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An algorithm for constructing gröbner bases from characteristic sets and its application to geometry

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Abstract

In Ritt's method, a prime ideal is given by a characteristic set. A characteristic set of a prime ideal is generally not a set of generators of this ideal. In this paper we present a simple algorithm for constructing Gröbner bases of a prime ideal from its characteristic set. We give a method for finding new theorems in geometry as an application of this algorithm.

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Author notes

  1. Jin-Gen Yang

    Present address: Department of Mathematics, Fudan University, Shanghai, China

Authors and Affiliations

  1. Institute for Computing Science, University of Texas at Austin, 78712, Austin, TX, USA

    Shang-Ching Chou

  2. Department of Mathematics, University of Texas at Austin, 78712, Austin, TX, USA

    William F. Schelter & Jin-Gen Yang

Authors
  1. Shang-Ching Chou
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  2. William F. Schelter
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  3. Jin-Gen Yang
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Additional information

Communicated by John E. Hopcroft.

The first author was supported by NSF Grants Nos. DCR-8503498 and CCR-8702108. The computer facility was supported by the NSF/CER Grant at the University of Texas.

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Chou, SC., Schelter, W.F. & Yang, JG. An algorithm for constructing gröbner bases from characteristic sets and its application to geometry. Algorithmica 5, 147–154 (1990). https://doi.org/10.1007/BF01840382

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  • DOI: https://doi.org/10.1007/BF01840382

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