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.