Gröbner Bases: A Computational Approach to Commutative Algebra / Edition 1

Gröbner Bases: A Computational Approach to Commutative Algebra / Edition 1

by Thomas Becker, Volker Weispfenning, H. Kredel
     
 

ISBN-10: 0387979719

ISBN-13: 9780387979717

Pub. Date: 04/08/1993

Publisher: Springer New York

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

Overview

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.

Product Details

ISBN-13:
9780387979717
Publisher:
Springer New York
Publication date:
04/08/1993
Series:
Graduate Texts in Mathematics Series, #141
Edition description:
1st ed. 1993. Corr. 2nd printing 1998
Pages:
576
Product dimensions:
9.21(w) x 6.14(h) x 1.38(d)

Related Subjects

Table of Contents

1: Commutative Rings with Unity. 2: Polynomial Rings. 3: Vector Spaces and Modules. 4: Orders and Abstract Reduction Relations. 5: Gr bner Bases. 6: First Applications of Gr bner Bases. 7: Field Extensions and the Hilbert Nullstellensatz. 8: Decomposition, Radical, and Zeroes of Ideals. 9: Linear Algebra in Residue Class Rings. 10: Variations on Gr bner Bases.

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