PolynomialTraits_d::PrincipalSturmHabichtSequence Concept Reference

Definition

Note: This functor is optional!

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 \( f\).

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. More...
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

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.