Applications of Polynomial Systems (CBMS Regional Conference Series in Mathematics) - Softcover

David A. Cox (author)

Softcover

ISBN 10: 1470451379 ISBN 13: 9781470451370

Publisher: American Mathematical Society, 2020

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 Bezier 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 this title

About the Author

David A. Cox, Amherst College, MA.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2020
• Language: English
• ISBN 10: 1470451379
• ISBN 13: 9781470451370
• Binding: Paperback
• Number of pages: 260