Tomás Recio

Robert M. Corless, Arthur C. Norman, Tomas Recio et al.

Today, symbolic mathematical computation is taken for granted as part of the scientific infrastructure, but it has not always been so. This paper provides a historical survey of the discipline's formative decade, 1965-1975, viewed from a 50 year perspective. This span of years saw the evolution from a few specialized programs with naive algorithms to integrated systems with substantial capabilities. We highlight some of the important early figures in the field and the innovations upon which the current generation of systems and algorithms are built. By revisiting a period unfamiliar to most current readers, this survey aims to shed light on once-pressing issues that are now largely resolved and to highlight how some of today's challenges were recognized earlier than expected.

Belén Ariño-Morera, Zoltán Kovács, Tomás Recio et al.

We address, through the automated reasoning tools in GeoGebra Discovery, a problem from a regional phase of the Austrian Mathematics Olympiad 2023. Trying to solve this problem gives rise to four different kind of feedback: the almost instantaneous, automated solution of the proposed problem; the measure of its complexity, according to some recent proposals; the automated discovery of a generalization of the given assertion, showing that the same statement is true over more general polygons than those mentioned in the problem; and the difficulties associated to the analysis of the surprising and involved high number of degenerate cases that appear when using the LocusEquation command in this problem. In our communication we will describe and reflect on these diverse issues, enhancing its exemplar role for showing some of the advantages, problems, and current fields of development of GeoGebra Discovery.

Zoltán Kovács, Tomás Recio, M. Pilar Vélez

In our contribution we describe some on-going improvements concerning the Automated Reasoning Tools developed in GeoGebra Discovery, providing different examples of the performance of these new features. We describe the new ShowProof command, that outputs both the sequence of the different steps performed by GeoGebra Discovery to confirm a certain statement, as well as a number intending to grade the difficulty or interest of the assertion. The proposal of this assessment measure, involving the comparison of the expression of the thesis (or conclusion) as a combination of the hypotheses, will be developed.

Zoltán Kovács, Tomás Recio, M. Pilar Vélez

In our contribution we will reflect, through a collection of selected examples, on the potential impact of the GeoGebra Discovery application on different social and educational contexts.

Teresa Gomez-Diaz, Tomas Recio

Background: Evaluation of the quality of research software is a challenging and relevant issue, still not sufficiently addressed by the scientific community. Methods: Our contribution begins by defining, precisely but widely enough, the notions of research software and of its authors followed by a study of the evaluation issues, as the basis for the proposition of a sound assessment protocol: the CDUR procedure. Results: CDUR comprises four steps introduced as follows: Citation, to deal with correct RS identification, Dissemination, to measure good dissemination practices, Use, devoted to the evaluation of usability aspects, and Research, to assess the impact of the scientific work. Conclusions: Some conclusions and recommendations are finally included. The evaluation of research is the keystone to boost the evolution of the Open Science policies and practices. It is as well our belief that research software evaluation is a fundamental step to induce better research software practices and, thus, a step towards more efficient science.

Zoltán Kovács, Tomás Recio, M. Pilar Vélez

We introduce and discuss, through a computational algebraic geometry approach, the automatic reasoning handling of propositions that are simultaneously true and false over some relevant collections of instances. A rigorous, algorithmic criterion is presented for detecting such cases, and its performance is exemplified through the implementation of this test on the dynamic geometry program GeoGebra.