Universal characteristic decomposition of radical differential ideals

We call a differential ideal universally characterizable, if it is characterizable w.r.t. any ranking on partial derivatives. We propose a factorization-free algorithm that represents a radical differential ideal as a finite intersection of universally characterizable ideals. The algorithm also constructs a universal characteristic set for each universally characterizable component, i.e., a finite set of differential polynomials that contains a characterizing set of the ideal w.r.t. any ranking. As a part of the proposed algorithm, the following problem of satisfiability by a ranking is efficiently solved: given a finite set of differential polynomials with a derivative selected in each polynomial, determine whether there exists a ranking w.r.t. which the selected derivatives are leading derivatives and, if so, construct such a ranking.