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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Volkmar Felsch.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains, for each Z-class representative of the irreducible
## maximal finite integral matrix groups of dimension 11,
##
## [1] a quadratic form (as lower triangle of the Gram matrix),
## [2] a list of matrix generators.
##
#############################################################################
##
## Quadratic form and matrix generators for the Z-class representatives of
## the irreducible maximal finite integral matrix groups of dimension 11.
##
IMFList[11].matrices := [
[ # Z-class [11][01]
[[1],
[0,1],
[0,0,1],
[0,0,0,1],
[0,0,0,0,1],
[0,0,0,0,0,1],
[0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,1]],
[[[0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,0]],
[[0,-1,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,0]]]],
[ # Z-class [11][02]
[[2],
[0,2],
[1,0,2],
[0,1,0,2],
[0,0,1,0,2],
[0,0,0,1,0,2],
[0,0,0,0,1,0,2],
[0,0,0,0,0,1,0,2],
[0,0,0,0,0,0,1,0,2],
[1,0,0,0,0,0,0,1,0,2],
[0,1,0,0,0,0,0,0,1,0,2]],
[[[1,0,-1,1,1,-1,-1,1,1,-1,0],
[-1,0,1,0,-1,0,1,-1,-1,1,1],
[1,0,-1,1,1,-1,-1,1,0,-1,0],
[-1,0,1,0,-1,0,1,0,-1,0,1],
[0,0,0,0,0,0,-1,0,0,0,0] ,
[0,0,0,0,0,0,0,0,0,-1,0],
[0,0,0,0,-1,0,0,0,0,0,0],
[0,0,0,0,0,1,0,-1,0,0,0],
[0,0,-1,0,0,0,0,0,0,0,0],
[0,-1,0,1,0,0,0,0,0,0,1],
[-1,0,0,0,0,0,0,-1,0,1,0]],
[[-1,-1,1,0,-1,0,1,0,-1,0,1],
[0,0,0,0,1,0,-1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,-1,0],
[0,0,0,0,1,0,-1,0,1,0,-1],
[0,0,0,0,0,0,0,-1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,-1],
[0,0,0,0,0,-1,0,0,0,0,0],
[0,0,0,0,0,0,1,0,-1,0,0],
[0,1,-1,-1,1,0,-1,0,1,0,-1],
[0,-1,0,0,0,0,1,0,-1,0,1],
[0,0,-1,0,1,0,-1,0,0,0,0]]]],
[ # Z-class [11][03]
[[11],
[-9,11],
[7,-9,11],
[-5,7,-9,11],
[3,-5,7,-9,11],
[-1,3,-5,7,-9,11],
[-1,-1,3,-5,7,-9,11],
[3,-1,-1,3,-5,7,-9,11],
[-5,3,-1,-1,3,-5,7,-9,11],
[7,-5,3,-1,-1,3,-5,7,-9,11],
[-9,7,-5,3,-1,-1,3,-5,7,-9,11]],
[[[0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,0]],
[[1,0,-1,-1,-1,0,0,0,1,0,0],
[0,0,1,1,1,0,0,0,-1,0,1],
[0,0,0,0,-1,0,0,0,1,0,-1],
[0,0,0,0,0,-1,0,0,-1,0,1],
