Resumen de Dealing with degeneracies in automated theorem proving in geometry: A zero-dimensional approach
Zoltán Kovács, Tomás Jesús Recio Muñiz, Luis Felipe Tabera Alonso, María Pilar Vélez Melón
In the presentation we will start by reporting, using various examples to present the current development in GeoGebra of geometric automated reasoning tools by means of computational algebraic geometry algorithms. "Ve will then introduce andanalyze the case of the degeneracy conditions that so often arise in the automated deduction in geometry context, proposing two different ways for dealing with them. The first is to work with the saturation of the hypotheses ideal with respect to the ring ofgeometrically independent variables, as a way to globally handle the statement over all non-degenerate components. The second is to consider the reformulation of the given hypotheses ideal considering the independent variables as invertible parameters, exploiting the specific properties of this zero-dimensional case to analyze the truth of the statement over each non-degenerate component.
