عنوان

Gröbner bases :

0387979719

3540979719

9780387979717

9783540979715

bnb

b412197

Gröbner bases :

[Book]

a computational approach to commutative algebra /

Thomas Becker, Volker Weispfenning, in cooperation with Heinz Kredel

xxii, 574 pages :

illustrations ;

25 cm

Graduate texts in mathematics ;

141

Includes bibliographical references (pages 531-559) and index

5.1. Term Orders and Polynomial Reductions. 5.2. Grobner Bases -- Existence and Uniqueness. 5.3. Grobner Bases -- Construction. 5.4. Standard Representations. 5.5. Improved Grobner Basis Algorithms. 5.6. The Extended Grobner Basis Algorithm -- 6. First Applications of Grobner Bases. 6.1. Computation of Syzygies. 6.2. Basic Algorithms in Ideal Theory. 6.3. Dimension of Ideals. 6.4. Uniform Word Problems -- 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 -- 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 -- 9. Linear Algebra in Residue Class Rings. 9.1. Grobner Bases and Reduced Terms. 9.2. Computing in Finitely Generated Algebras. 9.3. Dimensions and the Hilbert Function -- 10. Variations on Grobner Bases. 10.1. Grobner Bases over PID's and Euclidean Domains. 10.2. Homogeneous Grobner Bases. 10.3. Homogenization. 10.4. Grobner Bases for Polynomial Modules. 10.5. Systems of Linear Equations. 10.6. Standard Bases and the Tangent Cone. 10.7. Symmetric Functions -- Appendix: Outlook on Advanced and Related Topics. Complexity of Grobner Basis Constructions. Term Orders and Universal Grobner Bases. Comprehensive Grobner Bases. Grobner Bases and Automatic Theorem Proving. Characteristic Sets and Wu-Ritt Reduction. Term Rewriting. Standard Bases in Power Series Rings. Non-Commutative Grobner Bases. Grobner Bases and Differential Algebra

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0

Gröbner bases.

Algebra-- Data processing

Gröbner bases

Algèbre commutative

base Gröbner

calcul formel

Becker, Thomas,1952-

Kredel, Heinz

Weispfenning, Volker,1944-

20160712055524.0

[Book]

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