PolynomialTraits_d::PrincipalSturmHabichtSequence

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PolynomialTraits_d::PrincipalSturmHabichtSequence

Note: This functor is optional!

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.

Operations

template<typename OutputIterator>
OutputIterator	fo ( 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.

template<typename OutputIterator>
OutputIterator	fo ( 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.