Giac and GeoGebra – Improved Gröbner Basis Computations

Kovács, Zoltán; Parisse, Bernard

doi:10.1007/978-3-319-15081-9_7

Cited by 38 publications

(23 citation statements)

References 7 publications

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“…We refer, for precise details and examples to illustrate the difficulties and the adopted technical solutions, to the basic document [12] and, for recent updates, to [13,15] or [17]. The algorithms described in these papers are implemented in GeoGebra through the embedded computer algebra system Giac [18,19].…”

Section: Complicationsmentioning

confidence: 99%

Dealing with Degeneracies in Automated Theorem Proving in Geometry

et al. 2021

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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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Section: Complicationsmentioning

confidence: 99%

Dealing with Degeneracies in Automated Theorem Proving in Geometry

et al. 2021

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“…Since GeoGebra 4.4 fast solution of a system of equations in several variables is performed in a very efficient way because Giac uses an effective method to compute the Gröbner basis of a so-called polynomial ideal. Also, a related operation called elimination was done quickly enough to support real-time animation of symbolic locus visualizations (see KOVÁCS and PARISSE, 2015).…”

Section: Geogebra's Automated Reasoning Toolsmentioning

confidence: 99%

On a problem that was not interesting for Erdős

Kovács

2021

IGISP

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Estudamos um problema na geometria euclidiana elementar utilizando múltiplas abordagens. Concluímos que o estudo assistido por computador de hoje pode introduzir novos métodos para compreender melhor as relações e conceitos. Nomeadamente, usando as Ferramentas de Raciocínio Automático do GeoGebra, vários detalhes do problema original podem ser colocados em um contexto algébrico e, portanto, sua investigação automatizada é possível, em algum sentido, mecanicamente. Ainda assim, o pensamento criativo e a reformulação do problema em um cenário diferente continua sendo útil.

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“…That is, the current technical hierarchy allows using Maple/SyNRAC [12], Maple/RegularChains [6], and Reduce/Redlog [11] in the near future, but for the moment only Mathematica's [25] RQE subsystem, QEPCAD B [4,9] and Tarski [23] are available for the end user. GeoGebra internally uses the Giac computer algebra system to perform symbolic computations [17].…”

Section: Multiple Ways For Users To Enter Inputmentioning

confidence: 99%

Supporting Proving and Discovering Geometric Inequalities in GeoGebra by using Tarski

Brown

Kovács

Vajda

2021

Electron. Proc. Theor. Comput. Sci.

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We introduce a system of software tools that can automatically prove or discover geometric inequalities. The system, called GeoGebra Discovery, consisting of an extended version of GeoGebra, a controller web service realgeom, and the computational tool Tarski (with the extensive help of the QEPCAD B system) successfully solves several non-trivial problems in Euclidean planar geometry related to inequalities.

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Giac and GeoGebra – Improved Gröbner Basis Computations

Cited by 38 publications

References 7 publications

Dealing with Degeneracies in Automated Theorem Proving in Geometry

Dealing with Degeneracies in Automated Theorem Proving in Geometry

On a problem that was not interesting for Erdős

Supporting Proving and Discovering Geometric Inequalities in GeoGebra by using Tarski

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