PolynomialTraits_d::SturmHabichtSequenceWithCofactors Concept Reference

Definition

Note: This functor is optional!

Computes the Sturm-Habicht polynomials of a polynomial \( f\) of degree \( n\), as defined in the documentation of PolynomialTraits_d::SturmHabichtSequence. Moreover, for \( \mathrm{Stha}_i(f)\), polynomials \( u_i\) and \( v_i\) with \( \deg u_i\leq n-i-2\) and \( \deg v_i\leq n-i-1\) are computed such that \( \mathrm{Sres}_i(p,q)=u_i f + v_i f'\). \( u_i\) and \( v_i\) are called the cofactors of \( \mathrm{Stha}_i(f)\).

The result is written in three output ranges, each of length \( \min\{n,m\}+1\), starting with the \( 0\)-th Sturm-Habicht polynomial \( \mathrm{Stha_0(f)}\) and the corresponding cofactors.

Refines:

AdaptableBinaryFunction

CopyConstructible

DefaultConstructible

See Also

Polynomial_d

PolynomialTraits_d

PolynomialTraits_d::Resultant

PolynomialTraits_d::SturmHabichtSequence

PolynomialTraits_d::PrincipalSturmHabichtSequence

PolynomialTraits_d::PolynomialSubresultantsWithCofactors

Operations
template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	operator() (Polynomial_d f, OutputIterator1 stha, OutputIterator2 co_f, OutputIterator3 co_fx)
	computes the Sturm-Habicht sequence of \( f\), and the cofactors, with respect to the outermost variable. More...
template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >
OutputIterator1	operator() (Polynomial_d f, OutputIterator1 stha, OutputIterator2 co_f, OutputIterator3 co_fx, int i)
	computes the Sturm-Habicht sequence of \( f\), and the cofactors, with respect to \( x_i\). More...

Member Function Documentation

template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 >

OutputIterator1 PolynomialTraits_d::SturmHabichtSequenceWithCofactors::operator()	(	Polynomial_d	f,
		OutputIterator1	stha,
		OutputIterator2	co_f,
		OutputIterator3	co_fx
	)

computes the Sturm-Habicht sequence of \( f\), 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::SturmHabichtSequenceWithCofactors::operator()	(	Polynomial_d	f,
		OutputIterator1	stha,
		OutputIterator2	co_f,
		OutputIterator3	co_fx,
		int	i
	)

computes the Sturm-Habicht sequence of \( f\), and the cofactors, with respect to \( x_i\).

Each element is of type PolynomialTraits_d::Polynomial_d.