  Given a vertex algebra $\mathcal{V}$ and a subalgebra $\mathcal{A}\subset
\mathcal{V}$, the commutant $\text{Com}(\mathcal{A},\mathcal{V})$ is the
subalgebra of $\mathcal{V}$ which commutes with all elements of $\mathcal{A}$.
This construction is analogous to the ordinary commutant in the theory of
associative algebras, and is important in physics in the construction of coset
conformal field theories. When $\mathcal{A}$ is an affine vertex algebra,
$\text{Com}(\mathcal{A},\mathcal{V})$ is closely related to rings of invariant
functions on arc spaces. We find strong finite generating sets for a family of
examples where $\mathcal{A}$ is affine and $\mathcal{V}$ is a
$\beta\gamma$-system, $bc$-system, or $bc\beta\gamma$-system.
