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CGAL 6.0 - 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. | |
| 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.