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A Course in Computational Algebraic Number Theory

  • Henri Cohen

Part of the Graduate Texts in Mathematics book series (GTM, volume 138)

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Henri Cohen
    Pages 108-150
  3. Henri Cohen
    Pages 151-217
  4. Henri Cohen
    Pages 218-296
  5. Henri Cohen
    Pages 297-359
  6. Henri Cohen
    Pages 360-411
  7. Henri Cohen
    Pages 412-436
  8. Henri Cohen
    Pages 437-468
  9. Henri Cohen
    Pages 469-497
  10. Back Matter
    Pages 498-536

About this book

Introduction

With the advent of powerful computing tools and numerous advances in math­ ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al­ gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli­ cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.

Keywords

Algorithms Computer Algebra Factorisation Primality Symbolic Computation algebra algorithm computer number theory

Authors and affiliations

  • Henri Cohen
    • 1
  1. 1.U.F.R. de Mathématiques et InformatiqueUniversité Bordeaux ITalence CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02945-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08142-2
  • Online ISBN 978-3-662-02945-9
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site
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