  In this paper, we investigate the relative Gel'fand-Kalinin-Fuks cohomology
groups of the formal Hamiltonian vector fields on R^4. In the case of formal
Hamiltonian vector fields on R^2, we computed the relative
Gel'fand-Kalinin-Fuks cohomology groups of weight <20 in the paper by
Mikami-Nakae-Kodama. The main strategy there was decomposing the Gel'fand-Fucks
cochain complex into irreducible factors and picking up the trivial
representations and their concrete bases, and ours is essentially the same.
  By computer calculation, we determine the relative Gel'fand-Kalinin-Fuks
cohomology groups of the formal Hamiltonian vector fields on R^4 of weights 2,
4 and 6. In the case of weight 2, the Betti number of the cohomology group is
equal to 1 at degree 2 and is 0 at any other degree. In weight 4, the Betti
number is 2 at degree 4 and is 0 at any other degree, and in weight 6, the
Betti number is 0 at any degree.
