Applications of polynomial systems
著者
書誌事項
Applications of polynomial systems
（Regional conference series in mathematics, no. 134）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c2020
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注記
Other contributions: Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, Jessica Sidman
"With support from the National Science Foundation"
"NSF-CBMS Regional Conference in the Mathematical Sciences on Applications of Polynomial Systems held at Texas Christian University June 4-8, 2018"--T.p. verso
"Applied mathematics"--Cover
Includes bibliographical references (p. 225-241) and index
内容説明・目次
内容説明
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.
目次
Elimination theory
Numerical algebraic geometry
Geometric modeling
Rigidity theory
Chemical reaction networks
Illustration credits
Bibliography
Index
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