On Reconstruction of Algebraic Numbers

  • Claus Fieker
  • Carsten Friedrichs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1838)

Abstract

Let L be a number field and \(\mathfrak{a}\) be an ideal of some order of L. Given an algebraic number α mod \(\mathfrak{a}\) and some bounds we show how to effectively reconstruct a number b if it exists such that b is smaller then the given bound and ba mod \(\mathfrak{a}\).

The first application is an algorithm for the computation of n-th roots of algebraic numbers. Secondly, we get an algorithm to factor polynomials over number fields which generalizes the Hensel-factoring method. Our method uses only integral LLL-reductions in contrast to the real LLL-reductions suggested by [6,8].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Claus Fieker
    • 1
  • Carsten Friedrichs
    • 1
  1. 1.Fachbereich 3, Sekr. MA 8-1Technische Universität BerlinBerlinGermany

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