Algorithms and Computation in Mathematics

Computations in Algebraic Geometry with Macaulay 2

Editors: Eisenbud, D., Grayson, D.R., Stillman, M., Sturmfels, B. (Eds.)

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eBook $69.99
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  • ISBN 978-3-662-04851-1
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  • ISBN 978-3-642-07592-6
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About this Textbook

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.

Table of contents (11 chapters)

  • Ideals, Varieties and Macaulay 2

    Sturmfels, Bernd

    Pages 3-15

  • Projective Geometry and Homological Algebra

    Eisenbud, David

    Pages 17-40

  • Data Types, Functions, and Programming

    Grayson, Daniel R. (et al.)

    Pages 41-53

  • Teaching the Geometry of Schemes

    Smith, Gregory G. (et al.)

    Pages 55-70

  • Monomial Ideals

    Hoşten, Serkan (et al.)

    Pages 73-100

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-662-04851-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-3-540-42230-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-3-642-07592-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Computations in Algebraic Geometry with Macaulay 2
Editors
  • David Eisenbud
  • Daniel R. Grayson
  • Mike Stillman
  • Bernd Sturmfels
Series Title
Algorithms and Computation in Mathematics
Series Volume
8
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-04851-1
DOI
10.1007/978-3-662-04851-1
Hardcover ISBN
978-3-540-42230-3
Softcover ISBN
978-3-642-07592-6
Series ISSN
1431-1550
Edition Number
1
Number of Pages
XV, 329
Number of Illustrations and Tables
1 b/w illustrations
Topics