# Cat::Field

Category of fields

## Description

`Cat::Field` represents the category of fields.

A `Cat::Field` is a factorial domain, an Euclidean domain and a skew field. As a Euclidean domain, it has a commutative multiplication `*` (`_mult`) and as a skew field, the multiplication is invertible.

Many of the methods defined for factorial and Euclidean domains are trivial for a field.

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## Mathematical Methods

### `associates` — Test for associate elements

`associates(x, y)`

### `_divide` — Exact division

`_divide(x, y)`

### `divide` — Division with remainder

`divide(x, y)`

### `divides` — Test if division is exact

`divides(x, y)`

### `euclideanDegree` — Return Euclidean degree

`euclideanDegree(x)`

### `factor` — Unique factorization

`factor(x)`

### `gcd` — Greatest common divisor

`gcd(x, …)`

### `irreducible` — Test if element is irreducible

`irreducible(x)`

### `isUnit` — Test if element is an unit

`isUnit(x)`

### `quo` — Return Euclidean quotient

`quo(x, y)`

### `rem` — Return Euclidean remainder

`rem(x, y)`

### `sqrfree` — Square-free factorization

`sqrfree(x)`

### `unitNormal` — Unit normal form

`unitNormal(x)`

### `unitNormalRep` — Unit normal representation

`unitNormalRep(x)`