PolynomialTraits_d::PolynomialSubresultants Class Reference

#include <Concepts/PolynomialTraits_d--PolynomialSubresultants.h>

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.

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 \( x_i\). More...

Member Function Documentation

operator()() [1/2]

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.

operator()() [2/2]

template<typename OutputIterator >

OutputIterator PolynomialTraits_d::PolynomialSubresultants::operator()	(	Polynomial_d	p,
		Polynomial_d	q,
		OutputIterator	out,
		int	i
	)

computes the polynomial subresultants of \( p\) and \( q\), with respect to the variable \( x_i\).