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  • © 2005

Using Algebraic Geometry

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

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eBook USD 69.99
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  • ISBN: 978-0-387-27105-7
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Softcover Book USD 89.99
Price excludes VAT (USA)
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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
  2. Introduction

    Pages 1-25
  3. Resultants

    Pages 77-136
  4. Modules

    Pages 189-246
  5. Free Resolutions

    Pages 247-304
  6. Algebraic Coding Theory

    Pages 451-493
  7. Back Matter

    Pages 533-572

About this book

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

  • Department of Mathematics, Amherst College, Amherst, USA

    David A. Cox

  • Department of Mathematics, College of the Holy Cross, Worcester, USA

    John Little

  • Department of Mathematics, Mount Holyoke College, South Hadley, USA

    Donal O’shea

Bibliographic Information

Buying options

eBook USD 69.99
Price excludes VAT (USA)
  • ISBN: 978-0-387-27105-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 89.99
Price excludes VAT (USA)
Hardcover Book USD 119.99
Price excludes VAT (USA)