|
#############################################################################
##
## 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 Q-class representative of the irreducible
## maximal finite integral matrix groups of dimension 15,
##
## [1] a quadratic form (as lower triangle of the Gram matrix),
## [2] a list of matrix generators.
##
#############################################################################
##
## Quadratic form and matrix generators for the Q-class representatives of
## the irreducible maximal finite integral matrix groups of dimension 15.
##
IMFList[15].matrices := [
[ # Q-class [15][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],
[0,0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]],
[[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1],
[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0]],
[[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]]]],
[ # Q-class [15][02]
[[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],
[1,1,1,1,1,1,1,1,1,1,1,2],
[1,1,1,1,1,1,1,1,1,1,1,1,2],
[1,1,1,1,1,1,1,1,1,1,1,1,1,2],
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,2]],
[[[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1],
[0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0],
[0,0,0,0,0,0,0,0,-1,0,0,0,0,1,0],
[0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0],
[0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0],
[0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0],
[0,0,0,-1,0,0,0,0,0,0,0,0,0,1,0],
[0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0],
[0,-1,0,0,0,0,0,0,0,0,0,0,0,1,0],
[-1,0,0,0,0,0,0,0,0,0,0,0,0,1,0]],
[[-1,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0],
[0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0],
[0,0,0,0,0,0,0,0,-1,0,0,0,0,1,0],
[0,0,0,0,0,0,0,-1,0,0,0,0,0,1,0],
[0,0,0,0,0,0,-1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0],
[0,0,0,0,-1,0,0,0,0,0,0,0,0,1,0],
[0,0,0,-1,0,0,0,0,0,0,0,0,0,1,0],
[0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0],
[0,-1,0,0,0,0,0,0,0,0,0,0,0,1,0]]]],
[ # Q-class [15][03]
[[3],
[-1,3],
[1,-1,3],
[1,1,-1,3],
[1,1,-1,1,3],
[-1,-1,0,-1,-1,3],
[1,0,-1,1,1,-1,3],
[1,-1,1,-1,0,1,-1,3],
[1,-1,1,0,-1,1,-1,1,3],
[0,1,1,0,0,-1,-1,0,0,3],
[1,-1,0,1,0,-1,1,-1,0,-1,3],
[-1,1,-1,0,1,1,0,0,-1,-1,-1,3],
[1,0,1,1,0,0,-1,1,1,0,0,0,3],
[1,0,1,0,1,0,-1,1,1,0,0,0,1,3],
[0,-1,0,-1,-1,1,0,1,1,0,-1,0,-1,-1,3]],
[[[-1,-1,0,0,0,-1,1,0,1,1,0,1,0,0,0],
[1,1,1,0,1,1,-1,-1,-1,-1,0,-1,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0],
[0,0,0,0,0,0,0,-1,0,0,0,0,0,1,1],
[-1,0,1,0,1,0,1,0,1,0,0,0,0,0,0],
[-1,0,0,0,0,0,0,1,0,0,1,0,0,0,0],
[0,0,0,0,0,-1,0,0,1,0,0,1,0,0,0],
[-1,0,0,0,0,0,1,1,0,1,1,0,0,0,0],
[-1,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,1,0,-1,-1,0,0,-1,1,0,1],
[0,-1,0,1,-1,-1,0,0,1,0,-1,1,-1,0,-1],
[1,1,0,-1,0,1,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0],
[-1,0,1,0,0,0,1,0,0,0,0,0,0,0,0],
[0,0,-1,-1,0,0,0,0,0,1,1,0,1,0,0]],
[[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[1,0,-1,-1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
[1,1,0,0,-1,0,0,0,0,0,0,0,0,0,0],
[-1,-1,0,0,0,-1,0,0,0,0,0,0,0,0,0],
[-1,0,1,1,0,0,1,1,0,0,0,0,0,0,0],
[1,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0],
[-1,-1,0,0,1,-1,0,0,1,0,0,0,0,0,0],
[1,1,-1,-1,0,1,0,0,0,1,1,0,0,0,0],
[0,-1,0,1,0,0,0,0,0,0,-1,0,0,0,0],
[0,0,0,0,-1,-1,0,0,0,0,0,1,0,0,0],
[1,0,-1,-1,0,0,0,-1,0,0,0,0,1,0,0],
