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On the complexity of the Gröbner-bases algorithm over K[x,y,z]

  • Franz Winkler
Groebner Basis Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 174)

Abstract

In /Bu65/, /Bu70/, /Bu76/ B. Buchberger presented an algorithm which, given a basis for an ideal in K[x1,...,xn] (the ring of polynomials in n indeterminates over the field K), constructs a so-called Gröbner-basis for the ideal. The importance of Gröbner-bases for effectively carrying out a large number of construction and decision problems in polynomial ideal theory has been investigated in /Bu65/, /Wi78/, /WB81/, /Bu83b/. For the case of two variables B. Buchberger /Bu79/, /Bu83a/ gave bounds for the degrees of the polynomials which are generated by the Gröbner-bases algorithm. However, no bound has been known until now for the case of more than two variables. In this paper we give such a bound for the case of three variables.

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References

  1. /Bu65/.
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Franz Winkler
    • 1
  1. 1.Institut für Mathematik Arbeitsgruppe CAMPJohannes Kepler UniversitätLinzAustria

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