Gröbner Bases

A Computational Approach to Commutative Algebra

  • Thomas Becker
  • Volker Weispfenning

Part of the Graduate Texts in Mathematics book series (GTM, volume 141)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Thomas Becker, Volker Weispfenning
    Pages 1-13
  3. Thomas Becker, Volker Weispfenning
    Pages 15-59
  4. Thomas Becker, Volker Weispfenning
    Pages 61-118
  5. Thomas Becker, Volker Weispfenning
    Pages 119-139
  6. Thomas Becker, Volker Weispfenning
    Pages 141-185
  7. Thomas Becker, Volker Weispfenning
    Pages 187-242
  8. Thomas Becker, Volker Weispfenning
    Pages 243-292
  9. Thomas Becker, Volker Weispfenning
    Pages 293-333
  10. Thomas Becker, Volker Weispfenning
    Pages 335-421
  11. Thomas Becker, Volker Weispfenning
    Pages 423-452
  12. Thomas Becker, Volker Weispfenning
    Pages 453-509
  13. Back Matter
    Pages 511-576

About this book

Introduction

The origins of the mathematics in this book date back more than two thou­ sand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Eu­ clid. The word "algorithm" as well as the key word "algebra" in the title of this book come from the name and the work of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who was born in what is now Uzbek­ istan and worked in Baghdad at the court of Harun al-Rashid's son. The word "algorithm" is actually a westernization of al-Khowarizmi's name, while "algebra" derives from "al-jabr," a term that appears in the title of his book Kitab al-jabr wa'l muqabala, where he discusses symbolic methods for the solution of equations. This close connection between algebra and al­ gorithms lasted roughly up to the beginning of this century; until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations. During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid's time, namely, the axiomatic method.

Keywords

Abstract algebra Algebra Algebraic structure Finite Morphism Vector space axiom of choice equation function mathematics theorem

Authors and affiliations

  • Thomas Becker
    • 1
  • Volker Weispfenning
    • 1
  1. 1.Fakultät für Mathematik und Informatik Universität PassauPassauGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0913-3
  • Copyright Information Springer-Verlag New York, Inc. 1993
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6944-1
  • Online ISBN 978-1-4612-0913-3
  • Series Print ISSN 0072-5285
  • About this book