Each user defined variable has a type.
Rings are a basic concept of Macaulay .
The major type of data which Macaulay manipulates are matrices with polynomial entries. In order to optimize calculations every matrix must be defined over a base ring. A ring contains necessary information such as the number of variables, their names, and the monomial order being used. The system uses this information to compact the monomials into as small a space as possible. See Chapter 5 for details.