Overview
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
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Table of contents (6 chapters)
Keywords
About this book
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.
Reviews
“The book is well-written and includes many examples. Each chapter begins with a summary that motivates the … mathematics to follow, and every method is accompanied by an algorithms … . The book contains many new results and concepts, along with known ideas drawn from a widely scattered literature. … Overall, this book is a worthy contribution to both linear and commutative algebra.” (David A. Cox, Computeralgebra Rundbrief, 2017)
“The book is a textbook for advanced undergraduate and for graduate courses. Surprisingly, the experienced reader will also find new and unexpected aspects. I like the humorous style of the authors. The funny quotations help one enjoy the topic.” (Mathematical Reviews, 2017)
Authors and Affiliations
About the authors
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.
Bibliographic Information
Book Title: Computational Linear and Commutative Algebra
Authors: Martin Kreuzer, Lorenzo Robbiano
DOI: https://doi.org/10.1007/978-3-319-43601-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-43599-2Published: 16 September 2016
Softcover ISBN: 978-3-319-82865-7Published: 14 June 2018
eBook ISBN: 978-3-319-43601-2Published: 06 September 2016
Edition Number: 1
Number of Pages: XVIII, 321
Number of Illustrations: 1 b/w illustrations
Topics: Commutative Rings and Algebras, Linear and Multilinear Algebras, Matrix Theory