Abstract
A branch of the Automated Deduction in Geometry (ADG) theory deals with the automatic proof and discovery of theses holding on a given collection of hypotheses. The mechanical proof and derivation of such statements, through computational complex algebraic geometry methods, will be exemplify in this paper through the performance of GeoGebra Automated Reasoning Tools. Then we will refer to some challenging issues that rise in this context, regarding the translation in algebraic terms of the given geometric facts, the verification or the finding of the sought properties, and the interpretation of the outcome. We will show how some of these involved issues could be be better approached through the collaboration of Maple packages for polynomial ideal manipulation, requiring, as well, diverse theoretical concepts recently introduced by the authors.
The authors are partially supported by FEDER/Ministerio de Ciencia, Innovación y Universidades – Agencia Estatal de Investigación/MTM2017-88796-P (Symbolic Computation: new challenges in Algebra and Geometry and their applications).
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Kovács, Z., Recio, T., Vélez, M.P. (2021). Merging Maple and GeoGebra Automated Reasoning Tools. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds) Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, vol 1414. Springer, Cham. https://doi.org/10.1007/978-3-030-81698-8_17
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