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URN: urn:nbn:de:0030-drops-10219
URL: http://drops.dagstuhl.de/opus/volltexte/2007/1021/

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

Bounds and algebraic algorithms in differential algebra: the ordinary case

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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.

BibTeX - Entry

@InProceedings{morenomaza_et_al:DSP:2007:1021,
  author =	{Marc Moreno Maza and Oleg Golubitsky and Marina V. Kondratieva and Alexey Ovchinnikov},
  title =	{Bounds and algebraic algorithms in differential algebra: the ordinary case},
  booktitle =	{Challenges in Symbolic Computation Software},
  year =	{2007},
  editor =	{Wolfram Decker and Mike Dewar and Erich Kaltofen and Stephen Watt },
  number =	{06271},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2007/1021},
  annote =	{Keywords: Differential algebra, Rosenfeld Groebner Algorithm}
}

Keywords: Differential algebra, Rosenfeld Groebner Algorithm
Seminar: 06271 - Challenges in Symbolic Computation Software
Issue date: 2007
Date of publication: 21.05.2007


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