Using Maple’s RegularChains library to automatically classify plane geometric loci Francisco Botana 1 andTom´asRecio 2 1 Universidad de Vigo, Spain fbotana@uvigo.es, http://webs.uvigo.es/fbotana/ 2 Universidad de Cantabria, Spain tomas.recio@unican.es, http://www.recio.tk 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. 1 Introduction A Dynamic Geometry System (DGS) is a computer program that allows an accurate on–screen drawing of geometric diagrams and their interactive manip- ulation by mouse dragging or similar device. A key issue of these systems is their ability to display the trajectory of a point that depends on another one bound to a linear path, that is, a geometric locus. Traditionaly, DGS strategy to display loci consists of sampling the linear path and, for each sample, plotting the corresponding position of the locus point. Some ad–hoc heuristics are then applied to join contiguous points, ending with a visually continuous locus. A locus can be seen as the projection on the space of its coordinates of the surface defined by the problem constraints, and Gr¨obner based elimination was proposed as a technique to find algebraic knowledge about loci [1]. Nevertheless, since Zariski closures are obtained as result, loci equations can include spurious points, and complete 1–dimensional objects can even appear due to construction degeneracies. A finer analysis of loci problems can be done through a recently proposed taxonomy [2], and it has been implemented using the Gr¨obnerCover algorithm [3]. Here we describe an alternative implementation of the taxonomy using Maple’s RegularChains library. The results seem to be competitive when dealing with the above class of loci. Despite license problems can emerge when