Symbolic Computation Group
David R. Cheriton School of Computer Science


Friday, March 7, 2003, at U. of Waterloo.
Abstract:
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
Buchbergerlike algorithm.

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