Pensieve Header: Wheeled Semi-Symmetrized calculus in the 2D quotient: Solving for the “conj” coefficients, IV.

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\w-Computations"];
<< "Wheeled Semi-Symmetrized 2D Calculus.m"

conj3 works only in the feedback-only case

conj3[y_,x_][μ_] := Module[
{γ},
γ = Coefficient[μ, ar[y,x]];
μCollect[μ /. W[ws_] :> W[ws*(c[y]γ+1)]]
];

μ3 = W[1] + (Subscript[α, 1]) ar[1,1] + (Subscript[α, 3]) ar[1,2] + (Subscript[α, 4]) ar[1,3];
μ3 = W[1] + (Subscript[α, 1]) ar[1,1] + (Subscript[α, 2]) ar[2,1] + (Subscript[α, 3]) ar[1,2] + (Subscript[α, 4]) ar[1,3];
Riffle[
ComposeList[
ops={conj3[1,3], conj3[1,2], hm[2,3,2]},
μ3 = W[1] + (Subscript[α, 1]) ar[1,1] + (Subscript[α, 2]) ar[2,1] + (Subscript[α, 3]) ar[1,2] + (Subscript[α, 4]) ar[1,3]
]// μForm,
ops
]

Riffle[
ComposeList[
ops={hm[2,3,2], conj3[1,2]},
μ3 
]// μForm,
ops
]

(μ2 = W[1]+ α ar[1,1] + β ar[1,2] + γ ar[2,1] +δ ar[2,2]) // μForm

μ2 // hfac[2, {1}->2, 3] // hm[2,3,2] // μForm

Riffle[
ComposeList[
ops={hfac[2, {1}->2, 3], conj3[1,2], conj[1,3], hm[2,3,2]},
μ2
]// μForm,
ops
]