  We describe an essential improvement of our recent algorithm for computing
cohomology of Lie (super)algebra based on partition of the whole cochain
complex into minimal subcomplexes. We replace the arithmetic of rational
numbers or integers by a much cheaper arithmetic of a modular field and use the
inequality between the dimensions of cohomology H over any modular field F_p =
Z/pZ and over Q: dim H(F_p) >= dim H(Q). With this inequality we can, by
computing over arbitrary F_p, quickly find the (usually, rare) subcomplexes for
which dim H(F_p) > 0 and then carry out the full computation over Q within
these subcomplexes. We also present the results of application of the
corresponding C program to the Lie superalgebra of special vector fields
preserving an "odd-symplectic" structure on the (2|2)-dimensional
supermanifold. For this algebra, we found some new basis elements of the
cohomology in the trivial module.
