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Simulating Buchberger's algorithm by Knuth-Bendix completion

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Rewriting Techniques and Applications (RTA 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 488))

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Abstract

We present a canonical term rewriting system whose initial model is isomorphic to GF(q)[x 1,...,x n ]. Using this set of rewrite rules and additional ground equations specifying an ideal we can simulate Buchberger's algorithm for polynomials over finite fields using Knuth-Bendix term completion modulo AC. In order to simplify our proofs we exhibit a critical pair criterion which transforms critical pairs into simpler ones.

This work is part of the Ph.D. research of the author supervised by Prof. R. Loos.

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Authors and Affiliations

  1. Wilhelm-Schickard-Institut, Universität Tübingen, D-7400, Tübingen, Fed. Rep. of Germany

    Reinhard Bündgen

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  1. Reinhard Bündgen
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Ronald V. Book

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© 1991 Springer-Verlag Berlin Heidelberg

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Bündgen, R. (1991). Simulating Buchberger's algorithm by Knuth-Bendix completion. In: Book, R.V. (eds) Rewriting Techniques and Applications. RTA 1991. Lecture Notes in Computer Science, vol 488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53904-2_112

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  • DOI: https://doi.org/10.1007/3-540-53904-2_112

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53904-9

  • Online ISBN: 978-3-540-46383-2

  • eBook Packages: Springer Book Archive

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