PolynomialTraits_d::PrincipalSubresultants Concept Reference

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 $x_i$.

Member Function Documentation

operator()()

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.