|
#############################################################################
##
## 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 dimensions 1 to 9,
##
## [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 representative of
## the irreducible maximal finite integral matrix groups of dimension 1.
##
IMFList[1].matrices := [
[ # Z-class [01][01]
[[1]],
[[[-1]]]]
];
MakeImmutable( IMFList[1].matrices );
#############################################################################
##
## Quadratic form and matrix generators for the Z-class representatives of
## the irreducible maximal finite integral matrix groups of dimension 2.
##
IMFList[2].matrices := [
[ # Z-class [02][01]
[[1],
[0,1]],
[[[0,1],
[1,0]],
[[-1,0],
[0,1]]]],
[ # Z-class [02][02]
[[2],
[-1,2]],
[[[0,-1],
[1,1]],
[[0,1],
[1,0]]]]
];
MakeImmutable( IMFList[2].matrices );
#############################################################################
##
## Quadratic form and matrix generators for the Z-class representatives of
## the irreducible maximal finite integral matrix groups of dimension 3.
##
IMFList[3].matrices := [
[ # Z-class [03][01]
[[1],
[0,1],
[0,0,1]],
[[[1,0,0],
[0,0,1],
[0,1,0]],
[[0,0,-1],
[1,0,0],
[0,1,0]]]],
[ # Z-class [03][02]
[[3],
[-1,3],
[-1,-1,3]],
[[[0,1,0],
[1,0,0],
[0,0,1]],
[[-1,0,0],
[0,0,-1],
[1,1,1]]]],
[ # Z-class [03][03]
[[2],
[1,2],
[1,1,2]],
[[[0,1,0],
[1,0,0],
[0,0,1]],
[[-1,1,0],
[0,1,-1],
[0,1,0]]]]
];
MakeImmutable( IMFList[3].matrices );
#############################################################################
##
## Quadratic form and matrix generators for the Z-class representatives of
## the irreducible maximal finite integral matrix groups of dimension 4.
##
IMFList[4].matrices := [
[ # Z-class [04][01]
[[1],
[0,1],
[0,0,1],
[0,0,0,1]],
[[[0,1,0,0],
[1,0,0,0],
[0,0,1,0],
[0,0,0,1]],
[[-1,0,0,0],
[0,0,1,0],
[0,0,0,1],
[0,1,0,0]]]],
[ # Z-class [04][02]
[[2],
[1,2],
[0,1,2],
[0,1,0,2]],
[[[-1,1,-1,-1],
[-1,0,0,0],
[0,-1,1,0],
[0,-1,0,1]],
[[0,1,-1,-1],
[0,0,0,-1],
[-1,1,0,-1],
[0,-1,0,0]]]],
[ # Z-class [04][03]
[[2],
[-1,2],
[0,0,2],
[0,0,-1,2]],
[[[0,1,0,0],
[1,0,0,0],
[0,0,1,0],
[0,0,0,1]],
[[0,-1,0,0],
[1,1,0,0],
[0,0,1,0],
[0,0,0,1]],
[[0,0,1,0],
[0,0,0,1],
[1,0,0,0],
[0,1,0,0]]]],
[ # Z-class [04][04]
[[4],
[-2,4],
[-2,1,4],
[1,-2,-2,4]],
[[[0,1,0,0],
[1,0,0,0],
[0,0,0,1],
[0,0,1,0]],
[[0,-1,0,0],
[1,1,0,0],
[0,0,0,-1],
[0,0,1,1]],
[[1,0,0,0],
[0,0,1,0],
[0,1,0,0],
[0,0,0,1]]]],
[ # Z-class [04][05]
[[2],
[1,2],
[1,1,2],
[1,1,1,2]],
[[[0,0,0,1],
[-1,0,0,1],
[0,-1,0,1],
[0,0,-1,1]],
[[0,1,0,0],
[1,0,0,0],
[0,0,1,0],
[0,0,0,1]]]],
[ # Z-class [04][06]
[[4],
[-1,4],
[-1,-1,4],
[-1,-1,-1,4]],
[[[1,1,1,1],
[-1,0,0,0],
[0,-1,0,0],
[0,0,-1,0]],
[[0,1,0,0],
[1,0,0,0],
[0,0,1,0],
[0,0,0,1]]]]
];
MakeImmutable( IMFList[4].matrices );
#############################################################################
##
## Quadratic form and matrix generators for the Z-class representatives of
## the irreducible maximal finite integral matrix groups of dimension 5.
##
IMFList[5].matrices := [
[ # Z-class [05][01]
[[1],
[0,1],
[0,0,1],
[0,0,0,1],
[0,0,0,0,1]],
[[[-1,0,0,0,0],
[0,1,0,0,0],
[0,0,0,1,0],
[0,0,0,0,1],
[0,0,1,0,0]],
[[0,1,0,0,0],
[0,0,1,0,0],
[0,0,0,1,0],
[1,0,0,0,0],
[0,0,0,0,1]]]],
[ # Z-class [05][02]
[[2],
[1,2],
[0,1,2],
[0,0,1,2],
[0,0,1,0,2]],
[[[-1,2,-2,1,1],
[0,1,-1,1,1],
[0,0,0,1,0],
[0,0,1,0,-1],
[0,0,-1,1,0]],
[[0,1,0,0,0],
[0,0,1,0,0],
[1,-1,1,0,0],
[1,-1,1,0,-1],
[1,-1,1,-1,0]]]],
[ # Z-class [05][03]
[[4],
[0,4],
[0,0,4],
[0,0,0,4],
[2,2,2,2,5]],
[[[-1,0,0,0,0],
[0,1,0,0,0],
[0,0,0,1,0],
[-1,-1,-1,-1,2],
[-1,0,0,0,1]],
[[0,1,0,0,0],
[0,0,1,0,0],
[0,0,0,1,0],
[1,0,0,0,0],
[0,0,0,0,1]]]],
[ # Z-class [05][04]
[[5],
[-1,5],
[-1,-1,5],
[-1,-1,-1,5],
[-1,-1,-1,-1,5]],
[[[0,1,0,0,0],
[1,0,0,0,0],
[0,0,1,0,0],
[0,0,0,1,0],
[0,0,0,0,1]],
[[-1,0,0,0,0],
[0,0,-1,0,0],
[0,0,0,-1,0],
[0,0,0,0,-1],
[1,1,1,1,1]]]],
[ # Z-class [05][05]
[[2],
[1,2],
[1,1,2],
[1,1,1,2],
[1,1,1,1,2]],
[[[0,1,0,0,0],
[1,0,0,0,0],
[0,0,1,0,0],
[0,0,0,1,0],
[0,0,0,0,1]],
[[-1,1,0,0,0],
[0,1,-1,0,0],
[0,1,0,-1,0],
[0,1,0,0,-1],
[0,1,0,0,0]]]],
[ # Z-class [05][06]
[[4],
[1,4],
[-2,1,4],
[-2,-2,1,4],
[-2,1,1,1,4]],
[[[1,0,0,0,0],
[1,-1,1,-1,1],
[0,0,1,0,0],
[0,0,0,1,0],
[0,0,0,0,1]],
[[-1,1,-1,1,-1],
[0,0,-1,0,0],
[0,0,0,-1,0],
[1,0,1,0,0],
[1,0,0,0,1]]]],
[ # Z-class [05][07]
[[3],
[1,3],
[-1,1,3],
[-1,-1,1,3],
[-1,1,1,1,3]],
[[[1,0,0,0,0],
[0,1,0,1,-1],
[0,0,1,0,0],
[0,0,0,0,1],
[0,0,0,1,0]],
[[0,-1,0,-1,1],
[0,0,-1,0,0],
[1,0,0,0,0],
[0,1,0,0,0],
[0,1,-1,1,0]]]]
];
MakeImmutable( IMFList[5].matrices );
