Dealing with degeneracies in automated theorem proving in geometryA zero-dimensional approach
- Zoltán Kovács 1
- Tomas Recio 2
- Tabera, Luis F. 3
- M. Pilar Vélez 2
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1
Private University College of Education of the Diocese of Linz
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Private University College of Education of the Diocese of Linz
Linz, Austria
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2
Universidad Nebrija
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3
Universidad de Cantabria
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- Galindo Pastor, Carlos (coord.)
- Gimenez, Philippe (coord.)
- Hernando Carrillo, Fernando (coord.)
- Monserrat Delpalillo, Francisco José (coord.)
- Moyano-Fernández, Julio José (coord.)
Argitaletxea: Servei de Comunicació i Publicacions ; Universitat Jaume I
ISBN: 978-84-19647-46-7
Argitalpen urtea: 2023
Orrialdeak: 111-114
Biltzarra: Encuentro de Álgebra Computacional y Aplicaciones (17. 2022. Castelló de la Plana)
Mota: Biltzar ekarpena
Laburpena
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.