(* ::Package:: *)

(************************************************************************)
(* This file was generated automatically by the Mathematica front end.  *)
(* It contains Initialization cells from a Notebook file, which         *)
(* typically will have the same name as this file except ending in      *)
(* ".nb" instead of ".m".                                               *)
(*                                                                      *)
(* This file is intended to be loaded into the Mathematica kernel using *)
(* the package loading commands Get or Needs.  Doing so is equivalent   *)
(* to using the Evaluate Initialization Cells menu command in the front *)
(* end.                                                                 *)
(*                                                                      *)
(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
(* automatically each time the parent Notebook file is saved in the     *)
(* Mathematica front end.  Any changes you make to this file will be    *)
(* overwritten.                                                         *)
(************************************************************************)



(* ::Input::Initialization:: *)
Subscript[DP, x_->Subscript[D, \[Alpha]_],y_->Subscript[D, \[Beta]_]][P_][f_]:=Total[CoefficientRules[P,{x,y}]/.({m_,n_}->c_):>c D[f,{\[Alpha],m},{\[Beta],n}]]


(* ::Input::Initialization:: *)
Subscript[\[CapitalLambda], k_][h_,e_,l_,f_,\[Alpha]_,\[Beta]_,\[Delta]_] :=Subscript[\[CapitalLambda], k][h,e,l,f,\[Alpha],\[Beta],\[Delta]]=Module[{\[Lambda]},
\[Lambda]=Normal@Series[E^((f \[Alpha]+e \[Beta])/(1-\[Alpha] \[Beta] \[Epsilon])) (1-\[Alpha] \[Beta] \[Epsilon])^(-2 l+h/\[Epsilon]), {\[Epsilon],0,k}]/.E^_->1;
Collect[Subscript[DP, \[Alpha]->Subscript[D, f],\[Beta]->Subscript[D, e]][\[Lambda]][E^((f \[Alpha]+e \[Beta]+e f \[Delta])/(1+h \[Delta]))]/.E^_->1,\[Epsilon],Simplify]];


(* ::Input::Initialization:: *)
\[Epsilon] /: \[Epsilon]^p_ /; p>1 :=0;


(* ::Input::Initialization:: *)
CF[\[DoubleStruckCapitalE]1n[\[Omega]_,L_,Q_,P_]] := \[DoubleStruckCapitalE]1n[Together[\[Omega]], Together[L], Together[Q],Together[P]];
\[DoubleStruckCapitalE]1n /: \[DoubleStruckCapitalE]1n[\[Omega]1_,L1_,Q1_,P1_]\[DoubleStruckCapitalE]1n[\[Omega]2_,L2_,Q2_,P2_] := CF@\[DoubleStruckCapitalE]1n[\[Omega]1 \[Omega]2,L1+L2,Q1+Q2,P1+P2];
\[DoubleStruckCapitalE]1n[\[Omega]1_,L1_,Q1_,P1_] \[Congruent] \[DoubleStruckCapitalE]1n[\[Omega]2_,L2_,Q2_,P2_] := Simplify[\[Omega]1==\[Omega]2\[And]L1==L2\[And]Q1==Q2\[And]P1==P2];


(* ::Input::Initialization:: *)
\[DoubleStruckCapitalE]1n[\!\(\*SubsuperscriptBox[\(X\), \(i_, j_\), \(+\)]\)]:=\[DoubleStruckCapitalE]1n[1, Subscript[h, i] Subscript[l, j],\!\(
\*SubsuperscriptBox[\(h\), \(i\), \(-1\)] \((
\*SuperscriptBox[\(E\), 
SubscriptBox[\(h\), \(i\)]] - 1)\) 
\*SubscriptBox[\(e\), \(i\)] 
\*SubscriptBox[\(f\), \(j\)]\),SuperPlus[P]];
\[DoubleStruckCapitalE]1n[\!\(\*SubsuperscriptBox[\(X\), \(i_, j_\), \(-\)]\)]:=\[DoubleStruckCapitalE]1n[1, -Subscript[h, i] Subscript[l, j],\!\(
\*SubsuperscriptBox[\(h\), \(i\), \(-1\)] \((
\*SuperscriptBox[\(E\), \(-
\*SubscriptBox[\(h\), \(i\)]\)] - 1)\) 
\*SubscriptBox[\(e\), \(i\)] 
\*SubscriptBox[\(f\), \(j\)]\),SuperMinus[P]];
\[DoubleStruckCapitalE]1n[p_Times] := \[DoubleStruckCapitalE]1n /@ p;


