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A Dynamic Symbolic Geometry Environment Based on the GröbnerCover Algorithm for the Computation of Geometric Loci and Envelopes

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Intelligent Computer Mathematics (CICM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7961))

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Abstract

An enhancement of the dynamic geometry system GeoGebra for the automatic symbolic computation of algebraic loci and envelopes is presented. Given a GeoGebra construction, the prototype, after rewriting the construction as a polynomial system in terms of variables and parameters, uses an implementation of the recent GröbnerCover algorithm to obtain the algebraic description of the sought locus/envelope as a locally closed set. The prototype shows the applicability of these techniques in general purpose dynamic geometry systems.

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References

  1. Botana, F., Valcarce, J.L.: A software tool for the investigation of plane loci. Mathematics and Computers in Simulation 61(2), 139–152 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Botana, F.: A symbolic companion for interactive geometric systems. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds.) Calculemus/MKM 2011. LNCS, vol. 6824, pp. 285–286. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. GeoGebra: http://www.geogebra.org (last accessed January 2013)

  4. JSXGraph: http://jsxgraph.org/ (last accessed January 2013)

  5. Gerhäuser, M., Wassermann, A.: Automatic calculation of plane loci using Gröbner bases and integration into a dynamic geometry system. In: Schreck, P., Narboux, J., Richter-Gebert, J. (eds.) ADG 2010. LNCS, vol. 6877, pp. 68–77. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Escribano, J., Botana, F., Abánades, M.A.: Adding remote computational capabilities to dynamic geometry systems. Mathematics and Computers in Simulation 80, 1177–1184 (2010)

    Article  MathSciNet  Google Scholar 

  7. Sendra, J.R., Sendra, J.: Algebraic analysis of offsets to hypersurfaces. Matematische Zeitschrift 234, 697–719 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  8. Montes, A., Wibmer, M.: Gröbner bases for polynomial systems with parameters. Journal of Symbolic Computation 45, 1391–1425 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Guzmán, M.: La experiencia de descubrir en Geometría. Nivola (2002)

    Google Scholar 

  10. Locus/Envelope Prototype: (2012), http://193.146.36.205:8080/GgbSageDirect/LocusEnvelope/

  11. Simple sagecell server: https://github.com/sagemath/sagecell (last accessed January 2013)

  12. Botana, F.: On the parametric representation of dynamic geometry constructions. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2011, Part IV. LNCS, vol. 6785, pp. 342–352. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. CES Felipe II, Universidad Complutense de Madrid, C/ Capitán 39, 28300, Aranjuez, Spain

    Miguel A. Abánades

  2. Depto. de Matemática Aplicada I, Universidad de Vigo, Campus A Xunqueira, 36005, Pontevedra, Spain

    Francisco Botana

Authors
  1. Miguel A. Abánades
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  2. Francisco Botana
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Editor information

Editors and Affiliations

  1. Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Jacques Carette

  2. School of Informatics, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, Scotland, UK

    David Aspinall

  3. School of Computer Science, University of Birmingham, Edgbaston, B15 2TT, Birmingham, UK

    Christoph Lange

  4. Faculty of Informatics, Department of Computer Graphics and Design, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic

    Petr Sojka

  5. Johannes Kepler University Linz (JKU), RISC, Altenberger Strasse 69, 4040, Linz, Austria

    Wolfgang Windsteiger

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Abánades, M.A., Botana, F. (2013). A Dynamic Symbolic Geometry Environment Based on the GröbnerCover Algorithm for the Computation of Geometric Loci and Envelopes. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds) Intelligent Computer Mathematics. CICM 2013. Lecture Notes in Computer Science(), vol 7961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39320-4_27

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  • DOI: https://doi.org/10.1007/978-3-642-39320-4_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39319-8

  • Online ISBN: 978-3-642-39320-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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