2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144676Differential invariants of a (pseudo)group action can vary when restricted to invariant submanifolds (differential equations). The algebra is still governed by the Lie-Tresse theorem, but may change a lot. We describe in details the case of the motion group $O(n)\ltimes\R^n$ acting on the full (unconstraint) jet-space as well as on some invariant equations.Differential Geometrytext