Ferres-López, EnriqueRoanes Lozano, EugenioMartínez Zarzuelo, AngélicaSánchez, Fernando2024-12-132024-12-132023-02-06E. Ferres-López, E. Roanes-Lozano, A. Martínez-Zarzuelo, F. Sánchez. One-sided differentiability: a challenge for computer algebra systems. Electronic Research Archive. 2023, 31(3), 1737-1768. https://doi.org/10.3934/era.20230902688-159410.3934/era.2023090https://hdl.handle.net/20.500.14352/112579This work was partially supported by the research projects PGC2018-096509-B-I00 and PID2021-122905NB-C21 (Government of Spain). Referencias bibliográficas: • E. Ferres-López, E. Roanes-Lozano, Una breve nota didáctica sobre la evaluación de funciones fuera de su dominio usando software matemático, Boletín de la Sociedad Puig Adam, 113 (2022), 71–80. 2. • E. Ferres-López, E. Roanes-Lozano, A. 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Bernardin, A review of symbolic solvers, ACM SIGSAM Bull., 30 (1996), 9–20. https://doi.org/10.1145/231191.231193 • J. Monaghan, S. Sun, D. Tall, Construction of the limit concept with a computer algebra system, in Proceedings of the 18th Conference of the International Group for the Psychology of Mathematics Education, (1994), 279–286. Available from: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=332da54b21d4ac7877121501 f8ce0cae6fe6a343. • Mathematica Stack Exchange, What does True mean in this case? 2007. Available from: https://mathematica.stackexchange.com/questions/155021/what-does-true-mean-in-this-case.Computer Algebra Systems (CASs) are extremely powerful and widely used digital tools. Focusing on differentiation, CASs include a command that computes the derivative of functions in one variable (and also the partial derivative of functions in several variables). We will focus in this article on real-valued functions of one real variable. Since CASs usually compute the derivative of real-valued functions as a whole, the value of the computed derivative at points where the left deriva-tive and the right derivative are different (that we will call conflicting points) should be something like “undefined”, although this isn’t always the case: the output could strongly differ depending on the chosen CAS. We have analysed and compared in this article how some well-known CASs behave when addressing differentiation at the conflicting points of five different functions chosen by the au-thors. Finally, the ability for calculating one-sided limits of CASs allows to directly compute the result in these cumbersome cases using the formal definition of one-sided derivative, which we have also analysed and compared for the selected CASs. Regarding teaching, this is an important issue, as it is a topic of Secondary Education and nowadays the use of CASs as an auxiliary digital tool for teaching mathematics is very common.engAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/journal articlehttps://doi.org/10.3934/era.2023090https://www-scopus-com.bucm.idm.oclc.org/record/display.uri?eid=2-s2.0-85164589340&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28One-sided+differentiability%3A+a+challenge+for+computer+algebra+systems%29&sessionSearchId=0c5dcd17039c6481a084cc38bee123cf&relpos=0https://www.aimspress.com/journal/erahttps://www.aimspress.com/article/doi/10.3934/era.2023090open access372.8537.02:51004:37373.5004.4Computer algebra systemsOne-sided differentiabilityReal-valued functions of one real variableLimitsSoftware comparisonEnseñanza de las MatemáticasEnseñanza secundariaSoftware5801 Teoría y Métodos Educativos5802.03 Desarrollo de Asignaturas1203.10 Enseñanza Con Ayuda de Ordenador1203 Ciencia de Los Ordenadores