# AbelianSemiGroupΒΆ

the class of all additive (commutative) semigroups, i.e. a set with a commutative and associative operation +.

- *: (PositiveInteger, %) -> %
`n*x`

computes the left-multiplication of`x`

by the positive integer`n`

. This is equivalent to adding`x`

to itself`n`

times.

- +: (%, %) -> %
`x+y`

computes the sum of`x`

and`y`

.- =: (%, %) -> Boolean
- from BasicType
- ~=: (%, %) -> Boolean
- from BasicType
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory
- latex: % -> String
- from SetCategory