CGAL 6.0.1 - Algebraic Foundations
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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.
AdaptableBinaryFunction
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 . | |