#############################################################################
##
## Quadratic form and matrix generators for the Z-class representatives of
## the irreducible maximal finite integral matrix groups of dimension 6.
##
IMFList[6].matrices := [
[ # Z-class [06][01]
[[1],
[0,1],
[0,0,1],
[0,0,0,1],
[0,0,0,0,1],
[0,0,0,0,0,1]],
[[[0,1,0,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]],
[[-1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1],
[0,1,0,0,0,0]]]],
[ # Z-class [06][02]
[[2],
[1,2],
[0,1,2],
[0,0,1,2],
[0,0,0,1,2],
[0,0,0,1,0,2]],
[[[1,0,0,0,0,0],
[1,-1,2,-2,1,1],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]],
[[-1,1,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,1,-1,1,0,-1],
[0,-1,1,-1,1,0]]]],
[ # Z-class [06][03]
[[2],
[0,2],
[0,0,2],
[0,0,0,2],
[0,0,0,0,2],
[1,1,1,1,1,3]],
[[[0,1,0,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]],
[[-1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[-1,-1,-1,-1,-1,2],
[-1,0,0,0,0,1]]]],
[ # Z-class [06][04]
[[2],
[1,2],
[1,1,2],
[0,0,0,2],
[0,0,0,1,2],
[0,0,0,1,1,2]],
[[[0,1,0,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]],
[[-1,1,0,0,0,0],
[0,1,-1,0,0,0],
[0,1,0,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]],
[[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1],
[1,0,0,0,0,0],
[0,1,0,0,0,0],
[0,0,1,0,0,0]]]],
[ # Z-class [06][05]
[[3],
[-1,3],
[-1,-1,3],
[0,0,0,3],
[0,0,0,-1,3],
[0,0,0,-1,-1,3]],
[[[0,1,0,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]],
[[-1,0,0,0,0,0],
[0,0,-1,0,0,0],
[1,1,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]],
[[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1],
[1,0,0,0,0,0],
[0,1,0,0,0,0],
[0,0,1,0,0,0]]]],
[ # Z-class [06][06]
[[3],
[1,3],
[1,1,3],
[1,1,1,3],
[1,1,1,1,3],
[1,1,-1,-1,1,3]],
[[[1,0,-1,-1,1,-1],
[0,0,0,-1,0,0],
[0,1,-1,-1,1,-1],
[0,0,-1,0,0,0],
[1,1,-1,-1,0,-1],
[1,0,0,-1,0,-1]],
[[1,0,0,0,0,0],
[0,1,0,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[1,1,-1,-1,1,-2],
[1,1,-1,-1,0,-1]]]],
[ # Z-class [06][07]
[[2],
[-1,2],
[0,0,2],
[0,0,-1,2],
[0,0,0,0,2],
[0,0,0,0,-1,2]],
[[[0,-1,0,0,0,0],
[1,1,0,0,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1],
[0,0,1,0,0,0],
[0,0,0,1,0,0]],
[[0,1,0,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]],
[[0,0,0,0,-1,0],
[0,0,0,0,0,-1],
[-1,0,0,0,0,0],
[0,-1,0,0,0,0],
[0,0,-1,0,0,0],
[0,0,0,-1,0,0]]]],
[ # Z-class [06][08]
[[2],
[0,2],
[-1,0,2],
[0,-1,-1,2],
[0,0,0,-1,2],
[0,0,0,0,-1,2]],
[[[0,0,1,0,0,0],
[1,1,1,1,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1],
[-1,0,-1,-1,-1,-1]],
[[0,0,-1,0,0,0],
[1,1,1,1,0,0],
[0,0,0,-1,0,0],
[0,-1,0,0,0,0],
[-1,0,-1,-1,-1,0],
[0,0,0,0,0,-1]]]],
[ # Z-class [06][09]
[[4],
[1,4],
[-2,1,4],
[-2,-2,1,4],
[1,-2,-2,1,4],
[1,1,-2,-2,1,4]],
[[[-1,0,-1,0,0,0],
[-1,0,0,-1,0,0],
[0,0,0,-1,0,-1],
[0,1,0,0,1,-1],
[0,0,0,1,0,0],
[0,0,0,1,-1,1]],
[[1,-1,1,1,-1,1],
[1,-1,0,0,-1,0],
[0,0,0,-1,0,0],
[0,1,0,0,1,0],
[0,1,0,1,0,0],
[0,0,0,0,0,-1]]]],
[ # Z-class [06][10]
[[4],
[2,4],
[2,2,4],
[-2,-1,-1,4],
[-1,-2,-1,2,4],
[-1,-1,-2,2,2,4]],
[[[0,0,0,-1,0,0],
[0,0,0,0,-1,0],
[0,0,0,0,0,-1],
[1,0,0,1,0,0],
[0,1,0,0,1,0],
[0,0,1,0,0,1]],
[[0,0,0,1,-1,0],
[0,0,0,0,-1,1],
[0,0,0,0,-1,0],
[1,-1,0,0,0,0],
[0,-1,1,0,0,0],
[0,-1,0,0,0,0]],
[[0,1,0,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,0,1,0],
[0,0,0,1,0,0],
[0,0,0,0,0,1]]]],
[ # Z-class [06][11]
[[6],
[-2,6],
[-2,-2,6],
[-3,1,1,6],
[1,-3,1,-2,6],
[1,1,-3,-2,-2,6]],
[[[0,0,0,-1,0,0],
[0,0,0,0,-1,0],
[0,0,0,0,0,-1],
[1,0,0,1,0,0],
[0,1,0,0,1,0],
[0,0,1,0,0,1]],
[[0,0,0,1,0,0],
[0,0,0,0,0,1],
[0,0,0,-1,-1,-1],
[1,0,0,0,0,0],
[0,0,1,0,0,0],
[-1,-1,-1,0,0,0]],
[[0,1,0,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,0,1,0],
[0,0,0,1,0,0],
[0,0,0,0,0,1]]]],
[ # Z-class [06][12]
[[6],
[-1,6],
[-1,-1,6],
[-1,-1,-1,6],
[-1,-1,-1,-1,6],
[-1,-1,-1,-1,-1,6]],
[[[0,-1,0,0,0,0],
[0,0,-1,0,0,0],
[0,0,0,-1,0,0],
[0,0,0,0,-1,0],
[0,0,0,0,0,-1],
[1,1,1,1,1,1]],
[[0,1,0,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]]]],
[ # Z-class [06][13]
[[2],
[1,2],
[1,1,2],
[1,1,1,2],
[1,1,1,1,2],
[1,1,1,1,1,2]],
[[[1,-1,0,0,0,0],
[1,0,-1,0,0,0],
[1,0,0,-1,0,0],
[1,0,0,0,-1,0],
[1,0,0,0,0,-1],
[1,0,0,0,0,0]],
[[0,1,0,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,0,0,0,0,1]]]],
[ # Z-class [06][14]
[[4],
[-1,4],
[-2,-1,4],
[1,-2,-1,4],
[1,1,-2,-1,4],
[-2,1,1,-2,-1,4]],
[[[0,-1,-1,-1,0,0],
[1,1,1,0,0,0],
[-1,0,0,0,0,-1],
[0,0,0,1,1,1],
[0,0,-1,-1,-1,0],
[0,0,1,0,0,0]],
[[0,0,0,0,0,-1],
[0,-1,0,-1,0,0],
[0,0,0,1,0,1],
[0,1,1,1,1,0],
[0,0,0,-1,-1,-1],
[1,0,0,0,0,1]]]],
[ # Z-class [06][15]
[[3],
[-1,3],
[-1,-1,3],
[1,-1,0,3],
[1,0,-1,-1,3],
[0,1,-1,1,-1,3]],
[[[0,0,0,-1,0,0],
[0,0,0,0,-1,0],
[-1,0,0,1,1,0],
[0,0,0,0,0,-1],
[0,-1,0,-1,0,1],
[0,0,-1,0,-1,-1]],
[[-1,0,0,0,0,0],
[0,0,0,1,0,0],
[0,0,0,0,1,0],
[0,1,0,0,0,0],
[0,0,1,0,0,0],
[0,0,0,0,0,1]]]],
[ # Z-class [06][16]
[[4],
[1,4],
[2,1,4],
[2,2,1,4],
[1,2,2,1,4],
[0,1,-1,-1,1,4]],
[[[0,-1,0,0,0,0],
[0,0,-1,0,0,0],
[0,0,0,-1,0,0],
[0,0,0,0,-1,0],
[-1,0,0,0,0,0],
[0,0,-1,0,1,-1]],
[[-1,0,1,0,0,0],
[0,-1,0,0,1,0],
[0,0,1,0,0,0],
[-1,-1,1,1,0,1],
[0,0,0,0,1,0],
[0,0,-1,0,1,-1]]]],
[ # Z-class [06][17]
[[5],
[1,5],
[-1,1,5],
[-1,-1,1,5],
[1,-1,-1,1,5],
[2,2,2,2,2,5]],
[[[0,-1,0,0,0,0],
[0,0,-1,0,0,0],
[0,0,0,-1,0,0],
[0,0,0,0,-1,0],
[-1,0,0,0,0,0],
[0,0,0,0,0,-1]],
[[0,0,0,0,0,1],
[0,-1,0,-1,0,1],
[1,0,1,0,0,-1],
[1,0,0,1,0,-1],
[0,0,-1,0,-1,1],
[1,0,0,0,0,0]]]]
];
MakeImmutable( IMFList[6].matrices );