(* ::Input::Initialization:: *)
Subscript[NO, Subscript[(x:f|e), i_] Subscript[l, j_]][\[DoubleStruckCapitalE]1n[\[Omega]_,L_,Q_,P_]] := With[{q=E^\[Gamma] \[Beta] Subscript[x, i]+\[Gamma] Subscript[l, j]},
CF[\[DoubleStruckCapitalE]1n[\[Omega],L,
E^\[Gamma] \[Beta] Subscript[x, i]+(Q/.Subscript[x, i]->0),
E^-q Subscript[DP, Subscript[l, j]->Subscript[D, \[Gamma]],Subscript[x, i]->Subscript[D, \[Beta]]][P][E^q]
]/.{\[Gamma]->\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(l\), \(j\)]]L\),\[Beta]->\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(x\), \(i\)]]Q\)}]];


(* ::Input::Initialization:: *)
Subscript[NO, Subscript[f, i_] Subscript[e, j_]->k_][\[DoubleStruckCapitalE]1n[\[Omega]_,L_,Q_,P_]]:=With[{q=\[Nu](-\[Alpha] \[Beta] Subscript[h, k]+\[Beta] Subscript[e, k]+\[Alpha] Subscript[f, k]+\[Delta] Subscript[e, k] Subscript[f, k])},
CF[\[DoubleStruckCapitalE]1n[\[Nu] \[Omega],L,
q+(Q/.Subscript[f, i]|Subscript[e, j]->0),
E^-q Subscript[DP, Subscript[f, i]->Subscript[D, \[Alpha]],Subscript[e, j]->Subscript[D, \[Beta]]][P][E^q]+(Subscript[\[CapitalLambda], 1][Subscript[h, k],Subscript[e, k],Subscript[l, k],Subscript[f, k],\[Alpha],\[Beta],\[Delta]]-1 /. \[Epsilon]->1)
]/.\[Nu]->(1+Subscript[h, k]\[Delta])^-1/.{\[Alpha]->\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(f\), \(i\)]]Q\)/.Subscript[e, j]->0,\[Beta]->\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(e\), \(j\)]]Q\)/.Subscript[f, i]->0,\[Delta]->\!\(
\*SubscriptBox[\(\[PartialD]\), \(
\*SubscriptBox[\(f\), \(i\)], 
\*SubscriptBox[\(e\), \(j\)]\)]Q\)}]];


(* ::Input::Initialization:: *)
Subscript[m, i_,j_->k_][Z_]:=Module[{x,z},CF[(Z//Subscript[NO, Subscript[f, i] Subscript[e, j]->x]//Subscript[NO, Subscript[l, i] Subscript[e, x]]//Subscript[NO, Subscript[f, x] Subscript[l, j]])/.Subscript[z_, i|j|x]->Subscript[z, k]]]


(* ::Input::Initialization:: *)
\[DoubleStruckCapitalE]1n[\[DoubleStruckCapitalE]1p[\[Omega]_,L_,Q_,P_]] := CF[PowerExpand/@CF[\[DoubleStruckCapitalE]1n[\[Omega]^-1,L,\[Omega]^-1 Q,\[Omega]^-4 P] /. Subscript[e, i_]:>(Subscript[t, i]-1)/Subscript[h, i] Subscript[e, i]/. Subscript[t, i_]:>E^Subscript[h, i]]];
CF[\[DoubleStruckCapitalE]1p[\[Omega]_,L_,Q_,P_]] := \[DoubleStruckCapitalE]1p[Together[\[Omega]], Together[L], Together[Q],Together[P]];
\[DoubleStruckCapitalE]1p[\[DoubleStruckCapitalE]1n[\[Omega]_,L_,Q_,P_]] := CF[\[DoubleStruckCapitalE]1p[\[Omega]^-1,L,\[Omega]^-1 Q,\[Omega]^-4 P] /. Subscript[e, i_]:>Subscript[h, i]/(Subscript[t, i]-1) Subscript[e, i]/. Subscript[h, i_]:>Log[Subscript[t, i]]];
\[DoubleStruckCapitalE]1p[\[Omega]1_,L1_,Q1_,P1_] \[Congruent] \[DoubleStruckCapitalE]1p[\[Omega]2_,L2_,Q2_,P2_] := Simplify[\[Omega]1==\[Omega]2\[And]L1==L2\[And]Q1==Q2\[And]P1==P2];


