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On One Method of Proving Inequalities in Automated Way

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Automated Deduction in Geometry (ADG 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6877))

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Abstract

The paper describes proving geometric inequalities in automated way without cell decomposition. Firstly an overview of known methods of proving inequalities is given including the method which is based on reduction of a conclusion polynomial to the canonical form modulo a hypotheses ideal. Then a parametrization method of proving geometric inequalities is introduced. Further a method of proving geometric inequalities which introduces an auxiliary polynomial is described.

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Author information

Authors and Affiliations

  1. Faculty of Education, University of South Bohemia, Jeronýmova 10, 371 15, České Budějovice, Czech Republic

    Pavel Pech

Authors
  1. Pavel Pech
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Editor information

Editors and Affiliations

  1. LSIIT, Pôle API, Boulevard Sébastien Brant, BP 10413, 67412, Illkirch Cédex, France

    Pascal Schreck  & Julien Narboux  & 

  2. Technische Universität München, Zentrum Mathematik (M10), Lehrstuhl für Geometrie und Visualisierung, Boltzmannstraße 3, 85748, Garching, Germany

    Jürgen Richter-Gebert

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Pech, P. (2011). On One Method of Proving Inequalities in Automated Way. In: Schreck, P., Narboux, J., Richter-Gebert, J. (eds) Automated Deduction in Geometry. ADG 2010. Lecture Notes in Computer Science(), vol 6877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25070-5_9

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  • DOI: https://doi.org/10.1007/978-3-642-25070-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25069-9

  • Online ISBN: 978-3-642-25070-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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