In this paper, we give three theoretical and practical contributions for solving polynomial ODE or PDE systems. The first one is practical: an algorithm which improves the purely algebraic part of Rosenfeld-Gröbner. It is a variant of lextriangular but does not need any Gröbner basis computation. The second one is theoretical: a characterization of the output of Rosenfeld-Gröbner and a clarification of the relationship between algebraic and differential characteristic sets. The third one is theoretical as well as practical: an algorithm to compute canonical representatives of differential polynomials modulo regular differential ideals without any use of Gröbner bases.