Software Using the Gröbner Cover for Geometrical Loci Computation and Classification

  • Miguel A. Abánades
  • Francisco Botana
  • Antonio Montes
  • Tomás Recio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)

Abstract

We describe here a properly recent application of the Gröbner Cover algorithm (GC) providing an algebraic support to Dynamic Geometry computations of geometrical loci. It provides a complete algebraic solution of locus computation as well as a suitable taxonomy allowing to distinguish the nature of the different components. We included a new algorithm Locus into the Singular grobcov.lib library for this purpose. A web prototype has been implemented using it in Geogebra.

Keywords

Locus Taxonomy Dynamical Geometry Groebner Cover 

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References

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    Abanades, M., Botana, F., Montes, A., Recio, T.: An Algebraic Taxonomy for Locus Computation in Dynamic Geometry. Computer Aided Design (to appear, 2014)Google Scholar
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    Montes, A.: Using Kapur-Sun-Wang algorithm for the Gröbner Cover. In: Sendra, R., Villarino, C. (eds.) Proceedings of EACA 2012, pp. 135–138. Universidad de Alcalá de Henares (2012)Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Miguel A. Abánades
    • 1
  • Francisco Botana
    • 2
  • Antonio Montes
    • 3
  • Tomás Recio
    • 4
  1. 1.Universidad Complutense de MadridSpain
  2. 2.Universidad de VigoSpain
  3. 3.Universitat Politècnica de CatalunyaSpain
  4. 4.Universidad de CantabriaSpain

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