[0,0,0,0,0,0,-1,0,1,0,-1],
[0,0,0,0,0,0,0,-1,-1,0,1],
[0,0,0,0,0,0,0,0,0,0,-1],
[0,0,0,0,0,0,0,0,0,-1,0],
[0,0,0,0,0,0,0,0,-1,0,0],
[0,0,0,-1,-1,0,0,0,1,0,0],
[0,1,1,1,1,0,0,0,-1,0,0]]]],
[ # Z-class [11][04]
[[11],
[-1,11],
[-1,-1,11],
[-1,-1,-1,11],
[-1,-1,-1,-1,11],
[-1,-1,-1,-1,-1,11],
[-1,-1,-1,-1,-1,-1,11],
[-1,-1,-1,-1,-1,-1,-1,11],
[-1,-1,-1,-1,-1,-1,-1,-1,11],
[-1,-1,-1,-1,-1,-1,-1,-1,-1,11],
[-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,11]],
[[[0,-1,0,0,0,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0,0,0,0],
[0,0,0,-1,0,0,0,0,0,0,0],
[0,0,0,0,-1,0,0,0,0,0,0],
[0,0,0,0,0,-1,0,0,0,0,0],
[0,0,0,0,0,0,-1,0,0,0,0],
[0,0,0,0,0,0,0,-1,0,0,0],
[0,0,0,0,0,0,0,0,-1,0,0],
[0,0,0,0,0,0,0,0,0,-1,0],
[0,0,0,0,0,0,0,0,0,0,-1],
[1,1,1,1,1,1,1,1,1,1,1]],
[[1,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0]]]],
[ # Z-class [11][05]
[[5],
[2,5],
[-1,2,5],
[-1,-1,2,5],
[-1,-1,-1,2,5],
[-1,-1,-1,-1,2,5],
[-1,-1,-1,-1,-1,2,5],
[-1,-1,-1,-1,-1,-1,2,5],
[-1,-1,-1,-1,-1,-1,-1,2,5],
[-1,-1,-1,-1,-1,-1,-1,-1,2,5],
[2,-1,-1,-1,-1,-1,-1,-1,-1,2,5]],
[[[0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,0]],
[[1,0,1,0,1,0,1,0,0,1,0],
[0,0,0,0,0,0,0,0,-1,1,-1],
[0,0,0,0,0,0,0,0,0,0,-1],
[0,0,0,0,0,0,0,0,0,-1,0],
[0,0,0,0,0,0,-1,1,-1,0,0],
[0,0,0,0,0,0,-1,0,0,0,0],
[0,0,0,0,-1,1,-1,0,0,0,0],
[0,0,0,0,-1,0,0,0,0,0,0],
[0,0,-1,1,-1,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0,0,0,0],
[0,1,0,0,1,0,1,0,1,0,1]]]],
[ # Z-class [11][06]
[[9],
[5,9],
[1,5,9],
[-3,1,5,9],
[-3,-3,1,5,9],
[-3,-3,-3,1,5,9],
[-3,-3,-3,-3,1,5,9],
[-3,-3,-3,-3,-3,1,5,9],
[-3,-3,-3,-3,-3,-3,1,5,9],
[1,-3,-3,-3,-3,-3,-3,1,5,9],
[5,1,-3,-3,-3,-3,-3,-3,1,5,9]],
[[[0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,0]],
[[-2,1,0,-1,1,-1,0,1,-1,0,1],
[-1,1,1,-1,1,0,0,1,0,0,1],
[0,0,1,-1,1,0,0,1,0,0,1],
[0,0,1,-1,1,1,-1,1,0,0,1],
[0,0,0,-1,1,0,-1,1,-1,0,0],
[0,0,0,0,0,0,0,0,-1,1,-1],
[1,-1,0,1,-1,0,0,0,0,0,-1],
[1,-2,1,1,-2,1,0,-1,1,-1,0],
[1,-1,0,1,-2,1,0,-1,1,-1,0],
[0,0,-1,1,-1,0,1,-1,0,0,0],
[-1,1,-1,0,0,0,0,0,0,0,0]]]],
[ # Z-class [11][07]
[[8],
[5,8],
[2,5,8],
[-1,2,5,8],
[-4,-1,2,5,8],
[-4,-4,-1,2,5,8],
[-4,-4,-4,-1,2,5,8],
