Abstract: Closed subsets of polynomial functors are highly symmetrical varieties that live in infinite dimensions. Due to these large symmetries, they can be defined by finitely many polynomial equations. This is a recent result of Draisma. In this talk, I will discuss how to make this and more recent results of Bik-Draisma-Eggermont-Snowden algorithmic. Our algorithms use classical elimination in finite but ever-increasing dimension, but also separate routines, with no classical analogue, which search for a certificate that one has found enough equations.