Bounds and algebraic algorithms in differential algebra: the ordinary case

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

doi:10.4230/DagSemProc.06271.4

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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

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 6271
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2007-05-21

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DOI: 10.4230/DagSemProc.06271.4
URN: urn:nbn:de:0030-drops-10219

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Keywords

Differential algebra
Rosenfeld Groebner Algorithm

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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.

Cite As Get BibTex

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

Author Details

Marc Moreno Maza

Oleg Golubitsky

Marina V. Kondratieva

Alexey Ovchinnikov

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