Canonical representatives for residue classes of a polynomial ideal

  • Authors:

  • Markus Lauer

  • Affiliations:

  • -

  • Venue:
  • SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
  • Year:
  • 1976

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Abstract

At the EUROSAM Conference 1974 it was conjectured that there exist probably no canonical forms for polynomial expressions under polynomial side relations. In 1965, however, Buchberger had already implemented a reduction algorithm solving the problem over fields. Positive results were also attained independently since 1974 by R. Shtokhamer and the author. In this note a general theorem on canonical representatives is obtained and by application to Buchberger's and Shtokhamer's algorithms it is proven that the stated problem is solved.