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Oberwolfach Seminars

Computational Algebraic Number Theory

Authors: Pohst, Michael

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eBook 24,60 €
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  • ISBN 978-3-0348-8589-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Softcover 31,15 €
price for Spain (gross)
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

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Introduction

    Pages 1-3

    Pohst, Michael E.

  • Topics from finite fields

    Pages 4-10

    Pohst, Michael E.

  • Topics from the geometry of numbers

    Pages 11-26

    Pohst, Michael E.

  • Algebraic number fields

    Pages 27-33

    Pohst, Michael E.

  • Computation of an integral basis

    Pages 34-43

    Pohst, Michael E.

Buy this book

eBook 24,60 €
price for Spain (gross)
  • ISBN 978-3-0348-8589-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 31,15 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Computational Algebraic Number Theory
Authors
Series Title
Oberwolfach Seminars
Series Volume
21
Copyright
1993
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8589-8
DOI
10.1007/978-3-0348-8589-8
Softcover ISBN
978-3-7643-2913-6
Series ISSN
1661-237X
Edition Number
1
Number of Pages
X, 90
Number of Illustrations
1 b/w illustrations
Topics