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A dynamic symbolic geometry environment based on the GröbnerCover algorithm for the computation of geometric loci and envelopes. (English) Zbl 1390.68774
Carette, Jacques (ed.) et al., Intelligent computer mathematics. MKM, Calculemus, DML, and systems and projects 2013, held as part of CICM 2013, Bath, UK, July 8–12, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-39319-8/pbk). Lecture Notes in Computer Science 7961. Lecture Notes in Artificial Intelligence, 349-353 (2013).
Summary: 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.
For the entire collection see [Zbl 1268.68008].

68W30 Symbolic computation and algebraic computation
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