PolynomialTraits_d::SturmHabichtSequenceWithCofactors

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PolynomialTraits_d::SturmHabichtSequenceWithCofactors

Note: This functor is optional!

Definition

Computes the Sturm-Habicht polynomials of a polynomial f of degree n, as defined in the documentation of PolynomialTraits_d::SturmHabichtSequence. Moreover, for Stha_i(f), polynomials u_i and v_i with deg u_i ≤ n-i-2 and deg v_i ≤ n-i-1 are computed such that Sres_i(p,q)=u_i f + v_i f'. u_i and v_i are called the cofactors of 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 Stha₀(f) and the corresponding cofactors.

Refines

AdaptableBinaryFunction
CopyConstructible
DefaultConstructible

Operations

template<typename OutputIterator1, typename OutputIterator2, typename OutputIterator3>
OutputIterator1	fo ( Polynomial_d f , OutputIterator1 stha , OutputIterator2 co_f , OutputIterator3 co_fx )
		computes the Sturm-Habicht sequence of f, and the cofactors, with respect to the outermost variable. Each element is of type PolynomialTraits_d::Polynomial_d.

template< typename OutputIterator1, typename OutputIterator2, typename OutputIterator3 >
OutputIterator1	fo ( Polynomial_d f , OutputIterator1 stha , OutputIterator2 co_f , OutputIterator3 co_fx , int i )
		computes the Sturm-Habicht sequence of f, and the cofactors, with respect to x_i. Each element is of type PolynomialTraits_d::Polynomial_d.