Computational Linear and Commutative Algebra, 1st ed. 2016

This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems.

This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to present it in their lively and humorous style, interspersing core content with funny quotations and tongue-in-cheek explanations.

Most of the material is not yet available in book form

Combines linear and commutative algebra in a novel, unified way

Every chapter starts with a lively and humorous introduction to the topic

Follows the two well-received and well-known volumes “Computational Commutative Algebra 1+2” by the same authors

Written by active researchers in computer algebra

Authors have extensive first-hand experience in developing and implementing computer algebra methods via the development of the computer algebra system CoCoA

CoCoA files for the examples available as Electronic Supplementary Material

Includes supplementary material: sn.pub/extras