CGAL 5.1.3  Polynomial

Computes the principal leading coefficients of the SturmHabicht 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 SturmHabicht polynomial, this methods returns the coefficient of \( x_i^j\).
Note that the degree of the \( j\)th SturmHabicht polynomial is at most \( j\), but the principal coefficient might be zero, thus, this functor does not necessarily give the leading coefficient of the SturmHabicht 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 SturmHabicht 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 SturmHabicht 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 SturmHabicht sequence of \( f\), with respect to the outermost variable.
Each element is of type PolynomialTraits_d::Coefficient_type
.