Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

Symbolic Computation versus Computer Algebra
Stephen M. Watt, University of Western Ontario
Friday, June 9, 2006, at U. of Waterloo.

Abstract:

We observe that "symbolic computation" and "computer algebra" are really two different things and that neither one sufficiently addresses the problems that arise in applications.

Symbolic computation may be seen as working with expression trees representing mathematical formulae and applying various rules to transform them. Computer algebra may be seen as developing constructive algorithms to compute quantities in various arithmetic domains, possibly involving indeterminates.

Symbolic computation allows a wider range of expression, but lacks efficient algorithms. It is often unclear what is the algebraic structure of a domain defined by rewrite rules. Computer algebra admits greater algorithmic precision, but is limited in the problems that it can model.

We argue that considerable work is still required to make symbolic computation more effective and computer algebra more expressive. We use polynomials with symbolic exponents, e.g. $x^{n^2 + n} - y^{2m}$, as an example that lies in the middle ground and we present algorithms for their factorization and gcd.

 

Last modified on Sunday, 04 November 2012, at 20:42 hours.