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Gröbner bases and applications /
This book provides an easy-to-read account of the theory of Gröbner bases and applications. It is in 2 parts, the first consists of tutorial lectures, and the second, 17 original research papers on Gröbner bases.
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, U.K. ; New York :
Cambridge University Press,
1998.
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| Colección: | London Mathematical Society lecture note series ;
251. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Contents; Preface; Programme Committee; Tutorials; Introduction to Grobner Bases; Outline; 1 Grobner Bases at Work; 1.1 Example: Fermat Ideals; 1.2 Example: Geometry Theorem Proving; 1.3 Example: Invariant Theory; 1.4 Example: Systems of Polynomial Equations; 2 The Main Theorem on Grobner Bases; 2.1 Polynomials; 2.2 Polynomial Ideals; 2.3 Admissible Orderings on Power Products; 2.4 Order Dependent Decomposition of Polynomials; 2.5 Admissible Orderings on Polynomials; 2.6 Reduction Modulo Polynomials; Definition (Reduction Modulo Polynomials)
- Proposition (Noetherianity of Reduction Modulo Polynomials)Proposition (Property of Reduction Algorithm):; Proposition (Property of Cofactor Algorithm); Proposition (Compatibility of Reduction); Proposition (Relation Between Reduction and Congruence); 2.7 Some General Properties of Noetherian ReductionRelations; 2.8 Grobner Bases; 2.9 S-Polynomials; 2.10 The Main Theorem: Algorithmic Characterizationof Grobner Bases by S-Polynomials; 2.11 An Algorithm for Constructing Grobner Bases; Proposition (Correctness of the Grobner-Basis Algorithm):; Definition (Reduced Grobner Bases)
- Proposition (Canonicality):2.12 Other Characterizations of Grobner Bases; 3 Applications of Grobner Bases; 3.1 Overview; 3.2 Ideal Membership, Canonical Simplification, IdealIdentity; 3.3 Radical Membership; 3.4 Computation in Residue Class Rings Modulo Ideals; 3.5 Leading Power Products; 3.6 Polynomial Equations; 3.7 Linear Syzygies; 3.8 Hilbert Functions; 3.9 Elimination Ideals; 3.10 Ideal Operations; 3.11 Algebraic Relations and Implicitization; 3.12 Inverse Mappings; 3.13 Miscellaneous; References; Symbolic Summation and Symbolic Integration; Introduction
- 1 Indefinite Summation and Integration1.1 Ore Operators, Ore Algebras, Annihilating Ideals; 1.2 Grobner Bases in Ore Algebras; Contiguity Relations for the Appell F4 Bivariate HypergeometricFunction; 1.3 5-Finite Functions; 1.4 Indefinite Summation and Integration; Particular Solutions; Multivariate Extension; 2 Definite Summation and Integration; 2.1 Creative Telescoping and Elimination by GrobnerBases; 2.2 Multiple Summations and Integrations; 2.3 Takayama's Algorithm and Grobner Bases of Modules; Gordon's Generalization of the Rogers-Ramanujan Identities
- 2.4 Zeilberger's Fast Algorithm and its <9-Finite ExtensionCalkin's Curious Identity; 3 Closure Properties; 3.1 Addition, Product and Derivation of 5-Finite Functionsby the FGLM Algorithm; 3.2 Indefinite Summation and Integration by GrobnerBases; 4 Dimension and Holonomy; Acknowledgements; References; Grobner Bases and Invariant Theory; 0 Introduction; 1 Basic definitions and problems; 2 Algorithms for finite groups; 3 Algorithms for linearly reductive groups; References; A Tutorial on Generic Initial Ideals; Why is the gin Borel-fixed?; Why does the rlex gin compute satiety and regularity?