A Symbolic Companion for Interactive Geometric Systems

  • Francisco Botana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6824)


We consider the problem of enriching a dynamic geometry system with new features from the field of Automated Deduction in Geometry. A prototype based on Sage,, that extends the current capabilities of the interactive environment GeoGebra,, is presented. The prototype provides a deeper knowledge of the different geometric objects in a construction. More precisely, an algebraic symbolic approach based on Groebner Bases is followed to implement a substitute for the numerical approach for property checking and locus plotting used by GeoGebra. As a result the system provides a certified answer in the case of a geometric query or the algebraic equation of the locus in the case of a locus construction. Note that knowing the equation of a locus is necessary to derive new geometric objects from the locus.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Francisco Botana
    • 1
  1. 1.Departamento de Matemática Aplicada IUniversidad de VigoPontevedraSpain

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