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The computer algebra system DERIVE had a very important impact in teaching mathematics with technology, mainly in the 1990’s. The authors analyze the possible reasons for its success and impact and give personal conclusions based on the facts collected. More than 10 years after it was discontinued it is still used for teaching and several scientific papers (most devoted to educational issues) still refer to it. A summary of the history, journals and conferences together with a brief bibliographic analysis are included., Ministerio de Ciencia e Innovación (MICINN), Comunidad de Madrid, Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

Tennis is a sport with a very complex technique. Amateur tennis players have trainers and/or coaches, but are not usually accompanied by them to championships. Curiously, in this sport, the result of many matches can be changed by a small hint like ‘hit the ball a little higher when serving’. However, the biomechanical of a tennis stroke is only clear to an expert. We, therefore, developed a prototype of a rule-based expert system (RBES) aimed at an amateur competition player that is not accompanied by his/her coach to a championship and is not serving as usual (the RBES is so far restricted to serving). The player has to answer a set of questions about how he/she is serving that day and his/her usual serving technique and the RBES obtains a diagnosis using logic inference about the possible reasons (according of the logic rules that have been previously given to the RBES). A certain knowledge of the tennis terminology and technique is required from the player, but that is something known at this level. The underlying logic is Boolean and the inference engine is algebraic (it uses Groebner bases)., Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

Planning the operations of Renfe Operadora trains on Adif's (Spanish) railway network is very complex. The reasons are the coexistence of two track gauges, two kinds of electrification systems and five types of signaling systems; together with fixed and variable gauge rolling stock, sometimes able to run under different types of electrification and signaling systems. There is even a multiple unit hybrid series (730). The authors have developed a microscopic simulation computer package that calculates timings and minimal paths, and estimates costs, consumptions and emissions. The package is topology-independent and can perform computations for any type of trains. We shall focus here on its use, the structure of its input files and its possibilities., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

Gröbner bases have been applied to a number of problems related to the verification of Knowledge-Based Systems (KBS) and other problems within graph theory. In particular, the authors have developed in previous papers algebraic approaches to decide whether a situation in a railway interlocking system is safe or not. These algebraic approaches stand out because of the briefness of the code (as they use implementations of well-known algorithms for solving linear or algebraic systems provided by computer algebra systems). The authors have also developed a matrix-based computer tool that helps an expert to check whether a proposed railway electrification scenario (given through the topology of the railway station and the position of the isolation devices and the position and state of the “electrical bypasses” and feeders) fulfills the mandatory requirements of the Spanish railway infrastructure administrator (ADIF) for 3000 V railway electrifications or not. The second author works in the field of railway electrifications and he compares the present-day methods for verification of railway electrifications with the way KBS were verified in the past (manually by experts). In this article we approach this latter problem using algebraic techniques. The new computer tool is based on an algebraic translation of the problem (instead of based on the use of matrices) and is really simple and fast. Determining which electrification sections are under electric tension is computed solving linear systems (because in this case the graph is undirected and no polynomials of degree >1 arise in the algebraic translation, so it is not necessary to use Gröbner bases, unlike in the two problems mentioned in the beginning of the Abstract). Therefore far bigger railway facilities can be addressed than if non-linear systems were involved., Ministerio de Ciencia e Innovación (MICINN), Comunidad de Madrid, Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

Organizar una Comunidad de Práctica para conocer y reflexionar sobre los diferentes enfoques de la formación de maestros y propuestas formativas del Departamento de DCESM para abordar la formación de maestros de forma integrada y multidisciplinar.

Este trabajo aborda el valor del tiempo actuando sobre una red ferroviaria o sus usuarios, destacando la importancia del diseño y la representación gráfica en este tipo de problemas. Se trata de ilustrarlo con cuatro aplicaciones independientes, cada una en un capítulo, implementadas en software científico de amplia difusión. El primer capítulo se ocupa de los tiempos de viaje de un tren de ancho variable en una red con tres tipos de infraestructura, dos anchos de vía y cambiadores de ancho. Utilizando la teoría de grafos en estas redes se consigue reducir la complejidad de un multigrafo a un grafo multicapa. En estas condiciones se consigue una ruta mínima con un algoritmo estándar como el de Dijkstra o Bellman-Ford. En el segundo capítulo, aplicando nuevamente las herramientas de la teoría de grafos, se afrontó el problema de recrear dinámicamente los planos esquemáticos históricos de unas redes ferroviarias sometidas a muchos cambios, como son las redes subterráneas de ”metro”. Nuevamente se consiguió un buen resultado reduciendo la evolución de la red de metro de Madrid a unos pocos grafos llamados etapas de las líneas. La aplicación transforma la cronología de la red en unas pocas etapas, a partir de las que se obtiene la red retrospectiva en cualquier instante...

Este trabajo aborda el valor del tiempo actuando sobre una red ferroviaria o sus usuarios, destacando la importancia del diseño y la representación gráfica en este tipo de problemas. Se trata de ilustrarlo con cuatro aplicaciones independientes, cada una en un capítulo, implementadas en software científico de amplia difusión. El primer capítulo se ocupa de los tiempos de viaje de un tren de ancho variable en una red con tres tipos de infraestructura, dos anchos de vía y cambiadores de ancho. Utilizando la teoría de grafos en estas redes se consigue reducir la complejidad de un multigrafo a un grafo multicapa. En estas condiciones se consigue una ruta mínima con un algoritmo estándar como el de Dijkstra o Bellman-Ford. En el segundo capítulo, aplicando nuevamente las herramientas de la teoría de grafos, se afrontó el problema de recrear dinámicamente los planos esquemáticos históricos de unas redes ferroviarias sometidas a muchos cambios, como son las redes subterráneas de ”metro”. Nuevamente se consiguió un buen resultado reduciendo la evolución de la red de metro de Madrid a unos pocos grafos llamados etapas de las líneas. La aplicación transforma la cronología de la red en unas pocas etapas, a partir de las que se obtiene la red retrospectiva en cualquier instante..., This work addresses the value of time acting on a railway network or its users,highlighting the importance of design and graphic representation in this type of problem. The idea is to illustrate it with four independent applications, each one in a chapter, implemented in widely used scientific software.• The first chapter deals with the travel times of a variable gauge train in a network with three kinds of infrastructure, two track gauges and gauge changers. Using graph theory in these networks it is possible to reduce the complexity of a multigraph to a multilayer graph. Under these conditions, a minimum path is achieved with a standard algorithm such as Dijkstra or Bellman-Ford.• Applying again the tools of graph theory, The second chapter addresses the problem of dynamically recreating historical rail network schemes that undergo many changes, such as metropolitan rail networks. Once again, a good result was achieved by reducing the evolution of the Madrid metro network to a few graphs, called stages. The application transforms the chronology of the network in a few stages, from which the retrospective network is obtained at any moment...