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Euclidean minima of totally real fields : Algorithmic determination.

Jean-Paul Cerri 1, 2
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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Contributor : Guillaume Hanrot <>
Submitted on : Monday, December 5, 2005 - 6:53:31 PM
Last modification on : Wednesday, April 15, 2020 - 3:00:10 PM

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



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