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Reasoning about Geometric Problems using an Elimination Method

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Automated Practical Reasoning

Part of the book series: Texts and Monographs in Symbolic Computation ((TEXTSMONOGR))

Abstract

The present work relates to a paper by (1991) in which he explained the reasoning about a set of selected, geometry-related problems by using the algebraic methods of characteristic sets (Ritt 1950; Wu 1984a, b), Gröbner bases (Buchberger 1985) and cylindrical algebraic decomposition (Collins 1975). Its main purpose is to demonstrate how to deal with the same set of geometric problems by using another algebraic method which is based on some elimination procedures proposed by (1993). We use the same formulations of the problems (with slight modifications when necessary) and the same set of illustrative examples given previously (Wang 1991). It is shown that for most of the examples our new method takes less computing time than the methods of characteristic sets and Gröbner bases do.

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Authors
  1. Dongming Wang
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Editors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes-Kepler-University Linz, Linz, Austria

    Jochen Pfalzgraf

  2. Laboratoire d’Informatique Fondamentale et d’Intelligence Artificielle, Institut National Polytechnique de Grenoble, Grenoble, France

    Dongming Wang

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© 1995 Springer-Verlag Wien

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Wang, D. (1995). Reasoning about Geometric Problems using an Elimination Method. In: Pfalzgraf, J., Wang, D. (eds) Automated Practical Reasoning. Texts and Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6604-8_8

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  • DOI: https://doi.org/10.1007/978-3-7091-6604-8_8

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82600-3

  • Online ISBN: 978-3-7091-6604-8

  • eBook Packages: Springer Book Archive

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