Bounds and algebraic algorithms in differential algebra: the ordinary case
Marc Moreno Maza, Oleg Golubitsky, M. V. Kondratieva, Alexey Vital'evich Ovchinnikov · Dagstuhl Seminar Proceedings · 2006
Consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials. This algorithm inputs a system of differential polynomials and a ranking on derivatives and constructs finitely many regular systems equivalent to the original one. The property of regularity allows to check consistency of the systems and membership to the corresponding differential ideals. We propose a bound on the orders of derivatives occurring in all intermediate and final systems computed by the Rosenfeld-Groebner algorithm and outline its proof. We also reduce the problem of conversion of a regular decomposition of a radical differential ideal from one ranking to another to a purely algebraic problem.