#include <Concepts/PolynomialTraits_d--GcdUpToConstantFactor.h>

Definition

This AdaptableBinaryFunction computes the \( gcd\) up to a constant factor (utcf) of two polynomials of type PolynomialTraits_d::Polynomial_d.

In case the base ring \( R\) (PolynomialTraits_d::Innermost_coefficient_type) is not a UniqueFactorizationDomain or not a Field the polynomial ring \( R[x_0,\dots,x_{d-1}]\) (PolynomialTraits_d::Polynomial_d) may not possesses greatest common divisors. However, since \( R\) is an integral domain one can consider its quotient field \( Q(R)\) for which \( gcd\)s of polynomials exist.

This functor computes \( gcd\_utcf(f,g) = D * gcd(f,g)\), for some \( D \in R\) such that \( gcd\_utcf(f,g) \in R[x_0,\dots,x_{d-1}]\). Hence, \( gcd\_utcf(f,g)\) may not be a divisor of \( f\) and \( g\) in \( R[x_0,\dots,x_{d-1}]\).

Refines:

AdaptableBinaryFunction

CopyConstructible

DefaultConstructible

See also: Polynomial_d; PolynomialTraits_d; PolynomialTraits_d::IntegralDivisionUpToConstantFactor; PolynomialTraits_d::UnivariateContentUpToConstantFactor; PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor

Types
typedef PolynomialTraits_d::Polynomial_d	result_type

typedef PolynomialTraits_d::Polynomial_d	first_argument_type

typedef PolynomialTraits_d::Polynomial_d	second_argument_type

Operations
result_type	operator() (first_argument_type f, second_argument_type g)
	Computes \( gcd(f,g)\) up to a constant factor. More...

Member Typedef Documentation

◆ first_argument_type

typedef PolynomialTraits_d::Polynomial_d PolynomialTraits_d::GcdUpToConstantFactor::first_argument_type

◆ result_type

typedef PolynomialTraits_d::Polynomial_d PolynomialTraits_d::GcdUpToConstantFactor::result_type

◆ second_argument_type

typedef PolynomialTraits_d::Polynomial_d PolynomialTraits_d::GcdUpToConstantFactor::second_argument_type

Member Function Documentation

◆ operator()()

result_type PolynomialTraits_d::GcdUpToConstantFactor::operator()	(	first_argument_type	f,
		second_argument_type	g
	)

Computes \( gcd(f,g)\) up to a constant factor.