2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127135We prove a double-exponential upper bound on the degree and on the complexity of constructing a Janet basis of a $D$-module. This generalizes a well known bound on the complexity of a Gröbner basis of a module over the algebra of polynomials. We would like to emphasize that the obtained bound can not be immediately deduced from the commutative case.Analysis of PDEsRings and Algebras68W40text