[-4,-4,-4,-4,-1,2,5,8],
[-1,-4,-4,-4,-4,-1,2,5,8],
[2,-1,-4,-4,-4,-4,-1,2,5,8],
[5,2,-1,-4,-4,-4,-4,-1,2,5,8]],
[[[0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,0]],
[[-2,0,1,0,-1,0,1,-1,-1,1,1],
[-1,0,1,1,-1,0,1,0,-1,1,1],
[0,0,0,1,0,-1,1,0,0,0,1],
[0,0,0,1,-1,0,1,0,0,0,1],
[1,-1,0,1,0,-1,1,1,0,-1,1],
[1,-1,-1,1,0,-1,0,1,0,-2,1],
[1,-1,-1,1,0,0,-1,1,0,-1,0],
[1,0,-1,0,1,0,-2,1,1,-1,-1],
[0,1,-1,-1,1,1,-2,0,1,0,-1],
[-1,1,0,-1,0,1,-1,0,0,1,-1],
[-1,0,1,-1,0,0,0,0,-1,1,0]]]],
[ # Z-class [11][08]
[[3],
[2,3],
[1,2,3],
[0,1,2,3],
[-1,0,1,2,3],
[-2,-1,0,1,2,3],
[-2,-2,-1,0,1,2,3],
[-1,-2,-2,-1,0,1,2,3],
[0,-1,-2,-2,-1,0,1,2,3],
[1,0,-1,-2,-2,-1,0,1,2,3],
[2,1,0,-1,-2,-2,-1,0,1,2,3]],
[[[0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,-1,1,0,0,0,-1,0],
[0,0,0,-1,0,1,0,0,-1,-1,1],
[0,0,-1,0,0,1,0,-1,-1,0,1],
[0,-1,0,0,0,1,-1,-1,0,0,1],
[-1,0,0,0,0,0,-1,0,0,0,1]],
[[-1,-1,0,0,1,0,-1,-1,0,1,1],
[0,-1,0,0,1,1,-1,-1,0,1,1],
[0,0,-1,0,1,1,0,-1,-1,1,1],
[0,0,0,-1,1,1,0,0,-1,0,1],
[0,0,0,0,0,1,0,0,0,-1,1],
[0,1,0,0,-1,1,0,1,0,-1,0],
[0,1,0,0,-1,0,0,1,0,-1,-1],
[-1,1,1,0,-1,-1,0,1,1,-1,-1],
[-1,0,1,1,-1,-1,-1,1,1,0,-1],
[-1,0,0,1,0,-1,-1,0,1,1,-1],
[-1,0,0,0,1,-1,-1,0,0,1,0]]]],
[ # Z-class [11][09]
[[2],
[1,2],
[1,1,2],
[1,1,1,2],
[1,1,1,1,2],
[1,1,1,1,1,2],
[1,1,1,1,1,1,2],
[1,1,1,1,1,1,1,2],
[1,1,1,1,1,1,1,1,2],
[1,1,1,1,1,1,1,1,1,2],
[1,1,1,1,1,1,1,1,1,1,2]],
[[[0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,1,-1],
[0,0,0,0,0,0,0,0,-1,1,0],
[0,0,0,0,0,0,0,-1,0,1,0],
[0,0,0,0,0,0,-1,0,0,1,0],
[0,0,0,0,0,-1,0,0,0,1,0],
[0,0,0,0,-1,0,0,0,0,1,0],
[0,0,0,-1,0,0,0,0,0,1,0],
[0,0,-1,0,0,0,0,0,0,1,0],
[0,-1,0,0,0,0,0,0,0,1,0],
[-1,0,0,0,0,0,0,0,0,1,0]],
[[-1,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,1,-1],
[0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,-1,1,0],
[0,0,0,0,0,0,0,-1,0,1,0],
[0,0,0,0,0,0,-1,0,0,1,0],
[0,0,0,0,0,-1,0,0,0,1,0],
[0,0,0,0,-1,0,0,0,0,1,0],
[0,0,0,-1,0,0,0,0,0,1,0],
[0,0,-1,0,0,0,0,0,0,1,0],
[0,-1,0,0,0,0,0,0,0,1,0]]]]
];
MakeImmutable( IMFList[11].matrices );
[ Dauer der Verarbeitung: 0.18 Sekunden
(vorverarbeitet)
]
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