Pensieve Header: Alexander blobs Results: R4 only, with f21==0.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2011-08\\w-Computations"];
<< "AlexanderBlobs-Program.m"

r[i_,j_] := Diag[1, ar[i,j]];
b[r[1,2],r[1,3]] + b[r[1,2],r[2,3]]

b[r[1,2],r[1,3]] + b[r[1,2],r[2,3]] + b[r[1,3],r[2,3]]

R[i_,j_] := DExp[r[i,j]];
ModDegree[4, R[1,2]]

ModDegree[7, R[1,2]**R[1,3]**R[2,3] - R[2,3]**R[1,3]**R[1,2]]

v[1]=0;

d=2;
ModDegree[d+1,
Print[
v[d]=v[d-1]-(1/2)Diag[1,ar[1,2]]
];
V=DExp[v[d]];
V**DExp[r[1,3]+r[2,3]]-R[1,3]**R[2,3]**V
]

d=3;
ModDegree[d+1,
Print[
v[d]=v[d-1]+(1/24) Diag[h[1],ar[1,2]]+(1/12) Diag[h[2],ar[1,2]]
];
V=DExp[v[d]];
V**DExp[r[1,3]+r[2,3]]-R[1,3]**R[2,3]**V
]

d=4;
ModDegree[d+1,
Print[
v[d]=v[d-1]
];
V=DExp[v[d]];
V**DExp[r[1,3]+r[2,3]]-R[1,3]**R[2,3]**V
]

d=5;
ModDegree[d+1,
Print[
c[d,0]=-1/720; c[d,1]=-1/480; c[d, 2]=-1/720;c[d,3]=-1/2880;
v[d]=v[d-1]+Sum[c[d, k]Diag[h[1]^k*h[2]^(d-2-k),ar[1,2]], {k, 0, d-2}]
];
V=DExp[v[d]];
V**DExp[r[1,3]+r[2,3]]-R[1,3]**R[2,3]**V
]

d=6;
ModDegree[d+1,
Print[
c[6,_] = 0;
v[d]=v[d-1]+Sum[c[d, k]Diag[h[1]^k*h[2]^(d-2-k),ar[1,2]], {k, 0, d-2}]
];
V=DExp[v[d]];
V**DExp[r[1,3]+r[2,3]]-R[1,3]**R[2,3]**V
]

d=7;
ModDegree[d+1,
Print[
c[7,0]=1/30240; c[7,1]=1/12096;c[7,2]=1/9072;c[7,3]=1/12096; c[7,4]=1/30240;c[7,5]=1/181440;
v[d]=v[d-1]+Sum[c[d, k]Diag[h[1]^k*h[2]^(d-2-k),ar[1,2]], {k, 0, d-2}]
];
V=DExp[v[d]];
V**DExp[r[1,3]+r[2,3]]-R[1,3]**R[2,3]**V
]

ModDegree[8, V**Adjoint[V]]

d=8;
ModDegree[d+1,
Print[
c[8,_] = 0;
v[d]=v[d-1]+Sum[c[d, k]Diag[h[1]^k*h[2]^(d-2-k),ar[1,2]], {k, 0, d-2}]
];
V=DExp[v[d]];
V**DExp[r[1,3]+r[2,3]]-R[1,3]**R[2,3]**V
]

d=9;
ModDegree[d+1,
Print[
c[9,0]=-1/1209600; c[9,1]=-1/345600;c[9,2]=-1/172800;c[9,3]=-1/138240; c[9,4]=-1/172800;c[9,5]=-1/345600; c[9,6]=-1/1209600; c[9,7]=-1/9676800;
v[d]=v[d-1]+Sum[c[d, k]Diag[h[1]^k*h[2]^(d-2-k),ar[1,2]], {k, 0, d-2}]
];
V=DExp[v[d]];
V**DExp[r[1,3]+r[2,3]]-R[1,3]**R[2,3]**V
]

ModDegree[10, V**Adjoint[V]]

v[9] /. Diag[hs_, ar[1,2]] :> hs /. {h[1] -> h1, h[2] -> h2}

-1209600*8*Table[c[9,k], {k,0,7}]

Table[Binomial[8,k], {k, 1, 8}]