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Reduced Gröbner Bases in Polynomial Rings over a Polynomial Ring

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Abstract.

We propose a new notion of reduced Gröbner bases in polynomial rings over a polynomial ring and we show that every ideal has a unique reduced Gröbner basis. We introduce an algorithm for computing them.

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Authors and Affiliations

  1. Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Katsusuke Nabeshima

  2. Research Institute for Symbolic Computation (RISC-Linz), Johannes Kepler Universität Linz, Altenberger Straße 69, A-4040, Linz, Austria (until September 2007)

    Katsusuke Nabeshima

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  1. Katsusuke Nabeshima
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Correspondence to Katsusuke Nabeshima.

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Nabeshima, K. Reduced Gröbner Bases in Polynomial Rings over a Polynomial Ring. Math.Comput.Sci. 2, 587–599 (2009). https://doi.org/10.1007/s11786-008-0060-8

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  • DOI: https://doi.org/10.1007/s11786-008-0060-8

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