2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129474This paper presents an algorithm to compute the value of the inverse Laplace transforms of rational functions with poles on arrangements of hyperplanes. As an application, we present an efficient computation of the partition function for classical root systems.55 pages, 14 figures. Maple programs available at http://www.math.polytechnique.fr/~vergne/work/IntegralPoints.htmlCombinatoricsRepresentation Theory52C07, 17B20; 05A15text