\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5 - Polynomial
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PolynomialTraits_d::PrincipalSubresultants Concept Reference

Definition

Note: This functor is optional!

Computes the principal subresultant of two polynomials \( p\) and \( q\) of type 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)

Refines:

AdaptableBinaryFunction

CopyConstructible

DefaultConstructible

See Also
Polynomial_d
PolynomialTraits_d
PolynomialTraits_d::Resultant
PolynomialTraits_d::PolynomialSubresultants
PolynomialTraits_d::PrincipalSturmHabichtSequence

Operations

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. More...
 
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 \( x_i\).
 

Member Function Documentation

template<typename OutputIterator >
OutputIterator PolynomialTraits_d::PrincipalSubresultants::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 PolynomialTraits_d::Coefficient_type.