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 b ≡a 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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Fieker, C., Friedrichs, C. (2000). On Reconstruction of Algebraic Numbers. In: Bosma, W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722028_16
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DOI: https://doi.org/10.1007/10722028_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67695-9
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