#############################################################################
##
## Quadratic form and matrix generators for the Z-class representatives of
## the irreducible maximal finite integral matrix groups of dimension 7.
##
IMFList[7].matrices := [
[ # Z-class [07][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]],
[[[0,1,0,0,0,0,0],
[0,0,1,0,0,0,0],
[0,0,0,1,0,0,0],
[1,0,0,0,0,0,0],
[0,0,0,0,1,0,0],
[0,0,0,0,0,1,0],
[0,0,0,0,0,0,1]],
[[-1,0,0,0,0,0,0],
[0,1,0,0,0,0,0],
[0,0,0,1,0,0,0],
[0,0,0,0,1,0,0],
[0,0,0,0,0,1,0],
[0,0,0,0,0,0,1],
[0,0,1,0,0,0,0]]]],
[ # Z-class [07][02]
[[2],
[1,2],
[0,1,2],
[0,0,1,2],
[0,0,0,1,2],
[0,0,0,0,1,2],
[0,0,0,0,1,0,2]],
[[[0,1,0,0,0,0,0],
[0,0,1,0,0,0,0],
[1,-1,1,0,0,0,0],
[1,-1,1,-1,2,-1,-1],
[0,0,0,0,1,0,0],
[0,0,0,0,0,1,0],
[0,0,0,0,0,0,1]],
[[-1,2,-2,2,-2,1,1],
[0,1,-1,2,-2,1,1],
[0,0,0,1,0,0,0],
[0,0,0,0,1,0,0],
[0,0,0,0,0,1,0],
[0,0,1,-1,1,0,-1],
[0,0,-1,1,-1,1,0]]]],
[ # Z-class [07][03]
[[4],
[0,4],
[0,0,4],
[0,0,0,4],
[0,0,0,0,4],
[0,0,0,0,0,4],
[2,2,2,2,2,2,7]],
[[[0,1,0,0,0,0,0],
[0,0,1,0,0,0,0],
[0,0,0,1,0,0,0],
[1,0,0,0,0,0,0],
[0,0,0,0,1,0,0],
[0,0,0,0,0,1,0],
[0,0,0,0,0,0,1]],
[[-1,0,0,0,0,0,0],
[0,1,0,0,0,0,0],
[0,0,0,1,0,0,0],
[0,0,0,0,1,0,0],
[0,0,0,0,0,1,0],
[-1,-1,-1,-1,-1,-1,2],
[-1,0,0,0,0,0,1]]]],
[ # Z-class [07][04]
[[7],
[-1,7],
[-1,-1,7],
[-1,-1,-1,7],
[-1,-1,-1,-1,7],
[-1,-1,-1,-1,-1,7],
[-1,-1,-1,-1,-1,-1,7]],
[[[0,1,0,0,0,0,0],
[1,0,0,0,0,0,0],
[0,0,1,0,0,0,0],
[0,0,0,1,0,0,0],
[0,0,0,0,1,0,0],
[0,0,0,0,0,1,0],
[0,0,0,0,0,0,1]],
[[-1,0,0,0,0,0,0],
[0,0,-1,0,0,0,0],
[0,0,0,-1,0,0,0],
[0,0,0,0,-1,0,0],
[0,0,0,0,0,-1,0],
[0,0,0,0,0,0,-1],
[1,1,1,1,1,1,1]]]],
[ # Z-class [07][05]
[[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]],
[[[0,1,0,0,0,0,0],
[1,0,0,0,0,0,0],
[0,0,1,0,0,0,0],
[0,0,0,1,0,0,0],
[0,0,0,0,1,0,0],
[0,0,0,0,0,1,0],
[0,0,0,0,0,0,1]],
[[-1,1,0,0,0,0,0],
[0,1,-1,0,0,0,0],
[0,1,0,-1,0,0,0],
[0,1,0,0,-1,0,0],
[0,1,0,0,0,-1,0],
[0,1,0,0,0,0,-1],
[0,1,0,0,0,0,0]]]],
[ # Z-class [07][06]
[[2],
[0,2],
[1,0,2],
[0,1,1,2],
[0,0,0,1,2],
[0,0,0,0,1,2],
[0,0,0,0,0,1,2]],
[[[1,-1,-1,1,0,0,0],
[0,0,0,1,0,0,0],
[1,0,0,0,0,0,0],
[0,0,1,0,0,0,0],
[0,-1,0,1,-1,0,0],
[0,0,0,0,0,-1,0],
[0,0,0,0,0,0,-1]],
[[-1,0,1,-1,1,-1,1],
[0,1,0,-1,1,-1,1],
[-1,0,0,0,0,0,0],
[0,0,-1,0,0,0,0],
[0,0,0,-1,0,0,0],
[0,0,0,0,-1,0,0],
[0,0,0,0,0,-1,0]]]],
[ # Z-class [07][07]
[[3],
[1,3],
[1,1,3],
[1,1,1,3],
[1,1,1,1,3],
[1,1,-1,-1,-1,3],
[1,1,1,1,1,-1,3]],
[[[0,0,0,0,0,0,1],
[0,0,0,0,0,-1,0],
[0,0,0,0,1,0,0],
[1,0,0,-1,0,-1,0],
[1,0,-1,0,0,-1,0],
[0,1,0,0,-1,-1,0],
[-1,-1,0,0,1,1,1]],
[[-2,-1,1,1,1,2,1],
[0,0,0,0,0,0,1],
[0,0,0,0,0,-1,0],
[-1,-1,0,1,0,1,1],
[-1,-1,1,0,0,1,1],
[0,1,0,0,0,0,0],
[-1,-1,0,0,1,1,1]]]]
];
MakeImmutable( IMFList[7].matrices );
