Pensieve header: ZeroCo, the global picture.

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\OneCo-1604\\Zero"];
<< ZeroLocal.m

Global Generalities

TSD for "Tail Scattering Data”

(Subscript[TSD[λ_], j_]) := Lookup[λ,j,UU@a[1,j,h∞]];
UU[u_] // γ_TSD := CF[u /. λ_a :> γ@λ];
TSD /: (((γ_TSD))^(-1)) := Module[{S=Keys@@γ,m},
m=Table[Coefficient[(Subscript[γ, i ]), a[j,h∞]],{i,S}, {j,S}] // Inverse;
TSD@\[LeftAssociation]Table[S[[α]]->
CF@UU@Sum[a[m[[α,β]],S[[β]],h∞], {β,Length@S}],
{α, Length@S}]\[RightAssociation]
];
a[f_,j_,k_] // γ_TSD := Module[{S=Keys@@γ, γi},
Switch[{MemberQ[S,j], MemberQ[S,k]},
{False,False}, UU@a[f,j,k],
{True,False}, (Subscript[γ, j]) /. a[g_,i_,h∞] :> a[f g,i,k],
{False, True}, (γi=(γ^(-1));
CF@Sum[
γ[bb[S⋃{j}][(Subscript[γi, i]), UU@a[f,j,k]]] /. {
a[_,i,h∞] :> 0, a[g_,l_,h∞] :> a[g/(Subscript[b, i]),l,i]},
{i,S}]),
{True,True}, ct[h∞,t∞][γ@a[f,j,h∞], γ@a[1,t∞,k]]
]];

Ea & R

Ea[t_,j_,k_]:=TSD[\[LeftAssociation]
j->CF@UU[a[1,j,h∞]],
k->CF@UU[a[(E^(t (Subscript[b, j]))),k,h∞]+a[-(((-1+(E^(t (Subscript[b, j])))) (Subscript[b, k]))/(Subscript[b, j])),j,h∞]]\[RightAssociation]];
R[j_,k_]:=Ea[1,j,k]

{(Subscript[Ea[t,1,2], 1]), (Subscript[Ea[t,1,2], 2])} /. t->0

{D[(Subscript[Ea[t,1,2], 1]), t],D[(Subscript[Ea[t,1,2], 2]), t]}

{D[(Subscript[Ea[t,1,2], 1]), t]-bb[1,2][UU[a[1,1,2]], (Subscript[Ea[t,1,2], 1])],
D[(Subscript[Ea[t,1,2], 2]), t]-bb[1,2][UU[a[1,1,2]], (Subscript[Ea[t,1,2], 2])]}

R[1,2][a[f,2,3]]

((Ea[t,3,5])^(-1))

Ea[-t,3,5]