SPRINGER GROEBNER BASES STATISTICS AND SOFTWARE SYSTEMS 2013 RETAIL EBOOK-kE

TITLE: GROEBNER BASES: STATISTICS AND SOFTWARE SYSTEMS
PUBLISHER: SPRINGER LANGUAGE: ENGLISH
LINK: http://is.gd/4sAuSu RELEASE TYPE: RETAIL
FORMAT: PDF RELEASE DATE: 2015.01.28
ISBN: 9784431545743 STORE DATE: 2013
SAVED.MONEY: 80 EURO DISKCOUNT: 03 x 05MB
AUTHOR: HIBI, TAKAYUKI (ED.)

BOOK

The idea of the Groebner 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
Groebner basis was independently introduced by Heisuke Hironaka
in 1964 and Bruno Buchberger in 1965. However, after the
discovery of the notion of the Groebner 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 Groebner basis. Since then, rapid development on
the Groebner basis has been achieved by many researchers
including Bernd Sturmfels

This book serves as a standard bible of the Groebner 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 Groebner basis, requiring no
special knowledge to understand those basic points

Starting from the introductory performance of the Groebner basis
(Chapter 1), a trip around mathematical software follows (Chapter
2). Then comes a deep discussion of how to compute the Groebner
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 Groebner basis of a toric ideal is a
fundamental tool of the Markov chain Monte Carlo method
Moreover, the Groebner basis of a toric ideal has had a great
influence on the study of convex polytopes (Chapter 5). In
addition, the Groebner 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