Grbner Bases: Statistics and Software Systems by Takayuki Hibi (English) Paperba

Description: Grbner Bases by Takayuki Hibi It provides all the fundamentals for graduate students to learn the ABCs of the Gröbner basis, requiring no special knowledge to understand those basic points.Starting from the introductory performance of the Gröbner basis (Chapter 1), a trip around mathematical software follows (Chapter 2). FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description The idea of the Gröbner basis first appeared in a 1927 paper by F. S. Macaulay, who succeeded in creating a combinatorial characterization of the Hilbert functions of homogeneous ideals of the polynomial ring. Later, the modern definition of the Gröbner basis was independently introduced by Heisuke Hironaka in 1964 and Bruno Buchberger in 1965. However, after the discovery of the notion of the Gröbner basis by Hironaka and Buchberger, it was not actively pursued for 20 years. A breakthrough was made in the mid-1980s by David Bayer and Michael Stillman, who created the Macaulay computer algebra system with the help of the Gröbner basis. Since then, rapid development on the Gröbner basis has been achieved by many researchers, including Bernd Sturmfels.This book serves as a standard bible of the Gröbner basis, for which the harmony of theory, application, and computation are indispensable. It provides all the fundamentals for graduate students to learn the ABCs of the Gröbner basis, requiring no special knowledge to understand those basic points.Starting from the introductory performance of the Gröbner basis (Chapter 1), a trip around mathematical software follows (Chapter 2). Then comes a deep discussion of how to compute the Gröbner basis (Chapter 3). These three chapters may be regarded as the first act of a mathematical play. The second act opens with topics on algebraic statistics (Chapter 4), a fascinating research area where the Gröbner basis of a toric ideal is a fundamental tool of the Markov chain Monte Carlo method. Moreover, the Gröbner basis of a toric ideal has had a great influence on the study of convex polytopes (Chapter 5). In addition, the Gröbner basis of the ring of differential operators gives effective algorithms on holonomic functions (Chapter 6). The third act (Chapter 7) is a collection of concrete examples and problems for Chapters 4, 5 and 6 emphasizing computation by using various softwaresystems. Back Cover The idea of the Grobner basis first appeared in a 1927 paper by F. S. Macaulay, who succeeded in creating a combinatorial characterization of the Hilbert functions of homogeneous ideals of the polynomial ring. Later, the modern definition of the Grobner basis was independently introduced by Heisuke Hironaka in 1964 and Bruno Buchberger in 1965. However, after the discovery of the notion of the Grobner basis by Hironaka and Buchberger, it was not actively pursued for 20 years. A breakthrough was made in the mid-1980s by David Bayer and Michael Stillman, who created the Macaulay computer algebra system with the help of the Grobner basis. Since then, rapid development on the Grobner basis has been achieved by many researchers, including Bernd Sturmfels. This book serves as a standard bible of the Grobner basis, for which the harmony of theory, application, and computation are indispensable. It provides all the fundamentals for graduate students to learn the ABC s of the Grobner basis, requiring no special knowledge to understand those basic points. Starting from the introductory performance of the Grobner basis (Chapter 1), a trip around mathematical software follows (Chapter 2). Then comes a deep discussion of how to compute the Grobner basis (Chapter 3). These three chapters may be regarded as the first act of a mathematical play. The second act opens with topics on algebraic statistics (Chapter 4), a fascinating research area where the Grobner basis of a toric ideal is a fundamental tool of the Markov chain Monte Carlo method. Moreover, the Grobner basis of a toric ideal has had a great influence on the study of convex polytopes (Chapter 5). In addition, the Grobner basis of the ring of differential operators gives effective algorithms on holonomic functions (Chapter 6). The third act (Chapter 7) is a collection of concrete examples and problems for Chapters 4, 5 and 6 emphasizing computation by using various software systems. " Table of Contents A Quick Introduction to Gröbner Bases.- Warm-up Drills and Tips for Mathematical Software.- Computation of Gröbner Bases.- Markov Bases and Designed Experiments.- Convex Polytopes and Gröbner Bases.- Gröbner Basis for Rings of Differential Operators and Applications.- Examples and Exercises. Long Description The idea of the Grobner basis first appeared in a 1927 paper by F. S. Macaulay, who succeeded in creating a combinatorial characterization of the Hilbert functions of homogeneous ideals of the polynomial ring. Later, the modern definition of the Grobner basis was independently introduced by Heisuke Hironaka in 1964 and Bruno Buchberger in 1965. However, after the discovery of the notion of the Grobner basis by Hironaka and Buchberger, it was not actively pursued for 20 years. A breakthrough was made in the mid-1980s by David Bayer and Michael Stillman, who created the Macaulay computer algebra system with the help of the Grobner basis. Since then, rapid development on the Grobner basis has been achieved by many researchers, including Bernd Sturmfels. This book serves as a standard bible of the Grobner basis, for which the harmony of theory, application, and computation are indispensable. It provides all the fundamentals for graduate students to learn the ABC s of the Grobner basis, requiring no special knowledgeto understand those basic points. Starting from the introductory performance of the Grobner basis (Chapter 1), a trip around mathematical software follows (Chapter 2). Then comes a deep discussion of how to compute the Grobner basis (Chapter 3). These three chapters may be regarded as the first act of a mathematical play. The second act opens with topics on algebraic statistics (Chapter 4), a fascinating research area where the Grobner basis of a toric ideal is a fundamental tool of the Markov chain Monte Carlo method. Moreover, the Grobner basis of a toric ideal has had a great influence on the study of convex polytopes (Chapter 5). In addition, the Grobner basis of the ring of differential operators gives effective algorithms on holonomic functions (Chapter 6). The third act (Chapter 7) is a collection of concrete examples and problems for Chapters 4, 5 and 6 emphasizing computation by using various software systems. " Feature Covers broad aspects of Gr Details ISBN443156215X Publisher Springer Verlag, Japan Year 2016 ISBN-10 443156215X ISBN-13 9784431562153 Format Paperback Language English Media Book DEWEY 519.5 Imprint Springer Verlag, Japan Subtitle Statistics and Software Systems Place of Publication Tokyo Country of Publication Japan Edited by Takayuki Hibi Publication Date 2016-08-27 Pages 474 Short Title Grobner Bases Author Takayuki Hibi Edition Description Softcover reprint of the original 1st ed. 2013 Alternative 9784431545736 Audience Professional & Vocational Illustrations 123 Illustrations, black and white; XV, 474 p. 123 illus. We've got this At The Nile, if you're looking for it, we've got it. 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