Foreword from the Editors

This issue of the Journal of Symbolic Computation collects selected papers on work presented at, or related to, the meeting MEGA 2005, held in Porto Conte, Alghero, Sardinia (Italy), May 27 June 1, 2005. MEGA is the acronym for “Effective Methods in Algebraic Geometry” (and its equivalent in Italian, French, Spanish, German, Russian, etc.), a series of (roughly) biennial conferences on computing in and with Algebraic Geometry: Theory, Algorithms, Implementations, Applications. Previous meetings were held in 1990 (Castiglioncello, Italy), 1992 (Nice, France), 1994 (Santander, Spain), 1996 (Eindhoven, Nederlands), 1998 (St. Malo, France), 2000 (Bath, United Kingdom) and 2003 (Kaiserslautern, Germany). On this occasion, MEGA was also an opportunity to celebrate the 60th birthday of Prof. Carlo Traverso (Università di Pisa), one of the founders of MEGA and the chairman of the 2005 Conference. A special session within this MEGA, with several talks by colleagues and friends on his work and achievements, was devoted to honor him. Next MEGA 2007 will take place on June 24-30, 2007, at Strobl am Wolfgangsee, Austria. MEGA is run by a Steering Committee with the help of a larger Advisory Board, which takes care of refereeing the submitted contributions, only for oral presentation at the Conference. Even at this stage the refereeing process is quite strict, to keep the high standards of MEGA, so that the Conference can be regarded as the premiere in its field, presenting recent and on-going major breakthroughs on its different topics of interest. Following the traditions of MEGA, at and after the Conference, a new call for papers is announced, inviting all the participants of MEGA to submit papers for a special issue in a prestigious journal. This invitation is also extended to any researcher interested in the topics of the MEGA. These papers are subject to a new refereeing procedure, under the independent responsibility of some appointed members of the Steering Committee. In this opportunity, this task was assigned to Prof. Alicia Dickenstein (Universidad de Buenos Aires), Prof. Patrizia Gianni (Università di Pisa) and Prof. Tomas Recio (Universidad de Cantabria). We decided immediately to attempt publishing for the second time the –so called– Proceedings of MEGA through the Journal of Symbolic Computation, because of its prestige and impact in our community. We would like to thank the Editor in Chief of the Journal of Symbolic Computation, Prof. Hoon Hong, who accepted without hesitation our proposal, for all his help along the editorial process. As guest editors of the Special Issue, we circulated a call for papers in July 2005, with November 2005 as deadline. We received 41 submissions, covering many different topics. After a detailed refereeing process, including in most cases three or four different reviews, thirteen papers have been finally selected. We must remark that many other contributions, with excellent reports, could not be accepted for this Special JSC-MEGA issue, because of the page limitations. Deciding the excellence among the best has been, perhaps, the most difficult task of the guest editors. On the other hand we are much indebted to the authors and the referees for their very professional cooperation and understanding of the hardships of our job. Concerning the contents of this issue, we are proud to remark that the selected papers cover a broad range of topics, including • the study of condition numbers for singular systems, generalizing results by Shub and Smale for regular homogeneous systems, as in the paper by Beltran and Pardo.