PolynomialTraits_d::SturmHabichtSequence

Note: This functor is optional!

Definition

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 x_i. The Sturm-Habicht sequence is similar to the polynomial subresultant sequence of f and its derivative f':=(∂f)/(∂x_i) with respect to x_i. The implementation is based on the following definition:

Let n:=deg f and δ_k:=(-1)^k(k+1)/2. For k ∈ {0, … ,n}, the k-th Sturm-Habicht polynomial of f is defined as:

where Sres_k(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).

Refines

Operations

See Also

Polynomial_d
PolynomialTraits_d
PolynomialTraits_d::Resultant
PolynomialTraits_d::PrincipalSturmHabichtSequence
PolynomialTraits_d::SturmHabichtSequenceWithCofactors
PolynomialTraits_d::PolynomialSubresultants