OutputIterator1 operator()(Polynomial_d f,
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OutputIterator1 stha,
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OutputIterator2 co_f,
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OutputIterator3 co_fx);}
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{ computes the Sturm-Habicht sequence of $f$, and the cofactors,
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with respect to the outermost variable. Each element is of type
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\ccc{PolynomialTraits_d::Polynomial_d}.}
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\ccMethod{template< typename OutputIterator1,
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typename OutputIterator2,
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typename OutputIterator3 >
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OutputIterator1 operator()(Polynomial_d f,
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OutputIterator1 stha,
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OutputIterator2 co_f,
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OutputIterator3 co_fx,
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int i);}
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{ computes the Sturm-Habicht sequence of $f$, and the cofactors,
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with respect to $x_i$. Each element is of type
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\ccc{PolynomialTraits_d::Polynomial_d}.}
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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::Resultant}\\
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\ccRefIdfierPage{PolynomialTraits_d::SturmHabichtSequence}\\
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\ccRefIdfierPage{PolynomialTraits_d::PrincipalSturmHabichtSequence}\\
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\ccRefIdfierPage{PolynomialTraits_d::PolynomialSubresultantsWithCofactors}\\
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\end{ccRefConcept}
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