CGAL 4.8.1 - Polynomial
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Note: This functor is optional!
Computes the Sturm-Habicht sequence (aka the signed subresultant sequence) of a polynomial f of type PolynomialTraits_d::Polynomial_d
with respect to a certain variable xi. The Sturm-Habicht sequence is similar to the polynomial subresultant sequence of f and its derivative f′:=∂f∂xi with respect to xi. The implementation is based on the following definition:
Let n:=degf and δk:=(−1)k(k+1)/2. For k∈{0,…,n}, the k-th Sturm-Habicht polynomial of f is defined as:
where Sresk(f,f′) is defined as in the concept PolynomialTraits_d::PolynomialSubresultants
.
The result is written in an output range, starting with the 0-th Sturm-Habicht polynomial (which is equal to the discriminant of f up to a multiple of the leading coefficient).
Operations | |
template<typename OutputIterator > | |
OutputIterator | operator() (Polynomial_d f, OutputIterator out) |
computes 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 Sturm-Habicht sequence of f with respect to the variable xi. | |
OutputIterator PolynomialTraits_d::SturmHabichtSequence::operator() | ( | Polynomial_d | f, |
OutputIterator | out | ||
) |
computes the Sturm-Habicht sequence of f, with respect to the outermost variable.
Each element is of type PolynomialTraits_d::Polynomial_d
.