/usr/share/gap/pkg/Polycyclic/gap/exam/matlib.gi is in gap-polycyclic 2.11-3.
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##
#W matexam.gi Polycyc BE & WN
##
## Some examples of polycylic matrix groups -- MatExamples
##
#############################################################################
##
#F MatExamples(n)
##
MatExamples := function( n )
local MG;
##
## Plesken/Nebe 1
##
if n = 1 then
MG := [];
MG[1] := [
[ 0, -1, 0, -1, 1, -1, 0, 0, 1, 0, 1, 1, 0, 1, 0, -1 ],
[ 0, 1, 1, 0, -1, 0, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0 ],
[ 0, 0, 1, -1, -1, 0, 0, -1, -1, 0, 0, 0, 0, 1, -1, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0 ],
[ 0, 1, 1, 2, 0, 1, 0, 0, 0, -1, -1, -1, -1, -1, 1, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 1, 1 ],
[ 0, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0 ],
[ 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 1, 0, 1, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1 ],
[ 0, 1, 0, 0, -1, 0, -1, 0, -1, 0, -1, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 1, 1, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0 ] ];
MG[2] := [
[ 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, 1, 0, 0, -1, 1 ],
[ 0, 2, -2, 1, -1, 0, -2, 2, 0, 0, -1, -1, -1, 1, 0, 0 ],
[ 0, 2, -1, 1, -1, 0, -1, 1, -1, -1, -1, -1, 0, 0, 0, 1 ],
[ 0, -1, -1, -1, 0, -1, 0, 0, 0, 1, 1, 1, 1, 0, -1, 0 ],
[ 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, -2, -1, -2, 0, 2, -2 ],
[ 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, -1, 0, 0, 1, 0, -1 ],
[ -1, -1, 0, 0, 0, 0, 0, -1, 1, 0, 1, 0, 0, -1, 0, 0 ],
[ -1, 1, 0, 0, -1, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 1 ],
[ 0, 2, -1, 1, -1, 0, -1, 1, -1, -1, -1, -1, 0, 0, 1, 1 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, -1, 0 ],
[ 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 1, 0, 0, 0, -1, 1 ],
[ 1, 1, -1, 0, -1, 0, -1, 1, -1, 0, 0, 0, 1, 1, -1, 1 ],
[ 0, 1, -1, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1, -1 ],
[ -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, -1, 0, 1, -1 ],
[ 1, -1, 0, -1, 0, 0, 0, 0, -1, 1, 1, 1, 1, 1, -2, 0 ],
[ 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, -1, -1, -1, 0, 1, 0 ] ];
MG[3] := [
[ -2, 1, 0, 1, -1, -1, -2, 0, 1, -1, 1, -2, -1, -1, 0, 0 ],
[ 0, -2, 0, -2, 0, 1, 3, -1, 1, 1, 1, 2, 1, 1, 0, 0 ],
[ 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, 0 ],
[ 1, -2, 0, -2, 2, 1, 3, -1, 0, 2, 0, 2, 0, 0, 0, -1 ],
[ 1, -1, 0, -1, 1, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1 ],
[ 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 1, 1 ],
