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This paper gives an exposition of well known results on vector partitionfunctions. The exposition is based on works of M. Brion, A. Szenes and M.Vergne and is geared toward explicit computer realizations. In particular, thepaper presents two algorithms for computing the vector partition function withrespect to a finite set of vectors $I$ as a quasipolynomial over a finite setof pointed polyhedral cones. We use the developed techniques to relate a resultof P. Tumarkin and A. Felikson (and present an independent proof in theparticular case of finite-dimensional root systems) to give bounds for theperiods of the Kostant partition functions of $E_6$, $E_7$, $E_8$, $F_4$, $G_2$(the periods are divisors of respectively 6, 12, 60, 12, 6).  The first of the described algorithms has been realized and is publiclyavailable under the Library General Public License v3.0 at{http://vectorpartition.sourceforge.net/}. We include (non-unique) partialfraction decompositions for the generating functions of the Kostant partitionfunction for $A_2$, $A_3$, $A_4$, $B_2$, $B_3$, $C_2$, $C_3$, $G_2$ in theappendix.

Partial fraction decompositions and an algorithm for computing the vector partition function