Computational Linear and Commutative Algebra

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 notavailable 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

Autorentext
Martin Kreuzer holds the Chair of Symbolic Computation at the University of Passau, Germany. Starting out in Commutative Algebra and Algebraic Geometry, his research interests have developed further into Computer Algebra and its applications, including industrial applications and algebraic cryptography. He is the author or co-author of five monographs on computational algebra, cryptography and logic.
In his spare time, he plays correspondence chess, for which he is an international grandmaster and a severalfold world team champion.

Lorenzo Robbiano is a retired professor at the University of Genova, Italy. He is the co-author (with Martin Kreuzer) of the two books Computational Commutative Algebra 1 and Computational Commutative Algebra 2.

Since 1987 he has been the team leader of the project CoCoA. His research interests have evolved from Algebraic Geometry to Commutative Algebra, and in the last years to Computer Algebra.

Inhalt
Foreword.- Introduction.- 1 Endomorphisms.- 2 Families of Commuting Endomorphisms.- 3 Special Families of Endomorphisms.- 4 Zero-Dimensional Affine Algebras.- 5 Computing Primary and Maximal Components.- 6 Solving Zero-Dimensional Polynomial Systems.- Notation.- References.- Index.