Seminars

Scalings form a class of group actions on affine spaces that have both theoretical and practical importance. A scaling is accurately described by an integer matrix. Tools from linear algebra over the integers are exploited to compute a minimal generating set of rational invariants, trivial rewriting and rational sections for such a group action. The primary tools used are Hermite normal forms and their unimodular multipliers.

The same information is sufficient to offer a complete symmetry reduction scheme for either polynomial systems or dynamical systems. A special case of the symmetry reduction algorithm applies to reduce the number of parameters in physical, chemical or biological models, which was the original motivation of this research in collaboration with George Labahn (U. of Waterloo, Canada).