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On the Need of Radical Ideals in Automatic Proving: A Theorem About Regular Polygons

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Automated Deduction in Geometry (ADG 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4869))

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Abstract

The paper deals with a problem of finding natural geometry problem, that is, not specifically built up for the only purpose of having some concrete property, where the hypothesis is not described by a radical ideal. This problem was posed by Chou long ago. Regular polygons in the Euclidean space E d and their existence in spaces of various dimensions are studied by the technique of Gröbner bases. When proving that regular pentagons and heptagons span spaces of even dimension one encounters the case that the ideal describing the hypotheses is not radical. Thus, in order to prove that \(H\Rightarrow T\) one needs to show that T belongs to the radical of the ideal describing H.

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Authors and Affiliations

  1. Pedagogical Faculty, University of South Bohemia, 371 15 České Budějovice, Czech Republic

    Pavel Pech

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  1. Pavel Pech
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Francisco Botana Tomas Recio

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Pech, P. (2007). On the Need of Radical Ideals in Automatic Proving: A Theorem About Regular Polygons. In: Botana, F., Recio, T. (eds) Automated Deduction in Geometry. ADG 2006. Lecture Notes in Computer Science(), vol 4869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77356-6_10

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  • DOI: https://doi.org/10.1007/978-3-540-77356-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77355-9

  • Online ISBN: 978-3-540-77356-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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