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Software Using the Gröbner Cover for Geometrical Loci Computation and Classification

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Mathematical Software – ICMS 2014 (ICMS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8592))

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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.

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References

  1. Abanades, M., Botana, F., Montes, A., Recio, T.: An Algebraic Taxonomy for Locus Computation in Dynamic Geometry. Computer Aided Design (to appear, 2014)

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  2. Kapur, D., Sun, Y., Wang, D.: A new algorithm for computing comprehensive Gröbner systems. In: Proceedings of ISSAC 2010, pp. 29–36. ACM Press, New York (2010)

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  3. Botana, F.: Locus Prototype (2012), http://webs.uvigo.es/fbotana/LocusGC/

  4. 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)

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  5. Montes, A., Wibmer, M.: Gröbner bases for polynomial systems with parameters. Jour. Symb. Comp. 45, 1391–1425 (2010)

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  6. Wibmer, M.: Gröbner bases for families of affine or projective schemes. Jour. Symb. Comp. 42, 803–834 (2007)

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  7. Singular, http://www.singular.uni-kl.de/ (last accessed February 2014)

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Author information

Authors and Affiliations

  1. Universidad Complutense de Madrid, Spain

    Miguel A. Abánades

  2. Universidad de Vigo, Spain

    Francisco Botana

  3. Universitat Politècnica de Catalunya, Spain

    Antonio Montes

  4. Universidad de Cantabria, Spain

    Tomás Recio

Authors
  1. Miguel A. Abánades
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  2. Francisco Botana
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  3. Antonio Montes
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  4. Tomás Recio
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Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Box 8205, 27695, Raleigh, NC, USA

    Hoon Hong

  2. Courant Institute, Dept. of Computer Science, New York Institute, 251 Mercer Street, 10012, New York, NY, USA

    Chee Yap

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© 2014 Springer-Verlag Berlin Heidelberg

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Abánades, M.A., Botana, F., Montes, A., Recio, T. (2014). Software Using the Gröbner Cover for Geometrical Loci Computation and Classification. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_74

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  • DOI: https://doi.org/10.1007/978-3-662-44199-2_74

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44198-5

  • Online ISBN: 978-3-662-44199-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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