An introduction to Gröbner bases / William W. Adams, Philippe Loustaunau.
Series Graduate studies in mathematics, v. 3Editor: Providence, R.I. : American Mathematical Society, c1994Descripción: xiii, 289 p. : il. ; 27 cmISBN: 0821838040Tema(s): Gröbner basesOtra clasificación: 13P10 (13-01 68W30)Chapter 1. Basic Theory of Gröbner Bases [1] 1.1. Introduction [1] 1.2. The Linear Case [7] 1.3. The One Variable Case [10] 1.4. Term Orders [18] 1.5. Division Algorithm [25] 1.6. Gröbner Bases [32] 1.7. S-Polynomials and Buchberger’s Algorithm [39] 1.8. Reduced Grobner Bases [46] 1.9. Summary [50] Chapter 2. Applications of Gröbner Bases [53] 2.1. Elementary Applications of Gröbner Bases [53] 2.2. Hilbert Nullstellensatz [61] 2.3. Elimination [69] 2.4. Polynomial Maps [79] 2.5. Some Applications to Algebraic Geometry [90] 2.6. Minimal Polynomials of Elements in Field Extensions [97] 2.7. The 3-Color Problem [102] 2.8. Integer Programming [105] Chapter 3. Modules and Gröbner Bases [113] 3.1. Modules [113] 3.2. Gröbner Bases and Syzygies [118] 3.3. Improvements on Buchberger’s Algorithm [124] 3.4. Computation of the Syzygy Module [134] 3.5. Gröbner Bases for Modules [140] 3.6. Elementary Applications of Gröbner Bases for Modules [152] 3.7. Syzygies for Modules [161] 3.8. Applications of Syzygies [171] 3.9. Computation of Hom [183] 3.10. Free Resolutions [194] Chapter 4. Gröbner Bases over Rings [201] 4.1. Basic Definitions [202] 4.2. Computing Gröbner Bases over Rings [212] 4.3. Applications of Gröbner Bases over Rings [225] 4.4. A Primality Test [237] 4.5. Grobner Bases over Principal Ideal Domains [246] 4.6. Primary Decomposition in R[x] for R a PID [259] Appendix A. Computations and Algorithms [275] Appendix B. Well-ordering and Induction [277] References [279] List of Symbols [283]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
Libros
|
Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 13 Ad211 (Browse shelf) | Available | A-7384 |
Browsing Instituto de Matemática, CONICET-UNS shelves, Shelving location: Libros ordenados por tema Close shelf browser
| 12 V554 Leçons sur la théorie des équations selon Galois : | 12 W127-2 Moderne Algebra / | 12 W784 The structure of fields / | 13 Ad211 An introduction to Gröbner bases / | 13 At872 Introduction to commutative algebra / | 13 C527 The construction and study of certain important algebras / | 13 D567 Topics in local algebra / |
Incluye referencias bibliográficas (p. 279-281) e índice.
Chapter 1. Basic Theory of Gröbner Bases [1] --
1.1. Introduction [1] --
1.2. The Linear Case [7] --
1.3. The One Variable Case [10] --
1.4. Term Orders [18] --
1.5. Division Algorithm [25] --
1.6. Gröbner Bases [32] --
1.7. S-Polynomials and Buchberger’s Algorithm [39] --
1.8. Reduced Grobner Bases [46] --
1.9. Summary [50] --
Chapter 2. Applications of Gröbner Bases [53] --
2.1. Elementary Applications of Gröbner Bases [53] --
2.2. Hilbert Nullstellensatz [61] --
2.3. Elimination [69] --
2.4. Polynomial Maps [79] --
2.5. Some Applications to Algebraic Geometry [90] --
2.6. Minimal Polynomials of Elements in Field Extensions [97] --
2.7. The 3-Color Problem [102] --
2.8. Integer Programming [105] --
Chapter 3. Modules and Gröbner Bases [113] --
3.1. Modules [113] --
3.2. Gröbner Bases and Syzygies [118] --
3.3. Improvements on Buchberger’s Algorithm [124] --
3.4. Computation of the Syzygy Module [134] --
3.5. Gröbner Bases for Modules [140] --
3.6. Elementary Applications of Gröbner Bases for Modules [152] --
3.7. Syzygies for Modules [161] --
3.8. Applications of Syzygies [171] --
3.9. Computation of Hom [183] --
3.10. Free Resolutions [194] --
Chapter 4. Gröbner Bases over Rings [201] --
4.1. Basic Definitions [202] --
4.2. Computing Gröbner Bases over Rings [212] --
4.3. Applications of Gröbner Bases over Rings [225] --
4.4. A Primality Test [237] --
4.5. Grobner Bases over Principal Ideal Domains [246] --
4.6. Primary Decomposition in R[x] for R a PID [259] --
Appendix A. --
Computations and Algorithms [275] --
Appendix B. --
Well-ordering and Induction [277] --
References [279] --
List of Symbols [283] --
MR, 95g:13025
Click on an image to view it in the image viewer
There are no comments on this title.