|
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
|
| |
|
Is AlgebraicStructureTraits::Type.
| |
|
| |
|
Is AlgebraicStructureTraits::Type.
| |
|
| |
|
Is AlgebraicStructureTraits::Type.
| |
|
|
| |
| returns gcd(x,y). | ||
|
| ||
|
|
| This operator is well defined if NT1 and NT2 are ExplicitInteroperable with coercion type AlgebraicStructureTraits::Type. |