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\newcommand{\E}{\mathrm{E}} \newcommand{\A}{\mathrm{A}} \newcommand{\R}{\mathrm{R}} \newcommand{\N}{\mathrm{N}} \newcommand{\Q}{\mathrm{Q}} \newcommand{\Z}{\mathrm{Z}} \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }
CGAL 4.14 - Polynomial
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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. 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

◆ 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.