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

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Symbolic and Algebraic Computation (EUROSAM 1979)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 72))

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Abstract

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.

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References

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Authors and Affiliations

  1. Institut für Mathematik Johannes-Kepler-Universität, A-4045, Linz, Austria

    B. Buchberger

Authors
  1. B. Buchberger
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Editor information

Edward W. Ng

Additional information

Dedicated to the 80th birthday of Prof. W. Gröbner

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© 1979 Springer-Verlag Berlin Heidelberg

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Buchberger, B. (1979). A criterion for detecting unnecessary reductions in the construction of Gröbner-bases. In: Ng, E.W. (eds) Symbolic and Algebraic Computation. EUROSAM 1979. Lecture Notes in Computer Science, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09519-5_52

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  • DOI: https://doi.org/10.1007/3-540-09519-5_52

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09519-4

  • Online ISBN: 978-3-540-35128-3

  • eBook Packages: Springer Book Archive

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