Pensieve header: Perturbative β-calculations.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2012-05\\beta5.1"];
<< betaCalculus.m

Clear[ℏ];
$PerturbativeDegree=8;
βSimplify[expr_]:= Replace[
Series[Normal[expr], {ℏ, 0, $PerturbativeDegree}],sd_SeriesData :> MapAt[Expand, sd, 3]
];
βCollect[B[ω_, μ_]] := B[
βSimplify[ω],
βSimplify[μ]
];
Unprotect[C];
{V,C,sol6}=Get["SolutionToDegree6-120523.m"];

The Knot-Theoretic Equations

{
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}]])
} /. sol6,
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}]])
} /. sol6,
eqns0 = GroupLikeQ[V0],
eqns1=HardR4[V0],
eqns2=TwistEq[V0],
eqns3 = And[(V0 // dη[1])==B[1,0], (V0 // dη[2])==B[1,0]],
eqns4 = V0**(V0 // dA[1] // dA[2]) == B[1,0],
eqns5 = CapEquation[V0, C0],
eqns6 = (C0 // tη[1])==B[1,0],
eqns7 = (V0 == Rot120[V0]),
eqns8 = V0**(V0 // dS[1] // dS[2]) == R[1,2]
}  // ColumnForm

eqns = (eqns0&&eqns1&&eqns2&&eqns3&&eqns4&&eqns5&&eqns6&&eqns8);

Timing[sol8=PerturbativeSolveAlways[eqns, ℏ, $PerturbativeDegree, {(Subscript[c, 1]),(Subscript[c, 2])}]]

{V0, C0} /. sol8

sol=Union[sol6, sol8]

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

sol1 = Union[
sol /. Thread[indvars -> 0],
Thread[indvars -> 0]
]

{V1,C1}={V0, C0} /. sol

False && Put[{V1, C1, sol}, "SolutionToDegree8-120524.m"]