![]() Dynamic Geometry programs turned out to be an ideal interface to introduce geometric information, and the extension of this software with convenient algebraic tools allowed the creation of a natural environment to work on automated proving in Geometry. Unfortunately, this translation of geometric properties into algebraic equations can be a tedious process. The GATPs based on algebraic techniques, such as Wu’s Method () or the Gröbner Basis method (), require frequently the manipulation of a large set of polynomials, which represents a given geometric construction. As the algorithmic basis for both instruments (scanning, real solving) are already internally available in GeoGebra (e.g., via the Tarski package), we conclude proposing the development and merging of such features in the future progress of GeoGebra automated reasoning tools. On the other hand, via a symbolic computation approach which currently requires the (tricky) use of a variety of real geometry concepts (determining the real roots of a bivariate polynomial p ( x, y ) by reducing it to a univariate case through discriminants and Sturm sequences, etc.), which leads to a complete resolution of the initial problem. ![]() On the one hand, through the introduction of the dynamic color scanning method, which allows to visualize on GeoGebra the set of real solutions of a given equation and to shed light on its geometry. In our paper we will explore the capabilities and limitations of these new tools, through the case study of a classic geometric inequality, showing how to overcome, by means of a double approach, the difficulties that might arise attempting to ‘discover’ it automatically. Recently developed GeoGebra tools for the automated deduction and discovery of geometric statements combine in a unique way computational (real and complex) algebraic geometry algorithms and graphic features for the introduction and visualization of geometric statements.
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