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Dealing with degeneracies in automated theorem proving in geometry

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

 Fuente: Mathematics, 2021, 9(16), 1964

 Editorial: MDPI

 Año de publicación: 2021

 Nº de páginas: 17

 Tipo de publicación: Artículo de Revista

 DOI: 10.3390/math9161964

 ISSN: 2227-7390

 Proyecto español: PID2020-113192GB-I00

 Url de la publicación: https://doi.org/10.3390/math9161964

Autoría

KOVÁCS, ZOLTÁN

TOMAS JESUS RECIO MUÑIZ

VÉLEZ, M. PILAR