Bøger af Bernard Mourrain

This volume contains the papers presented at 6th Conference on Geometric Modeling and Processing (GMP 2010) held in Castro Urdiales, Spain during June16-18,2010. GeometricModelingandProcessingisabiannualinternational conference series on geometric modeling, simulation and computing. Previously, GMPhasbeenheldinHongKong(2000), Saitama, Japan(2002), Beijing, China (2004), Pittsburgh, USA (2006) and Hangzhou, China (2008). GMP 2010 received a total of 30 submissions that were reviewed by three to four Program Committee members on average. While the number of subm- sions dropped signi?cantly from previous years, the quality did not and was still quite high overall. Based on the reviews received, the committee decided to - cept 20 papers for inclusion in the proceedings. Additionally, extended versions of selected papers were considered for a special issue of Computer-Aided - sign (CAD) and Computer-Aided Geometric Design (CAGD). The paper topics spanned a wide variety and include: - Solutions of transcendental equations - Volume parameterization - Smooth curves and surfaces - Isogeometric analysis - Implicit surfaces - Computational geometry Many people helped make this conference happen and we are grateful for their help. We would especially like to thank the Conference Chair, all of the authors who submitted papers, the ProgramCommittee members who reviewed the papers and all of the participants at the conference.

Les équations polynomiales apparaissent dans de nombreux domaines, pour modéliser des contraintes géométriques, des relations entre des grandeurs physiques, ou encore des propriétés satisfaites par certaines inconnues. Cet ouvrage est une introduction aux méthodes algébriques permettant de résoudre ce type d'équations. Nous montrons comment la géométrie des variétés algébriques définies par ces équations, leur dimension, leur degré, ou leurs composantes peuvent se déduire des propriétés des algèbres quotients correspondantes. Nous abordons pour cela des méthodes de la géométrie algébrique effective, telles que les bases de Grobner, la résolution par valeurs et vecteurs propres, les résultants, les bezoutiens, la dualité, les algèbres de Gorenstein et les résidus algébriques. Ces méthodes sont accompagnées d'algorithmes, d'exemples et d'exercices, illustrant leurs applications.