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)](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.41.6148&rep=rep1&type=pdf) for instance in pseudo code, but surprisingly I was not able to find any implementation online in Singular, Magma or similar.



Software for computing equivariants
The canonical reference appears to be Karin Gatermann's book:


*Gatermann, Karin*, [**Computer algebra methods for equivariant dynamical systems**](http://dx.doi.org/10.1007/BFb0104059), Lecture Notes in Mathematics. 1728. Berlin: Springer. xv, 153 p. (2000). [ZBL0944.65131](https://zbmath.org/?q=an:0944.65131).


In the book she frequently alludes to the *Maple* package *symmetry* which she uses to compute invariants and equivariants. 


