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

  • Polynomial Algorithms
  • Conference paper
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Eurocal '87 (EUROCAL 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 378))

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Abstract

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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References

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Remark

  • Mora,F. and Robbiano,L. (1987), The Gröbner Fan of an Ideal, preprint.

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  • Weispfenning,V. (1987), Constructing universal Gröbner bases, extended abstract.

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Authors and Affiliations

  1. Department of Mathematics, University of Technology Dresden, GDR

    Klaus-Peter Schemmel

Authors
  1. Klaus-Peter Schemmel
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Editor information

James H. Davenport

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© 1989 Springer-Verlag Berlin Heidelberg

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Schemmel, KP. (1989). An extension of buchberger's algorithm to compute all reduced gröbner bases of a polynomial ideal. In: Davenport, J.H. (eds) Eurocal '87. EUROCAL 1987. Lecture Notes in Computer Science, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51517-8_130

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  • DOI: https://doi.org/10.1007/3-540-51517-8_130

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51517-3

  • Online ISBN: 978-3-540-48207-9

  • eBook Packages: Springer Book Archive

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