Lecture Notes in Artificial Intelligence Edited by R. Goebel, J. Siekmann, and W. Wahlster
Subseries of Lecture Notes in Computer Science
6301
Thomas Sturm Christoph Zengler (Eds.)
Automated Deduction in Geometry 7th International Workshop, ADG 2008 Shanghai, China, September 22-24, 2008 Revised Papers
13
Series Editors Randy Goebel, University of Alberta, Edmonton, Canada Jörg Siekmann, University of Saarland, Saarbrücken, Germany Wolfgang Wahlster, DFKI and University of Saarland, Saarbrücken, Germany Volume Editors Thomas Sturm Max-Planck-Institut für Informatik, RG 1: Automation of Logic 66123 Saarbrücken, Germany E-mail:
[email protected] Christoph Zengler Universität Tübingen Wilhelm-Schickard-Institut für Informatik Symbolic Computation Group 72076 Tübingen, Germany E-mail:
[email protected]
ISSN 0302-9743 e-ISSN 1611-3349 e-ISBN 978-3-642-21046-4 ISBN 978-3-642-21045-7 DOI 10.1007/978-3-642-21046-4 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011926785 CR Subject Classification (1998): I.2.3, I.3.5, F.4.1, G.2-3, D.2.4 LNCS Sublibrary: SL 7 – Artificial Intelligence
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Preface
Automated Deduction in Geometry (ADG) 2008 continued an established and fruitful series of biannual international workshops in that area. Previous meetings have taken place in Toulouse (1996), Beijing (1998), Zurich (2000), Linz (2002), Gainesville (2004), and Pontevedra (2006). The seventh workshop was held at the East China Normal University (ECNU) in Shanghai during September 22–24, 2008. ADG 2008 was co-organized by the CAS-MPG Partner Institute for Computational Biology, the Shanghai Institute of Biology Sciences, and the Chinese Academy of Sciences. While the ADG workshops themselves are quite open also for the informal discussion of work in progress, the selected contributions for the proceedings generally undergo a very thorough and highly selective reviewing process. This publication in the LNAI series of selected papers from 2008 continues a tradition established with the first ADG in 1996. As the Chair of the Program Committee, I would like to thank in the first place all PC members, who are listed on the next page, for their competence and dedication during two refereeing processes: first for the workshop contributions and then for the selected papers published here; all this comprised a considerable timespan. Zhenbing Zeng did a perfect job with the local organization at the exceptionally interesting location in Shanghai. Manual Kauers and Christoph Zengler greatly supported me with the organization of the online reviewing process and the preparation of these proceedings. Jes´ us Escribano and Miguel Ab´ anades created and maintained a beautiful and informative website, which was most helpful for the organizers as well as for the attendees of the workshop. Last but not least, I particularly want to thank Tom´ as Recio and Dongming Wang for their advice that has accompanied my organizational work for more than two years. March 2011
Thomas Sturm
Organization
Invited Speakers Shang-Ching Chou Tetsuo Ida
Wichita State University, USA/Zhejiang University, China University of Tsukuba, Japan
Organizing Committee Zhengbing Zeng Miguel A. Ab´ anades Jes´ us Escribano Christoph Zengler
Shanghai, China, Chair Madrid, Spain Madrid, Spain T¨ ubingen, Germany
Program Committee Thomas Sturm Hirokazu Anai Francisco Botana Christopher Brown Giorgio Dalzotto Jacques Fleuriot Xiao-Shan Gao Hoon Hong Deepak Kapur Manuel Kauers Montserrat Manubens Pavel Pech Tom´as Recio Georg Regensburger J¨ urgen Richter-Gebert Pascal Schreck Meera Sitharam Dongming Wang Min Wu Bican Xia Zhenbing Zeng
MPI-INF, Saarbr¨ ucken, Germany, Chair Fujitsu Lab, Japan Pontevedra, Spain Annapolis, USA Pisa, Italy Edinburgh, UK Beijing, China Raleigh, USA Albuquerque, USA Linz, Austria Barcelona, Spain Ceske Budejovice, Czech Republic Santander, Spain Linz, Austria Munich, Germany Strasbourg, France Gainesville, USA) Beijing, China/Paris, France Shanghai, China Beijing, China Shanghai, China
Table of Contents
Contributed Papers Dynamical Systems of Simplices in Dimension Two or Three . . . . . . . . . . G´erald Bourgeois and S´ebastien Orange
1
On the Design and Implementation of a Geometric Knowledge Base . . . . Xiaoyu Chen, Ying Huang, and Dongming Wang
22
Proof Certificates for Algebra and Their Application to Automatic Geometry Theorem Proving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benjamin Gr´egoire, Lo¨ıc Pottier, and Laurent Th´ery
42
Multivariate Resultants in Bernstein Basis . . . . . . . . . . . . . . . . . . . . . . . . . . Deepak Kapur and Manfred Minimair
60
Unique Factorization Domains in the Java Computer Algebra System . . . Heinz Kredel
86
Automatic Verification of the Adequacy of Models for Families of Geometric Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aless Lasaruk and Thomas Sturm
116
Formalizing Projective Plane Geometry in Coq . . . . . . . . . . . . . . . . . . . . . . Nicolas Magaud, Julien Narboux, and Pascal Schreck
141
Linear Programming for Bernstein Based Solvers . . . . . . . . . . . . . . . . . . . . . Dominique Michelucci and Christoph F¨ unfzig
163
Offsetting Revolution Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fernando San Segundo and J. Rafael Sendra
179
An Introduction to Java Geometry Expert (Extended Abstract) . . . . . . . Zheng Ye, Shang-Ching Chou, and Xiao-Shan Gao
189
On the Heilbronn Optimal Configuration of Seven Points in the Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhenbing Zeng and Liangyu Chen
196
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
225
