  We compute explicitly the density of the invariant measure for the Reverse
algorithm which is absolutely continuous with respect to Lebesgue measure,
using a method proposed by Arnoux and Nogueira. We also apply the same method
on the unsorted version of Brun algorithm and Cassaigne algorithm. We
illustrate some experimentations on the domain of the natural extension of
those algorithms. For some other algorithms, which are known to have a unique
invariant measure absolutely continuous with respect to Lebesgue measure, the
invariant domain found by this method seems to have a fractal boundary, and it
is unclear that it is of positive measure.
