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