Computational Algebra

Abstract

Computer algebra, also known as symbolic computation, is an interdisciplinary area of mathematics and computer science. We develop algorithms for solving mathematical problems such as integrating algebraic formulae, factoring polynomials, and computing the complex roots of an analytic function. We also develop software systems (problem solving environments) like Maple for implementing these algorithms and use these systems for application in mathematics and the sciences.Our research is funded by MITACS and NSERC. Our MITACS project is called MOCAA, an anacronym for Mathematics of Computer Algebra and Analysis. Our NSERC project is entitled "Algorithms Data Structures and Algorithms for Polynomials over Finite, Algebraic Number and Function Fields". Both projects are supported by the Maple company. We are one of six international sites for the development of Maple.The MOCAA project is a joint project with investigators from Alberta, Ontario and Quebec. This project includes subprojects on (i) computing algebraic solution of (systems of) ordinary, partial and algebraic equations, (ii) special functions, their numerical evaluation, (iii) simplification of algebraic formula involving algebraic, elementary and special functions, and (iv) linear algebra over finite fields.The NSERC research project is aimed at developing data structures and algorithms for computing (i) polynomial greatest common divisors, (ii) factoring polynomials and (iii) computing Grobner bases. The fields which we will support include the rational numbers, finite fields, and algebraic number and function fields.Two other projects that we completed in 2004 are the development of an algorithm for computing all complex roots of an analytic function in a rectangular region, and a package for computing with polynomial ideals which includes algorithms for decomposing an ideal into prime(ary) ideals.

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