PolynomialTraits_d::GcdUpToConstantFactor

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[x₀,...,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 $$gcds of polynomials exist.

This functor computes $$gcd_utcf(f,g) = D * gcd(f,g), for some $$D R such that $$gcd_utcf(f,g) R[x₀,...,x_d-1]. Hence, $$gcd_utcf(f,g) may not be a divisor of $$f and $$g in $$R[x₀,...,x_d-1].

Refines

AdaptableBinaryFunction

Types

Operations

See Also

Polynomial_d
PolynomialTraits_d
PolynomialTraits_d::IntegralDivisionUpToConstantFactor
PolynomialTraits_d::UnivariateContentUpToConstantFactor
PolynomialTraits_d::SquareFreeFactorizeUpToConstantFactor