mirror of https://github.com/CGAL/cgal
56 lines
1.9 KiB
TeX
56 lines
1.9 KiB
TeX
\begin{ccRefConcept}{PolynomialTraits_d::PrincipalSubresultants}
|
|
|
|
\textbf{Note:} This functor is optional!
|
|
|
|
\ccDefinition
|
|
|
|
Computes the principal subresultant of two polynomials $p$ and $q$ of
|
|
type \ccc{PolynomialTraits_d::Coefficient_type}
|
|
with respect to the outermost variable.
|
|
The $i$-th principal subresultant, $\mathrm{sres}_i(p,q)$,
|
|
is defined as the coefficient at $t^i$ of the $i$-th polynomial
|
|
subresultant $\mathrm{Sres}_i(p,q)$. Thus, it is either the leading
|
|
coefficient of $\mathrm{Sres}_i$, or zero in the case where its degree is
|
|
below $i$.
|
|
|
|
The result is written in an output range, starting with the $0$-th
|
|
principal subresultant $\mathrm{sres}_0(p,q)$
|
|
,aka as the resultant of $p$ and $q$.
|
|
(Note that $\mathrm{sres}_0(p,q)=\mathrm{Sres}_0(p,q)$ by definition)
|
|
|
|
\ccRefines
|
|
\ccc{AdaptableBinaryFunction}\\
|
|
\ccc{CopyConstructible}\\
|
|
\ccc{DefaultConstructible}\\
|
|
|
|
\ccCreationVariable{fo}
|
|
|
|
\ccOperations
|
|
\ccMethod{template<typename OutputIterator>
|
|
OutputIterator operator()(Polynomial_d p,
|
|
Polynomial_d q,
|
|
OutputIterator out);}
|
|
{ computes the principal subresultants of $p$ and $q$,
|
|
with respect to the outermost variable. Each element is of type
|
|
\ccc{PolynomialTraits_d::Coefficient_type}.}
|
|
|
|
\ccMethod{template<typename OutputIterator>
|
|
OutputIterator operator()(Polynomial_d p,
|
|
Polynomial_d q,
|
|
OutputIterator out,
|
|
int i);}
|
|
{ computes the principal subresultants of $p$ and $q$,
|
|
with respect to the variable $x_i$.}
|
|
|
|
%\ccHasModels
|
|
|
|
\ccSeeAlso
|
|
|
|
\ccRefIdfierPage{Polynomial_d}\\
|
|
\ccRefIdfierPage{PolynomialTraits_d}\\
|
|
\ccRefIdfierPage{PolynomialTraits_d::Resultant}\\
|
|
\ccRefIdfierPage{PolynomialTraits_d::PolynomialSubresultants}\\
|
|
\ccRefIdfierPage{PolynomialTraits_d::PrincipalSturmHabichtSequence}\\
|
|
|
|
\end{ccRefConcept}
|