Definition

Note: This functor is optional!

Computes the polynomial subresultant of two polynomials $p$ and $q$ of degree $n$ and $m$ , respectively, as defined in the documentation of PolynomialTraits_d::PolynomialSubresultants. Moreover, for $\mathrm{Sres}_i(p,q)$ , polynomials $u_i$ and $v_i$ with $\deg u_i\leq m-i-1$ and $\deg v_i\leq n-i-1$ are computed such that $\mathrm{Sres}_i(p,q)=u_i p + v_i q$ . $u_i$ and $v_i$ are called the cofactors of $\mathrm{Sres}_i(p,q)$ .

The result is written in three output ranges, each of length $\min\{n,m\}+1$ , starting with the $0$ -th subresultant and the corresponding cofactors.

Refines:

AdaptableBinaryFunction

CopyConstructible

DefaultConstructible

See Also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::Resultant; PolynomialTraits_d::PolynomialSubresultants; PolynomialTraits_d::PrincipalSubresultants; PolynomialTraits_d::SturmHabichtSequenceWithCofactors

Operations
template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	operator() (Polynomial_d p, Polynomial_d q, OutputIterator1 sres, OutputIterator2 co_p, OutputIterator3 co_q)
	computes the subresultants of $p$ and $q$ , and the cofactors, with respect to the outermost variable. More...

template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	operator() (Polynomial_d p, Polynomial_d q, OutputIterator1 sres, OutputIterator2 co_p, OutputIterator3 co_q, int i)
	computes the subresultants of $p$ and $q$ , and the cofactors, with respect to $x_i$ . More...

Member Function Documentation

template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >

OutputIterator1 PolynomialTraits_d::PolynomialSubresultantsWithCofactors::operator()	(	Polynomial_d	p,
		Polynomial_d	q,
		OutputIterator1	sres,
		OutputIterator2	co_p,
		OutputIterator3	co_q
	)

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

Each element is of type PolynomialTraits_d::Polynomial_d.

template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >

OutputIterator1 PolynomialTraits_d::PolynomialSubresultantsWithCofactors::operator()	(	Polynomial_d	p,
		Polynomial_d	q,
		OutputIterator1	sres,
		OutputIterator2	co_p,
		OutputIterator3	co_q,
		int	i
	)

computes the subresultants of $p$ and $q$ , and the cofactors, with respect to $x_i$ .

Each element is of type PolynomialTraits_d::Polynomial_d.

Definition

Operations

Member Function Documentation