# ambient(Ring) -- ambient polynomial ring

## Synopsis

• 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).