Computations in Algebraic Geometry with Macaulay 2

  • David Eisenbud
  • Michael Stillman
  • Daniel R. Grayson
  • Bernd Sturmfels

Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 8)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Introducing Macaulay 2

    1. Front Matter
      Pages 1-1
    2. Bernd Sturmfels
      Pages 3-15
    3. David Eisenbud
      Pages 17-40
    4. Daniel R. Grayson, Michael E. Stillman
      Pages 41-53
    5. Gregory G. Smith, Bernd Sturmfels
      Pages 55-70
  3. Mathematical Computations

    1. Front Matter
      Pages 71-71
    2. Serkan Hoşten, Gregory G. Smith
      Pages 73-100
    3. Luchezar L. Avramov, Daniel R. Grayson
      Pages 131-178
    4. Michael Stillman, Bernd Sturmfels, Rekha Thomas
      Pages 179-214
    5. Wolfram Decker, David Eisenbud
      Pages 215-249
    6. Frank-Olaf Schreyer, Fabio Tonoli
      Pages 251-279
    7. Uli Walther
      Pages 281-323
  4. Back Matter
    Pages 325-329

About this book


Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re­ cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith­ mic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solv­ ing problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield new algorithms and emerging applications lead to new theoretical questions. This book presents algorithmic tools for algebraic geometry and experi­ mental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. A wide range of mathematical scientists should find these expositions valuable. This includes both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all.


Groebner bases algebraic geometry algorithms commutative algebra computer algebra system symbolic algebra syzygies

Editors and affiliations

  • David Eisenbud
    • 1
  • Michael Stillman
    • 2
  • Daniel R. Grayson
    • 3
  • Bernd Sturmfels
    • 4
  1. 1.Mathematical SciencesResearch InstituteBerkeleyUSA
  2. 2.Department of MathematicsCornell UniversityIthacaUSA
  3. 3.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  4. 4.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07592-6
  • Online ISBN 978-3-662-04851-1
  • Series Print ISSN 1431-1550
  • About this book