Computational Linear and Commutative Algebra

  • Martin Kreuzer
  • Lorenzo Robbiano

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Martin Kreuzer, Lorenzo Robbiano
    Pages 1-45
  3. Martin Kreuzer, Lorenzo Robbiano
    Pages 47-93
  4. Martin Kreuzer, Lorenzo Robbiano
    Pages 95-129
  5. Martin Kreuzer, Lorenzo Robbiano
    Pages 131-184
  6. Martin Kreuzer, Lorenzo Robbiano
    Pages 185-242
  7. Martin Kreuzer, Lorenzo Robbiano
    Pages 243-309
  8. Back Matter
    Pages 311-321

About this book

Introduction

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.

Keywords

commuting endomorphisms generalized eigenspace multiplication map zero-dimensional affine algebra primary decomposition polynomial system

Authors and affiliations

  • Martin Kreuzer
    • 1
  • Lorenzo Robbiano
    • 2
  1. 1.Fakultät für Informatik und MathematikUniversität PassauPassauGermany
  2. 2.Department of MathematicsUniversity of GenoaGenoaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-43601-2
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-43599-2
  • Online ISBN 978-3-319-43601-2
  • About this book