CGAL 4.7 - Polynomial
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:
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.