(* ::Input::Initialization:: *)
\[DoubleStruckCapitalE]1p/: \[DoubleStruckCapitalE]1p[\[Omega]1_,L1_,Q1_,P1_]\[DoubleStruckCapitalE]1p[\[Omega]2_,L2_,Q2_,P2_] := CF@\[DoubleStruckCapitalE]1p[\[Omega]1 \[Omega]2,L1+L2,\[Omega]2 Q1+\[Omega]1 Q2,\[Omega]2^4 P1+\[Omega]1^4 P2];


(* ::Input::Initialization:: *)
Subscript[NO, Subscript[f, i_] Subscript[e, j_]->k_][\[DoubleStruckCapitalE]1p[\[Omega]_,L_,Q_,P_]]:=Module[{\[Alpha],\[Beta],\[Delta],\[Mu],q,\[CapitalLambda]},
q=((1-Subscript[t, k])\[Alpha] \[Beta]+\[Beta] Subscript[e, k]+\[Delta] Subscript[e, k] Subscript[f, k]+\[Alpha] Subscript[f, k])/\[Mu];
\[CapitalLambda]=1/(2 Log[Subscript[t, k]]) \[Omega]^4 (-1+Subscript[t, k]) (\[Alpha]^2 \[Beta]^2+4 \[Alpha] \[Beta] \[Delta]+2 \[Delta]^2-4 \[Alpha] \[Beta] \[Delta]^2-4 \[Delta]^3+2 \[Delta]^4+4 \[Alpha] \[Beta] Subscript[l, k]+4 \[Delta] Subscript[l, k]-8 \[Alpha] \[Beta] \[Delta] Subscript[l, k]-12 \[Delta]^2 Subscript[l, k]+4 \[Alpha] \[Beta] \[Delta]^2 Subscript[l, k]+12 \[Delta]^3 Subscript[l, k]-4 \[Delta]^4 Subscript[l, k]-\[Alpha]^2 \[Beta]^2 Subscript[t, k]-4 \[Alpha] \[Beta] \[Delta] Subscript[t, k]-2 \[Delta]^2 Subscript[t, k]+8 \[Alpha] \[Beta] \[Delta]^2 Subscript[t, k]+8 \[Delta]^3 Subscript[t, k]-6 \[Delta]^4 Subscript[t, k]+8 \[Alpha] \[Beta] \[Delta] Subscript[l, k] Subscript[t, k]+12 \[Delta]^2 Subscript[l, k] Subscript[t, k]-8 \[Alpha] \[Beta] \[Delta]^2 Subscript[l, k] Subscript[t, k]-24 \[Delta]^3 Subscript[l, k] Subscript[t, k]+12 \[Delta]^4 Subscript[l, k] Subscript[t, k]-4 \[Alpha] \[Beta] \[Delta]^2 \!\(\*SubsuperscriptBox[\(t\), \(k\), \(2\)]\)-4 \[Delta]^3 \!\(\*SubsuperscriptBox[\(t\), \(k\), \(2\)]\)+6 \[Delta]^4 \!\(\*SubsuperscriptBox[\(t\), \(k\), \(2\)]\)+4 \[Alpha] \[Beta] \[Delta]^2 Subscript[l, k] \!\(\*SubsuperscriptBox[\(t\), \(k\), \(2\)]\)+12 \[Delta]^3 Subscript[l, k] \!\(\*SubsuperscriptBox[\(t\), \(k\), \(2\)]\)-12 \[Delta]^4 Subscript[l, k] \!\(\*SubsuperscriptBox[\(t\), \(k\), \(2\)]\)-2 \[Delta]^4 \!\(\*SubsuperscriptBox[\(t\), \(k\), \(3\)]\)+4 \[Delta]^4 Subscript[l, k] \!\(\*SubsuperscriptBox[\(t\), \(k\), \(3\)]\)+\[Alpha]^2 \[Delta] \!