#############################################################################
##
## Quadratic form and matrix generators for the Z-class representatives of
## the irreducible maximal finite integral matrix groups of dimension 8.
##
IMFList[8].matrices := [
[ # Z-class [08][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]],
[[[0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[-1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1],
[0,1,0,0,0,0,0,0]]]],
[ # Z-class [08][02]
[[2],
[1,2],
[0,1,2],
[0,0,1,2],
[0,0,0,1,2],
[0,0,0,0,1,2],
[0,0,0,0,0,1,2],
[0,0,0,0,0,1,0,2]],
[[[1,0,0,0,0,0,0,0],
[1,-1,2,-2,2,-2,1,1],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[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],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,1,-1,1,-1,1,0,-1],
[0,-1,1,-1,1,-1,1,0]]]],
[ # Z-class [08][03]
[[2],
[0,2],
[0,0,2],
[0,0,0,2],
[0,0,0,0,2],
[0,0,0,0,0,2],
[0,0,0,0,0,0,2],
[1,1,1,1,1,1,1,4]],
[[[0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[-1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[-1,-1,-1,-1,-1,-1,-1,2],
[-1,0,0,0,0,0,0,1]]]],
[ # Z-class [08][04]
[[2],
[1,2],
[0,1,2],
[0,1,0,2],
[0,0,0,0,2],
[0,0,0,0,1,2],
[0,0,0,0,0,1,2],
[0,0,0,0,0,1,0,2]],
[[[-1,1,-1,-1,0,0,0,0],
[-1,0,0,0,0,0,0,0],
[0,-1,1,0,0,0,0,0],
[0,-1,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[0,1,-1,-1,0,0,0,0],
[0,0,0,-1,0,0,0,0],
[-1,1,0,-1,0,0,0,0],
[0,-1,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0]]]],
[ # Z-class [08][05]
[[2],
[0,2],
[-1,0,2],
[0,-1,-1,2],
[0,0,0,-1,2],
[0,0,0,0,-1,2],
[0,0,0,0,0,-1,2],
[0,0,0,0,0,0,-1,2]],
[[[-1,-1,-1,-1,0,0,0,0],
[0,0,0,1,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,1,0,1,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[-1,0,-1,-1,-1,-1,-1,-1],
[0,1,0,1,1,1,1,1],
[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0]]]],
[ # Z-class [08][06]
[[4],
[2,4],
[0,2,4],
[0,2,0,4],
[-2,-1,0,0,4],
[-1,-2,-1,-1,2,4],
[0,-1,-2,0,0,2,4],
[0,-1,0,-2,0,2,0,4]],
[[[0,0,0,0,0,-1,1,1],
[0,0,0,0,0,0,0,1],
[0,0,0,0,1,-1,0,1],
[0,0,0,0,0,1,0,0],
[0,1,-1,-1,0,1,-1,-1],
[0,0,0,-1,0,0,0,-1],
[-1,1,0,-1,-1,1,0,-1],
[0,-1,0,0,0,-1,0,0]],
[[0,0,0,0,-1,1,-1,-1],
[0,0,0,0,-1,0,0,0],
[0,0,0,0,0,-1,1,0],
[0,0,0,0,0,-1,0,1],
[-1,1,-1,-1,0,0,0,0],
[-1,0,0,0,0,0,0,0],
[0,-1,1,0,0,0,0,0],
[0,-1,0,1,0,0,0,0]],
[[-1,1,-1,-1,0,0,0,0],
[-1,0,0,0,0,0,0,0],
[0,-1,1,0,0,0,0,0],
[0,-1,0,1,0,0,0,0],
[0,0,0,0,-1,1,-1,-1],
[0,0,0,0,-1,0,0,0],
[0,0,0,0,0,-1,1,0],
[0,0,0,0,0,-1,0,1]]]],
[ # Z-class [08][07]
[[2],
[-1,2],
[0,0,2],
[0,0,-1,2],
[0,0,0,0,2],
[0,0,0,0,-1,2],
[0,0,0,0,0,0,2],
[0,0,0,0,0,0,-1,2]],
[[[0,-1,0,0,0,0,0,0],
[1,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0]],
[[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]]]],
[ # Z-class [08][08]
[[4],
[-2,4],
[0,0,4],
[0,0,-2,4],
[-2,1,-1,-1,4],
[1,-2,2,-1,-2,4],
[1,-2,-1,2,-2,1,4],
[1,1,-1,-1,1,-2,-2,4]],
[[[-1,0,0,0,0,1,1,1],
[0,-1,0,0,-1,-1,-1,0],
[0,0,-1,0,0,0,0,0],
[0,0,0,-1,0,0,0,0],
[0,0,0,0,-1,-1,-1,-1],
[0,0,0,0,1,0,1,0],
[0,0,0,0,1,1,0,0],
[0,0,0,0,-1,0,0,0]],
[[0,0,1,0,0,-1,0,0],
[0,0,0,1,0,1,0,1],
[-1,0,0,0,0,0,1,1],
[0,-1,0,0,0,0,-1,0],
[1,1,0,0,1,1,1,0],
[-1,0,0,0,0,0,0,0],
[0,-1,0,0,0,-1,-1,-1],
[1,1,0,0,0,0,0,0]],
[[1,0,0,0,0,0,-1,-1],
[0,1,0,0,0,0,1,0],
[0,0,1,0,0,0,1,1],
[0,0,0,1,0,0,-1,0],
[0,0,0,0,1,0,1,0],
[0,0,0,0,0,1,0,1],
[0,0,0,0,0,0,-1,0],
[0,0,0,0,0,0,0,-1]]]],
[ # Z-class [08][09]
[[6],
[0,6],
[0,0,6],
[0,3,0,6],
[0,0,-3,0,6],
[3,0,0,0,0,6],
[3,-3,0,-3,3,3,8],
[0,0,3,-3,0,3,4,8]],
[[[-1,0,0,0,0,0,0,0],
[0,-1,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0],
[0,0,0,-1,0,0,0,0],
[0,0,0,0,-1,0,0,0],
[0,0,0,0,0,-1,0,0],
[-1,1,0,0,-1,0,1,-1],
[0,0,-1,1,-1,-1,1,0]],
[[0,-1,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,-1,0,0],
[0,0,0,-1,0,0,0,0],
[0,0,0,0,-1,-1,1,0],
[0,1,0,-1,-1,0,1,-1]],
[[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[-1,1,0,0,-1,0,2,-1],
[0,0,0,1,0,0,0,0],
[0,0,1,-1,1,1,-1,-1],
[0,0,0,0,0,1,0,0],
[0,0,1,-1,0,1,0,-1],
[-1,1,0,-1,-1,1,1,-1]]]],
[ # Z-class [08][10]
[[4],
[-2,4],
[-2,1,4],
