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Applications of Polynomial Systems

David A. Cox Amherst College, Amherst, MA
with contributions by Carlos D'Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, and Jessica Sidman.
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-1-4704-5137-0
Product Code: CBMS/134
List Price: $59.00 MAA Member Price:$53.10
AMS Member Price: $47.20 Electronic ISBN: 978-1-4704-5589-7 Product Code: CBMS/134.E List Price:$59.00
MAA Member Price: $53.10 AMS Member Price:$47.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $88.50 MAA Member Price:$79.65
AMS Member Price: $70.80 Click above image for expanded view Applications of Polynomial Systems David A. Cox Amherst College, Amherst, MA with contributions by Carlos D'Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, and Jessica Sidman. A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-1-4704-5137-0 Product Code: CBMS/134  List Price:$59.00 MAA Member Price: $53.10 AMS Member Price:$47.20
 Electronic ISBN: 978-1-4704-5589-7 Product Code: CBMS/134.E
 List Price: $59.00 MAA Member Price:$53.10 AMS Member Price: $47.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$88.50 MAA Member Price: $79.65 AMS Member Price:$70.80
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1342020; 250 pp
MSC: Primary 13; 14; Secondary 52; 62; 65; 68; 92;

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.

Graduate students and researchers interested in applications of algebraic geometry.

• Chapters
• Elimination theory
• Numerical algebraic geometry
• Geometric modeling
• Rigidity theory
• Chemical reaction networks

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 1342020; 250 pp
MSC: Primary 13; 14; Secondary 52; 62; 65; 68; 92;

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.