## `Cat::AbelianGroup` -- the category of abelian groups

#### Introduction

`Cat::AbelianGroup` represents the category of abelian groups.

#### Generating the category

`Cat::AbelianGroup()`

#### Categories

`Cat::CancellationAbelianMonoid`

#### Details

- An `Cat::AbelianGroup` is an abelian monoid with cancellation law where the operation `+` is invertible.

#### Method _negate: returns opposite

- `_negate(dom x)`
- - Must return the opposite of `x`.

#### Method equal: test for equality

- `equal(dom x, dom y)`
- - Returns `TRUE` iff `x` is equal to `y`. This implementation tests if `x` minus `y` is zero, using the method `"iszero"`.

#### Method intmult: returns integer multiple

- `intmult(dom x, DOM_INT n)`
- - Returns the integer multiple `n` times `x`. This method is implemented like ``repeated squaring'' using the domains method `"_plus"`.

#### Method _subtract: subtracts two elements

- `_subtract(dom x, dom y)`
- - Returns `x` minus `y` by adding `x` and the opposite of `y`.

#### Changes

- no changes

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