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# ambient(Ring) -- ambient polynomial ring

- Function: ambient
- Usage:
    `ambient R`
- Inputs:
  - R, a ring, a polynomial ring or a quotient of a polynomial ring
- Outputs:
  - a ring, the polynomial ring of which this ring is a quotient

## Description

    i1 : A = ZZ[a..d];

    i2 : B = A/(3*a^2-1);

    i3 : C = B/(a*b-3);

    i4 : describe C

            B
    o4 = -------
         a*b - 3

    i5 : ambient C

    o5 = B

    o5 : QuotientRing

If R is not a quotient of a polynomial ring, an error is given.

## Caveat

If the ring is a GaloisField, then the meaning is different. See ambient(GaloisField).

## Ways to use this method:

- `ambient(PolynomialRing)`
- `ambient(QuotientRing)`
- ambient(Ring) -- ambient polynomial ring

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/functions/ambient-doc.m2:40:0.