The main component of this project with MapleSoft, Inc., a software development and business consulting firm, will be to design a high performance implementation (in C) of a set of procedures the intern has created in Maple language. These procedures provide an environment for doing polynomial arithmetic in a ‘lazy’ way. That is, they allow the team to compute in a way where polynomial algebra is done only when absolutely necessary. Computing in this fashion will allow the researchers to approach the implementation of several computer algebra algorithms in a novel way. It is my hope that in doing so I will be able to improve these algorithms.