mirror of https://github.com/CGAL/cgal
44 lines
1.6 KiB
TeX
44 lines
1.6 KiB
TeX
\begin{ccRefConcept}{PolynomialTraits_d::Principal_subresultants}
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\ccDefinition
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Computes the principal subresultant of two polynomials $f$ and $g$ of
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type \ccc{PolynomialTraits_d::Polynomial_d}
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with respect a certain variable $x_i$.
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The principal subresultants are also known as {\it scalar} subresultants.
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The $j$th such principal subresultant is defined to be the coefficient
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of $x_i^j$ in the $j$-th subresultant polynomial of $f$ and $g$.
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Since the degree of the $j$-th subresultant polynomial is at most $j$,
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this principal coefficients are sometimes called the
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{\tt formal leading coefficients} (``formal'' because they might vanish).
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The result is written in an output range,
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starting with the $0$th principal subresultant
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(aka as the resultant of $f$ and $g$).
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\ccOperations
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\ccMethod{template<typename OutputIterator>
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OutputIterator operator()(Polynomial_d f,
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Polynomial_d g,
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OutputIterator out);}
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{ computes the principal subresultants of $f$ and $g$,
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with respect to the outermost variable. Each element is of type
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\ccc{PolynomialTraits_d::Coefficient_type}.}
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\ccMethod{template<typename OutputIterator>
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OutputIterator operator()(Polynomial_d f,
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Polynomial_d g,
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OutputIterator out,
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int i);}
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{ computes the principal subresultants of $f$ and $g$,
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with respect to the variable $x_i$.}
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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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\end{ccRefConcept}
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