[1,-2,-2,4],
[0,0,0,0,4],
[0,0,0,0,-2,4],
[0,0,0,0,-2,1,4],
[0,0,0,0,1,-2,-2,4]],
[[[0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[0,-1,0,0,0,0,0,0],
[1,1,0,0,0,0,0,0],
[0,0,0,-1,0,0,0,0],
[0,0,1,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0]]]],
[ # Z-class [08][11]
[[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]],
[[[0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[1,-1,0,0,0,0,0,0],
[1,0,-1,0,0,0,0,0],
[1,0,0,-1,0,0,0,0],
[1,0,0,0,-1,0,0,0],
[1,0,0,0,0,-1,0,0],
[1,0,0,0,0,0,-1,0],
[1,0,0,0,0,0,0,-1],
[1,0,0,0,0,0,0,0]]]],
[ # Z-class [08][12]
[[8],
[-1,8],
[-1,-1,8],
[-1,-1,-1,8],
[-1,-1,-1,-1,8],
[-1,-1,-1,-1,-1,8],
[-1,-1,-1,-1,-1,-1,8],
[-1,-1,-1,-1,-1,-1,-1,8]],
[[[0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[0,-1,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0],
[0,0,0,-1,0,0,0,0],
[0,0,0,0,-1,0,0,0],
[0,0,0,0,0,-1,0,0],
[0,0,0,0,0,0,-1,0],
[0,0,0,0,0,0,0,-1],
[1,1,1,1,1,1,1,1]]]],
[ # Z-class [08][13]
[[8],
[-4,8],
[-4,2,8],
[2,-4,-4,8],
[-4,2,2,-1,8],
[2,-4,-1,2,-4,8],
[2,-1,-4,2,-4,2,8],
[-1,2,2,-4,2,-4,-4,8]],
[[[0,0,0,0,-1,0,0,0],
[0,0,0,0,0,-1,0,0],
[0,0,0,0,0,0,-1,0],
[0,0,0,0,0,0,0,-1],
[1,0,0,0,1,0,0,0],
[0,1,0,0,0,1,0,0],
[0,0,1,0,0,0,1,0],
[0,0,0,1,0,0,0,1]],
[[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0]],
[[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[1,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,1]]]],
[ # Z-class [08][14]
[[2],
[1,2],
[1,1,2],
[1,1,1,2],
[0,0,0,0,2],
[0,0,0,0,1,2],
[0,0,0,0,1,1,2],
[0,0,0,0,1,1,1,2]],
[[[0,0,0,1,0,0,0,0],
[-1,0,0,1,0,0,0,0],
[0,-1,0,1,0,0,0,0],
[0,0,-1,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0]]]],
[ # Z-class [08][15]
[[4],
[-1,4],
[-1,-1,4],
[-1,-1,-1,4],
[0,0,0,0,4],
[0,0,0,0,-1,4],
[0,0,0,0,-1,-1,4],
[0,0,0,0,-1,-1,-1,4]],
[[[1,1,1,1,0,0,0,0],
[-1,0,0,0,0,0,0,0],
[0,-1,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0]]]],
[ # Z-class [08][16]
[[4],
[-2,4],
[1,-1,4],
[1,0,-1,4],
[-1,-1,1,1,4],
[-2,1,-2,1,1,4],
[0,1,-2,2,-1,2,4],
[2,-1,0,1,-2,0,1,4]],
[[[0,0,0,0,0,0,0,1],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0],
[0,1,0,0,1,-1,0,1],
[0,1,0,0,0,0,0,0],
[1,1,0,-1,1,0,0,0],
[0,0,1,0,0,0,0,0],
[1,0,0,0,0,0,0,0]],
[[-1,-1,0,0,0,-1,1,0],
[0,0,0,0,0,1,-1,0],
[0,0,0,-1,0,0,1,0],
[0,-1,1,1,-1,1,0,-1],
[1,0,1,0,-1,1,0,-1],
[0,0,1,1,-1,1,-1,0],
[0,0,0,0,1,0,0,1],
[-1,-1,0,1,-1,0,0,0]],
[[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,1,-1,1,-1,0],
[0,-1,1,1,-2,1,0,-1]]]],
[ # Z-class [08][17]
[[8],
[3,8],
[3,3,8],
[3,3,3,8],
[-3,2,2,2,8],
[-3,2,2,2,3,8],
[-2,-2,-2,-2,2,2,8],
[-2,-2,-2,3,2,2,3,8]],
[[[0,0,0,0,1,0,0,0],
[1,-1,0,0,1,0,0,0],
[1,0,-1,0,1,0,0,0],
[1,0,0,-1,1,0,0,0],
[1,0,0,-1,0,0,0,1],
[2,-1,-1,-1,1,1,-1,0],
[1,0,0,-1,0,1,-1,1],
[1,0,0,-1,0,1,0,0]],
[[0,0,0,0,-1,0,0,0],
[-1,1,0,0,-1,0,0,0],
[-1,0,1,0,-1,0,0,0],
[-1,0,0,1,-1,0,0,0],
[-1,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]],
[[1,-1,0,0,1,0,0,0],
[0,-1,0,0,0,0,0,0],
[-1,0,1,1,-1,-1,1,0],
[1,-1,0,0,0,1,0,0],
[0,0,0,0,-1,0,0,0],
[-1,0,0,1,-1,0,0,0],
[0,0,0,0,0,0,-1,0],
[1,0,0,-1,0,1,-1,1]]]],
[ # Z-class [08][18]
[[8],
[-2,8],
[-2,-2,8],
[-2,-2,-2,8],
[-4,1,1,1,8],
[1,-4,1,1,-2,8],
[1,1,-4,1,-2,-2,8],
[1,1,1,-4,-2,-2,-2,8]],
[[[0,0,0,0,1,1,1,1],
[0,0,0,0,-1,0,0,0],
[0,0,0,0,0,-1,0,0],
[0,0,0,0,0,0,-1,0],
[-1,-1,-1,-1,-1,-1,-1,-1],
[1,0,0,0,1,0,0,0],
[0,1,0,0,0,1,0,0],
[0,0,1,0,0,0,1,0]],
[[0,0,0,0,1,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1],
[1,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0]],
[[0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]]]],
[ # Z-class [08][19]
[[4],
[2,4],
[2,2,4],
[2,2,2,4],
[-2,-1,-1,-1,4],
[-1,-2,-1,-1,2,4],
[-1,-1,-2,-1,2,2,4],
[-1,-1,-1,-2,2,2,2,4]],
[[[0,0,0,-1,0,0,0,-1],
[1,0,0,-1,1,0,0,-1],
[0,1,0,-1,0,1,0,-1],
[0,0,1,-1,0,0,1,-1],
[0,0,0,1,0,0,0,0],
[-1,0,0,1,0,0,0,0],
[0,-1,0,1,0,0,0,0],
[0,0,-1,1,0,0,0,0]],
[[0,0,0,0,-1,0,0,0],
[0,0,0,0,0,-1,0,0],
[0,0,0,0,0,0,-1,0],
[0,0,0,0,0,0,0,-1],
[-1,0,0,0,0,0,0,0],
[0,-1,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0],
[0,0,0,-1,0,0,0,0]],
