Note: This functor is optional!

Computes the Sturm-Habicht polynomials of a polynomial $f$ of degree $n$, as defined in the documentation of PolynomialTraits_d::SturmHabichtSequence. Moreover, for $\mathrm{Stha}_i(f)$, polynomials $u_i$ and $v_i$ with $\deg u_i\leq n-i-2$ and $\deg v_i\leq n-i-1$ are computed such that $\mathrm{Sres}_i(p,q)=u_i f + v_i f'$. $u_i$ and $v_i$ are called the cofactors of $\mathrm{Stha}_i(f)$.

The result is written in three output ranges, each of length $\min\{n,m\}+1$, starting with the $0$-th Sturm-Habicht polynomial $\mathrm{Stha_0(f)}$ and the corresponding cofactors.

Refines:

AdaptableBinaryFunction

CopyConstructible

DefaultConstructible

See Also

Polynomial_d

PolynomialTraits_d

PolynomialTraits_d::Resultant

PolynomialTraits_d::SturmHabichtSequence

PolynomialTraits_d::PrincipalSturmHabichtSequence

PolynomialTraits_d::PolynomialSubresultantsWithCofactors