Gröbner bases and applications

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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.

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Title Statements

Full title :Gröbner bases and applications / edited by B. Buchberger & F. Winkler.

Summary

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.

Edition Statements

Publication Date:1998.

Publication Statements

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

Notes

Papers from an intensive course for researchers (Jan. 1998) and a conference "33 Years of Gröbner Bases" held at RISC-Linz, Feb. 2-4, 1998.

The Physical Object

Description:1 online resource (viii, 552 pages) : : illustrations

Edition Identifiers

ISBN:9781107362697, 1107362695, 9780511565847, 0511565844
oclc:ocn836870790
LC Classification:QA251.3
Dewey Decimal:512/.24

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 Char…