Computer Algebra - Richard Zippel

Research Summary

Currently, my activities in computer algebra fall into three different areas. We are continuing to develop a very flexible computer algebra substrate called Weyl, which extends Common Lisp to have symbolic computing facilities. This substrate has a functorial architecture that has been implemented using object oriented programming techniques. The functorial organization allows one to define algebraic structures over arbitrary algebraic domains. This approach permits algebraic structures like groups, rings and fields to be first class objects that can be manipulated by the user.

We have been attempting to link together Weyl with Bob's Constable's theorem proving system, Nuprl. This will allow us state and use theorem about algebraic structures when deciding which algorithms should be used Weyl.

In additon, I have been continuing my work on algorithms in computer algebra. Among the problems I have been studying include: algebraic function decomposition (with Dexter Kozen and Susan Landau) and primality testing of polynomials.