[ -1, 0, 0, 0, -1, 0, 0, 0, 1, -1, 1, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 0, -1, 0, -1, 1, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, -1 ],
[ 1, -1, 1, -1, 1, 1, 2, -1, 0, 1, -1, 1, 0, 0, 0, -1 ],
[ 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1 ],
[ 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0 ] ];
MG[4] := [
[ 0, 0, 0, 2, 0, 0, -1, 1, 0, 0, 0, -1, 0, -1, 0, 1 ],
[ 0, -1, 0, -1, 1, 0, 2, -1, 2, 0, 1, 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, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, 1, -2, 1, 0, 2, -2, 0, 0, 1, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, -1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, -1, 1, -1, 1, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, -1 ],
[ 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0 ] ];
MG[5] := [
[ 0, 1, -1, 1, -1, -1, -3, 1, -1, -1, 1, -1, 0, 1, 0, 2 ],
[ 1, -2, -1, -2, 1, -1, 1, 0, -1, 2, 1, 3, 2, 0, -2, -1 ],
[ 1, -2, 0, -2, 0, 0, 1, -1, 0, 2, 1, 2, 2, 1, -2, -1 ],
[ 0, 2, -1, 2, 0, 0, -2, 2, -1, -1, -1, -1, -1, 0, 1, 1 ],
[ 0, -3, 1, -3, 1, -1, 3, -2, 1, 3, 1, 2, 1, 0, -1, -2 ],
[ 1, 0, 0, -1, 0, 0, 1, 0, -1, 1, -1, 1, 1, 0, -1, -1 ],
[ -2, 1, 0, 2, 0, 0, -1, 0, 1, -2, 0, -2, -2, -1, 2, 1 ],
[ 0, -1, 1, 0, 0, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, -2, 0, -2, 0, 0, 1, -1, 0, 2, 1, 2, 1, 1, -2, -1 ],
[ 1, 1, -1, 0, 0, 0, 0, 1, -1, 0, -1, 1, 1, 0, 0, 0 ],
[ 0, 1, -1, 1, 0, -1, -2, 1, -1, -1, 0, 0, 0, 0, 0, 1 ],
[ 2, 0, -1, -1, 0, 0, 0, 1, -2, 1, 0, 2, 2, 1, -2, 0 ],
[ 1, -1, 0, -1, 0, 0, 1, 0, 0, 2, 0, 1, 1, 1, -1, -1 ],
[ -1, -1, 1, 0, 1, 0, 1, -1, 1, 0, 0, 0, -1, -1, 1, -1 ],
[ 1, 2, -1, 1, -1, 0, -2, 2, -2, -1, -1, 0, 1, 1, 0, 1 ],
[ 0, -2, 1, -2, 0, 0, 2, -2, 1, 2, 1, 1, 1, 0, -1, -1 ] ];
MG[6] := [
[ 0, 2, -3, 1, -1, -1, -4, 3, -2, -1, 1, -1, 1, 0, 0, 2 ],
[ -1, -1, 3, 1, 1, 2, 2, -1, 3, -1, 0, -2, -2, 0, 3, -1 ],
[ 0, -1, 1, 1, 2, 0, 0, 1, 1, 0, 0, 0, -2, 0, 1, -1 ],
[ -2, 1, -1, 1, -1, 0, -1, -1, 1, -2, 1, -2, -1, -2, 1, 2 ],
[ 1, -2, 3, -2, 2, 2, 6, -2, 3, 2, -2, 1, 0, 0, 1, -4 ],
[ 1, -1, 2, 0, 0, 2, 2, -1, 1, 1, -1, 0, 0, 1, 0, -1 ],
[ -2, 1, -1, 0, -1, -2, -1, -1, 0, -1, 1, -1, 0, -1, 1, 2 ],
[ -1, -1, 0, 0, 1, -2, -1, 0, 0, 0, 1, 1, -1, 0, 0, 0 ],
[ 0, -2, 1, -1, 2, 0, 1, 0, 1, 1, 1, 1, -1, 0, 0, -2 ],
[ 0, 1, 1, 2, -1, 2, 0, 0, 1, -1, -1, -2, -1, 0, 1, 1 ],
[ -2, 1, 0, 2, -1, 0, -2, 0, 1, -2, 1, -3, -1, -1, 2, 2 ],
[ 0, -1, 1, 1, 0, 1, -1, 0, 1, 0, 1, -1, -1, 1, 0, 0 ],
[ 0, -2, 1, -1, 2, 1, 3, -1, 2, 1, 0, 1, -1, -1, 0, -2 ],
[ 0, -1, 1, -2, 0, 0, 3, -2, 1, 1, 0, 1, 1, 0, 0, -1 ],
