Pensieve header: Testing and solving the overhand equation.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2012-05\\beta5.0"];
<< betaCalculus.m

Clear[ℏ];
$PerturbativeDegree=6;
βSimplify[expr_]:= Replace[
Series[Normal[expr], {ℏ, 0, $PerturbativeDegree}],sd_SeriesData :> MapAt[Expand, sd, 3]
];
βCollect[B[ω_, μ_]] := B[
βSimplify[ω],
βSimplify[μ]
];

{V1, C1, sol} = Get["SolutionToDegree6-120501.m"];

V1

Φ1=Φ[V1]

The Overhand Equation:

Φ1 // dΔ[1,0,1] // dS[2] // dS[3] // dm[0,3,0] // dm[1,2,1]

{
V0=βCollect[
B[ω[ℏ (Subscript[c, 1]),ℏ (Subscript[c, 2])],α[ℏ (Subscript[c, 1]),ℏ (Subscript[c, 2])]t[1]h[1]+β[ℏ (Subscript[c, 1]),ℏ (Subscript[c, 2])]t[1]h[2]+γ[ℏ (Subscript[c, 1]),ℏ (Subscript[c, 2])]t[2]h[1]+δ[ℏ (Subscript[c, 1]),ℏ (Subscript[c, 2])]t[2]h[2]]
] /. {
(ϵ:(α|β|γ|δ|ω|κ))[___] :> (Subscript[ϵ, 0]), Derivative[k___][(ϵ:(α|β|γ|δ|ω|κ))][___] :> (Subscript[ϵ, FromDigits[{k}]])
},
C0=βCollect[B[κ[ℏ (Subscript[c, 1])],0]] /. {
(ϵ:(α|β|γ|δ|ω|κ))[___] :> (Subscript[ϵ, 0]), Derivative[k___][(ϵ:(α|β|γ|δ|ω|κ))][___] :> (Subscript[ϵ, FromDigits[{k}]])
}
}

({V2, C2}={V0, C0} /. sol) // ColumnForm

Φ2=Φ[V2]

eqn=((Φ2 // dΔ[1,0,1] // dS[2] // dS[3] // dm[0,3,0] // dm[1,2,1])==B[1,0])

sol1 = PerturbativeSolveAlways[eqn, ℏ, $PerturbativeDegree, {(Subscript[c, 1]), (Subscript[c, 2])}]

indvars=Union[Cases[Last /@ #, (Subscript[ϵ_, k_]) :> (Subscript[ϵ, k]), Infinity]]& /@  {sol1}

({V3, C3} = {V2, C2} /. sol1 /. Thread[{(Subscript[γ, 12]),(Subscript[δ, 10]),(Subscript[δ, 23]),(Subscript[δ, 30]),(Subscript[δ, 41])} -> 0]) // ColumnForm

False && Put[{V3, C3, sol1}, "SolutionToDegree6-120518.m"]