Is there a program (in Macaulay2 or singular or Gap or whatever) which explicitly gives the ring structure of $Spec[V]^G$ where $V$ is an explicitly given affine variety (over $\mathbb{C}$) and $G$ a reductive group acting on $V$ ?

As a background: in supersymmetric quantum field theory, we often come across so-called Seiberg dualities, one of whose consequences is that two quotients $Spec[V]^G$ and $Spec[W]^H$ are the same. Therefore it's important for us to check the equality, but doing this by hand is often extremely tedious. So I'm looking for a way to automate it.