\(\*SubsuperscriptBox[\(f\), \(k\), \(2\)]\) (2-\[Delta]+\[Delta] Subscript[t, k])+2 \[Alpha] Subscript[f, k] (\[Alpha] \[Beta]+2 \[Delta]-2 \[Delta]^2+2 \[Delta]^2 Subscript[t, k]+2 \[Delta] Subscript[l, k] (1-\[Delta]+\[Delta] Subscript[t, k])^2)+\[Delta] \!\(\*SubsuperscriptBox[\(e\), \(k\), \(2\)]\) (\[Beta]+\[Delta] Subscript[f, k]) (\[Beta] (2-\[Delta]+\[Delta] Subscript[t, k])+\[Delta] Subscript[f, k] (4-3 \[Delta]+3 \[Delta] Subscript[t, k]))+2 Subscript[e, k] (\[Alpha] \[Delta]^2 \!\(\*SubsuperscriptBox[\(f\), \(k\), \(2\)]\) (3-2 \[Delta]+2 \[Delta] Subscript[t, k])+\[Beta] (\[Alpha] \[Beta]+2 \[Delta]-2 \[Delta]^2+2 \[Delta]^2 Subscript[t, k]+2 \[Delta] Subscript[l, k] (1-\[Delta]+\[Delta] Subscript[t, k])^2)+2 \[Delta] Subscript[f, k] (\[Delta] Subscript[l, k] (1-\[Delta]+\[Delta] Subscript[t, k])^2+(2-\[Delta]+\[Delta] Subscript[t, k]) (\[Alpha] \[Beta]+\[Delta]-\[Delta]^2+\[Delta]^2 Subscript[t, k]))));
CF[
\[DoubleStruckCapitalE]1p[\[Mu] \[Omega],L,\[Mu] \[Omega] q+\[Mu](Q/.Subscript[f, i]|Subscript[e, j]->0),\[Mu]^4 (Subscript[DP, Subscript[f, i]->Subscript[D, \[Alpha]],Subscript[e, j]->Subscript[D, \[Beta]]][P][E^q]/.E^_->1)+\[Omega]^4 \[CapitalLambda][k]]/.\[Mu]->1+(Subscript[t, k]-1)\[Delta]/.{\[Alpha]->\[Omega]^-1 (\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(f\), \(i\)]]Q\)/.Subscript[e, j]->0),\[Beta]->\[Omega]^-1 (\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(e\), \(j\)]]Q\)/.Subscript[f, i]->0),\[Delta]->\[Omega]^-1 \!\(
\*SubscriptBox[\(\[PartialD]\), \(
\*SubscriptBox[\(f\), \(i\)], 
\*SubscriptBox[\(e\), \(j\)]\)]Q\)}
]];


(* ::Input::Initialization:: *)
Subscript[NO, Subscript[l, j_] Subscript[(x:e|f), i_]->k_][\[DoubleStruckCapitalE]1p[\[Omega]_,L_,Q_,P_]]:=With[{q=E^\[Gamma] \[Beta] Subscript[x, k]+\[Gamma] Subscript[l, k]},CF[
\[DoubleStruckCapitalE]1p[\[Omega],\[Gamma] Subscript[l, k]+(L/.Subscript[l, j]->0),\[Omega] E^\[Gamma] \[Beta] Subscript[x, k]+(Q/.Subscript[x, i]->0),E^-q Subscript[DP, Subscript[l, j]->Subscript[D, \[Gamma]],Subscript[x, i]->Subscript[D, \[Beta]]][P][E^q]]/.{\[Gamma]->\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(l\), \(j\)]]L\),\[Beta]->\[Omega]^-1 \!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(x\), \(i\)]]Q\)}]];



