(* ::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:: *)
\[Rho]h=({
 {0, 0, -1},
 {0, 0, 0},
 {0, 0, 0}
});\[Rho]e=({
 {0, 0, 0},
 {0, 0, 1},
 {0, 0, 0}
}); \[Rho]l=({
 {0, 0, 0},
 {0, 1, 0},
 {0, 0, 0}
}); \[Rho]f=({
 {0, 1, 0},
 {0, 0, 0},
 {0, 0, 0}
}); \[Rho]0=({
 {0, 0, 0},
 {0, 0, 0},
 {0, 0, 0}
});
B[x_?MatrixQ, y_?MatrixQ] := x.y-y.x;


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


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


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


(* ::Input::Initialization:: *)
Subscript[NO, Subscript[f, i_] Subscript[e, j_]->k_][\[DoubleStruckCapitalE][\[Omega]_,L_,Q_]]:=CF[
\[DoubleStruckCapitalE][\[Nu] \[Omega],L,\[Nu](-\[Alpha] \[Beta] Subscript[h, k]+\[Beta] Subscript[e, k]+\[Alpha] Subscript[f, k]+\[Delta] Subscript[e, k] Subscript[f, k])+(Q/.Subscript[f, i]|Subscript[e, j]->0)]
/.\[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]]]



