Signature-based algorithms to compute Gröbner bases

  • Authors:

  • Christian Eder;John Edward Perry

  • Affiliations:

  • Universitat Kaiserslautern, Kaiserslautern, Germany;University of Southern Mississippi, Hattiesburg, MS, USA

  • Venue:
  • Proceedings of the 36th international symposium on Symbolic and algebraic computation
  • Year:
  • 2011

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Abstract

Abstract This paper describes a Buchberger-style algorithm to compute a Gröbner basis of a polynomial ideal, allowing for a selection strategy based on "signatures". We explain how three recent algorithms can be viewed as different strategies for the new algorithm, and how other selection strategies can be formulated. We describe a fourth as an example. We analyze the strategies both theoretically and empirically, leading to some surprising results.