A software tool for the investigation of plane loci. 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.

References in zbMATH (referenced in 19 articles )

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  1. Baydaş, Şenay; Karakaş, Bülent: The cissoid of Diocles in the Lorentz-Minkowski plane (2019)
  2. Botana, Francisco: A parametric approach to 3D dynamic geometry (2014)
  3. Botana, Francisco; Abánades, Miguel A.: Automatic deduction in (dynamic) geometry: Loci computation (2014)
  4. Montes, Antonio; Recio, Tomás: Generalizing the Steiner-Lehmus theorem using the Gröbner cover (2014)
  5. Botana, Francisco: Computing bisectors in a dynamic geometry environment (2013)
  6. Botana, Francisco: A symbolic companion for interactive geometric systems (2011)
  7. Gerhäuser, Michael; Wassermann, Alfred: Automatic calculation of plane loci using Gröbner bases and integration into a dynamic geometry system (2011)
  8. Escribano, Jesús; Botana, Francisco; Abánades, Miguel A.: Adding remote computational capabilities to dynamic geometry systems (2010) ioport
  9. Roanes-Lozano, Eugenio; van Labeke, Nicolas; Roanes-Macías, Eugenio: Connecting the 3D DGS Calques3D with the CAS Maple (2010)
  10. Guven, Bulent: Using dynamic geometry software to gain insight into a proof (2008) MathEduc
  11. Pech, Pavel: Selected topics in geometry with classical vs. computer proving (2007)
  12. Botana, Francisco; Recio, Tomás: Towards solving the dynamic geometry bottleneck via a symbolic approach (2006)
  13. Botana, Francisco; Valcarce, José L.: Automated discovery in elementary extrema problems (2006)
  14. Botana, Francisco; Valcarce, José L.: Automatic determination of envelopes and other derived curves within a graphic environment (2004)
  15. Recio, T.; Botana, F.: Where the truth lies (in automatic theorem proving in elementary geometry) (2004)
  16. Botana, Francisco: A web-based intelligent system for geometric discovery (2003)
  17. Botana, Francisco: Automatic determination of algebraic surfaces as loci of points (2003)
  18. Botana, F.; Valcarce, J. L.: A software tool for the investigation of plane loci (2003)
  19. Botana, F.: Interactive versus symbolic approaches to plane loci generation in dynamic geometry environments (2002)