Using Maple’s RegularChains Library to Automatically Classify Plane Geometric Loci

  • Francisco Botana
  • Tomás Recio
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)

Abstract

We report a preliminary discussion on the usability of the RegularChains library of Maple for the automatic computation of plane geometric loci and envelopes in graphical interactive environments. We describe a simple implementation of a recently proposed taxonomy of algebraic loci, and its extension to envelopes of families of curves is also discussed. Furthermore, we sketch how currently unsolvable problems in interactive environments can be approached by using the RegularChains library.

Keywords

parametrical systems solving constructible sets dynamic geometry 

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References

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    Botana, F., Valcarce, J.: A Software Tool for the Investigation of Plane. Loci. Math. Comput. Simul. 61, 139–152 (2003)CrossRefMATHMathSciNetGoogle Scholar
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    Abánades, M., Botana, F., Montes, A., Recio, T.: An Algebraic Taxonomy for Loci Computation in Dynamic Geometry. Comput. Aided Des. (submitted, 2014)Google Scholar
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    Montes, A., Wibmer, M.: Gröbner Bases for Polynomial Systems with Parameters. J. Symb. Comput. 45, 1391–1425 (2010)CrossRefMATHMathSciNetGoogle Scholar
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    Abánades, M.A., Botana, F., Montes, A., Recio, T.: Software Using the Gröbner Cover for Geometrical Loci Computation and Classification. In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 492–499. Springer, Heidelberg (2014)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Francisco Botana
    • 1
  • Tomás Recio
    • 2
  1. 1.Universidad de VigoSpain
  2. 2.Universidad de CantabriaSpain

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