Acknowledgements

The authors would like to thank Kurt Schneider and Stan Yoshinobu who wrote some of the Mathematica software and contributed heavily to the working of examples in this paper. In particular, they did substantial parts of the examples in § and §. Kurt Schneider did much of the work for the example in § and Stan Yoshinobu did much of the work in the example in §.

Victor Shih and Mike Moore contributed to the C++ coding behind the NCProcess command.

We would like to thank Johan Kaashoek, Nicholas Young and Hugo Woerderman for providing problems and comments on our computer generated solutions. Johan Kaashoek deserves special thanks for detailed and valuable help.

We would also like to thank Roger Germundsson for helpful discussions involving commutative Gröbner Basis.