[[0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1]]]],
[ # Z-class [08][20]
[[4],
[0,4],
[0,0,4],
[1,1,-1,4],
[0,0,0,1,4],
[1,-1,1,1,-1,4],
[-1,-1,-1,0,1,1,4],
[1,1,1,-1,1,0,1,4]],
[[[0,-1,0,1,-1,-1,0,1],
[0,0,0,-1,0,0,0,0],
[-1,0,-1,0,0,1,-1,1],
[0,0,0,0,0,-1,0,0],
[0,0,0,0,0,0,-1,0],
[0,0,-1,0,0,0,0,0],
[0,0,0,0,0,0,0,-1],
[0,0,0,0,-1,0,0,0]],
[[0,0,0,0,0,0,0,-1],
[-1,-1,0,1,0,0,-1,1],
[0,0,1,1,-1,-1,1,0],
[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,-1,0,0,0,0],
[-1,0,0,0,0,0,0,0]]]],
[ # Z-class [08][21]
[[3],
[1,3],
[0,0,3],
[0,0,-1,3],
[0,1,-1,0,3],
[-1,0,1,0,-1,3],
[-1,0,0,-1,1,1,3],
[1,0,1,0,1,0,1,3]],
[[[-1,1,-1,-1,-1,0,-1,1],
[0,0,-1,-1,0,1,-1,1],
[-1,0,0,0,0,0,-1,1],
[0,0,-1,0,0,0,0,0],
[1,0,0,0,0,0,0,0],
[0,-1,0,0,0,0,0,0],
[1,-1,1,0,1,0,0,-1],
[0,0,0,0,0,0,-1,0]],
[[-1,1,-1,-1,-1,0,-1,1],
[0,1,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0],
[0,0,0,0,0,1,0,0],
[0,0,1,0,1,0,0,-1],
[0,0,0,1,0,0,0,0],
[0,0,1,1,0,-1,1,-1],
[0,0,0,0,0,0,0,-1]]]],
[ # Z-class [08][22]
[[6],
[-2,6],
[2,-2,6],
[3,-1,3,6],
[3,1,1,1,6],
[-1,3,1,1,0,6],
[1,3,-1,2,3,3,6],
[0,0,2,3,1,3,3,6]],
[[[0,0,-1,0,1,1,-1,0],
[0,1,1,0,0,-1,0,0],
[0,0,0,0,0,1,0,0],
[0,0,-1,1,1,1,-1,0],
[-1,0,0,0,1,0,0,0],
[0,0,1,0,0,0,1,-1],
[-1,0,0,1,1,0,0,-1],
[-1,-1,0,1,1,1,0,-1]],
[[0,0,-1,1,0,0,-1,0],
[-1,0,1,0,0,-1,1,0],
[0,0,-1,0,0,0,0,0],
[0,0,-1,1,0,0,0,0],
[-1,0,0,1,0,0,0,-1],
[-1,-1,0,0,0,0,1,0],
[-1,0,0,1,0,0,0,0],
[0,0,0,0,-1,0,1,0]],
[[1,0,0,-1,0,0,0,1],
[0,0,0,0,0,1,0,-1],
[1,1,1,-1,-1,-1,0,1],
[1,1,0,0,0,0,-1,1],
[0,0,1,-1,0,0,1,0],
[0,0,0,0,0,1,-1,0],
[0,0,0,0,0,1,0,0],
[0,1,0,0,0,0,-1,1]]]],
[ # Z-class [08][23]
[[8],
[-4,8],
[-1,2,8],
[2,-4,-4,8],
[2,-1,-4,2,8],
[-4,2,2,-1,-4,8],
[-1,-1,2,-1,2,-1,8],
[2,-1,-1,-1,-1,2,-4,8]],
[[[0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,1,0],
[1,1,-1,0,-1,0,1,0],
[0,0,1,0,1,0,-1,0],
[-1,0,1,1,0,-1,0,1],
[1,0,0,0,0,1,0,-1],
[0,0,0,0,-1,-1,0,0],
[0,0,0,0,0,1,0,0]],
[[-1,-1,1,0,1,0,-1,0],
[0,0,-1,0,-1,0,1,0],
[0,0,0,0,0,0,0,-1],
[0,0,0,0,0,0,-1,0],
[-1,0,0,0,0,-1,0,1],
[1,0,-1,-1,0,1,0,-1],
[0,0,0,0,0,-1,0,0],
[0,0,0,0,1,1,0,0]]]],
[ # Z-class [08][24]
[[6],
[-1,6],
[0,-1,6],
[1,0,3,6],
[-1,-2,3,1,6],
[1,1,2,1,3,6],
[-1,2,-2,1,-1,2,6],
[0,2,3,2,2,3,1,6]],
[[[0,1,0,0,1,-1,0,0],
[0,0,-1,0,0,1,-1,0],
[0,0,-1,1,0,0,0,0],
[-1,0,-1,1,-1,1,-1,0],
[0,0,0,0,0,0,1,0],
[0,0,-1,0,0,0,0,1],
[-1,-1,-1,0,-1,1,-1,1],
[0,0,-1,0,0,0,0,0]],
[[1,0,1,-1,0,-1,1,0],
[0,0,-1,0,0,1,-1,0],
[0,0,1,0,0,0,0,-1],
[0,-1,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0],
[0,0,1,-1,0,0,0,0],
[-1,-1,-1,0,-1,1,-1,1],
[0,0,0,0,0,0,-1,0]],
[[1,0,0,0,0,0,0,0],
[0,1,1,0,0,0,0,-1],
[0,0,0,0,0,0,0,1],
[0,0,0,0,0,1,0,0],
[-1,-1,-1,1,-1,1,-1,1],
[0,0,0,1,0,0,0,0],
[0,0,1,0,0,0,1,-1],
[0,0,1,0,0,0,0,0]]]],
[ # Z-class [08][25]
[[4],
[2,4],
[2,1,4],
[-1,0,-1,4],
[0,-1,2,0,4],
[1,1,0,2,1,4],
[0,1,2,1,1,1,4],
[-1,-1,1,0,1,1,2,4]],
[[[1,-1,0,0,0,0,0,0],
[1,0,-1,0,1,-1,0,0],
[1,0,0,0,0,0,0,0],
[0,0,-1,-1,0,0,1,0],
[0,0,1,0,-1,0,0,0],
[1,0,-1,0,0,-1,0,1],
[1,1,-1,0,1,-1,0,1],
[0,1,0,0,0,0,-1,1]],
[[-1,0,1,0,0,1,-1,0],
[-1,0,1,0,0,1,0,-1],
[0,1,0,1,1,-1,-1,1],
[0,0,-1,0,0,0,1,0],
[0,1,0,1,0,-1,-1,1],
[-1,0,1,0,-1,1,0,0],
[1,1,-1,1,1,-1,0,1],
[1,0,0,1,0,-1,0,1]],
[[1,-1,0,0,0,0,0,0],
[0,-1,0,0,0,0,0,0],
[0,-1,1,0,-1,1,0,0],
[0,1,0,1,1,-1,-1,1],
[0,0,0,0,0,1,0,0],
[0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,1,0]]]],
[ # Z-class [08][26]
[[14],
[1,14],
[7,-4,14],
[-4,7,-5,14],
[4,-4,5,-5,14],
[4,-4,5,-5,-1,14],
[-5,-1,-1,4,5,-1,14],
[1,5,-4,1,-1,5,5,14]],
[[[0,0,1,0,0,-1,0,1],
[-1,0,0,0,1,0,-1,1],
[1,0,0,-1,-1,-1,1,0],
[-1,0,0,0,1,0,-1,0],
[1,0,0,0,0,0,0,0],
[0,-1,1,0,-1,-1,0,1],
[0,0,0,0,0,0,-1,0],
[-1,0,1,0,0,0,-1,1]],
[[1,0,0,0,0,0,0,0],
[0,-1,0,1,0,0,-1,1],
[0,0,1,0,0,0,0,0],
[0,0,0,0,-1,0,0,0],
[0,0,1,0,0,-1,0,1],
[0,0,0,-1,0,0,0,0],
[-1,0,1,0,0,-1,-1,1],
[0,-1,0,0,0,-1,-1,1]],
[[0,0,0,0,0,0,0,-1],
[-1,0,0,1,1,1,-1,0],
[1,0,0,0,-1,0,1,-1],
[-1,0,1,1,1,0,-1,1],
[1,0,-1,0,0,0,1,-1],
[0,1,0,-1,-1,0,1,-1],
[0,0,0,0,0,0,1,0],
[-1,0,0,0,0,0,0,0]]]]
];
MakeImmutable( IMFList[8].matrices );
