My main area of research is computer algebra which is also known as symbolic computation. I am interested in the problems of algebraic simplification and computing with polynomials over number fields, finite fields, and function fields, in particular polynomial GCD computation, polynomial factorization, and Groebner basis computation. And I work in computer algebra systems design, in particular Maple and data structures for polynomials. I also have an interest in automatic differentiation, applications of computer algebra, cryptography and algebraic geometry.
I am perhaps best known for my contributions to the Maple project. Maple started as a university research project at Waterloo in 1980. I became involved in the project as a graduate student in 1983 and continue to be involved in the Maple project at Simon Fraser University through an NSERC research grant and a MITACS research grant. There I am directing the computational algebra group at SFU and also presently directing the CECM, the centre for experimental and constructive mathematics.