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# GaloisField -- the class of all Galois fields

### Menu

- GF -- make a finite field
- order -- a key used internally
- ambient(GaloisField) -- corresponding quotient ring

## Functions and methods returning a Galois field:

- `GF(Ring)` -- see GF -- make a finite field
- `GF(ZZ)` -- see GF -- make a finite field
- `GF(ZZ,ZZ)` -- see GF -- make a finite field

## Methods that use a Galois field:

- ambient(GaloisField) -- corresponding quotient ring
- `describe(GaloisField)` -- see describe -- real description
- `dim(GaloisField)` -- see dim(Ring) -- compute the Krull dimension
- `flattenRing(GaloisField)` -- see flattenRing -- write a ring as a (quotient of a) polynomial ring
- `isField(GaloisField)` -- see isField -- whether something is a field
- `isFinitePrimeField(GaloisField)` -- see isFinitePrimeField -- whether a ring is a finite prime field
- map(GaloisField,GaloisField) (missing documentation)
- `precision(GaloisField)` -- see precision

## For the programmer

The object GaloisField is a type, with ancestor classes EngineRing < Ring < Type < MutableHashTable < HashTable < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/doc_rings.m2:229:0.