Solving Polynomial Equation Systems Ii

This volume focuses on Buchberger theory and its application to the algorithmic view of commutative algebra. The presentation is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in its algorithmization.

The second volume of a comprehensive treatise. This part focuses on Buchberger theory and its application to the algorithmic view of commutative algebra.

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.

Computational algebra; computational number theory; commutative algebra; handbook; reference; algorithmic; modern.

The second volume of a comprehensive treatise. This part focuses on Buchberger theory and its application to the algorithmic view of commutative algebra.

Covers extensions of Buchberger's Theory and Algorithm, and promising recent alternatives to Gröbner bases.