#############################################################################
##
## Quadratic form and matrix generators for the Z-class representatives of
## the irreducible maximal finite integral matrix groups of dimension 9.
##
IMFList[9].matrices := [
[ # Z-class [09][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]],
[[[-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],
[0,0,0,0,1,0,0,0,0],
[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],
[0,0,1,0,0,0,0,0,0]],
[[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],
[1,0,0,0,0,0,0,0,0],
[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]]]],
[ # Z-class [09][02]
[[2],
[1,2],
[0,1,2],
[0,0,1,2],
[0,0,0,1,2],
[0,0,0,0,1,2],
[0,0,0,0,0,1,2],
[0,0,0,0,0,0,1,2],
[0,0,0,0,0,0,1,0,2]],
[[[-1,2,-2,2,-2,2,-2,1,1],
[0,1,-1,2,-2,2,-2,1,1],
[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],
[0,0,1,-1,1,-1,1,0,-1],
[0,0,-1,1,-1,1,-1,1,0]],
[[0,1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0],
[1,-1,1,0,0,0,0,0,0],
[1,-1,1,-1,2,-2,2,-1,-1],
[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]]]],
[ # Z-class [09][03]
[[4],
[0,4],
[0,0,4],
[0,0,0,4],
[0,0,0,0,4],
[0,0,0,0,0,4],
[0,0,0,0,0,0,4],
[0,0,0,0,0,0,0,4],
[2,2,2,2,2,2,2,2,9]],
[[[-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],
[0,0,0,0,1,0,0,0,0],
[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],
[-1,-1,-1,-1,-1,-1,-1,-1,2],
[-1,0,0,0,0,0,0,0,1]],
[[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],
[1,0,0,0,0,0,0,0,0],
[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]]]],
[ # Z-class [09][04]
[[2],
[1,2],
[1,1,2],
[0,0,0,2],
[0,0,0,1,2],
[0,0,0,1,1,2],
[0,0,0,0,0,0,2],
[0,0,0,0,0,0,1,2],
[0,0,0,0,0,0,1,1,2]],
[[[0,1,0,0,0,0,0,0,0],
[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]],
[[-1,1,0,0,0,0,0,0,0],
[0,1,-1,0,0,0,0,0,0],
[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]],
[[0,0,0,1,0,0,0,0,0],
[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],
[1,0,0,0,0,0,0,0,0],
[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],
[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],
[0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1]]]],
[ # Z-class [09][05]
[[3],
[-1,3],
[-1,-1,3],
[0,0,0,3],
[0,0,0,-1,3],
[0,0,0,-1,-1,3],
[0,0,0,0,0,0,3],
[0,0,0,0,0,0,-1,3],
[0,0,0,0,0,0,-1,-1,3]],
[[[0,1,0,0,0,0,0,0,0],
[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]],
[[-1,0,0,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0,0],
[1,1,1,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0],
[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]],
[[0,0,0,1,0,0,0,0,0],
[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],
[1,0,0,0,0,0,0,0,0],
[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],
[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],
[0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1]]]],
[ # Z-class [09][06]
[[2],
[1,2],
[1,1,2],
[0,0,0,2],
[0,0,0,1,2],
[0,0,0,1,1,2],
[0,0,0,0,0,0,2],
[0,0,0,0,0,0,1,2],
[0,1,1,0,1,1,0,1,3]],
[[[0,1,0,0,0,0,0,0,0],
[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],
[1,-1,0,0,0,0,0,0,1]],
[[-1,1,0,0,0,0,0,0,0],
[0,1,-1,0,0,0,0,0,0],
[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],
[1,0,-1,0,0,0,0,0,1]],
[[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],
[1,-1,-1,1,-1,-1,1,-1,2],
[1,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1]],
[[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],
[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],
[0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1]]]],
[ # Z-class [09][07]
[[4],
[0,4],
[0,0,4],
[0,0,0,4],
[0,0,0,0,4],
[0,0,0,0,0,4],
[0,0,0,0,0,0,4],
[0,0,0,2,2,2,2,6],
[2,2,2,0,0,2,2,1,6]],
[[[1,0,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0],
[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]],
[[0,0,1,0,0,0,0,0,0],
[-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],
[0,0,0,0,1,0,0,0,0],
[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],
[-1,0,0,0,0,0,0,0,1]],
[[0,0,0,-1,0,0,0,0,0],
[0,0,0,0,-1,0,0,0,0],
[-1,-1,-1,-1,-1,-2,-2,2,2],
[0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0,0],
[-1,0,0,0,0,0,0,0,0],
[0,-1,0,0,0,0,0,0,0],
[0,0,1,0,0,1,1,0,-1],
[-1,-1,-1,-1,-1,-1,-1,1,1]],
[[0,0,0,-1,0,0,0,0,0],
[0,0,0,0,-1,0,0,0,0],
[-1,-1,-1,-1,-1,-2,-2,2,2],
[-1,0,0,0,0,0,0,0,0],
[0,-1,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,1,0,0],
[0,0,1,0,0,1,1,0,-1],
[-1,-1,-1,-1,-1,-1,-1,1,2]]]],
[ # Z-class [09][08]
[[3],
[-1,3],
[-1,-1,3],
[0,0,0,3],
[0,0,0,-1,3],
[0,0,0,-1,-1,3],
[-1,1,1,1,-1,1,3],
[1,-1,1,1,1,-1,0,3],
[1,1,-1,-1,1,1,0,0,3]],
[[[1,1,1,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0,0],
[0,-1,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0],
[0,-1,-1,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1]],
[[0,1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0],
[0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1],
[0,0,0,0,0,0,1,0,0]],
[[0,0,1,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0],
[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],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,1,0,0]],
[[0,-1,-1,0,0,0,1,0,0],
[0,1,1,1,0,1,-1,0,0],
[0,0,0,-1,0,-1,1,0,0],
[0,0,0,0,-1,-1,0,0,1],
[-1,-1,0,0,0,0,0,0,1],
[1,1,0,0,1,1,0,0,-1],
[1,1,1,0,0,0,0,0,0],
[-1,-1,-1,-1,-1,-1,1,1,1],
[0,0,0,1,1,1,0,0,0]]]],
[ # Z-class [09][09]
[[4],
[2,4],
[2,2,4],
[2,1,1,4],
[1,2,1,2,4],
[1,1,2,2,2,4],
[2,1,1,2,1,1,4],
[1,2,1,1,2,1,2,4],
[1,1,2,-1,1,0,0,2,4]],
[[[1,0,0,0,0,0,0,0,0],
[1,0,0,-1,1,0,0,0,-1],
[1,-1,1,-1,1,0,0,0,-1],
[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],
[1,-1,0,-1,1,0,0,1,-1],
[1,-1,0,-1,1,0,0,0,0]],
[[0,1,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0],
[0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0],
[-1,1,-1,1,-1,1,1,-1,2],
[0,1,-1,0,-1,1,1,-1,1]],
[[0,0,1,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0],
[1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0],
[0,0,0,0,1,0,0,0,0],
[0,0,0,1,0,0,0,0,0],
[-1,1,-1,1,-1,1,1,-1,2],
[0,0,0,0,0,0,0,1,0],
[1,-1,1,-1,1,-1,0,1,-1]],
[[1,-1,0,0,0,0,-1,1,0],
[0,0,0,0,0,0,-1,1,0],
[0,0,0,1,-1,0,-1,1,0],
[1,-2,2,-1,1,-1,-1,2,-2],
[1,-1,1,-1,1,-1,-1,2,-2],
[1,-1,1,-1,0,0,-1,2,-2],
[0,-1,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,1,0],
[0,1,-1,1,-1,0,0,0,1]]]],
[ # Z-class [09][10]
[[4],
[2,4],
[2,2,4],
[2,1,1,4],
[1,2,1,2,4],
[1,1,2,2,2,4],
[2,1,1,2,1,1,4],
[1,2,1,1,2,1,2,4],
[1,1,2,1,1,2,2,2,4]],
[[[0,1,0,0,0,0,0,0,0],
[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],
[0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,1]],
