Classification of quintic eutactic forms

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...

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Bibliographic Details
Published in:Mathematics of computation 2001-01, Vol.70 (233), p.395-417
Main Author: Batut, Christian
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
Determinants
Equivalence relation
Exact sciences and technology
Hyperplanes
Mathematical lattices
Mathematical vectors
Mathematics
Matrices
Number theory
Perfection
Polynomials
Sciences and techniques of general use
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Summary: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.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-00-01295-3