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Automatic Discovery of Geometry Theorems Using Minimal Canonical Comprehensive Groebner Systems
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.Comment: 25 pages, 8 figure