  We develop an algorithm for recognizing whether a character belongs to
$\Sigma^m$. In order to apply it we just need to know that the ambient group is
of type $\mathrm{FP}_m$ or of type $\mathrm{F}_2$ and that the word problem is
solvable for this group. Then finite data is sufficient proof of membership in
$\Sigma^m$, not just for the given character but also for a neighborhood of it.
