#%Format: latex
#%This file can be pasted directly to GAP
\Read("D5.txt");
#\table
#=D5+A6+A4+2A2&&E7-3333&(1,0)&\tref{arg.D5.ir}%
 \size(7,5,3);#\cr%
#D5+A14&&E7-9111=1&(0,1)&\tref{arg.D5.ir}%
 \size(15,\0,1);#\cr%
#D5+A12+A2&&E7-9111=2&(1,0)&\tref{arg.D5.ir}%
 \size(13,3);#\cr%
#=D5+A10+A4&\same3 &E7-9111=2&(1,0)&\tref{arg.D5.ir}%
 \Size(DS(AA(lbb, [5,11]), A(x^2*y*x*(y*x^2)^3, 1), bb));#\cr%
#D5+A8+A6&&E7-5511=\-1&(0,1)&\tref{arg.D5.ir}%
 \size(9,7,\0,\0,1);#\cr%
#D5+A10+A4&\same3 &E7-5511=2&(0,1)&\tref{arg.D5.ir}%
 \size(11,\0,1);#\cr%
#D5+A8+A4+A2&\same4 &E7-5511=3&(1,0)&\tref{arg.D5.ir}%
 \size(9,3);#\cr%
#=D5+A6+2A4&\same5 &E7-5511=3&(1,0)&\tref{arg.D5.ir}%
 \size(5,7);#\cr%
#\midrule
#=D5+A8+A4+A2&\same4 &[fig.d5-ir]=1&(0,1)&\tref{arg.D5.genuine}%
 \inf(x*y*x^2);#%
 \size2(9,0,3,5);#\cr%
#D5+A6+2A4&\same5 &[fig.d5-ir]=2&(1,0)&\tref{arg.D5.genuine}%
 \inf(x*y*x^2);#%
 \size2(5,7,0,5);#\cr%
#D5+A10+2A2&&[fig.d5-ir]=3&(1,0)&\tref{arg.D5.genuine}%
 \inf(x*y*x^2);#%
 \size2(11,3,3);#\cr%
#=D5+(A8+3A2)&&[fig.d5-ir]=4&(1,0)&\tref{arg.D5+(A8+3A2)}%
 #% see below
 #\cr%
#\endtable
#\endinput


## The computation for D5+(A8+3A2) (torus type)
# the path from R_1 to R_2:
p := (x*y)^3*x^2*y;
# relevant elements from R_2:
bg := bm(p, [(G.1*G.2)^2*G.3/(G.3*(G.1*G.2)^2), (G.1*G.2)^2]);
# the group:
g := G/[G.3*G.1*G.2/rho,           # from R_1
        G.2*G.3*G.2/(G.3*G.2*G.3), # explicit simplified relation from
                                   # the triangle adjacent to R_1
        RA(x, 9),
        bg[1],                     # from R_2
        RA(p*x, 3), RA(p*x^2, 3),  # the two other triangles
        G.3*rho^3/bg[2]];          # the relation at infinity
simplify(g.2/g.3);
