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.

Definition

Types

Operations