[1,0,0,0,0,-1,-1,0,1,-1,-1,0,-1,-1,-1],
[-1,0,1,0,1,0,0,0,0,0,1,0,0,0,1]]]],
[ # Q-class [15][04]
[[3],
[1,3],
[0,-1,3],
[0,1,-1,3],
[0,-1,0,0,3],
[0,0,0,-1,-1,3],
[-1,-1,1,0,1,1,3],
[0,0,-1,0,0,0,-1,3],
[-1,-1,0,-1,0,1,1,-1,3],
[0,1,0,0,0,1,1,-1,1,3],
[0,-1,0,-1,0,1,1,1,1,0,3],
[1,1,0,0,-1,0,-1,1,0,0,1,3],
[0,0,-1,1,1,0,1,0,0,1,0,-1,3],
[0,1,1,0,0,-1,0,0,-1,1,0,1,0,3],
[0,0,0,-1,1,0,1,-1,1,1,1,0,1,1,3]],
[[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,-1,0,0,0,1,-1,0,0,0],
[0,0,0,0,-1,-1,1,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,1,-1,0,0,0,0,0],
[0,-1,-1,-1,0,0,1,0,-1,0,-1,1,0,0,0],
[0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0],
[-1,1,1,-1,0,-1,0,0,-1,1,0,1,1,-2,0],
[0,-1,0,1,0,1,0,1,0,0,-1,0,-1,0,1],
[0,0,0,0,0,1,0,0,0,-1,0,0,0,1,0],
[0,0,1,0,0,0,0,1,0,0,-1,0,0,-1,1],
[-1,0,1,0,0,0,-1,0,-1,1,0,0,0,-1,1],
[0,1,0,0,0,0,1,0,0,-1,0,0,0,0,0],
[0,1,1,0,0,0,-1,0,0,0,1,-1,0,0,0],
[1,0,0,1,0,1,0,1,1,-1,-1,-1,-1,1,1]],
[[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[1,0,0,0,-1,-1,1,1,1,0,0,-1,0,0,0],
[-1,1,1,0,1,0,-1,0,-1,1,1,0,0,-1,0],
[0,-1,0,1,0,0,0,0,-1,1,0,0,-1,-1,1],
[0,0,-1,-1,0,0,1,-1,0,-1,0,1,1,1,-1],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
[0,-1,0,1,0,1,-1,0,0,0,0,0,0,1,0],
[0,0,-1,-1,0,0,1,-1,0,-1,0,0,0,1,-1],
[0,1,0,0,0,0,1,0,0,-1,0,0,0,0,0],
[1,-1,-1,0,0,1,1,0,1,-1,-1,0,0,2,-1],
[1,0,-1,0,0,1,0,0,1,-1,0,-1,0,2,-1],
[-1,0,1,0,0,0,0,0,-2,1,0,1,0,-2,1],
[1,0,0,1,-1,0,1,2,1,0,-1,-1,-1,0,1],
[1,-1,-1,0,-1,0,2,1,0,0,-2,0,-1,0,1]]]],
[ # Q-class [15][05]
[[2],
[1,2],
[1,1,2],
[1,1,1,2],
[1,1,1,1,2],
[0,0,0,0,0,2],
[0,0,0,0,0,1,2],
[0,0,0,0,0,1,1,2],
[0,0,0,0,0,1,1,1,2],
[0,0,0,0,0,1,1,1,1,2],
[0,0,0,0,0,0,0,0,0,0,2],
[0,0,0,0,0,0,0,0,0,0,1,2],
[0,0,0,0,0,0,0,0,0,0,1,1,2],
[0,0,0,0,0,0,0,0,0,0,1,1,1,2],
[0,0,0,0,0,0,0,0,0,0,1,1,1,1,2]],
[[[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1],
[0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0],
[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0]],
[[-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0],
[0,-1,0,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]],
[[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]]]],
[ # Q-class [15][06]
[[3],
[1,3],
[1,1,3],
[1,1,1,3],
[1,1,1,1,3],
[-1,1,0,0,0,3],
[-1,0,1,0,0,1,3],
[-1,0,0,1,0,1,1,3],
[-1,0,0,0,1,1,1,1,3],
[0,-1,1,0,0,-1,1,0,0,3],
[0,-1,0,1,0,-1,0,1,0,1,3],
[0,-1,0,0,1,-1,0,0,1,1,1,3],
[0,0,-1,1,0,0,-1,1,0,-1,1,0,3],
[0,0,-1,0,1,0,-1,0,1,-1,0,1,1,3],
[0,0,0,-1,1,0,0,-1,1,0,-1,1,-1,1,3]],
[[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,-1,1,-1],
[0,0,0,0,0,0,0,-1,1,0,0,0,0,0,-1],
[0,0,0,0,0,0,0,0,0,0,-1,1,0,0,-1],
[0,0,0,-1,1,0,0,0,0,0,0,0,0,0,-1],
[0,0,0,0,0,0,-1,0,1,0,0,0,0,-1,0],
[0,0,0,0,0,0,0,0,0,-1,0,1,0,-1,0],
[0,0,-1,0,1,0,0,0,0,0,0,0,0,-1,0],
[0,0,0,0,0,1,0,0,-1,0,0,1,0,0,0],
[-1,0,0,0,1,0,0,0,-1,0,0,0,0,0,0],
[0,-1,0,0,1,0,0,0,0,0,0,-1,0,0,0]],
[[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
[-1,1,0,0,0,-1,0,0,0,0,0,0,0,0,0],
[-1,0,1,0,0,0,-1,0,0,0,0,0,0,0,0],
[-1,0,0,0,1,0,0,0,-1,0,0,0,0,0,0],
[-1,0,0,1,0,0,0,-1,0,0,0,0,0,0,0],
[0,-1,1,0,0,0,0,0,0,-1,0,0,0,0,0],
[0,-1,0,0,1,0,0,0,0,0,0,-1,0,0,0],
[0,-1,0,1,0,0,0,0,0,0,-1,0,0,0,0],
[0,0,-1,0,1,0,0,0,0,0,0,0,0,-1,0],
[0,0,-1,1,0,0,0,0,0,0,0,0,-1,0,0],
[0,0,0,1,-1,0,0,0,0,0,0,0,0,0,1]]]]
];
MakeImmutable( IMFList[15].matrices );
[ Dauer der Verarbeitung: 0.18 Sekunden
(vorverarbeitet)
]
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