Symbolic Computation Group

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

Standard bases in bifurcation theory
Karin Gatermann, University of Western Ontario
Friday, March 7, 2003, at U. of Waterloo.


We consider singularity theory in bifurcation theory in the sense of Golubitsky, Stewart, Schaeffer. One is interested in typical local bifurcation scenarios, that means the real solutions of a system of equation depending on a parameter. The theory requires the study of algebraic objects over local rings, such as codimension and representatives of quotients giving the universal unfolding. These are typical tasks of Computer Algebra. For ideals in local rings there exists standard bases with respect to semigroup orders with implementation available in Singular. Serkan Hosten and I generalized this concept to mixed modules over local rings as needed in the bifurcation theory context. The Mora normal form algorithm is generalzed as well as the Buchberger-like algorithm.

Computational examples illustrate the benefits of our methods. Moreover, we like to improve the existing classification by computer algebra methods. We will show experimentel results on this too.


Last modified on Sunday, 04 November 2012, at 15:42 hours.