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Abstract: In this paper we study the algorithmic problem of finding the ring of integers of a given algebraic number field. In practice, this problem is often considered to be wellsolved, but theoretical results indicate that it is intractable for number fields that are defined by equations with very large coefficients. Such fields occur in the number field sieve algorithm for factoring integers. Applying a variant of a standard algorithm for finding rings of integers, one finds a subring of the number... (Update)
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...to work with ideals and algebraic integers. We first have to compute an integral basis of O. In general, this is a hopeless task (see [13, 2] for a survey) but for the number fields NFS encounters (small degree and large discriminant) this can be done by the so called round...
...efficient algorithm known at the present time. For some practical advice on how to compute such a divisor, the reader is referred to Section 7 of [4]. the model of computation that we will be using is that of a Turing machine. We say that a language L is polynomial time...
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BibTeX entry: (Update)
J. Buchmann, H. W. Lenstra, Jr., Approximating rings of integers in number fields, in preparation. http://citeseer.ist.psu.edu/721825.html More
@misc{ buchmann-approximating,
author = "J. Buchmann and H. Lenstra",
title = "Approximating rings of integers in number fields",
text = "J. Buchmann, H. W. Lenstra, Jr., Approximating rings of integers in number
fields, in preparation.",
url = "citeseer.ist.psu.edu/721825.html" }
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