Symbolic Computation Group

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 polynomial systems whose solution set is invariant by a finite abelian group action.

This is joint work with Evelyne Hubert (France)