**CBMS Regional Conference Series in Mathematics**

Volume: 134;
2020;
250 pp;
Softcover

MSC: Primary 13; 14;
Secondary 52; 62; 65; 68; 92

**Print ISBN: 978-1-4704-5137-0
Product Code: CBMS/134**

List Price: $59.00

AMS Member Price: $47.20

MAA Member Price: $53.10

**Electronic ISBN: 978-1-4704-5589-7
Product Code: CBMS/134.E**

List Price: $59.00

AMS Member Price: $47.20

MAA Member Price: $53.10

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#### Supplemental Materials

# Applications of Polynomial Systems

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*David A. Cox*

with contributions by Carlos D'Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, and Jessica Sidman.

A co-publication of the AMS and CBMS

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.

#### Readership

Graduate students and researchers interested in applications of algebraic geometry.

#### Table of Contents

# Table of Contents

## Applications of Polynomial Systems

- Cover Cover11
- Title page iii4
- Preface vii8
- Chapter 1. Elimination Theory 112
- Chapter 2. Numerical Algebraic Geometry 4556
- Chapter 3. Geometric Modeling 89100
- Chapter 4. Rigidity Theory 137148
- Chapter 5. Chemical Reaction Neworks 179190
- Illustration Credits 223234
- Bibliography 225236
- Index 243254
- Back Cover Back Cover1264