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\newcommand{\E}{\mathrm{E}} \newcommand{\A}{\mathrm{A}} \newcommand{\R}{\mathrm{R}} \newcommand{\N}{\mathrm{N}} \newcommand{\Q}{\mathrm{Q}} \newcommand{\Z}{\mathrm{Z}} \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }
CGAL 5.0.4 - Polynomial
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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

See also
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}.