Gröbner Bases and Applications

by Buchberger, Bruno

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Title Statements

Full title :Gröbner Bases and Applications.

Summary

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?

How is the gin computed?

Comprehensive account of theory and applications of Gröbner bases, co-edited by the subject's inventor.

Edition Statements

Publication Date:1998.
Edition:Online-ausg

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge
Language:eng
Publication Date:1998.

The Physical Object

Description:Online-Ressource (1 online resource (562 Seiten))

Edition Identifiers

ISBN:9781107367609, 1107367603, 9780511565847, 0511565844, 9780521632980, 0521632986
DOI:10.1017/CBO9780511565847
oclc:ocn846961631
LC Classification:QA251.3 .G76 1998
Dewey Decimal:512.24