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Computational Algebraic Number Theory

  • Book
  • © 1993

Overview

Authors:
  1. Michael E. Pohst

    1. Fachbereich 3 Mathematik, Technische Universität Berlin, Berlin 12, Germany

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Part of the book series: Oberwolfach Seminars (OWS, volume 21)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Michael E. Pohst
    Pages 1-3

  3. Topics from finite fields

    • Michael E. Pohst
    Pages 4-10

  4. Topics from the geometry of numbers

    • Michael E. Pohst
    Pages 11-26

  5. Algebraic number fields

    • Michael E. Pohst
    Pages 27-33

  6. Computation of an integral basis

    • Michael E. Pohst
    Pages 34-43

  7. Computation of the unit group

    • Michael E. Pohst
    Pages 44-60

  8. Computation of the class group

    • Michael E. Pohst
    Pages 61-75

  9. Back Matter

    Pages 76-90
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Keywords

About this book

Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker Vereinigung initiated an introductory graduate seminar on this topic in Düsseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields. Contents: Introduction • Topics from finite fields • Arithmetic and polynomials • Factorization of polynomials • Topics from the geometry of numbers • Hermite normal form • Lattices • Reduction • Enumeration of lattice points • Algebraic number fields • Introduction • Basic Arithmetic • Computation of an integral basis • Integral closure • Round-Two-Method • Round-Four-Method • Computation of the unit group • Dirichlet's unit theorem and a regulator bound • Two methods for computing r independent units • Fundamental unit computation • Computation of the class group • Ideals and class number • A method for computing the class group • Appendix • The number field sieve • KANT • References • Index

Authors and Affiliations

  • Fachbereich 3 Mathematik, Technische Universität Berlin, Berlin 12, Germany

    Michael E. Pohst

Bibliographic Information

  • Book Title: Computational Algebraic Number Theory

  • Authors: Michael E. Pohst

  • Series Title: Oberwolfach Seminars

  • DOI: https://doi.org/10.1007/978-3-0348-8589-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1993

  • Softcover ISBN: 978-3-7643-2913-6Published: 01 September 1993

  • eBook ISBN: 978-3-0348-8589-8Published: 06 December 2012

  • Series ISSN: 1661-237X

  • Series E-ISSN: 2296-5041

  • Edition Number: 1

  • Number of Pages: X, 90

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Number Theory, Science, Humanities and Social Sciences, multidisciplinary

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