PolynomialTraits_d::PrincipalSubresultants Class Reference

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

Definition

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)

Note

This functor is optional.

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 \( x_i\). More...

Member Function Documentation

operator()() [1/2]

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.

operator()() [2/2]

template<typename OutputIterator >

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

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