Skip to main content
Springer Nature Link
Log in

Structural Gröbner Basis Detection

  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

 We determine the computational complexity of deciding whether m polynomials in n variables have relatively prime leading terms with respect to some term order. This problem in NP-complete in general, but solvable in polynomial time in two different situations, when m is fixed and when n−m is fixed. Our new algorithm for the second case determines a candidate set of leading terms by solving a maximum matching problem. This reduces the problem to linear programming.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA 94720, USA (e-mail: bernd@math.berkeley.edu), , , , , , US

    Bernd Sturmfels

  2. Fachbereich Mathematik, Universität Trier, Universitätsring, 15, D-54286 Trier, Germany (e-mail: wiegelm@uni-trier.de), , , , , , DE

    Markus Wiegelmann

Authors
  1. Bernd Sturmfels
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Markus Wiegelmann
    View author publications

    You can also search for this author inPubMed Google Scholar

Additional information

Received: May 9, 1996; revised version: December 19, 1996

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sturmfels, B., Wiegelmann, M. Structural Gröbner Basis Detection. AAECC 8, 257–263 (1997). https://doi.org/10.1007/s002000050063

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002000050063