ACM SIGSAM Bulletin, Vol 37, No 1, March 2003 Abstracts of the Eighth Spanish Meeting on Computer Algebra and Applications: EACA-2002 Communicated by Philippe Gimenez Departamento de ´ Algebra, Geometr´ ıa y Topolog´ ıa. Facultad de Ciencias. Universidad de Valladolid. E-47005 Valladolid, Spain. pgimenez@agt.uva.es This is the collection of the abstracts of the talks given during the EACA-2002, the Eighth Spanish Meeting on Computer Algebra and Applications held in Pe ˜ naranda de Duero (Burgos, Spain) on September 11-13, 2002. The main goal of the EACA–Meetings is to provide a forum for researchers from Computer Algebra and researchers that essentially use these techniques in their investigation. As in previous events of the series (Santander 1995, Sevilla 1996, Granada 1997, Sig¨ uenza 1998, Tenerife 1999, Barcelona 2000 and Ezcaray 2001), participation of young researchers was specially encouraged. The EACA-2002 was supported by Universidad de Valladolid, Ministerio de Ciencia y Tecnolog´ ıa (Acci ´ on Especial BFM2001-4832-E), Consejer´ ıa de Educaci´ on y Cultura de la Junta de Castilla y Le´ on, Real Sociedad Matem´ atica Espa˜ nola, SUN Microsystems S.A. and Addlink Software Cient´ ıfico S.L. The contributed papers were selected by the Scientific Committee which consisted of Mar´ ıa Emilia Alonso, Isabel Bermejo, Jos´ e Luis Bueso, Francisco J. Castro-Jim´ enez, Juan Elias, Philippe Gimenez, Laureano Gonz´ alez-Vega, Antonio Montes, Tomas Recio, Julio Rubio and Juan Rafael Sendra. The first six abstracts (Carlos Andradas, Bruno Buchberger, Juan Elias, Ioannis Z. Emiris, Aron Simis and Uli Walther) correspond to the invited lectures. Characterization and description of basic semialgebraic sets Carlos Andradas carlos andradas@mat.ucm.es Dpto de Algebra, Universidad Complutense de Madrid, 28040 Madrid, Spain. The description of a semialgebraic set (that is, the equations and inequations used to write it down) is highly non unique. The number of unions, inequalities and degree of the polynomials involved is often called the complexity of the set and determines some properties of it, like the possible topological types, etc. It has been known since the eighties that the number of unions and inequalities required to described a semialgebraic set can be bounded in terms only of its dimension, at the cost of increasing the degrees of the polynomials used in the description. In the lecture we will review these results and some open questions related to them, paying attention to the lack of constructive methods to rewrite a semialgebraic set. 16