Computing nullity and kernel vectors using NF-package: Counterexamples

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 $\N_{R^\circ}$.