## `Cat::GcdDomain` -- the category of integral domains with gcd

#### Introduction

`Cat::GcdDomain` represents the category of integral domains with a gcd.

#### Generating the category

`Cat::GcdDomain()`

#### Categories

`Cat::IntegralDomain`

#### Details

- A `Cat::GcdDomain` is an integral domain where the greatest common divisor of two elements can be computed by the method `"gcd"`.

#### Method gcd: greatest common divisor

- `gcd(dom x...)`
- - Must return the greatest common divisor of its arguments.
  - The method must satisfy the following conditions:
    1. `x` and `y` must divide `dom::gcd(x,y)`,
    2. if `z` divides both `x` and `y`, then `z` must divide `dom::gcd(x,y)`,
    3. if a domain has the axiom `Ax::canonicalUnitNormal` then `dom::gcd(x,y)` must be equal to `dom::unitNormal(dom::gcd(x,y))`.
    Remember that `x` divides `y` if `_divide(x,y)` does not return `FAIL`.

#### Method lcm: least common multiple

- `lcm(dom x...)`
- - Returns the least common multiple of its arguments. The implementation provided here uses the method `"gcd"` to compute the result.

#### Changes

- no changes

Do you have questions or comments?
Copyright © SciFace Software GmbH & Co. KG 2000