PolynomialTraits_d::PolynomialSubresultantsWithCofactors Concept Reference Definition 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. NoteThis functor is optional. Refines AdaptableBinaryFunction CopyConstructible DefaultConstructible See alsoPolynomial_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. 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 \( x_i\). Member Function Documentation operator()() [1/2] 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. operator()() [2/2] 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. PolynomialTraits_dPolynomialSubresultantsWithCofactors Generated by 1.17.0

Definition

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.

Note

This functor is optional.

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.
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 \( x_i\).

Member Function Documentation

operator()() [1/2]

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.

operator()() [2/2]

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.