2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106324We use a version of localization in equivariant cohomology for the norm-square of the moment map, described by Paradan, to give several weighted decompositions for simple polytopes. As an application, we study Euler-Maclaurin formulas.Revision: changed content of last theorem; corrected typosCombinatoricsSymplectic Geometry52B; 65B15; 53D20; 55N91text