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Graduate texts in mathematics, vol.141: Gröbner bases. A computational approach to commutative algebra - Thomas Becker, Volker Weispfenning
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Graduate texts in mathematics, vol.141: Gröbner bases. A computational approach to commutative algebra - Première édition

1993, ISBN: 9780387979717

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Thomas Becker, Volker Weispfenning:

Graduate texts in mathematics, vol.141: Gröbner bases. A computational approach to commutative algebra - Première édition

1993, ISBN: 9780387979717

Edition reliée

Mitarbeiter: Heinz Kredel, Springer, Gebundene Ausgabe, Auflage: 1st ed. 1993. Corr. 2nd printing 1998, 598 Seiten, Publiziert: 1993-04-08T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: … Plus…

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Gröbner Bases A Computational Approach to Commutative Algebra 1st ed. 1993. Corr. 2nd printing 1998 - Thomas Becker, H. Kredel, Volker Weispfenning
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Gröbner Bases A Computational Approach to Commutative Algebra 1st ed. 1993. Corr. 2nd printing 1998 - Première édition

1993

ISBN: 9780387979717

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1993, ISBN: 0387979719

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Graduate texts in mathematics, vol.141: Gröbner bases. A computational approach to commutative algebra

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.

Informations détaillées sur le livre - Graduate texts in mathematics, vol.141: Gröbner bases. A computational approach to commutative algebra


EAN (ISBN-13): 9780387979717
ISBN (ISBN-10): 0387979719
Version reliée
Livre de poche
Date de parution: 1998
Editeur: Springer
574 Pages
Poids: 1,046 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2007-06-04T12:42:19+02:00 (Paris)
Page de détail modifiée en dernier sur 2024-02-23T09:33:39+01:00 (Paris)
ISBN/EAN: 9780387979717

ISBN - Autres types d'écriture:
0-387-97971-9, 978-0-387-97971-7
Autres types d'écriture et termes associés:
Auteur du livre: heinz becker, volker beck, weispfenning volker becker thomas, weiß heinz, kredel, weispfennig, buchberger
Titre du livre: computational commutative algebra, groebner, grabner, 141, gröbner bases, approach mathematics, graduate text mathematics, graduate texts mathematics


Données de l'éditeur

Auteur: Thomas Becker; Volker Weispfenning
Titre: Graduate Texts in Mathematics; Gröbner Bases - A Computational Approach to Commutative Algebra
Editeur: Springer; Springer US
576 Pages
Date de parution: 1993-04-08
New York; NY; US
Poids: 2,250 kg
Langue: Anglais
106,99 € (DE)
109,99 € (AT)
118,00 CHF (CH)
POD
XXII, 576 p.

BB; Group Theory and Generalizations; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Gruppen und Gruppentheorie; Verstehen; Abstract algebra; Algebra; Algebraic structure; Finite; Morphism; Vector space; axiom of choice; equation; function; mathematics; theorem; Algebra; Group Theory and Generalizations; Algebra; Algebra; BC; EA

0 Basics.- 0.1 Natural Numbers and Integers.- 0.2 Maps.- 0.3 Mathematical Algorithms.- Notes.- 1 Commutative Rings with Unity.- 1.1 Why Abstract Algebra?.- 1.2 Groups.- 1.3 Rings.- 1.4 Subrings and Homomorphisms.- 1.5 Ideals and Residue Class Rings.- 1.6 The Homomorphism Theorem.- 1.7 Gcd’s, Lcm’s, and Principal Ideal Domains.- 1.8 Maximal and Prime Ideals.- 1.9 Prime Rings and Characteristic.- 1.10 Adjunction, Products, and Quotient Rings.- Notes.- 2 Polynomial Rings.- 2.1 Definitions.- 2.2 Euclidean Domains.- 2.3 Unique Factorization Domains.- 2.4 The Gaussian Lemma.- 2.5 Polynomial Gcd’s.- 2.6 Squarefree Decomposition of Polynomials.- 2.7 Factorization of Polynomials.- 2.8 The Chinese Remainder Theorem.- Notes.- 3 Vector Spaces and Modules.- 3.1 Vector Spaces.- 3.2 Independent Sets and Dimension.- 3.3 Modules.- Notes.- 4 Orders and Abstract Reduction Relations.- 4.1 The Axiom of Choice and Some Consequences in Algebra.- 4.2 Relations.- 4.3 Foundedness Properties.- 4.4 Some Special Orders.- 4.5 Reduction Relations.- 4.6 Computing in Algebraic Structures.- Notes.- 5 Gröbner Bases.- 5.1 Term Orders and Polynomial Reductions.- 5.2 Gröbner Bases—Existence and Uniqueness.- 5.3 Gröbner Bases—Construction.- 5.4 Standard Representations.- 5.5 Improved Gröbner Basis Algorithms.- 5.6 The Extended Gröbner Basis Algorithm.- Notes.- 6 First Applications of Gröbner Bases.- 6.1 Computation of Syzygies.- 6.2 Basic Algorithms in Ideal Theory.- 6.3 Dimension of Ideals.- 6.4 Uniform Word Problems.- Notes.- 7 Field Extensions and the Hilbert Nullstellensatz.- 7.1 Field Extensions.- 7.2 The Algebraic Closure of a Field.- 7.3 Separable Polynomials and Perfect Fields.- 7.4 The Hilbert Nullstellensatz.- 7.5 Height and Depth of Prime Ideals.- 7.6 Implicitization of Rational Parametrizations.- 7.7 Invertibility of Polynomial Maps.- Notes.- 8 Decomposition, Radical, and Zeroes of Ideals.- 8.1 Preliminaries.- 8.2 The Radical of a Zero-Dimensional Ideal.- 8.3 The Number of Zeroes of an Ideal.- 8.4 Primary Ideals.- 8.5 Primary Decomposition in Noetherian Rings.- 8.6 Primary Decomposition of Zero-Dimensional Ideals.- 8.7 Radical and Decomposition in Higher Dimensions.- 8.8 Computing Real Zeroes of Polynomial Systems.- Notes.- 9 Linear Algebra in Residue Class Rings.- 9.1 Gröbner Bases and Reduced Terms.- 9.2 Computing in Finitely Generated Algebras.- 9.3 Dimensions and the Hilbert Function.- Notes.- 10 Variations on Gröbner Bases.- 10.1 Gröbner Bases over PID’s and Euclidean Domains.- 10.2 Homogeneous Gröbner Bases.- 10.3 Homogenization.- 10.4 Gröbner Bases for Polynomial Modules.- 10.5 Systems of Linear Equations.- 10.6 Standard Bases and the Tangent Cone.- 10.7 Symmetric Functions.- Notes.- Appendix: Outlook on Advanced and Related Topics.- Complexity of Gröbner Basis Constructions.- Term Orders and Universal Gröbner Bases.- Comprehensive Gröbner Bases.- Gröbner Bases and Automatic Theorem Proving.- Characteristic Sets and Wu-Ritt Reduction.- Term Rewriting.- Standard Bases in Power Series Rings.- Non-Commutative Gröbner Bases.- Gröbner Bases and Differential Algebra.- Selected Bibliography.- Conference Proceedings.- Books and Monographs.- Articles.- List of Symbols.

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