A criterion for detecting unnecessary reductions in the construction of Gröbner-bases

  • B. Buchberger
1. Simplification
Part of the Lecture Notes in Computer Science book series (LNCS, volume 72)


We present a new criterion that may be applied in an algorithm for constructing Gröbner-bases of polynomial ideals. The application of the criterion may drastically reduce the number of reductions of polynomials in the course of the algorithm. Incidentally, the new criterion allows to derive a realistic upper bound for the degrees of the polynomials in the Gröbner-bases computed by the algorithm in the case of polynomials in two variables.


Polynomial Ideal Algorithmic Construction Common Multiple Termination Proof Residue Class Ring 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • B. Buchberger
    • 1
  1. 1.Institut für Mathematik Johannes-Kepler-UniversitätLinzAustria

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