An extension of buchberger's algorithm to compute all reduced gröbner bases of a polynomial ideal

  • Klaus-Peter Schemmel
Polynomial Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 378)


In this paper we present for the bivariate case an algorithm to compute all possible reduced Gröbner bases of a polynomial ideal. This algorithm is an extension of Buchberger's one, which is based on the possibility to classify and to handle easy all term orderings in case of two variables. The constructed algorithm is interesting for the study of complexity of constructing Gröbner bases in dependence of the chosen term ordering and may lead to new insights on the question which is the best term ordering for quick termination.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Klaus-Peter Schemmel
    • 1
  1. 1.Department of MathematicsUniversity of Technology DresdenGDR

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