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A software tool for the investigation of plane loci

Author

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  • Botana, F.
  • Valcarce, J.L.

Abstract

We describe the capabilities of Lugares for obtaining the equations and graphs of plane loci. Lugares is a Windows program written in Prolog that offers a standard dynamic geometry environment and uses the symbolic capabilities of CoCoA, a computer algebra system specialized in Groebner basis computations, or Mathematica. The main novelty in Lugares consists of the link between the dynamic geometry paradigm and a symbolic approach to automatic discovery in geometry. Through this link Lugares determines as a locus almost any algebraic curve specified by geometric conditions.

Suggested Citation

  • Botana, F. & Valcarce, J.L., 2003. "A software tool for the investigation of plane loci," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(2), pages 139-152.
    • Handle: RePEc:eee:matcom:v:61:y:2003:i:2:p:139-152
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    Cited by:

    1. Botana, Francisco & Valcarce, José L., 2004. "Automatic determination of envelopes and other derived curves within a graphic environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 67(1), pages 3-13.
    2. Montes, Antonio & Recio, Tomás, 2014. "Generalizing the Steiner–Lehmus theorem using the Gröbner cover," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 104(C), pages 67-81.
    3. Escribano, Jesús & Botana, Francisco & Abánades, Miguel A., 2010. "Adding remote computational capabilities to Dynamic Geometry Systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(6), pages 1177-1184.
    4. Roanes-Lozano, Eugenio & van Labeke, Nicolas & Roanes-Macías, Eugenio, 2010. "Connecting the 3D DGS Calques3D with the CAS Maple," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(6), pages 1153-1176.
    5. Botana, Francisco, 2014. "A parametric approach to 3D dynamic geometry," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 104(C), pages 3-20.

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