[ 1, 1, -1, 1, -2, 1, -2, 1, -1, 0, 0, -1, 1, 1, -1, 2 ],
[ 1, -1, 1, -1, 1, 0, 2, 0, 1, 2, -1, 1, 0, 1, 0, -2 ] ];
MG[7] := [
[ 0, 0, 1, -1, -1, -1, 0, -2, 0, 1, -1, -1, 0, 0, -1, -1 ],
[ 0, 0, 0, 1, 1, 0, 0, 1, 0, -1, 0, 0, 0, 1, 2, 1 ],
[ 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1 ],
[ 0, 0, -2, 1, 0, 1, 0, 3, 0, -1, 2, 1, 2, 1, 1, 2 ],
[ 0, 0, -1, 0, 0, 0, 0, 1, 0, -1, 1, 1, 1, 1, 1, 1 ],
[ 1, 0, 0, -1, 0, 0, 0, 0, -1, 1, -1, 1, 0, 1, -1, -1 ],
[ 0, 0, 1, 0, 0, 0, 0, -1, 0, 1, -1, -1, -1, -1, 0, 0 ],
[ 1, 1, 0, 1, 0, 1, 0, 1, -1, 0, -1, -1, 0, -1, 0, 1 ],
[ -1, 0, 0, 1, 1, 0, 0, 0, 1, -2, 0, 0, -1, 0, 2, 0 ],
[ -1, -1, 1, -1, 1, -1, 1, -2, 1, 0, 0, 0, -1, 0, 1, -1 ],
[ 0, -1, 1, 0, 1, 0, 1, -1, 1, 0, 0, 0, -1, 0, 1, 0 ],
[ 1, 1, -1, 1, 0, 1, 0, 2, -1, 0, 0, 0, 1, 0, 0, 1 ],
[ 0, 1, -1, 1, 0, 1, 0, 2, 0, -1, 0, 0, 0, 0, 1, 1 ],
[ -1, 0, 0, 0, 0, -1, 0, -1, 1, -1, 0, 0, -1, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 1, 0, 1, 0, -1, 0, 0, 0, 0, 1, 1 ] ];
MG[8] := [
[ -1, 0, 0, -1, 0, -1, -1, -1, 0, 0, 1, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, -1, -1, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0 ],
[ 0, 1, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -1, 0, 1, 2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 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, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, -1, 0, 0, 0, 0, 0 ],
[ 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, 0, 0, 0, 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, 1, 0, 0, 0, 0, 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, 1 ] ];
MG[9] := [
[ -1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 1, 0, 0, -1, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, -1, 1, -2, 1, -1, 0, 1, 0, -1, -1 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1 ],
[ 2, -1, 1, -1, 0, 1, 0, 0, -2, 2, -2, 1, 0, 1, -2, -1 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 0 ],
[ -1, 0, 0, -1, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, -1 ],
[ -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0 ],
[ 1, -1, 0, 0, 0, 1, 0, 1, -1, 1, 0, 1, 1, 1, -1, 0 ],
[ 1, 1, 0, 1, 0, 0, -1, 1, -1, 0, -1, -1, 0, 0, 0, 0 ],
[ -1, 1, 0, 1, 0, -1, -1, 0, 0, -1, 0, -1, 0, -1, 1, 0 ],
[ 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, -1, 0, -1, 1, 0 ],
[ 1, -1, 0, -1, 0, 0, 0, 0, -1, 1, 0, 1, 1, 1, -1, 0 ],
[ 1, 0, 0, -1, 0, 0, 0, 0, -1, 1, -1, 1, 0, 1, -1, -1 ],
[ 0, 1, 0, 1, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 1, 1 ],
[ 1, 0, 0, 0, 0, 1, 0, 1, -1, 1, -1, 0, 0, 0, -1, 0 ] ];
return Group(MG, MG[1]^0 );
elif n = 2 then
MG := [];
