2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167334We describe an algorithm to decompose rational functions from which we determine the poset of groups fixing these functions.25 pages, 2 data tables; to be published in LMS Journal of Computation and Mathematics. v2: page format adjustmentNumber TheorySymbolic ComputationRepresentation Theory11F11, 30F35 (Primary); 68W30 (Secondary)text