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arXiv · 1604.06606

Reduced normal form of local integral bases

Nathália Moraes de Oliveira·Enric Nart
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Abstract

We introduce a canonical form for reduced bases of integral closures of discrete valuation rings, and we describe an algorithm for computing a basis in reduced normal form. This normal form has the same applications as the Hermite normal form: identification of isomorphic objects, construction of global bases by patching local ones, etc. but in addition the bases are reduced, which is a crutial property for several important applications. Except for very particular cases, a basis in Hermite normal form cannot be reduced.

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Nathália Moraes de Oliveira, Enric Nart. 2016-04-22. Reduced normal form of local integral bases. https://arxiv.org/abs/1604.06606

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