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Structural Gröbner Basis Detection

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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.

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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
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  2. Markus Wiegelmann
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Received: May 9, 1996; revised version: December 19, 1996

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

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

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