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International Conference on Intelligent Computer Mathematics

CICM 2011: Intelligent Computer Mathematics pp 45–57Cite as

Proof Assistant Decision Procedures for Formalizing Origami

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 6824)

Abstract

Origami constructions have interesting properties that are not covered by standard euclidean geometry. Such properties have been shown with the help of computer algebra systems. Proofs performed with computer algebra systems can be accompanied by proof documents, still they lack complete mathematical rigorousity, like the one provided by proof assistant checked proofs. Transforming such proofs to machine checkable proof scripts poses a number of challenges.

In this paper we describe issues that arise when proving properties of origami constructions using proof assistant decision procedures. We examine the strength of Gröbner Bases implementations comparing proof assistants with each other and with the implementations provided in computer algebra systems. We show ad-hoc decision procedures that can be used to optimize the proofs. We show how maximum equilateral triangle inscribed in a square construction can be formalized. We show how a equation system solving mechanism can be embedded in a CAS decision procedure of a proof assistant.

Keywords

  • Decision Procedure
  • Equilateral Triangle
  • Computer Algebra
  • Computer Algebra System
  • Linear Factor

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • DOI: 10.1007/978-3-642-22673-1_4
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Author information

Authors and Affiliations

  1. Symbolic Computation Research Group, University of Tsukuba, Japan

    Cezary Kaliszyk & Tetsuo Ida

Authors
  1. Cezary Kaliszyk
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  2. Tetsuo Ida
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Editor information

Editors and Affiliations

  1. Departments of Computer Science and Mathematics Sciences, University of Bath, BA2 7AY, United Kingdom

    James H. Davenport

  2. Department of Computing and Software, McMaster University, 1280 Main Street West, L8SK1, Hamilton, Ontario, Canada

    William M. Farmer

  3. Institute for Computing and Information Sciences, Radboud University, Heyendaalseweg 135, 6525 AJ, Nijmegen, The Netherlands

    Josef Urban

  4. Department of Computer Science, Jacobs University Bremen, Campus Ring 12, 28759, Bremen, Germany

    Florian Rabe

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Kaliszyk, C., Ida, T. (2011). Proof Assistant Decision Procedures for Formalizing Origami. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds) Intelligent Computer Mathematics. CICM 2011. Lecture Notes in Computer Science(), vol 6824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22673-1_4

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  • DOI: https://doi.org/10.1007/978-3-642-22673-1_4

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  • Print ISBN: 978-3-642-22672-4

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