MG[1] := [
[ 2, -1, -1, 3 ],
[ -1, 0, 1, -4 ],
[ 0, 1, 2, -2 ],
[ -1, 1, 2, -4 ]];
MG[2] := [
[ 1, 1, 1, -2 ],
[ 1, 1, -1, 1 ],
[ -2, 1, 0, -3 ],
[ -1, 1, 0, -2 ]];
MG[3] := [
[ 1, 0, -1, 0 ],
[ -2, 5, 5, -11 ],
[ -1, 0, 2, 0 ],
[ -1, 1, 2, -2 ]];
MG[4] := [
[ 0, 3, 2, -7 ],
[ -1, 6, 4, -13 ],
[ -1, 2, 1, -5 ],
[ -1, 3, 2, -7 ]];
MG[5] := [
[ 0, 4, 5, -12 ],
[ 2, -4, 1, 5 ],
[ 1, -4, -1, 8 ],
[ 1, -3, 0, 5 ]];
MG[6] := [
[ 1, 0, -1, 0 ],
[ -2, 5, 5, -11 ],
[ -1, 0, 2, 0 ],
[ -1, 1, 2, -2 ]];
return Group( MG, MG[1]^0 );
elif n = 3 then
MG := [];
MG[1] := [
[ 5, 3, 3, -5 ],
[ 7, 4, 5, -8 ],
[ 2, 1, 2, -2 ],
[ 10, 6, 7, -11 ]];
MG[2] := [
[ -2, -4, -3, 5 ],
[ 4, 7, 5, -8 ],
[ -3, -3, -3, 4 ],
[ 1, 2, 1, -2 ]];
MG[3] := [
[ 1, -1, 0, 1 ],
[ -4, -2, -2, 5 ],
[ -4, -2, -3, 3 ],
[ -3, -2, -2, 4 ]];
MG[4] := [
[ 8, 8, 3, -10 ],
[ -13, -14, -5, 17 ],
[ -13, -14, -5, 18 ],
[ -8, -9, -3, 11 ]];
MG[5] := [
[ 0, -1, -1, 2 ],
[ 2, 2, 1, -1 ],
[ 2, 3, 1, -5 ],
[ 3, 3, 1, -3 ]];
MG[6] := [
[ 2, 1, 0, 0 ],
[ 3, 2, 0, 0 ],
[ -7, -8, -3, 11 ],
[ -1, -3, -2, 7 ]];
return Group( MG, MG[1]^0 );
elif n = 4 then
MG :=
[ [ [ -492568055, -715902540, -559233360, 913773168 ],
[ 853152732, 1239979321, 968620464, -1582701120 ],
[ 796991748, 1158354480, 904858501, -1478515764 ],
[ 543797628, 790360020, 617396520, -1008810083 ] ],
[ [ -348686135, -530151780, -271469520, 913773168 ],
[ -603941868, -918249479, -470198736, 1582701120 ],
[ -215499732, -327651600, -167777219, 564742596 ],
[ -793008492, -1205711460, -617396520, 2078172517 ] ],
[ [ -151935722, -225045135, -150030090, 330066198 ],
[ 45009027, 58106404, 90018054, 0 ],
[ 105021063, 150030090, 133121449, -165033099 ],
[ -45009027, -75015045, 0, 193133485 ] ],
[ [ 13, 0, -21, 0 ],
[ 147, 181, 105, -231 ],
[ -21, 0, 34, 0 ],
[ 84, 105, 63, -134 ] ],
[ [ 670415977, 715902540, 271469520, -913773168 ],
[ 1161194148, 1239979321, 470198736, -1582701120 ],
[ -1084755588, -1158354480, -439246739, 1478515764 ],
[ 607257732, 648459180, 245895000, -827688875 ] ],
[ [ 814297897, 530151780, 559233360, -913773168 ],
[ -1410405012, -918249479, -968620464, 1582701120 ],
[ 503263572, 327651600, 345625141, -564742596 ],
[ -358046868, -233107740, -245895000, 401786125 ] ],
[ [ 141577573978831, 92174617804950, 97230886083807, -158872797828558 ],
[ -245219551343241, -159651121205951, -168408834761919, 275175757779087 ],
[ 87499752763389, 56967046703190, 60091992355948, -98188788945456 ],
[ -62251695137616, -40529202794985, -42752445237981, 69856409444878 ] ]
];
return Group( MG, MG[1]^0 );
fi;
return fail;
end;
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