Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathématiques et Applications (MATHAPPLIC, volume 59)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
From the reviews;
"The book under review … is devoted to a systematic study of the solutions of polynomial equations in various aspects. The general purpose of this series is to introduce engineers and applied scientists to aspects of theoretical concepts and their applications. The contents of the present volume introduces a potential reader to methods of commutative algebra, algebraic geometry and analysis. … it might be used for a practitioner to become familiar with the power of parts of ‘pure Mathematics’ in applied fields." (Peter Schenzel, Zentralblatt MATH, Vol. 1127 (4), 2008)
"This is a very interesting book which would make a useful textbook for a course in algorithmic algebra and computational algebraic geometry at the Master’s or doctoral level. … authors have collected in this text all the experience they gained by teaching a course on the subject at the (French) DEA level in Mathematics at the University of Nice. … Throughout the book there are interesting exercises, as well as an extensive list of algorithms and a pointer to the Maple package multires … ." (Carlos D’ Andrea, Mathematical Reviews, Issue 2008 i)
Authors and Affiliations
Bibliographic Information
Book Title: Introduction à la résolution des systèmes polynomiaux
Authors: Mohamed Elkadi, Bernard Mourrain
Series Title: Mathématiques et Applications
DOI: https://doi.org/10.1007/978-3-540-71647-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2007
Softcover ISBN: 978-3-540-71646-4Published: 24 May 2007
eBook ISBN: 978-3-540-71647-1Published: 23 May 2007
Series ISSN: 1154-483X
Series E-ISSN: 2198-3275
Edition Number: 1
Number of Pages: VIII, 308
Number of Illustrations: 14 b/w illustrations
Topics: Commutative Rings and Algebras, Computational Mathematics and Numerical Analysis, Algebraic Geometry, Numerical Analysis, General Algebraic Systems