Classification of quintic eutactic forms-Reference-Cited by-同舟云学术

Classification of quintic eutactic forms

Published:2000-07-21 Issue:233 Volume:70 Page:395-417
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Batut Christian

Abstract

From the classical Voronoi algorithm, we derive an algorithm to classify quadratic positive definite forms by their minimal vectors; we define some new invariants for a class, for which several conjectures are proposed. Applying the algorithm to dimension 5 we obtain the table of the 136 classes in this dimension, we enumerate the 118 eutactic quintic forms, and we verify the Ash formula.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/2001-70-233/S0025-5718-00-01295-3/S0025-5718-00-01295-3.pdf

Reference13 articles.

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2. On the existence of eutactic forms;Ash, Avner;Bull. London Math. Soc.,1980

3. [Ba] J.-L. Baril, Autour de l’algorithme de Voronoi: constructions de réseaux euclidiens, Thèse Bordeaux (1996).

4. [Bv] C. Bavard, Une formule d’Euler pour les classes minimales de réseaux, preprint.

5. Sur la classification des réseaux eutactiques;Bergé, Anne-Marie;J. London Math. Soc. (2),1996

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