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 Dusseldorf. 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
General
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