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