License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.06271.4
URN: urn:nbn:de:0030-drops-10219
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2007/1021/
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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:DagSemProc.06271.4,
  author =	{Moreno Maza, Marc and Golubitsky, Oleg and Kondratieva, Marina V. and Ovchinnikov, Alexey},
  title =	{{Bounds and algebraic algorithms in differential algebra: the ordinary case}},
  booktitle =	{Challenges in Symbolic Computation Software},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{6271},
  editor =	{Wolfram Decker and Mike Dewar and Erich Kaltofen and Stephen Watt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2007/1021},
  URN =		{urn:nbn:de:0030-drops-10219},
  doi =		{10.4230/DagSemProc.06271.4},
  annote =	{Keywords: Differential algebra, Rosenfeld Groebner Algorithm}
}

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

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