Hermite and Smith normal form algorithms over Dedekind domains. (English) Zbl 0853.11100

Summary: 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.


11Y40 Algebraic number theory computations
13P99 Computational aspects and applications of commutative rings
11R99 Algebraic number theory: global fields
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
11R04 Algebraic numbers; rings of algebraic integers
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