Subring is a type that stores information associated to a subring of a polynomial ring, such as a set of subring generators and a reference to the polynomial ring it is contained in. An instance of a Subring is constructed with the function subring.
Every instance of Subring is guaranteed to have the following keys:

ambientRing: The polynomial or quotient ring that contains the subring instance's generators.

generators: A onerow matrix, the generators of the subring.

cache: Contains unspecified information. The contents of the cache may effect performance, but should never effect the result of a computation.

subductionQuotientRing: the polynomial ring with one variable for each generator of the subring