#%Format: latex
#%This file can be pasted directly to GAP
\Read("E6.txt");
#\table
#=(3E6)+A1\\\2&&E6-31&(1,0)&\tref{arg.two.E}%
 #% Perturbations of torus type:
 \group1e(1);#%
 \simplify(g.1/g.2);#\cr%
#2E6+E7&&E6-21=\-1&(1,0)&\tref{arg.two.E}%
 \Size(group1e(\0,1));#\cr%
#\midrule
#=(2E6+2A2)+A3\\\2&&E6-3333&(1,0)&\eqref{eq.(2E6+2A2)+A3}%
 \group1e(4,3);#%
 \qsize(g.1^2);#%
 \StructureDescription(qgroup(g.1^2));#%
 #% Perturbations not of torus type:
 \Size(group1e(4,1));#\cr%
#=2E6+A7&&E6-5511=\-1,\ \moreref{fig.E8.ir}{E8-31}{--1}&%
 #(0,1)&\tref{arg.E6.loop}%
 \size1l(\0,\0,1);#\cr%
#=2E6+A4+A3.1\\\1&\same1 &E6-5511=2,\ \moreref{fig.E6.snail}{s31}{}&%
 #(1,0)&\tref{arg.E6.snail}#\cr%
#=2E6+A4+A3.2\\\1&\same1 &E6-6321=1,\ \moreref{fig.E8.ir}{E8-31}{--3}&%
 #(1,0)&\tref{arg.2E6+A4+A3.2}%
 \size1l(5,4);#%
 #% Perturbations:
 \size1l(1,4);#%
 \size1l(5,2);#\cr%
#=(2E6+A5)+A2.1\\\2&\same2 &E6-6321=2&(1,0)&\eqref{eq.(2E6+A5)+A2.1}%
 \group1e(3,6);#%
 #% This returns 48 vs. 12 for $\Gamma$:
 \qsize(g.1^3);#%
 \StructureDescription(qgroup(g.1^3));#%
 #% Alexander module:
 \AbelianInvariants(h);#%
 #% Perturbations of torus type:
 \group1e(3,3);#%
 \simplify(g.1/g.2);#%
 \group1e(1,6);#%
 \simplify(g.1/g.2);#%
 #% Perturbations not of torus type:
 \Size(group1e(3,2));#\cr%
#=(2E6+A5)+A2.2\\\2&\same2 &E6-6321=2,\ \moreref{fig.E8.ir}{E8-31}{--2}&%
 #(1,0)&\eqref{eq.(2E6+A5)+A2.2}%
 \group1l(3,6);#%
 #% This returns 48 vs. 12 for $\Gamma$:
 \qsize(g.1^3);#%
 \StructureDescription(qgroup(g.1^3));#%
 #% Alexander module:
 \AbelianInvariants(h);#%
 #% Perturbations of torus type:
 \group1l(3,3);#%
 \simplify(g.1/g.2);#%
 \group1l(1,6);#%
 \simplify(g.1/g.2);#%
 #% Perturbations not of torus type:
 \size1l(3,2);#\cr%
#=2E6+A6+A1&&E6-6321=3&(0,1)&\tref{arg.two.E}%
 \Size(group1e(7,2));#\cr%
#=E6+E7+A6&&E6+7-5511=\-1,\ \moreref{fig.E8.ir}{E8-21}{--1}&%
 #(0,1)&\tref{arg.E6.loop}%
 \size1l(\0,\0,1);#\cr%
#=E6+E7+A4+A2.1&\same23 &E6+7-5511=2,\ \moreref{fig.E6.snail}{s21}{}&%
 #(1,0)&\tref{arg.E6.snail}#\cr%
#=E6+E7+A4+A2.2&\same23 &E6+7-6321=2,\ \moreref{fig.E8.ir}{E8-21}{--2}&%
 #(1,0)&\tref{arg.E6.loop}%
 \size1l(3,4);#\cr%
#\midrule\changelines
#=E6+E7+D6&&E6+7-411&(1,0)&\tref{arg.E6+E7}%
 #% This applies to all remaining curves:
 \Size(DS(fixed, [rho^3], E7([])));#\cr%
#E6+E7+D5+A1&&E6+7-411&(1,0)&\tref{arg.E6+E7}#\cr%
#E6+E7+2A3&&E6+7-6321=1,\ \moreref{fig.E8.r}{E8-21-r}{}&%
 #(1,0)&\tref{arg.E6.loop}%
 \size2l(4,4);#\cr%
#E6+E7+A4+2A1&&E6+7-4422=1&(1,0)&\tref{arg.E6+E7}#\cr%
#=E6+E7+A3+A2+A1&&E6+7-4422=2&(1,0)&\tref{arg.E6+E7}#\cr%
#\endtable
#\endinput


## Further processing for 2E6+A4+A3.2
size1l(5,4);
StructureDescription(h);
# Abelianization splits:
Order(g.1);
Order(g.2);
Order(g.3);
# The product is not direct:
c := Centralizer(g, h);
AbelianInvariants(c);
Size(c);
Size(Intersection(c, h));
