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Zbl 0769.11028
Jaquet-Chiffelle, David-Olivier
Complete enumeration of classes of perfect septenary forms. (Énumération complète des classes de formes parfaites en dimension 7.) (French)
[J] Ann. Inst. Fourier 43, No.1, 21-55 (1993). ISSN 0373-0956; ISSN 1777-5310/e

The reader will find here a detailed description of the methods and algorithms used in order to prove that there are only 33 classes of perfect septenary forms, as well as a recapitulative table of the results. He will find in particular a generalization of Vorono\" i's algorithm applied in depth, recursively, to the faces of the domains.
[D.-O.Jaquet-Chiffelle (Neuchâtel)]

MSC 2000:: *11H55 Quadratic forms

Keywords: perfect quadratic forms; perfect lattices; entactic lattices; extremal lattices; Vorono\" i domain; minimal vectors; Hermite invariant; algorithms; perfect septenary forms; generalization of Vorono\" i's algorithm

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