Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond

✍ Scribed by Teo Mora

• Publisher: Cambridge University Press
• Year: 2016
• Tongue: English
• Leaves: 834
• Series: Encyclopedia of mathematics and its applications 88 99 157 158
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Content: 1. Solving polynomial equation systems --
2. Macaulay's Paradigm and Gröbner Technology --
3. Algebraic Solving --
4. Buchberger Theory and Beyond.

✦ Subjects

Equations -- Numerical solutions;Polynomials;Iterative methods (Mathematics);Équations -- Solutions numériques;Polynômes;Itération (Mathématiques);Polynomen;Vergelijkingen (wiskunde);Gröbner-Basis;Algebraische Gleichung;Polynomes;Itération (mathématiques);Equations algébriques