Parameterizing invariant spaces

I've been working on extending SageMath's capabilities to calculate parameterizations for invariant rings of matrix groups over finite fields. While the general linear group's invariants can be parameterized using Dickson invariants, it's more challenging for smaller groups like the special linear group. I aim to implement known methods for computing these spaces, like subring decomposition, to make them more accessible and known to researchers. I also plan to tackle invariant rings of characteristic 0 representations of finite groups, focusing on permutation representations.