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Experiments on Automatic Inclusion of Some Non-degeneracy Conditions Among the Hypotheses in Locus Equation Computations

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Intelligent Computer Mathematics (CICM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11617))

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Abstract

In automated reasoning in geometry, in particular in computing locus equations, degenerate components usually play an important role. Although degeneracy may have multiple meanings by considering different mathematical traditions, avoiding degenerate components is useful from the geometrical point of view.

Computation of locus equations is usually based on elimination of variables. In most cases the graphical output is checked after the computations and then the degenerate components will be removed manually. In our experiments we prescribe non-degeneracy before starting any computations and expect disappearing of the degenerate components automatically.

In this paper we investigate if such assumptions may be automatized, and if they can help in improving the output by getting the degenerate components automatically removed, and whether the calculation is still feasible due to the higher amount of computations. Our experiments have already been tried in an implementation of our algorithm in GeoGebra 5.0.524.0.

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Notes

  1. 1.

    Frame per second.

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Acknowledgments

We are thankful to Tomás Recio for his numerous suggestions on improving this paper. The first author was partially supported by a grant MTM2017-88796-P from the Spanish MINECO (Ministerio de Economia y Competitividad) and the ERDF (European Regional Development Fund).

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Authors and Affiliations

  1. The Private University College of Education of the Diocese of Linz, Salesianumweg 3, 4020, Linz, Austria

    Zoltán Kovács

  2. Faculty of Education, University of South Bohemia, Jeronýmova 10, 370 01, České Budějovice, Czech Republic

    Pavel Pech

Authors
  1. Zoltán Kovács
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  2. Pavel Pech
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Corresponding author

Correspondence to Zoltán Kovács .

Editor information

Editors and Affiliations

  1. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  2. University of St. Andrews, St. Andrews, UK

    Edwin Brady

  3. University of Applied Sciences, Neu-Ulm, Germany

    Andrea Kohlhase

  4. University of Bologna, Bologna, Italy

    Claudio Sacerdoti Coen

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Kovács, Z., Pech, P. (2019). Experiments on Automatic Inclusion of Some Non-degeneracy Conditions Among the Hypotheses in Locus Equation Computations. In: Kaliszyk, C., Brady, E., Kohlhase, A., Sacerdoti Coen, C. (eds) Intelligent Computer Mathematics. CICM 2019. Lecture Notes in Computer Science(), vol 11617. Springer, Cham. https://doi.org/10.1007/978-3-030-23250-4_10

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  • DOI: https://doi.org/10.1007/978-3-030-23250-4_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-23249-8

  • Online ISBN: 978-3-030-23250-4

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