  We present an effective algorithm for computing the standard cohomology
spaces of finitely generated Lie (super) algebras over a commutative field K of
characteristic zero. In order to reach explicit representatives of some
generators of the quotient space Z^k/B^k of cocycles Z^k modulo coboundaries
B^k, we apply Groebner bases techniques (in the appropriate linear setting) and
take advantage of their strength. Moreover, when the considered Lie (super)
algebras enjoy a grading -- a case which often happens both in representation
theory and in differential geometry --, all cohomology spaces Z^k/B^k naturally
split up as direct sums of smaller subspaces, and this enables us, for higher
dimensional Lie (super) algebras, to improve the computer speed of
calculations. Lastly, we implement our algorithm in the Maple software and
evaluate its performances via some examples, most of which have several
applications in the theory of Cartan-Tanaka connections.
