Cat::CancellationAbelianMonoid
-- the category of abelian monoids with cancellationCat::CancellationAbelianMonoid
represents the category
of abelian monoids with cancellation.
Cat::CancellationAbelianMonoid()
Cat::AbelianMonoid
Cat::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.