Miguel Abánades | Universidad Rey Juan Carlos (original) (raw)

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Papers by Miguel Abánades

The Intergeo File Format in Progress Miguel Abánades1, Francisco Botana2, Jesús Escribano3, Maxim... more The Intergeo File Format in Progress Miguel Abánades1, Francisco Botana2, Jesús Escribano3, Maxim Hendriks4, Ulrich Kortenkamp5, Yves Kreis6, Paul Libbrecht7, Daniel Marques8, Christian Mercat9 1 CES Felipe II-UCM, Aranjuez, Spain 2 Universidad de ...

Gaceta De La Real Sociedad Matematica Espanola, 2009

... En los últimos tiempos han aparecido interesantes aplicaciones en este sentido. En esta nota,... more ... En los últimos tiempos han aparecido interesantes aplicaciones en este sentido. En esta nota, entre otras aplicaciones, destacaremos el programa GeoGebra, un sistema de geometrıa dinámica de gran ayuda para la ense˜nanza de la Geometrıa. ... 3.1.1. El caso de GeoGebra ...

Journal of Pure and Applied Algebra, 1999

We show that the ring of bounded meromorphic functions on an irreducible compact real analytic se... more We show that the ring of bounded meromorphic functions on an irreducible compact real analytic set of dimension d is a Prüfer domain of dimension d. Consequently, every finitely generated ideal in this ring can be generated by d+1 elements, and we show that this bound is sharp.

Computational Science – ICCS 2007, 2007

, an open web-based tool to determine equations of geometric loci specified using Cabri Geometry ... more , an open web-based tool to determine equations of geometric loci specified using Cabri Geometry and The Geometer's Sketchpad, is described. A geometric construction of a locus is uploaded to a Java Servlet server, where two computer algebra systems, CoCoA and Mathematica, following the Groebner basis method, compute the locus equation and its graph. Moreover, an OpenMath description of the geometric construction is given. GLI can be efficiently used in mathematics education, as a supplement of the locus functions of the standard dynamic geometry systems. The system is located at

Towards Mechanized Mathematical Assistants, 2007

A prototype for a web application designed to symbolically process locus, proof and discovery tas... more A prototype for a web application designed to symbolically process locus, proof and discovery tasks on geometric diagrams created with the commercial dynamic geometry systems Cabri, The Geometer’s Sketchpad and Cinderella is presented. The application, named LAD (acronym for Locus-Assertion-Discovery) and thought of as a remote add-on for the considered DGS, follows the Groebner basis method relying on CoCoA and

This paper describes some examples of fruitful cooperation between geometric software tools (in p... more This paper describes some examples of fruitful cooperation between geometric software tools (in particular, GeoGebra) and a free open source computer algebra system, Sage (Software for Algebra and Geometry Experimentation). We collect some of our efforts for enhancing mathematics education via technologically rich environments. We show that a math teacher with no specialized programming knowledge can mix widespread resources to

EPTCS, 2012

We present a symbolic tool that provides robust algebraic methods to handle automatic deduction t... more We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer algebra system Sage, corresponding to two different ways of coding a geometric construction. In one worksheet, diagrams constructed with the open source dynamic geometry system GeoGebra are accepted. In this worksheet, Groebner bases are used to either compute the equation of a geometric locus in the case of a locus construction or to determine the truth of a general geometric statement included in the GeoGebra construction as a boolean variable. In the second worksheet, locus constructions coded using the common file format for dynamic geometry developed by the Intergeo project are accepted for computation. The prototype and several examples are provided for testing. Moreover, a third Sage worksheet is presented in which a novel algorithm to eliminate extraneous parts in symbolically computed loci has been implemented. The algorithm, based on a recent work on the Groebner cover of parametric systems, identifies degenerate components and extraneous adherence points in loci, both natural byproducts of general polynomial algebraic methods. Detailed examples are discussed.

Computer-Aided Design, 2014

2011 11th International Conference on Intelligent Systems Design and Applications, 2011

This paper presents a Named Entity Recognition (NER) system based on Hidden Markov Models. The sy... more This paper presents a Named Entity Recognition (NER) system based on Hidden Markov Models. The system design is language independent, and the target language and scope of the NER is determined by the training corpus. The NER is formed by two subsystems that detect and label the entities independently. Each subsystem implements a different approach of that statistical theory, showing that each component may complement the results of the other one. Unlike most of the previous works, two labels are returned when the components provide different results. This redundancy is an advantage when human supervision is mandatory at the end of the process such as in intelligence environments.

Mathematics and Computers in Simulation, 2010

A Dynamic Geometry System (DGS) is a computer application that allows the exact drawing and dynam... more A Dynamic Geometry System (DGS) is a computer application that allows the exact drawing and dynamic manipulation of geometric constructions. DGS have been the paradigm of new technologies applied to Math education, but some authors have claimed that some symbolic capabilities should be added to this systems. We present an example of communication between the commercial DGS Cabri, The Geometer's Sketchpad and Cinderella and two Computer Algebra Systems (CAS), Mathematica and CoCoA. The tool is a web application designed to symbolically process locus, proof and discovery tasks on geometric diagrams. Named LAD (Locus-Assertion-Discovery), it is a remote add-on for the three DGS. LAD is a prototype oriented to research users. We also describe LADucation, a one-click educational version of LAD. By just uploading the file generated by the considered DGS, graphs and equations of geometric loci are computed.

Computer Applications in Engineering Education, 2012

ABSTRACT We present the experience of the authors teaching mathematics to freshmen engineering st... more ABSTRACT We present the experience of the authors teaching mathematics to freshmen engineering students with the help of the open source computer algebra system Sage. We describe some teaching resources and present an ad hoc distribution of Sage used by the authors. Comput Appl Eng Educ © 2012 Wiley Periodicals, Inc.

Computer Applications in Engineering Education, 2011

Dynamic Geometry, also known as Interactive Geometry, refers to computer programs where accurate ... more Dynamic Geometry, also known as Interactive Geometry, refers to computer programs where accurate construction of (generally) planar drawings can be made. The key characteristic of this software is that, when dragging certain elements of the configuration, the geometric properties of the construction are preserved. In this paper, we describe an educational web-based application that complements standard dynamic geometry programs in a mathematically sound manner. We put the focus on computing the geometric locus of distinguished points in linkages and other geometric constrained configurations, since knowing the equations of such loci is a typical engineering task. The tool is located at

ABSTRACT We describe here a properly recent application of the Gröbner cover algorithm (GC) provi... more ABSTRACT We describe here a properly recent application of the Gröbner cover algorithm (GC) providing an algebraic support to dynamic geometry computations of geometrical loci. It provides a complete algebraic solution of locus computation as well as a suitable taxonomy allowing to distinguish the nature of the different components. We included a new algorithm Locus into the Singular grobcov.lib library for this purpose. A web prototype has been implemented using it in Geogebra.