  A computational technique for calculating nullity vectors and kernel vectors,
using the new Finsler package, is introduced. As an application, three
interesting counterexamples are given. The first counterexample shows that the
two distributions $\mathrm{Ker}_R$ and $\N_R$ do not coincide. The second shows
that the nullity distribution $\N_{P^\circ}$ is not completely integrable. The
third shows that the nullity distribution $\N_\mathfrak{R}$ is not a
sub-distribution of the nullity distribution $\N_{R^\circ}$.
