TITLE: Software for computing equivariants
QUESTION [6 upvotes]: If $\Gamma$ is a finite group with action on two vector spaces $\mathbb R^n$ and $\mathbb R^m$ denoted by $\gamma_n$ and $\gamma_m$ respectively, the fundamental equivariants are the polynomials $f: \mathbb R^n \rightarrow \mathbb R^m$ that commute with $\Gamma$, i.e. $$\gamma_m \cdot f(x) = f(\gamma_n^{-1} \cdot x) \quad \forall x \in \mathbb R^n.$$
It it well known that this set is a finitely generated free module over the ring of primary invariants. 
Is there any software available to compute a set of generators of the module of equivariants? 
An algorithm is described in page 12 of this paper "Zeros of equivariant vector fields..."  by P. Worfolk (citeseerx link, unrestricted) for instance in pseudo code, but surprisingly I was not able to find any implementation online in Singular, Magma or similar.

REPLY [2 votes]: The canonical reference appears to be Karin Gatermann's book:
Gatermann, Karin, Computer algebra methods for equivariant dynamical systems, Lecture Notes in Mathematics. 1728. Berlin: Springer. xv, 153 p. (2000). ZBL0944.65131.
In the book she frequently alludes to the Maple package symmetry which she uses to compute invariants and equivariants.