  Let g be a real form of a simple complex Lie algebra. Based on ideas of
Djokovic and Vinberg, we describe an algorithm to compute representatives of
the nilpotent orbits of g using the Kostant-Sekiguchi correspondence. Our
algorithms are implemented for the computer algebra system GAP and, as an
application, we have built a database of nilpotent orbits of all real forms of
simple complex Lie algebras of rank at most 8. In addition, we consider two
real forms g and g' of a complex simple Lie algebra g^c with Cartan
decompositions g= k+p and g'=k'+p'. We describe an explicit construction of an
isomorphism g -> g', respecting the given Cartan decompositions, which fails if
and only if g and g' are not isomorphic. This isomorphism can be used to map
the representatives of the nilpotent orbits of g to other realisations of the
same algebra.
