2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77383We present an algorithm to compute the action of the Hecke operators on the top dimensional integral cohomology of certain torsion-free arithmetic subgroups of algebraic groups of Q-rank one. This generalizes the modular symbol algorithm to a setting including Bianchi groups and Hilbert modular groups. In addition, we generalize some results of Voronoi for real positive-definite quadratic forms to self-adjoint homogeneous cones of arbitrary Q-rank.19 pages, 5 figures, AMS-LaTeX, uses psfrag.sty, to appear in Journal of Number TheoryNumber Theory11F75text