Let G be a group acting``nicely" on a space, $X$, with some structure(topological, differentiable, algebraic, combinatorial.). A basic problem is to find an effective way of determining if two points $x,y$ are in the same orbit (or at least in an appropriate closure of an orbit). In this lecture I will look at methods that can be used in concert with computers to approach such problems through the determination of "enough" computable invariant functions. There will be several examples including measures of quantum entanglement.