Énumération complète des classes de formes parfaites en dimension 7

David-Olivier Jaquet-Chiffelle

Annales de l'institut Fourier (1993)

  • Volume: 43, Issue: 1, page 21-55
  • ISSN: 0373-0956

Abstract

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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 Voronoï’s algorithm applied in depth, recursively, to the faces of the domains.

How to cite

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Jaquet-Chiffelle, David-Olivier. "Énumération complète des classes de formes parfaites en dimension 7." Annales de l'institut Fourier 43.1 (1993): 21-55. <http://eudml.org/doc/74989>.

@article{Jaquet1993,
abstract = {Le lecteur trouvera ici une description détaillée des méthodes et algorithmes utilisés pour démontrer qu’il n’y a que 33 classes de formes parfaites en dimension 7, ainsi qu’un tableau récapitulatif des résultats.Il trouvera, en particulier, une généralisation de l’algorithme de Voronoï appliquée en profondeur, récursivement, aux faces des domaines},
author = {Jaquet-Chiffelle, David-Olivier},
journal = {Annales de l'institut Fourier},
keywords = {perfect quadratic forms; perfect lattices; entactic lattices; extremal lattices; Voronoï domain; minimal vectors; Hermite invariant; algorithms; perfect septenary forms; generalization of Voronoï’s algorithm},
language = {fre},
number = {1},
pages = {21-55},
publisher = {Association des Annales de l'Institut Fourier},
title = {Énumération complète des classes de formes parfaites en dimension 7},
url = {http://eudml.org/doc/74989},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Jaquet-Chiffelle, David-Olivier
TI - Énumération complète des classes de formes parfaites en dimension 7
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 1
SP - 21
EP - 55
AB - Le lecteur trouvera ici une description détaillée des méthodes et algorithmes utilisés pour démontrer qu’il n’y a que 33 classes de formes parfaites en dimension 7, ainsi qu’un tableau récapitulatif des résultats.Il trouvera, en particulier, une généralisation de l’algorithme de Voronoï appliquée en profondeur, récursivement, aux faces des domaines
LA - fre
KW - perfect quadratic forms; perfect lattices; entactic lattices; extremal lattices; Voronoï domain; minimal vectors; Hermite invariant; algorithms; perfect septenary forms; generalization of Voronoï’s algorithm
UR - http://eudml.org/doc/74989
ER -

References

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