FoCM 2014 conference

Workshop B7 - Symbolic Analysis

December 17, 17:30 ~ 17:55 - Room A11

## Invariants of Finite Abelian Groups and their use in Symmetry Reduction of Dynamical Systems

### George Labahn

### University of Waterloo, Canada - glabahn@uwaterloo.ca

We describe the computation of rational invariants of the linear action of a finite abelian group in the non-modular case and investigate its use in symmetry reductions of dynamical and polynomial systems. Finite abelian subgroups of $GL(n,K)$ can be diagonalized which allows the group action to be accurately described by an integer matrix of exponents. We can make use of integer linear algebra to compute both a minimal generating set of invariants and the substitution to rewrite any invariant in terms of this generating set. The set of invariants provide a symmetry reduction scheme for dynamical and polynomial systems whose solution set is invariant by a finite abelian group action. A special case of the symmetry reduction algorithm applies to reduce the number of parameters in physical, chemical or biological models.

Joint work with Evelyne Hubert (INRIA Mediterranee, France).