Solving polynomial equation systems. Volume 4, Buchberger's theory and beyond / Teo Mora.

Format:

Book

Author/Creator:

Mora, Teo, author.

Series:

Encyclopedia of mathematics and its applications ; v. 158.

Encyclopedia of mathematics and its applications ; volume 158

Language:

English

Subjects (All):

Equations--Numerical solutions.

Equations.

Polynomials.

Iterative methods (Mathematics).

Physical Description:

1 online resource (xi, 820 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2016.

Summary:

In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.

Contents:

1. Solving polynomial equation systems

2. Macaulay's Paradigm and Gröbner Technology

3. Algebraic Solving

Notes:

Title from publisher's bibliographic system (viewed on 05 Apr 2016).

Includes bibliographical references and index.

ISBN:

1-316-37958-2

1-316-38318-0

1-316-35918-2

1-316-36038-5

1-316-35978-6

1-316-38498-5

1-316-27190-0