# AbelianGroupΒΆ

The class of abelian groups, i.e. additive monoids where each element has an additive inverse.

- 0: %
- from AbelianMonoid

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

is the product of`x`

by the integer`n`

.- *: (NonNegativeInteger, %) -> %
- from AbelianMonoid
- *: (PositiveInteger, %) -> %
- from AbelianSemiGroup
- +: (%, %) -> %
- from AbelianSemiGroup

- -: % -> %
`-x`

is the additive inverse of`x`

.

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

is the difference of`x`

and`y`

i.e.`x + (-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
- opposite?: (%, %) -> Boolean
- from AbelianMonoid
- sample: %
- from AbelianMonoid
- subtractIfCan: (%, %) -> Union(%, failed)
- from CancellationAbelianMonoid
- zero?: % -> Boolean
- from AbelianMonoid