A Symbolic Companion for Interactive Geometric Systems
We consider the problem of enriching a dynamic geometry system with new features from the field of Automated Deduction in Geometry. A prototype based on Sage, sagemath.org, that extends the current capabilities of the interactive environment GeoGebra, geogebra.org, is presented. The prototype provides a deeper knowledge of the different geometric objects in a construction. More precisely, an algebraic symbolic approach based on Groebner Bases is followed to implement a substitute for the numerical approach for property checking and locus plotting used by GeoGebra. As a result the system provides a certified answer in the case of a geometric query or the algebraic equation of the locus in the case of a locus construction. Note that knowing the equation of a locus is necessary to derive new geometric objects from the locus.