Gröbner Bases
A Computational Approach to Commutative Algebra
Seiten
1998
|
Corr. 2nd printing
Springer Berlin (Hersteller)
978-3-540-97971-5 (ISBN)
Springer Berlin (Hersteller)
978-3-540-97971-5 (ISBN)
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This book provides a comprehensive treatment of Gröbner 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 asa textbook. At the same time, the comprehensive treatment makes it a valuable source of reference on Gröbner 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.
1: Commutative Rings with Unity.
2: Polynomial Rings.
3: Vector Spaces and Modules.
4: Orders and Abstract Reduction Relations.
5: Gröbner 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 Gröbner Bases.
| Reihe/Serie | Graduate Texts in Mathematics ; 141 |
|---|---|
| Sprache | deutsch |
| Gewicht | 966 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Schlagworte | Algebra • HC/Mathematik/Arithmetik, Algebra • Kommutative Algebra |
| ISBN-10 | 3-540-97971-9 / 3540979719 |
| ISBN-13 | 978-3-540-97971-5 / 9783540979715 |
| Zustand | Neuware |
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