Softcover ISBN:  9781470451370 
Product Code:  CBMS/134 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
Electronic ISBN:  9781470455897 
Product Code:  CBMS/134.E 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 134; 2020; 250 ppMSC: 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 twentyfirst 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, fourbar mechanisms, border rank, font design, StewartGough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bézier patches, CayleyMenger 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.ReadershipGraduate students and researchers interested in applications of algebraic geometry.

Table of Contents

Chapters

Elimination theory

Numerical algebraic geometry

Geometric modeling

Rigidity theory

Chemical reaction networks


Additional Material

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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 twentyfirst 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, fourbar mechanisms, border rank, font design, StewartGough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bézier patches, CayleyMenger 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