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Hermite and Smith normal form algorithms over Dedekind domains
1996
Mathematics of Computation
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. The goal of this paper is to explain how to generalize to a Dedekind domain R many of the algorithms which are usually associated with a Euclidean domain, such as the Hermite Normal
doi:10.1090/s0025-5718-96-00766-1
fatcat:ntkddvvffzfs3comev4k7zqk4a