Automatic Discovery of Geometry Theorems Using Minimal Canonical Comprehensive Gröbner Systems

The main proposal in this paper is the merging of two techniques that have been recently developed. On the one hand, we consider a new approach for computing some specializable Grobner basis, the so called Minimal Canonical Comprehensive Grobner Systems (MCCGS) that is -roughly speaking- a computational procedure 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 is related to automatic theorem discovery in elementary geometry. Automatic discovery aims to obtain complementary (equality and inequality type) 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.

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