  We apply some recent developments of Baldoni-Beck-Cochet-Vergne on vector
partition function, to Kostant's and Steinberg's formulae, for classical Lie
algebras $A\_r$, $B\_r$, $C\_r$, $D\_r$. We therefore get efficient {\tt Maple}
programs that compute for these Lie algebras: the multiplicity of a weight in
an irreducible finite-dimensional representation; the decomposition
coefficients of the tensor product of two irreducible finite-dimensional
representations. These programs can also calculate associated Ehrhart
quasipolynomials.
