Loading [MathJax]/extensions/TeX/newcommand.js
\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 4.14 - Polynomial
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PolynomialTraits_d::PolynomialSubresultants Concept Reference

Definition

Computes the polynomial subresultant of two polynomials p and q of type PolynomialTraits_d::Polynomial_d with respect to outermost variable. Let p=\ccSum{i=0,\ldots,n}{} p_i x^i and q=\ccSum{i=0,\ldots,m}{} q_i x^i, where x is the outermost variable. The i-th subresultant (with i=0,\ldots,\min\{n,m\}) is defined by.

subresultant_def.png

where p_i and q_i are set to zero if i<0. In the case that n=m, \mathrm{Sres_n} is set to q.

The result is written in an output range, starting with the 0-th subresultant \mathrm{Sres}_0(p,q) (aka as the resultant of p and q).

Note
This functor is optional.
Refines:

AdaptableBinaryFunction

CopyConstructible

DefaultConstructible

See also
Polynomial_d
PolynomialTraits_d
PolynomialTraits_d::Resultant
PolynomialTraits_d::PrincipalSubresultants
PolynomialTraits_d::PolynomialSubresultantsWithCofactors
PolynomialTraits_d::SturmHabichtSequence

Operations

template<typename OutputIterator >
OutputIterator operator() (Polynomial_d p, Polynomial_d q, OutputIterator out)
 computes the polynomial 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 polynomial subresultants of p and q, with respect to the variable x_i.
 

Member Function Documentation

◆ operator()()

template<typename OutputIterator >
OutputIterator PolynomialTraits_d::PolynomialSubresultants::operator() ( Polynomial_d  p,
Polynomial_d  q,
OutputIterator  out 
)

computes the polynomial subresultants of p and q, with respect to the outermost variable.

Each element is of type PolynomialTraits_d::Polynomial_d.