PolynomialTraits_d::GcdUpToConstantFactor Concept Reference

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.