#%Format: latex
#%This file can be pasted directly to GAP
\Read("E7.txt");
#\table
#\splitting{D_3+D_3}
#=E7+A7+A3+A2\\\1&&E7-6321=1&(2,0)&\\
 #% First curve
 \size2(8,4,3);
 \StructureDescription(h);
 #% Perturbations:
 \IdFunc(size(1,4,3));
 \IdFunc(size(8,1,3));
 #% Second curve
 \size2(4,8,3);
 \StructureDescription(h);
 #% Perturbations:
 \IdFunc(size(1,8,3));
 \IdFunc(size(4,1,3)); #\note2\!\!\!\!&\QG8\cr
#E7+A9+A2+A1&&E7-6321=4&(0,1)&\\
 \size2(10,\0,1);#\note2&0\cr
#E7+A11+A1\\\1&&E7-8211=2&(0,1)&\\
 \size2(12,\0,1,\0,2);
 #% Hence also irreducible perturbations have trivial groups:
 \Size(g)/Size(Centralizer(g,h)); #\note2&\CG3\cr
#E7+D12&&E7-411=1&(1,0)&\tref{arg.E7.D}&0\cr
#E7+D5+A7&&E7-411=1&(0,1)&\\
 \size2(8,\0,1);#\note2&0\cr
#=2E7+A5\\\1&&E7-21=1&(0,1)&\\
 \size2(6,\0,1);
 #% Hence also irreducible perturbations have trivial groups:
 \Size(g)/Size(Centralizer(g,h)); #\note2&\CG3\cr
#\midrule\splitting{D_5+D_1}
#E7+A5+A4+A3&&E7-6321=2&(1,0)&\\
 \size2(5,4);#\note2&0\cr
#E7+A7+A4+A1&&E7-6321=\-3&(0,1)&\\
 \size2(5,8,\0,1);#\note2&0\cr
#E7+A7+2A2+A1\\\1&&E7-6321=5&(1,0)&\\
 \size2(3,8,\0,3);
 \StructureDescription(h); #\note2&\SL(2,\FF5)\cr
#E7+A9+A3&&E7-8211=1&(1,0)&\\
 \size2(4,\0,\0,1);#\note2&0\cr
#E7+A9+A2+A1&&E7-8211=3&(1,0)&\\
 \size2(3,\0,\0,2);#\note2&0\cr
#E7+D10+A2&&E7-411=2&(1,0)&\\
 \size2(3,\0,\0,1);#\note2&0\cr
#E7+D7+A5&&E7-411=2&(1,0)&\tref{arg.E7.D}&0\cr
#E7+D5+A5+A2&&E7-411=2&(1,0)&\\
 \size2(3,6);#\note2&0\cr
#2E7+A3+A2\\\1&&E7-21=2&(1,0)&\\
 \size2(3,4);
 \StructureDescription(h); #\note2&\SL(2,\FF5)\cr
#2E7+D5&&E7-E7&(1,0)&\tref{arg.E7.D}&0\cr
#\midrule\splitting{D_4+D_2}
#E7+A5+A4+A3\\\1&&E7-6321=2&(1,0)&\\
 \size3(4,5,6);
 \StructureDescription(h);
 #% Perturbations:
 \IdFunc(size(1,5,6));
 \IdFunc(size(4,5,3));
 #\note3&\SL(2,\FF5)\cr
#E7+A7+A4+A1&&E7-6321=\-3&(0,1)&\\
 \size3(8,5,2);#\note3&0\cr
#=E7+A7+2A2+A1\\\1&&E7-6321=5&(1,0)&\tref{arg.E7.infty}
 \AbelianInvariants(group3(8,3,\0,3)); #%> [ 3, 3 ]
 \AbelianInvariants(DerivedSubgroup(h)); #%> [ 0, 0 ]
 #&\infty\cr
#E7+A9+A3&&E7-8211=1&(1,0)&\\
 \size3(\0,4,\0,1);#\note3&0\cr
#E7+A9+A2+A1&&E7-8211=3&(1,0)&\\
 \size3(\0,3,\0,2);#\note3&0\cr
#E7+D10+A2&&E7-411=2&(1,0)&\tref{arg.E7.D}&0\cr
#=E7+D7+A5&&E7-411=2&(1,0)&\tref{arg.E7.D}
 #% Because of the D-region, have to use another central element
 \Size(DS(Union(fixed, D(x^2, 3), [G.2])));
 #&0\cr
#E7+D5+A5+A2\\\1&&E7-411=2&(1,0)&\\
 \size3(6,3);
 \Size(g)/Size(Centralizer(g,h));
 #% Perturbations:
 \IdFunc(size(3,3));
 #\note3&\CG3\cr
#=2E7+A3+A2\\\1&&E7-21=2&(1,0)&\tref{arg.E7.infty}
 \AbelianInvariants(group3(4,3)); #%> [ 3, 3 ]
 \AbelianInvariants(DerivedSubgroup(h)); #%> [ 0, 0 ]
 #&\infty\cr
#=2E7+D5\\\1&&E7-E7&(1,0)&\tref{arg.E7.D}
 #% Because of the D_region, have to use another central element
 \Size(DS(fixed, E7([]), [G.2]));
 \Size(g)/Size(Centralizer(g,h));
 #&\CG3\cr
#\midrule\splitting{D_3+D_2+D_1}
#=E7+2A5+2A1\\\1&&[fig.E7.r3]E7-4422=1&(1,0)&\tref{arg.E7.infty}
 \AbelianInvariants(group4(6,6,2)); #%> [ 0, 0, 0, 0 ]
 #% Perturbations:
 \IdFunc(size(3,3,2));
 \IdFunc(size(6,3,1));
 \IdFunc(size(3,6,1));
 #&\infty\cr
#=E7+A5+2A3+A1\\\1&\same1 &[fig.E7.r3]E7-4422=2&(1,0)&\tref{arg.E7.infty}
 \AbelianInvariants(group4(4,6,4)); #%> [ 0, 0, 3 ]
 #% Perturbations:
 \IdFunc(size(1,3,4));
 \IdFunc(size(4,3,1));
 \IdFunc(size(1,6,1));
 #&\infty\cr
#E7+A5+2A3+A1\\\1&\same1 &[fig.E7.r3]E7-4422=2&(1,0)&\\
 \size4(6,4,4);
 \StructureDescription(h); #\note4&\SL(2,\FF5)\cr
 #% Perturbations:
 \IdFunc(size(3,1,4));
 \IdFunc(size(3,4,1));
 \IdFunc(size(6,1,1));
#=E7+D8+A3+A1\\\1&\same2 &[fig.E7.r3]E7-222&(1,0)&%
 #\tref{arg.E7.D}, \tref{arg.E7.infty}
 #% Because of the D_region, we have to use another central element
 \AbelianInvariants(DS(fixed, A(x, 4), D(x^2, 4), [G.1^2, G.2]));
 #&\infty\cr
#E7+D8+A3+A1&\same2 &[fig.E7.r3]E7-222&(1,0)&\tref{arg.E7.D}&0\cr
#E7+D6+2A3\\\1&&[fig.E7.r3]E7-222&(1,0)&\\
 \size4(4,4);
 \StructureDescription(h); #\note4&\QG8\cr
 #% Perturbations:
 \IdFunc(size(1,1));
 \IdFunc(size(1,4,1));
 \IdFunc(size(4,1,1));
#E7+2D6&&[fig.E7.r3]E7-00&(1,0)&\tref{arg.E7.D}&0\cr
#\endtable
#\endinput
