Grobner Bases: A Computational Approach to Commutative Algebra

Becker, Thomas & Volker Weispfennig, in cooperation with Heinz Kredel

ISBN 10: 0387979719 / ISBN 13: 9780387979717

Published by Springer-Verlag (1993), New York, 1993

About this Item

Ex-library. Library stamps and markings. ; xxii, [1], 574, [2] pages. Hardcover. Papered boards. Page dimensions: 234 x 152mm. Contents: Preface; How to Use This Book; List of Algorithms; Basics; Commutative Rings with Unity; Polynomial Rings; Vector Spaces and Modules; Orders and Abstract Reduction Relations; Grobner Bases; First Applications of Grobner Bases; Field Extensions and the Hilbert Nullstellensatz; Decomposition, Radical, and Zeroes of Ideals; Linear Algebra in Residue Class Rings; Variations on Grobner Bases; Appendix: Outlook on Advanced and Related Topics; Selected Bibliography; List of Symbols; Index. ; Graduate Texts in Mathematics; Ex-Library; Vol. 141; 8vo.

Seller Inventory # 10874

Bibliographic Details

• Title: Grobner Bases: A Computational Approach to Commutative Algebra
• Publisher: Springer-Verlag (1993), New York
• Publication Date: 1993
• Language: English
• ISBN 10: 0387979719
• ISBN 13: 9780387979717
• Binding: Hardcover
• Edition: First Edition.
• Condition: Good+
• Dust Jacket Condition: No Dust Jacket

About this title

Synopsis

The origins of the mathematics in this book date back more than two thou­ sand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Eu­ clid. The word "algorithm" as well as the key word "algebra" in the title of this book come from the name and the work of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who was born in what is now Uzbek­ istan and worked in Baghdad at the court of Harun al-Rashid's son. The word "algorithm" is actually a westernization of al-Khowarizmi's name, while "algebra" derives from "al-jabr," a term that appears in the title of his book Kitab al-jabr wa'l muqabala, where he discusses symbolic methods for the solution of equations. This close connection between algebra and al­ gorithms lasted roughly up to the beginning of this century; until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations. During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid's time, namely, the axiomatic method.

Synopsis

This book provides a comprehensive treatment of Gr bner bases theory embedded in an introduction to commutative algebra from a computational point of view. The centerpiece of Gr bner bases theory is the Buchberger algorithm, which provides a common generalization of the Euclidean algorithm and the Gaussian elimination algorithm to multivariate polynomial rings. The book explains how the Buchberger algorithm and the theory surrounding it are eminently important both for the mathematical theory and for computational applications. A number of results such as optimized version of the Buchberger algorithm are presented in textbook format for the first time. This book requires no prerequisites other than the mathematical maturity of an advanced undergraduate and is therefore well suited for use as a textbook. At the same time, the comprehensive treatment makes it a valuable source of reference on Gr bner bases theory for mathematicians, computer scientists, and others. Placing a strong emphasis on algorithms and their verification, while making no sacrifices in mathematical rigor, the book spans a bridge between mathematics and computer science.