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

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 Hardcover 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 Gr 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. Feature Covers broad aspects of Gr Details ISBN4431545735 Publisher Springer Verlag, Japan Year 2014 ISBN-10 4431545735 ISBN-13 9784431545736 Format Hardcover Short Title GROBNER BASES 2013/E Language English Media Book Imprint Springer Verlag, Japan Subtitle Statistics and Software Systems Place of Publication Tokyo Country of Publication Japan Edited by Takayuki Hibi Edition 2013th Pages 474 DOI 10.1007/978-4-431-54574-3 Author Takayuki Hibi Edition Description 2013 ed. Publication Date 2014-01-17 Alternative 9784431562153 DEWEY 005.55 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. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96402867;

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