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Bounds and algebraic algorithms in differential algebra: the ordinary case

Authors Marc Moreno Maza, Oleg Golubitsky, Marina V. Kondratieva, Alexey Ovchinnikov



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Author Details

Marc Moreno Maza
Oleg Golubitsky
Marina V. Kondratieva
Alexey Ovchinnikov

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Marc Moreno Maza, Oleg Golubitsky, Marina V. Kondratieva, and Alexey Ovchinnikov. Bounds and algebraic algorithms in differential algebra: the ordinary case. In Challenges in Symbolic Computation Software. Dagstuhl Seminar Proceedings, Volume 6271, pp. 1-9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2007)
https://doi.org/10.4230/DagSemProc.06271.4

Abstract

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.
Keywords
  • Differential algebra
  • Rosenfeld Groebner Algorithm

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