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2006-55

Classification of eight dimensional perfect forms

by Mathieu Dutour Sikiric, Achill Schürmann, Frank Vallentin.


Series: 2006-55, Preprints

MSC:
11H55 Quadratic forms (reduction theory, extreme forms, etc.)

Abstract:
In this paper, we classify the perfect lattices in dimension 8. There are 10916 of them. Our classification heavily relies on exploiting symmetry in polyhedral computations. Here we describe algorithms making the classification possible.

Keywords:
perfect forms, perfect lattices, Hermite's constant