Details:
Title  Minimal generating sets of nonmodular invariant rings of finite groups  Author(s)  Simon A. King  Type  Article in Journal  Abstract  It is a classical problem to compute a minimal set of invariant polynomials generating the invariant ring of a finite group as a subalgebra. We present here a new algorithmic solution in the nonmodular case. Our algorithm only involves very basic operations and is based on wellknown ideas. In contrast to the algorithm of Kemper and Steel, it does not rely on the computation of primary and (irreducible) secondary invariants. In contrast to the algorithm of Thiéry, it is not restricted to permutation representations. With the first implementation of our algorithm in Singular, we obtained minimal generating sets for the natural permutation action of the cyclic groups of order up to 12 in characteristic 0 and of order up to 15 for finite fields. This was far out of reach for implementations of previously described algorithms. By now our algorithm has also been implemented in Magma. As a byproduct, we obtain a new algorithm for the computation of irreducible secondary invariants that, in contrast to previously studied algorithms, does not involve a computation of all reducible secondary invariants.  Keywords  Invariant ring, Fundamental invariants, Irreducible secondary invariants, Truncated Gröbner basis  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S074771711200079X 
Language  English  Journal  Journal of Symbolic Computation  Volume  48  Number  0  Pages  101  109  Year  2013  Edition  0  Translation 
No  Refereed 
No 
