Applications of Polynomial Systems

Cox, David A.; D'Andrea, Carlos (CON); Dickenstein, Alicia (CON); Hauenstein, Jonathan (CON); Schenck, Hal (CON)

ISBN 10: 1470451379 / ISBN 13: 9781470451370

Published by American Mathematical Society, 2020

Unread book in perfect condition. Seller Inventory # 40566575

Synopsis:

Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert. Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border rank, font design, Stewart-Gough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bézier patches, Cayley-Menger varieties, and toric varieties; and algebraic objects such as resultants, Rees algebras, approximation complexes, matroids, and toric ideals. Two important subthemes that appear in multiple chapters are toric varieties and algebraic statistics. The book also discusses the history of elimination theory, including its near elimination in the middle of the twentieth century. The main goal is to inspire the reader to learn about the topics covered in the book. With this in mind, the book has an extensive bibliography containing over 350 books and papers.

About the Author: David A. Cox: Amherst College, Amherst, MA

Bibliographic Details

Title: Applications of Polynomial Systems
Publisher: American Mathematical Society
Publication Date: 2020
Binding: Soft cover
Condition: As New