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

Abstract

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.

Conferences on Intelligent Computer Mathematics, CICM 2013, 8-12 July 2013, Bath, UK 5 pages, 2 figures