Automatic Discovery of Geometry Theorems Using Minimal Canonical Comprehensive Groebner Systems

Abstract

The main idea in this paper is merging two techniques that have been recently developed. On the one hand, we consider MCCGS, standing for Minimal Canonical Comprehensive Groebner Systems, a recently introduced computational tool yielding "good" bases for ideals of polynomials over a field depending on several parameters, that specialize "well", for instance, regarding the number of solutions for the given ideal, for different values of the parameters. The second ingredient concerns automatic theorem discovery in elementary geometry. Automatic discovery aims to obtain complementary hypotheses for a (generally false) geometric statement to become true. The paper shows how to use MCCGS for automatic discovering of theorems and gives relevant examples.