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# ambient -- ambient free module of a subquotient, or ambient ring

## Description

Each module M in Macaulay2 is a quotient, submodule or subquotient of a free module, called the ambient free module of M.

The ambient ring of a quotient ring R/I is the polynomial ring of that it is a quotient. The ambient ring of a Galois field is the quotient ring that it was constructed from.

## See also

- GF -- make a finite field
- cover -- get the covering free module
- super -- get the ambient module

## Ways to use ambient:

- ambient(GaloisField) -- corresponding quotient ring
- ambient(Matrix) -- get the map between the ambient free modules
- ambient(Module) -- ambient free module
- `ambient(PolynomialRing)` -- see ambient(Ring) -- ambient polynomial ring
- `ambient(QuotientRing)` -- see ambient(Ring) -- ambient polynomial ring
- ambient(Ring) -- ambient polynomial ring

## For the programmer

The object ambient is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/functions/ambient-doc.m2:18:0.