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Using Algebraic Geometry

  • David A. Cox
  • John Little
  • Donal O’shea

Part of the Graduate Texts in Mathematics book series (GTM, volume 185)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Pages 1-25
  3. Pages 77-136
  4. Pages 189-246
  5. Pages 247-304
  6. Pages 451-493
  7. Back Matter
    Pages 533-572

About this book

Introduction

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gröbner bases and resultants.

The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gröbner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.

For the new edition, the authors have added a unified discussion of how matrices can be used to specify monomial orders; a revised presentation of the Mora normal form algorithm; two sections discussing the Gröbner fan of an ideal and the Gröbner Walk basis conversion algorithm; and a new chapter on the theory of order domains, associated codes, and the Berlekamp-Massey-Sakata decoding algorithm. They have also updated the references, improved some of the proofs, and corrected typographical errors.

David Cox is Professor of Mathematics at Amherst College. John Little is Professor of Mathematics at College of the Holy Cross. Dona

l O’Shea is the Elizabeth T. Kennan Professor of Mathematics and Dean of Faculty at Mt. Holyoke College. These authors also co-wrote the immensely successful book, Ideals, Varieties, and Algorithms.

Keywords

Splines algorithms coding theory combinatorics computer geometry programming

Authors and affiliations

  • David A. Cox
    • 1
  • John Little
    • 2
  • Donal O’shea
    • 3
  1. 1.Department of MathematicsAmherst CollegeAmherstUSA
  2. 2.Department of MathematicsCollege of the Holy CrossWorcesterUSA
  3. 3.Department of MathematicsMount Holyoke CollegeSouth HadleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b138611
  • Copyright Information Springer Science+Business Media, Inc. 2005
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-20706-3
  • Online ISBN 978-0-387-27105-7
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site