Satisfiability Checking and Symbolic Computation

Symbolic Computation and Satisfiability Checking are viewed as individual research areas, but they share common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite these commonalities, the two communities are currently only weakly connected. We introduce a new project SC-square to build a joint community in this area, supported by a newly accepted EU (H2020-FETOPEN-CSA) project of the same name. We aim to strengthen the connection between these communities by creating common platforms, initiating interaction and exchange, identifying common challenges, and developing a common roadmap. This abstract and accompanying poster describes the motivation and aims for the project, and reports on the first activities.Comment: 3 page Extended Abstract to accompany an ISSAC 2016 poster. Poster available at http://www.sc-square.org/SC2-AnnouncementPoster.pd

The importance of being zero

2018 International Symposium on Symbolic and Algebraic Computation (ISSAC), July 2018, New York, NY, United StatesWe present a deterministic algorithm for deciding if a polynomial ideal, with coefficients in an algebraically closed field K of characteristic zero, of which we know just some very limited data, namely:the number n of variables, and some upper bound for the geometric degree of its zero set in Kn, is or not the zero ideal. The algorithm performs just a finite number of decisions to check whether a point is or not in the zero set of the ideal. Moreover, we extend this technique to test, in the same fashion, if the elimination of some variables in the given ideal yields or not the zero ideal. Finally, the role of this technique in the context of automated theorem proving of elementary geometry statements, is presented, with references to recent documents describing the excellent performance of the already existing prototype version, implemented in GeoGebra.Ministerio de Economía y CompetitividadEuropean Regional Development Fun

Diseño de experiencias de aula usando razonamiento automático con GeoGebra

Las últimas versiones de GeoGebra disponen de herramientas y comandos que permiten hacer razonamiento automático en geometría (GGB-ART); esto es, derivar, descubrir y/o demostrar, de modo general y riguroso, propiedades sobre una construcción geométrica representada en GeoGebra. El propósito de esta comunicación es exponer, a través de diversos ejemplos, las posibilidades de GGB-ART, así como plantear el diseño de experimentos de aula para estimar el posible impacto de estas herramientas en la enseñanza y el aprendizaje de las Matemáticas. Para ello consideramos que es necesario comenzar promoviendo la reflexión colectiva sobre las oportunidades y diferencias –frente a la metodología tradicional-- que plantearía el uso escolar de los comandos de GGB-ART. En definitiva, se trata de avanzar hacia un marco en el que desarrollar experiencias de aula que aprovechen estas herramientas, tanto en un contexto escolar clásico (como utensilio auxiliar del currículo tradicional) como en un contexto curricular diferente, en el que se asuma la disponibilidad y popularización de una especie de “calculadora geométrica” entre el alumnado