Pensieve Header: A failed attempt to solve the two F equations with analytic hair using Full Scattering, where F is written as an exponential.

Ouch! f1 and f2 were treated as constants rather than functions!

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\ScatterAndGlow"];
<< ScatterAndGlow-090103.m

F=S[Exp[-1/4 Ar[2,1]+1/4 Ar[1,2]+Y[1,2,1,AH[f1]]+Y[1,2,2,AH[f2]]]]

Short[
F21 = S[Exp[-1/4 Ar[1,2]+1/4 Ar[2,1]+Y[2,1,2,AH[f1]]+Y[2,1,1,AH[f2]]]]
]

Short[lhs1 = Ar[3,0] // S[Exp[Ar[1,3]+Ar[2,3]]] // F]

Short[rhs1 = Ar[3,0] // F // S[sigma[1,3],sigma[2,3]]]

lhs2=Ar[1,0] // F21 // S[sigma[1,2]]// S[Exp[1/2 Ar[1,1]]] // S[Exp[1/2 Ar[2,2]]]

rhs2=Ar[1,0] // S[Exp[Expand[1/2(Ar[1,1]+Ar[1,2]+Ar[2,1]+Ar[2,2])]]] // F

The following was aborted after a day of computation:

sol=Solve[
{
Coefficient[lhs1, Y[1,2,0]] == Coefficient[rhs1, Y[1,2,0]],
Coefficient[lhs2, Y[1,2,0]] == Coefficient[rhs2, Y[1,2,0]]
},
{f1, f2}
]

To do

Print lhs1 and rhs1 in full.

See if matters can be simplified by picking specific coefficients of or values for x[3].