An evaluation approach to computing invariants rings of permutation groups

Abstract

Using evaluation at appropriately chosen points, we propose a Gröbner basis free approach for calculating the secondary invariants of a finite permutation group. This approach allows for exploiting the symmetries to confine the calculations into a smaller quotient space, which gives a tighter control on the algorithmic complexity, especially for large groups. This is confirmed by extensive benchmarks using a Sage implementation.

18 pages, 4 figures, In Proceedings of MEGA 2011, March 2011