Definition

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.

Note: This functor is optional.

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.

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 $x_i$ .

Member Function Documentation

◆ operator()() [1/2]

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.

◆ operator()() [2/2]