A ring map is a map (homomorphism) between two polynomial rings,
.
If the ring R has n variables, then a ring map f is completely
determined by the image 
of each variable 
of R. In
Macaulay, a ring map from any ring R to a ring S is given
as a 1 by n matrix f whose base ring is S. Since ring maps
are represented as matrices in Macaulay, any matrix operation can be
used to create a ring map. For an example of a ring map, see the
rmap command below.
One can also use the commands rmap and imap to create ring maps. rmap is used to create a general ring map, while imap is used to create an ``identity'' map: map each variable of R to the variable with the same name in S. The command edit-map allows you to modify an existing ring map. The command ev allows you to evaluate the image of a matrix under a specified ring map. The command fetch is used to map a matrix to a new ring using an ``identity'' map as above. Finally, the pmap command displays a ring map.
Whenever a ring is expected as a parameter and a matrix is given, the ring used is the base ring of the specified matrix. This actually holds more generally thoughout Macaulay: whenever a ring is expected, any user defined variable with the same base ring can be used.
As always in Macaulay, either ring R or S can be a quotient ring (see section 5.3).
This set of commands has many uses, including: dehomogenizing an ideal or matrix, changing to generic coordinates, changing the monomial order and adding new variables.