CGAL 4.14 - Polynomial
PolynomialTraits_d::PseudoDivision Concept Reference

## Definition

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

Given $$f$$ and $$g \neq 0$$ this functor computes quotient $$q$$ and remainder $$r$$ such that $$D \cdot f = g \cdot q + r$$ 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:

AdaptableFunctor

CopyConstructible

DefaultConstructible

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

## Types

typedef void result_type

## Operations

result_type operator() (PolynomialTraits_d::Polynomial_d f, PolynomialTraits_d::Polynomial_d g, PolynomialTraits_d::Polynomial_d &q, PolynomialTraits_d::Polynomial_d &r, PolynomialTraits_d::Coefficient_type &D)
Computes the pseudo division with respect to the outermost variable $$x_{d-1}$$.