Modular methods are effective ways to control intermediate expression swell. In a joint work by X. Dahan, M. Moreno Maza, E. Schost, W. Wu and myself, we discovered a new way of encoding the solution set of a non-linear system with finitely many solutions; we call it the equiprojectable decomposition. Its computational properties lead us to a sharp modular method and our experimentation shows the capacity of this approach to solve problems out of reach of other symbolic solvers. When studying the complexity of this method, we show how asymptotically fast algorithms for polynomials over fields can be adapted to more general domains with potential of automatic case discussion.