PolynomialTraits_d::GcdUpToConstantFactor

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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

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	fo ( first_argument_type f , second_argument_type g )
		Computes gcd(f,g) up to a constant factor.