#%Format: latex
#%This file can be pasted directly to GAP
\Read("E8.txt");
#\table
#E8+A5+2A3&&E8-6321-r=1&(1,0)&\\
 \size2(4,4,6);#\note2\cr
#E8+A7+A3+A1&&E8-6321-r=\-2&(0,1)&\\
 \size2(8,4,2);#\note2\cr
#E8+A7+A2+2A1&&E8-6321-r=3&(1,0)&\tref{lem.E8.loop}\cr
#E8+A5+A4+2A1&&E8-4422-r=1&(1,0)&\\
 \size2(6,5,2);#\note2\cr
#E8+A5+A3+A2+A1&&E8-4422-r=2&(1,0)&\\
 \size2(6,3,4);#\note2\cr
#E8+A4+2A3+A1&&E8-4422-r=3&(1,0)&\\
 \size2(4,5,4);#\note2\cr
#E8+A9+A2&\same1 &E8-8211-r=1&(1,0)&\\
 \size2(10,3,\0);#\note2\cr
#E8+A9+2A1&&E8-8211-r=2&(1,0)&\tref{lem.E8.loop}\cr
#E8+D8+A2+A1&&E8-222-r&(1,0)&\\
 \size2(\0,3,2);#\note2\cr
#E8+D7+A3+A1&&E8-222-r&(1,0)&\\
 \size2(4,\0,2);#\note2\cr
#=E8+D6+A3+A2\\\1&&E8-222-r&(1,0)&\tref{arg.E8+D6+A3+A2}%
 \size2(4,3,\0);#%
 #% Perturbations:
 \size2(2,3,\0);#%
 \size2(4,1,\0);#%
 \size(4,3,1);#\cr
#E8+D10+A1&&E8-411-r&(1,0)&\tref{lem.E8.loop}\cr
#=E8+D6+A5&&E8-411-r&(1,0)&\tref{arg.E8+E6+D5}%
 \size2(6,\0,6);#\cr
#E8+D5+A5+A1&&E8-411-r&(1,0)&\tref{lem.E8.loop}\cr
#E8+E7+A3+A1&&E8-21-r&(1,0)&\tref{lem.E8.loop}\cr
#=E8+D6+D5&&E8-00-r&(1,0)&\tref{lem.E8.loop}\cr
#=E8+E7+D4&&\omit\tab isotrivial\!\!\!\hss&(1,0)&\tref{arg.E8+E7+D4}\cr
#\endtable
#\endinput

## Further processing for E8+D6+A3+A2
sh := size2(4,3,0);
# Sizes are equal, hence the last relation can be omitted
sh = size2(4,0,0);
StructureDescription(h);
# (g.1*g.2)^2 is central, hence so is (g.1*g.2)^2*g.2^-3

## Further processing for E8+D6+A5
Size(DS(Union(fixed, A(x*y*x*y*x^2, 1), [G.2^3])));
