|
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 ∈ R is said to divide b ∈ R, iff ∃ r ∈ R such that a ⋅ r = b. Thus, 0 is divided by every element of the Ring, in particular by itself.
AdaptableBinaryFunction
| AlgebraicStructureTraits::Gcd::result_type | |
|
Is AlgebraicStructureTraits::Type.
| |
| AlgebraicStructureTraits::Gcd::first_argument | |
|
Is AlgebraicStructureTraits::Type.
| |
| AlgebraicStructureTraits::Gcd::second_argument | |
|
Is AlgebraicStructureTraits::Type.
| |
| result_type | gcd ( first_argument_type x , second_argument_type y ) | |
| returns gcd(x,y). | ||
| template <class NT1, class NT2> | ||
| result_type | gcd ( NT1 x , NT2 y ) | This operator is defined if NT1 and NT2 are ExplicitInteroperable with coercion type AlgebraicStructureTraits::Type. |