Domains in Domains are functions which return tables of operations for manipulating objects in the domain.  For example, Integers() returns a table of operations for computing with integers including `+` addition, `-` subtraction, `*` multiplication, etc.

Domains can be parameterized by other domains and values; for example, the domain $\mathrm{DenseUnivariatePolynomial}\left(R\,x\right)$ takes a coefficient ring R and a variable x as a parameter. The coefficient ring must be a Domains domain which belongs to the category Ring; that is, it must support all the operations of a ring.  The variable x must be a name.

All domains support belongs to the category Set which supports the operations

=, <>  -- boolean equality of domains elements

Input -- for converting expressions into the domain data representation

Output -- for converting from the domain representation to an output form

Random -- for generating a pseudo-random value from the domain

Type -- for testing if a value is a valid domain element

The command show(D, operations) can be used to print out all the operations that are defined for a domain.  Operations marked by -- are not implemented. A list of the domains constructors in Domains is

In addition, there are some special domains that use the Maple representation for polynomials to try to get back some efficiency for integer and rational coefficients.