Gröbner Bases. Graduate Texts in Mathematics, Band 141

Seitenzahl:

574

Gewicht:

1046 g

Auflage:

1993. Corr. 2nd.

Erschienen bei:

Springer

Beschreibung

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.

Kurzbeschreibung

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. TOC: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.

Portrait

Professor für Organisation und Wirtschaftsinformatik im Fachbereich Wirtschaftswissenschaften an der FH Mainz. Er lehrt u.a. in den Bereichen Business Intelligence, IT-Strategie und IT-Controlling und Projektmanagement. Zudem ist er Leiter des IT-Management und Projektleiter Digitale Archive beim ZDF. Seine Forschungsthemen sind u.a. Collaborative Business Intelligence, IT-Organisation und Projektmanagement und betriebliche Anwendungssoftware.

Mehr über...

Mehr über:  Algebra, Datenverarbeitung / Anwendungen / Mathematik, Statistik, Kommutation - kommutativ, kommutativ ( Kommutation ), Statistik. Kommutation - kommutativ. kommutativ ( Kommutation ) Mathematik

Mehr von: 

Mehr von:  Thomas Becker, Volker Weispfenning, Springer