期刊
MATHEMATICS
卷 9, 期 16, 页码 -出版社
MDPI
DOI: 10.3390/math9161964
关键词
automated theorem proving in geometry; automated deduction in geometry; automated reasoning in geometry; Dynamic Geometry; GeoGebra; computational algebraic geometry
类别
资金
- Spanish MICINN [PID2020-113192GB-I00]
The study focuses on the development of geometric automated reasoning tools in GeoGebra software through computational algebraic geometry algorithms. It introduces two different ways for dealing with the degeneracy conditions that often arise in geometry context.
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.
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