Computer Algebra

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Computer algebra is the field where computers are applied to the problems of mathematics which are not necessarily numerical. This includes symbolic computation which manipulates symbolic expressions according to mathematical rules, as well as applications such as modeling groups and operators. The techniques are extremely useful for doing tedious derivations and solving certain classes of equations.

Research focus is primarily on applications and extensions of SymbolicC++, a symbolic computation system written completely in C++. SymbolicC++ is applied to problems involving Lie series techniques, energy eigenvalue motion, commutation relations in quantum mechanics and quantum computation. The combination of symbolic and numerical computation permits calculations with high precision where pure numerical techniques accumulate errors.

We recently supervised a postgraduate student (MSc in Computer Science) who implemented Gröbner basis techniques for Symbolic C++. This will aid us in the symbolic solving of nonlinear multivariate polynomial equations.