Suggestions are welcome.
The above works in Release 4. In Release 3 'Domains' was called 'Gauss'. Maple has a package for dealing with finite fields. I found it a bit cumbersome and did a series of worksheets designed to make it easier to do computations over a given finite field. FiniteFields The notes for release V 4 suggest that Domains will make it easier to do computations in different settings in the future, but I have not explored this yet.