On the Parametric Representation of Dynamic Geometry Constructions

This paper describes an ongoing implementation of an open source library dealing with parametric representation of dynamic geometry constructions. We show how some current issues in standard dynamic geometry environments, such as computing envelopes of lines which are not primitive objects known by the geometric system, can be efficiently solved using the correspondence between geometry and algebra. We also propose enriching the tool (or macro) mechanism, available in some environments, with our parametric approach. Finally, some problems arising from the algebraic method considered are also studied.