  Computation of homology or cohomology is intrinsically a problem of high
combinatorial complexity. Recently we proposed a new efficient algorithm for
computing cohomologies of Lie algebras and superalgebras. This algorithm is
based on partition of the full cochain complex into minimal subcomplexes. The
algorithm was implemented as a C program LieCohomology. In this paper we
present results of applying the program LieCohomology to the algebra of
hamiltonian vector fields H(2|0). We demonstrate that the new approach is much
more efficient comparing with the straightforward one. In particular, our
computation reveals some new cohomological classes for the algebra H(2|0) (and
also for the Poisson algebra Po(2|0)).
