PolynomialTraits_d::PseudoDivision

Definition

This AdaptableFunctor computes the pseudo division of two polynomials $$f and $$g.

Given $$f and $$g 0 this functor computes quotient $$q and remainder $$r such that $$D · f = g · q + r and $$degree(r) < degree(g), where $$ D = leading_coefficient(g)^{max(0, degree(f)-degree(g)+1)}

This functor is useful if the regular division is not available, which is the case if PolynomialTraits_d::Coefficient_type is not a Field. Hence in general it is not possible to invert the leading coefficient of $$g. Instead $$f is extended by $$D allowing integral divisions in the internal computation.

Refines

Types

Operations

See Also

Polynomial_d
PolynomialTraits_d
PolynomialTraits_d::PseudoDivision
PolynomialTraits_d::PseudoDivisionRemainder
PolynomialTraits_d::PseudoDivisionQuotient