Cat::CancellationAbelianMonoid
-- the category of abelian monoids with cancellation
IntroductionCat::CancellationAbelianMonoid represents the category
of abelian monoids with cancellation.
Generating
the categoryCat::CancellationAbelianMonoid()
Cat::AbelianMonoid
DetailsCat::CancellationAbelianMonoid is an abelian monoid
where the cancellation law holds according to the operation
+, i.e. a + b = a + c implies b =
c._subtract(dom x, dom
y)z such that x =
y + z or FAIL if z
dosn't exist. The result is unique due to the cancellation law.equal(dom x, dom
y)TRUE if x - y exists
and is equal to zero. Returns FAIL if x -
y returns FAIL."iszero" is used to test for zero._negate(dom x)x by computing 0 -
x or FAIL if the subtraction fails.intmult(dom x, DOM_INT n)n-fold sum of x. The integer
n may also be negative. In this case the opposite of
x is computed. If no opposite exists then
FAIL is returned, otherwise the -n-fold sum
of the opposite is returned.