An evaluation approach to computing invariants rings of permutation   groups
  Using evaluation at appropriately chosen points, we propose a Gr\"obner 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. 
Nicolas Borie and Nicolas M. Thi\'ery
math.CO