PolynomialTraits_d::PrincipalSturmHabichtSequence Concept Reference

Definition

Computes the principal leading coefficients of the Sturm-Habicht sequence of a polynomials \( f\) of type PolynomialTraits_d::Polynomial_d with respect a certain variable \( x_i\). This means that for the \( j\)-th Sturm-Habicht polynomial, this methods returns the coefficient of \( x_i^j\).

Note that the degree of the \( j\)-th Sturm-Habicht polynomial is at most \( j\), but the principal coefficient might be zero, thus, this functor does not necessarily give the leading coefficient of the Sturm-Habicht polynomials.

In case that PolynomialTraits_d::Coefficient_type is RealEmbeddable, the function CGAL::number_of_real_roots can be used on the resulting sequence to count the number of distinct real roots of the polynomial \( f\).

Note

This functor is optional.

Refines

AdaptableBinaryFunction

CopyConstructible

DefaultConstructible

See also

Polynomial_d

PolynomialTraits_d

CGAL::number_of_real_roots()

PolynomialTraits_d::Resultant

PolynomialTraits_d::SturmHabichtSequence

PolynomialTraits_d::PrincipalSubresultants

Operations
template<typename OutputIterator >
OutputIterator	operator() (Polynomial_d f, OutputIterator out)
	computes the principal coefficients of the Sturm-Habicht sequence of \( f\), with respect to the outermost variable.
template<typename OutputIterator >
OutputIterator	operator() (Polynomial_d f, OutputIterator out, int i)
	computes the principal coefficients of the Sturm-Habicht sequence of \( f\) with respect to the variable \( x_i\).

Member Function Documentation

operator()()

template<typename OutputIterator >

OutputIterator PolynomialTraits_d::PrincipalSturmHabichtSequence::operator()	(	Polynomial_d	f,
		OutputIterator	out
	)

computes the principal coefficients of the Sturm-Habicht sequence of \( f\), with respect to the outermost variable.

Each element is of type PolynomialTraits_d::Coefficient_type.