(* ::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:: *)
\[DoubleStruckCapitalE] /: \[DoubleStruckCapitalE][Q1_]\[DoubleStruckCapitalE][Q2_] := Simp@\[DoubleStruckCapitalE][Q1+Q2]


(* ::Input::Initialization:: *)
Simp[\[Omega]_. \[DoubleStruckCapitalE][Q_]] := Simplify[\[Omega]]\[DoubleStruckCapitalE][Simplify[Q]];
\[Omega]1_. \[DoubleStruckCapitalE][Q1_] \[Congruent] \[Omega]2_. \[DoubleStruckCapitalE][Q2_] := Simplify[\[Omega]1==\[Omega]2\[And]Q1==Q2];


(* ::Input::Initialization:: *)
NO[Subscript[u, i_],Subscript[c, j_],k_][\[Omega]_. \[DoubleStruckCapitalE][Q_]] := Simp@Module[{\[Alpha]=\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(c\), \(j\)]]Q\),\[Beta]=\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(u\), \(i\)]]Q\), \[CapitalTheta]=Q/.Subscript[c, j]|Subscript[u, i]->0}, \[Omega] \[DoubleStruckCapitalE][E^-\[Alpha] \[Beta] Subscript[u, k]+\[Alpha] Subscript[c, k]+\[CapitalTheta]]];
NO[Subscript[w, i_],Subscript[c, j_],k_][\[Omega]_. \[DoubleStruckCapitalE][Q_]] := Simp@Module[{\[Alpha]=\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(c\), \(j\)]]Q\),\[Beta]=\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(w\), \(i\)]]Q\), \[CapitalTheta]=Q/.Subscript[c, j]|Subscript[w, i]->0}, \[Omega] \[DoubleStruckCapitalE][E^\[Alpha] \[Beta] Subscript[w, k]+\[Alpha] Subscript[c, k]+\[CapitalTheta]]];
NO[Subscript[w, i_],Subscript[u, j_],k_][\[Omega]_. \[DoubleStruckCapitalE][Q_]] := Simp@Module[{\[Alpha]=\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(w\), \(i\)]]Q\)/.Subscript[u, j]->0, \[Beta]=\!\(
\*SubscriptBox[\(\[PartialD]\), 
SubscriptBox[\(u\), \(j\)]]Q\)/.Subscript[w, i]->0, \[Delta]=\!\(
\*SubscriptBox[\(\[PartialD]\), \(
\*SubscriptBox[\(w\), \(i\)], 
\*SubscriptBox[\(u\), \(j\)]\)]Q\),\[CapitalTheta]=Q/.Subscript[w, i]|Subscript[u, j]->0,\[Nu]},
\[Nu]=(1+Subscript[b, k] \[Delta])^-1;
\[Nu] \[Omega] \[DoubleStruckCapitalE][-Subscript[b, k]\[Nu] \[Alpha] \[Beta]+\[Nu] \[Beta] Subscript[u, k]+\[Nu] \[Delta] Subscript[u, k] Subscript[w, k]+\[Nu] \[Alpha] Subscript[w, k] +\[CapitalTheta]]
];


(* ::Input::Initialization:: *)
m[i_,j_,k_][Z_] :=Simp@Module[{a},(Z /. Subscript[b, i|j]->Subscript[b, k] // NO[Subscript[w, i],Subscript[c, j],a]//NO[Subscript[u, i],Subscript[c, a],a]//NO[Subscript[w, a],Subscript[u, j],a]) /. {Subscript[c, i]->Subscript[c, k],Subscript[w, j]->Subscript[w, k],Subscript[y_, a]:>Subscript[y, k]}]


(* ::Input::Initialization:: *)
\[Sigma][i_,j_][\[ScriptCapitalE]_] := \[ScriptCapitalE] /. {Subscript[b, i]->Subscript[b, j], Subscript[c, i]->Subscript[c, j], Subscript[u, i]->Subscript[u, j], Subscript[w, i]->Subscript[w, j]}


(* ::Input::Initialization:: *)
Rp[i_,j_]:=\[DoubleStruckCapitalE][Subscript[b, i] Subscript[c, j]+(E^Subscript[b, i]-1)/Subscript[b, i] Subscript[u, i] Subscript[w, j]];
Rm[i_,j_]:=\[DoubleStruckCapitalE][-Subscript[b, i] Subscript[c, j]+(E^-Subscript[b, i]-1)/Subscript[b, i] Subscript[u, i] Subscript[w, j]];



