I have an linearly reductive algebraic group $G$ acting regularly on an affine variety $X$(over an algebraically closed field of characteristic 0). I want to compute the invariant ring $\mathbb{K}[X]^{G}$. Now I don't expect to be able to find a software that can do this for any such $X$ and $G$, but I'm hoping I can find a software which can do it for some special cases.
I would be grateful if someone can suggest me what are those softwares and for what cases of $G$ and $X$ do they work.
