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A dynamic symbolic geometry environment based on the GröbnerCover algorithm for the computation of geometric loci and envelopes

An enhancement of the dynamic geometry system GeoGebra for the automatic symbolic computation of algebraic loci and envelopes is presented. Given a GeoGebra construction, the prototype, after rewriting the construction as a polynomial system in terms of variables and parameters, uses an implementation of the recent GröbnerCover algorithm to obtain the algebraic description of the sought locus/envelope as a locally closed set. The prototype shows the applicability of these techniques in general purpose dynamic geometry systems.

preprint2013arXivOpen access
Miguel A. AbánadesFrancisco Botana
math.AG
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Open access2 authors1 topic
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Miguel A. AbánadesFrancisco Botana

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