Symbolic computation

General.Symbolic Computation (also known as Computer Algebra) is the study of algorithms and their implementations for computations involving mathematical symbols, not just numbers. This has been elegantly described by a number of people:

``Computer algebra evolved as a discipline, linking algorithmic and abstract algebra in its most general sense to methods of computer science, and providing a new methodical tool in the border area between applied mathematics and computer science.'' --- Steering committee of the Fachgruppe of computer algebra, Handbook of Computer Algebra, p. 1

``Computer algebra systems have significantly influenced scientific research in many fields, among them mathematics, computer science, physics, chemistry, engineering. They have supplemented the well-established numerical packages by new tools aimed at problems that require exact answersi, or a closed-form analysis of the dependence of a problem class on certain parameters. ... They have become absolutely indispensable ..." --- Erich Kaltofen, Handbook of Computer Algebra, p. 4

``The Purpose of Computing is Insight, not Numbers'' --- R. W. Hamming

Maple is a commercial product for symbolic computation, distributed by Maplesoft (see www.maplesoft.com), but there are other such commercial products, such as Mathematica (see www.wolfram.com). There also exists good free software to do this kind of thing. At present, the packages are all under continuous development, and their capabilities are being extended to solve harder and harder problems, for use in industrial mathematics. Some examples of such problems include analysis of mathematical models used in the pulp and paper industry or in robotics, car parts manufactured with the help of Computer Aided Geometric Design, and solution of equations arising in mathematical biology (specifically to do with pigment regeneration characteristics in the human eye).

The Department of Applied Mathematics at UWO is one of the co-sponsors of the Ontario Research Centre for Computer Algebra, where further development is under way. ORCCA (on the Computer Science side) also has projects on making the use of such systems easier, notably by work on MathML and on mathematical handwriting recognition.

Recent papers.

Research groups.

• Rob Corless
  • Official web page
  • Personal

• David Jeffrey
  • Official web page
  • Personal

• Greg Reid
  • Official web page
  • Personal