# Euclidean minima of totally real fields : Algorithmic determination.

1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : This article deals with the determination of the Euclidean minimum $M(K)$ of a totally real number field $K$ of degree $n\geq 2$, using techniques from the geometry of numbers. Our improvements of existing algorithms allow us to compute Euclidean minima for fields of degree $2$ to $8$ and small discriminants, most of which were previously unknown. Tables are given at the end of this paper.
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Journal articles
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https://hal.inria.fr/inria-00000904
Contributor : Guillaume Hanrot <>
Submitted on : Monday, December 5, 2005 - 6:53:31 PM
Last modification on : Thursday, January 11, 2018 - 6:20:00 AM

### Citation

Jean-Paul Cerri. Euclidean minima of totally real fields : Algorithmic determination.. Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2005, 76, pp.1547-1575. ⟨10.1090/S0025-5718-07-01932-1⟩. ⟨inria-00000904⟩

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