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Mathematics of Computation

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Hermite and Smith normal form algorithms over Dedekind domains

Author: Henri Cohen
Journal: Math. Comp. 65 (1996), 1681-1699
MSC (1991): Primary 11Y40
MathSciNet review: 1361805
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Abstract: We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.

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Additional Information

Henri Cohen
Affiliation: Laboratoire A2X, UMR 9936 du C.N.R.S., Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France

Keywords: Dedekind domain, Hermite normal form, Smith normal form, relative extensions of number fields
Received by editor(s): January 11, 1995
Received by editor(s) in revised form: July 19, 1995
Article copyright: © Copyright 1996 American Mathematical Society