AlgebraicStructureTraits::Gcd

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 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.

Refines

AdaptableBinaryFunction

Types

Operations

See Also

AlgebraicStructureTraits