Hermite and Smith normal form algorithms over Dedekind domains

Cohen, Henri

doi:10.1090/S0025-5718-96-00766-1

Hermite and Smith normal form algorithms over Dedekind domains
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Math. Comp. 65 (1996), 1681-1699 Request permission

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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