RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra i Analiz, 2008, Volume 20, Issue 5, Pages 41–82 (Mi aa530)  

This article is cited in 1 scientific paper (total in 1 paper)

Research Papers

Complexity of the Standard Basis of a $D$-Module

D. Yu. Grigorieva, A. L. Chistovb

a CNRS, IRMAR, Université de Rennes, Rennes, France
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: A double-exponential upper bound is obtained for the degree and for the complexity of constructing a standard basis of a $D$-module. This generalizes a well-known bound for the complexity of a Gröbner basis of a module over the algebra of polynomials. It should be emphasized that the bound obtained cannot be deduced immediately from the commutative case. To get the bound in question, a new technique is elaborated for constructing all the solutions of a linear system over a homogeneous version of a Weyl algebra.

Keywords: Weyl algebra, Janet basis, Gröbner basis

Full text: PDF file (499 kB)
References: PDF file   HTML file

English version:
St. Petersburg Mathematical Journal, 2009, 20:5, 709–736

Bibliographic databases:

MSC: 16Z05
Received: 30.03.2007

Citation: D. Yu. Grigoriev, A. L. Chistov, “Complexity of the Standard Basis of a $D$-Module”, Algebra i Analiz, 20:5 (2008), 41–82; St. Petersburg Math. J., 20:5 (2009), 709–736

Citation in format AMSBIB
\Bibitem{GriChi08}
\by D.~Yu.~Grigoriev, A.~L.~Chistov
\paper Complexity of the Standard Basis of a~$D$-Module
\jour Algebra i Analiz
\yr 2008
\vol 20
\issue 5
\pages 41--82
\mathnet{http://mi.mathnet.ru/aa530}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2492359}
\zmath{https://zbmath.org/?q=an:1206.16050}
\transl
\jour St. Petersburg Math. J.
\yr 2009
\vol 20
\issue 5
\pages 709--736
\crossref{https://doi.org/10.1090/S1061-0022-09-01069-3}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000270134200003}


Linking options:
  • http://mi.mathnet.ru/eng/aa530
  • http://mi.mathnet.ru/eng/aa/v20/i5/p41

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Shibuta T., Tajima Sh., “An Algorithm For Computing the Truncated Annihilating Ideals For An Algebraic Local Cohomology Class”, Computer Algebra in Scientific Computing, Casc 2014, Lecture Notes in Computer Science, 8660, eds. Gerdt V., Koepf W., Seiler W., Vorozhtsov E., Springer-Verlag Berlin, 2014, 447–459  crossref  mathscinet  zmath  isi
  • Алгебра и анализ St. Petersburg Mathematical Journal
    Number of views:
    This page:195
    Full text:51
    References:41
    First page:17

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017