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Mathematics of Computation

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Classification of quintic eutactic forms

Author: Christian Batut
Journal: Math. Comp. 70 (2001), 395-417
MSC (2000): Primary 11H55, 11H56; Secondary 11E10
Published electronically: July 21, 2000
MathSciNet review: 1803130
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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.

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Additional Information

Christian Batut
Affiliation: A2X, Mathématiques, Université Bordeaux I, 351, cours de la Libération, 33405 Talence cedex, France

Keywords: Quadratic form, minimal vectors, eutactic form
Received by editor(s): February 13, 1997
Received by editor(s) in revised form: June 19, 1997
Published electronically: July 21, 2000
Article copyright: © Copyright 2000 American Mathematical Society