Elimination theory for differential difference polynomials

  • Authors:

  • E. L. Mansfield;A. Szanto

  • Affiliations:

  • University of Kent, Canterbury, United Kingdom;North Carolina State University, Raleigh, NC

  • Venue:
  • ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
  • Year:
  • 2003

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Abstract

In this paper we give an elimination algorithm for differential difference polynomial systems. We use the framework of a generalization of Ore algebras, where the independent variables are non-commutative. We prove that for certain term orderings, Buchberger's algorithm applied to differential difference systems terminates and produces a Gröbner basis. Therefore, differential-difference algebras provide a new instance of non-commutative graded rings which are effective Gröbner structures.