Geodesic
Reduced normal form of local integral bases
Nathália Moraes de Oliveira 1   ; Enric Nart 1
1 Departament de Matemàtiques Universitat Autónoma de Barcelona Edifici C E-08193 Bellaterra, Barcelona, Catalonia, Spain
Acta Arithmetica, Tome 178 (2017) no. 2, pp. 181-200 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 crucial property for several important applications. Except for very particular cases, a basis in Hermite normal form cannot be reduced.
DOI : 10.4064/aa8509-10-2016
Keywords: introduce canonical form reduced bases integral closures discrete valuation rings describe algorithm computing basis reduced normal form normal form has applications hermite normal form identification isomorphic objects construction global bases patching local etc addition bases reduced which crucial property several important applications except particular cases basis hermite normal form cannot reduced

Nathália Moraes de Oliveira  1   ; Enric Nart  1

1 Departament de Matemàtiques Universitat Autónoma de Barcelona Edifici C E-08193 Bellaterra, Barcelona, Catalonia, Spain 
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Nathália Moraes de Oliveira; Enric Nart. Reduced normal form of local integral bases. Acta Arithmetica, Tome 178 (2017) no. 2, pp. 181-200. doi: 10.4064/aa8509-10-2016

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