  We report on some computations with reachable elements in simple Lie algebras
of exceptional type within the SLA package of GAP4. These computations confirm
the classification of such elements by Elashvili and Grelaud. Secondly they
answer a question from Panyushev. Thirdly they show in what way a recent result
of Yakimova for the Lie algebras of classical type extends to the exceptional
types.