[[-1,1,0,0,0,0,0,0,0],
[0,1,-1,0,0,0,0,0,0],
[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],
[0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,-1,1,0],
[0,0,0,0,0,0,0,1,-1],
[0,0,0,0,0,0,0,1,0]],
[[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],
[0,1,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,1,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,1]]]],
[ # Z-class [09][11]
[[9],
[-3,9],
[-3,-3,9],
[-3,1,1,9],
[1,-3,1,-3,9],
[1,1,-3,-3,-3,9],
[-3,1,1,-3,1,1,9],
[1,-3,1,1,-3,1,-3,9],
[1,1,-3,1,1,-3,-3,-3,9]],
[[[0,1,0,0,0,0,0,0,0],
[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],
[0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,1]],
[[-1,0,0,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0,0],
[1,1,1,0,0,0,0,0,0],
[0,0,0,-1,0,0,0,0,0],
[0,0,0,0,0,-1,0,0,0],
[0,0,0,1,1,1,0,0,0],
[0,0,0,0,0,0,-1,0,0],
[0,0,0,0,0,0,0,0,-1],
[0,0,0,0,0,0,1,1,1]],
[[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],
[0,1,0,0,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,1,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,1]]]],
[ # Z-class [09][12]
[[6],
[-2,6],
[-2,-2,6],
[3,-1,-1,6],
[-1,3,-1,-2,6],
[-1,-1,3,-2,-2,6],
[3,-1,-1,1,1,1,6],
[-1,3,-1,1,1,1,2,6],
[-1,-1,3,1,1,1,2,2,6]],
[[[0,0,0,0,0,0,0,0,1],
[0,0,1,0,0,-1,1,0,-1],
[0,1,0,0,-1,0,0,0,0],
[0,0,0,-1,-1,-1,0,0,1],
[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],
[0,0,0,0,0,-1,0,0,0],
[0,1,-1,0,-1,0,0,-1,1]],
[[-1,-1,-1,1,1,1,0,0,0],
[0,1,0,0,-1,0,0,-1,1],
[0,0,1,0,0,-1,0,1,-1],
[0,0,0,1,1,1,0,0,0],
[0,0,0,0,-1,0,0,0,0],
[0,0,0,0,0,-1,0,0,0],
[0,-1,-1,1,1,1,-1,0,0],
[1,0,0,0,0,0,-1,0,1],
[1,0,0,0,0,0,-1,1,0]],
[[1,0,0,0,0,0,0,0,0],
[0,0,0,-1,-1,-1,0,1,0],
[0,0,1,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0],
[0,-1,0,-1,0,-1,0,1,0],
[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]]]],
[ # Z-class [09][13]
[[8],
[4,8],
[4,4,8],
[0,0,0,8],
[0,0,0,4,8],
[0,0,0,4,4,8],
[0,0,0,0,0,0,8],
[0,0,0,0,0,0,4,8],
[4,4,4,4,4,4,4,4,9]],
[[[1,0,0,0,0,0,0,0,0],
[0,0,1,0,0,0,0,0,0],
[0,1,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0],
[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,-1,0,0,0,0,0,0],
[0,1,-1,0,0,0,0,0,0],
[1,0,-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,-1,0,0,0,0,0,1]],
[[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],
[-1,-1,-1,-1,-1,-1,-1,-2,4],
[-1,-1,-1,-1,-1,-1,-1,-1,4],
[-1,-1,-1,-1,-1,-1,-2,-1,4],
[0,1,-1,0,0,0,0,0,0],
[-1,1,0,0,0,0,0,0,0],
[-1,0,-1,-1,-1,-1,-1,-1,3]],
[[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],
[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],
[0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1]]]],
[ # Z-class [09][14]
[[6],
[-2,6],
[-2,-2,6],
[3,-1,-1,6],
[-1,3,-1,-2,6],
[-1,-1,3,-2,-2,6],
[3,-1,-1,3,-1,-1,6],
[-1,3,-1,-1,3,-1,-2,6],
[-1,-1,3,-1,-1,3,-2,-2,6]],
[[[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],
[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],
[0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1]],
[[-1,0,0,1,0,0,0,0,0],
[0,-1,0,0,1,0,0,0,0],
[0,0,-1,0,0,1,0,0,0],
[0,0,0,1,0,0,-1,0,0],
[0,0,0,0,1,0,0,-1,0],
[0,0,0,0,0,1,0,0,-1],
[0,0,0,1,0,0,0,0,0],
[0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,1,0,0,0]],
[[0,1,0,0,0,0,0,0,0],
[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],
[0,0,0,1,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,1]],
[[-1,0,0,0,0,0,0,0,0],
[0,0,-1,0,0,0,0,0,0],
[1,1,1,0,0,0,0,0,0],
[0,0,0,-1,0,0,0,0,0],
[0,0,0,0,0,-1,0,0,0],
[0,0,0,1,1,1,0,0,0],
[0,0,0,0,0,0,-1,0,0],
[0,0,0,0,0,0,0,0,-1],
[0,0,0,0,0,0,1,1,1]]]],
[ # Z-class [09][15]
[[9],
[-1,9],
[-1,-1,9],
[-1,-1,-1,9],
[-1,-1,-1,-1,9],
[-1,-1,-1,-1,-1,9],
[-1,-1,-1,-1,-1,-1,9],
[-1,-1,-1,-1,-1,-1,-1,9],
[-1,-1,-1,-1,-1,-1,-1,-1,9]],
[[[0,1,0,0,0,0,0,0,0],
[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]],
[[-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],
[1,1,1,1,1,1,1,1,1]]]],
[ # Z-class [09][16]
[[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]],
[[[0,1,0,0,0,0,0,0,0],
[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]],
[[-1,1,0,0,0,0,0,0,0],
[0,1,-1,0,0,0,0,0,0],
[0,1,0,-1,0,0,0,0,0],
[0,1,0,0,-1,0,0,0,0],
[0,1,0,0,0,-1,0,0,0],
[0,1,0,0,0,0,-1,0,0],
[0,1,0,0,0,0,0,-1,0],
[0,1,0,0,0,0,0,0,-1],
[0,1,0,0,0,0,0,0,0]]]],
[ # Z-class [09][17]
[[8],
[3,8],
[3,3,8],
[3,3,3,8],
[3,3,3,3,8],
[3,3,3,3,3,8],
[3,3,3,3,3,3,8],
[3,3,3,3,3,3,3,8],
[-3,-3,2,2,2,2,2,2,8]],
[[[1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,-1],
[0,-1,1,0,0,0,0,0,-1],
[0,-1,0,1,0,0,0,0,-1],
[0,-1,0,0,1,0,0,0,-1],
[0,-1,0,0,0,1,0,0,-1],
[0,-1,0,0,0,0,1,0,-1],
[0,-1,0,0,0,0,0,1,-1],
[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,-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],
[-3,-3,1,1,1,1,1,1,-4],
[-1,0,1,0,0,0,0,0,-1]]]],
[ # Z-class [09][18]
[[4],
[2,4],
[2,2,4],
[2,2,2,4],
[2,2,2,2,4],
[2,2,2,2,2,4],
[2,2,2,2,2,2,4],
[2,2,2,2,2,2,2,4],
[0,0,0,2,2,2,2,2,5]],
[[[-1,0,0,0,0,0,0,0,0],
[-1,1,0,0,0,0,0,0,0],
[-1,0,1,0,0,0,0,0,0],
[-1,0,0,1,0,0,0,0,0],
[-1,0,0,0,1,0,0,0,0],
[-1,0,0,0,0,1,0,0,0],
[-1,0,0,0,0,0,1,0,0],
[-1,0,0,0,0,0,0,1,0],
[0,0,0,0,0,0,0,0,1]],
[[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],
[1,1,1,-1,-1,-1,-1,-1,2],
[1,1,1,0,-1,-1,-1,-1,1]]]],
[ # Z-class [09][19]
[[12],
[2,12],
[2,-3,12],
[-3,2,2,12],
[3,3,-2,3,12],
[3,3,3,-2,2,12],
[-3,-3,2,2,3,3,12],
[-2,3,3,3,2,-3,-2,12],
[3,-2,-2,3,2,-3,3,-3,12]],
[[[1,-1,-1,1,0,0,0,0,-1],
[0,0,0,0,0,-1,0,0,0],
[0,-1,-1,0,0,1,0,1,0],
[-1,0,1,-1,1,0,-1,0,1],
[0,0,0,0,0,0,-1,0,0],
[0,0,-1,0,0,0,0,0,0],
[-1,0,0,0,0,1,-1,0,1],
[0,0,0,0,0,0,0,1,0],
[-1,0,1,0,1,0,-1,-1,0]],
[[1,-1,-1,1,-1,1,0,1,0],
[0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,1],
[0,0,0,0,1,0,0,0,0],
[0,-1,-1,0,0,1,0,1,0],
[-1,0,0,0,0,1,-1,0,1],
[0,0,-1,0,0,0,0,0,0],
[0,0,0,0,0,0,1,0,0],
[1,-1,-1,1,0,0,0,0,-1]]]],
[ # Z-class [09][20]
[[4],
[-2,4],
[-1,2,4],
[-1,2,0,4],
[0,0,-1,-1,4],
[-1,0,0,0,1,4],
[1,1,0,2,0,0,4],
[2,-1,1,-1,-1,1,1,4],
[-1,2,1,1,-1,-1,2,0,4]],
[[[0,1,0,-1,-1,0,1,-1,-1],
[-1,0,-1,0,0,0,0,1,0],
[0,1,-1,0,0,0,0,1,0],
[-1,-1,0,0,0,0,1,0,0],
[-1,0,0,0,0,-1,0,1,-1],
[-1,0,0,0,1,-1,0,1,0],
[-1,0,0,0,0,0,1,0,-1],
[0,1,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0]],
[[0,0,0,0,0,0,1,0,0],
[0,0,0,1,0,0,-1,0,0],
[-1,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,-1,1,0],
[0,0,-1,0,0,0,0,0,0],
[0,1,-1,-1,-1,0,0,0,0],
[1,0,0,1,0,1,-1,0,1],
[0,0,0,0,0,0,0,0,1],
[1,-1,1,1,0,1,-1,-1,1]]]]
];
MakeImmutable( IMFList[9].matrices );
[ Dauer der Verarbeitung: 0.22 Sekunden
(vorverarbeitet)
]
|
