Dealing with Degeneracies in Automated Theorem Proving in Geometry

We report, through different examples, the current development in GeoGebra, a widespread Dynamic Geometry software, of geometric automated reasoning tools by means computational algebraic geometry algorithms. Then we introduce and analyze case degeneracy conditions that so often arise deduction context, proposing two ways for dealing with them. One is working saturation hypotheses ideal respect to ring geometrically independent variables, as way globally handle statement over all non-degenerate components. The second considering reformulation given ideal—considering variables invertible parameters—and developing exploiting specific properties this zero-dimensional individually truth