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

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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.

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Editorial Reviews

The centerpiece of Grobner basis theory is the Buchberger algorithm, the importance of which is explained, as it spans mathematical theory and computational applications. This comprehensive treatment is useful as a text and as a reference for mathematicians and computer scientists and requires no prerequisites other than the mathematical maturity of an advanced undergraduate. Strong emphasis is placed on algorithms and their verification, with no sacrifices in mathematical rigor. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780387979717
  • Publisher: Springer New York
  • Publication date: 4/8/1993
  • Series: Graduate Texts in Mathematics Series, #141
  • Edition description: 1st ed. 1993. Corr. 2nd printing 1998
  • Edition number: 1
  • Pages: 576
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.38 (d)

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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