CGAL 4.14 - Polynomial
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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 | 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. | |
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
.