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Gröbner bases in exterior algebra

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Abstract

We show that the Buchberger algorithm for commutative polynomials over a field may be generalised to an algebraic structure which embeds such polymomials, the exterior polynomial algebra, and which is a natural domain for linear geometry. In particular, those finite sets of exterior polynomials which induce confluent reduction relations are characterised, and a means of algorithmically constructing them from a given set presented. A distinguished subset of such bases consists of the exterior algebra version of Gröbner bases. We characterise such bases and demonstrate how to construct them algorithmically from a given finite set of exterior polynomials.

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  1. Department of Mathematics, University of Tasmania, G.P.O. Box 252C, 7001, Hobart, Tasmania, Australia

    Timothy Stokes

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  1. Timothy Stokes
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Stokes, T. Gröbner bases in exterior algebra. J Autom Reasoning 6, 233–250 (1990). https://doi.org/10.1007/BF00244487

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  • DOI: https://doi.org/10.1007/BF00244487

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