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CGAL 6.0.1 - Algebraic Foundations
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AlgebraicStructureTraits_::Gcd Concept Reference

Definition

AdaptableBinaryFunction providing the gcd.

The greatest common divisor ( gcd) of ring elements x and y is the unique ring element d (up to a unit) with the property that any common divisor of x and y also divides d. (In other words: d is the greatest lower bound of x and y in the partial order of divisibility.) We demand the gcd to be unit-normal (i.e. have unit part 1).

gcd(0,0) is defined as 0, since 0 is the greatest element with respect to the partial order of divisibility. This is because an element a \in R is said to divide b \in R, iff \exists r \in R such that a \cdot r = b. Thus, 0 is divided by every element of the Ring, in particular by itself.

Refines
AdaptableBinaryFunction
See also
AlgebraicStructureTraits

Types

typedef unspecified_type result_type
 Is AlgebraicStructureTraits::Type.
 
typedef unspecified_type first_argument
 Is AlgebraicStructureTraits::Type.
 
typedef unspecified_type second_argument
 Is AlgebraicStructureTraits::Type.
 

Operations

result_type operator() (first_argument_type x, second_argument_type y)
 returns gcd(x,y).
 
template<class NT1 , class NT2 >
result_type operator() (NT1 x, NT2 y)
 This operator is defined if NT1 and NT2 are ExplicitInteroperable with coercion type AlgebraicStructureTraits::Type.