 CGAL 4.7 - Polynomial
PolynomialTraits_d::PrincipalSubresultants Concept Reference

Definition

Note: This functor is optional!

Computes the principal subresultant of two polynomials $$p$$ and $$q$$ of type PolynomialTraits_d::Coefficient_type with respect to the outermost variable. The $$i$$-th principal subresultant, $$\mathrm{sres}_i(p,q)$$, is defined as the coefficient at $$t^i$$ of the $$i$$-th polynomial subresultant $$\mathrm{Sres}_i(p,q)$$. Thus, it is either the leading coefficient of $$\mathrm{Sres}_i$$, or zero in the case where its degree is below $$i$$.

The result is written in an output range, starting with the $$0$$-th principal subresultant $$\mathrm{sres}_0(p,q)$$ ,aka as the resultant of $$p$$ and $$q$$. (Note that $$\mathrm{sres}_0(p,q)=\mathrm{Sres}_0(p,q)$$ by definition)

Refines:
Polynomial_d
PolynomialTraits_d
PolynomialTraits_d::Resultant
PolynomialTraits_d::PolynomialSubresultants
PolynomialTraits_d::PrincipalSturmHabichtSequence

Operations

template<typename OutputIterator >
OutputIterator operator() (Polynomial_d p, Polynomial_d q, OutputIterator out)
computes the principal subresultants of $$p$$ and $$q$$, with respect to the outermost variable. More...

template<typename OutputIterator >
OutputIterator operator() (Polynomial_d p, Polynomial_d q, OutputIterator out, int i)
computes the principal subresultants of $$p$$ and $$q$$, with respect to the variable $$x_i$$.

Member Function Documentation

template<typename OutputIterator >
 OutputIterator PolynomialTraits_d::PrincipalSubresultants::operator() ( Polynomial_d p, Polynomial_d q, OutputIterator out )

computes the principal subresultants of $$p$$ and $$q$$, with respect to the outermost variable.

Each element is of type PolynomialTraits_d::Coefficient_type.