Mathematics of Computer Algebra and Analysis

Computer algebra systems such as Maple compute using mathematical formulae as well as numbers, mechanizing the mathematics used in education and research labs. This project focuses on the design and implementation of algorithms for these systems. Emphasis is placed on efficiency that allows large and complex problems of the type encountered in industrial settings to be solved. In the past year the team has made major advances in the core tools that are needed to solve these complex problems. These include a new compact way to represent the core tools (polynomials) and their fundamental arithmetic operations. Additional advances also include new algorithms for computing the greatest common divisors of polynomials, which have been incorporated into Maple. The latter advance provides a huge improvement for important operations such as the simplification of large complex formulae. It is the inability of Maple and other computer algebra systems to efficiently simplify large formulae that has often been a key problem in preventing the system from solving industrial sized problems.