(* ::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:: *)
SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\OneCo-1606"];
<< NOE-1.m


(* ::Input::Initialization:: *)
ECAllButOne={Subscript[f, 2][x_,y_]:>y Subscript[f, 9][x,y]+y^2 Subscript[f, 26][x,y]-Subscript[g, 6][x],Subscript[f, 3][x_,z_]:>x^2 Subscript[f, 18][x,z],Subscript[f, 4][x_,y_]:>y Subscript[f, 13][x,y]-Subscript[g, 1][x],Subscript[f, 5][x_,y_]:>y^2 Subscript[f, 26][x,y],Subscript[f, 8][x_,z_]:>0,Subscript[f, 10][x_,z_]:>2 x Subscript[f, 18][x,z],Subscript[f, 11][x_,y_]:>2 x Subscript[f, 18][x,y]-2 E^x x Subscript[f, 18][x,y]-Subscript[g, 4][x],Subscript[f, 12][x_,z_]:>0,Subscript[f, 13][x_,z_]:>x Subscript[f, 22][x,z]-Subscript[g, 3][z],Subscript[f, 14][x_,y_]:>y Subscript[f, 22][x,y]-Subscript[g, 2][x],Subscript[f, 15][x_,y_]:>1/((-1+E^y) x) (-x y Subscript[f, 23][x,y]+E^y x y Subscript[f, 23][x,y]+x Subscript[g, 2][x]-E^x x Subscript[g, 2][x]-E^y x Subscript[g, 2][x]+E^(x+y) x Subscript[g, 2][x]-E^y y Subscript[g, 2][y]+E^(x+y) y Subscript[g, 2][y]-y Subscript[g, 3][y]+E^x y Subscript[g, 3][y]-y Subscript[g, 4][y]+E^x y Subscript[g, 4][y]+8 y^2 Subscript[g, 5][y]-8 E^x y^2 Subscript[g, 5][y]-16 E^y y^2 Subscript[g, 5][y]+8 E^(2 y) y^2 Subscript[g, 5][y]+16 E^(x+y) y^2 Subscript[g, 5][y]-8 E^(x+2 y) y^2 Subscript[g, 5][y]+4 y Subscript[g, 7][y]-4 E^x y Subscript[g, 7][y]-4 E^y y Subscript[g, 7][y]+4 E^(x+y) y Subscript[g, 7][y]),Subscript[f, 16][x_,z_]:>0,Subscript[f, 17][x_,y_]:>2 y Subscript[f, 26][x,y],Subscript[f, 18][x_,y_]:>-((Subscript[f, 19][x,y]+4 Subscript[g, 5][x]-8 E^x Subscript[g, 5][x]+4 E^(2 x) Subscript[g, 5][x])/(2 (-1+E^x))),Subscript[f, 19][x_,y_]:>1/((-1+E^x) (-1+E^y) x^2 y) (-1+2 E^x-E^(2 x)+E^y-2 E^(x+y)+E^(2 x+y)+2 x^2 y Subscript[f, 20][x,y]-2 E^y x^2 y Subscript[f, 20][x,y]+x y Subscript[g, 4][x]-E^x x y Subscript[g, 4][x]-E^y x y Subscript[g, 4][x]+E^(x+y) x y Subscript[g, 4][x]+y^2 Subscript[g, 4][y]-2 E^x y^2 Subscript[g, 4][y]+E^(2 x) y^2 Subscript[g, 4][y]-4 y^3 Subscript[g, 5][y]+8 E^x y^3 Subscript[g, 5][y]-4 E^(2 x) y^3 Subscript[g, 5][y]+8 E^y y^3 Subscript[g, 5][y]-4 E^(2 y) y^3 Subscript[g, 5][y]-16 E^(x+y) y^3 Subscript[g, 5][y]+8 E^(2 x+y) y^3 Subscript[g, 5][y]+8 E^(x+2 y) y^3 Subscript[g, 5][y]-4 E^(2 x+2 y) y^3 Subscript[g, 5][y]-E^y y Subscript[h, 1][]+2 E^(x+y) y Subscript[h, 1][]-E^(2 x+y) y Subscript[h, 1][]),Subscript[f, 21][x_,z_]:>0,Subscript[f, 22][x_,z_]:>(-x Subscript[f, 23][x,z]-4 Subscript[g, 7][z]+4 E^x Subscript[g, 7][z])/((-1+E^x) x),Subscript[f, 24][x_,z_]:>0,Subscript[f, 25][x_,z_]:>0,Subscript[g, 1][y_]:>y Subscript[g, 2][y]+Subscript[h, 1][],Subscript[g, 2][y_]:>1/(2 y^2) E^-y (-2+2 E^y-2 y^2 Subscript[g, 3][y]+8 y^3 Subscript[g, 5][y]-16 E^y y^3 Subscript[g, 5][y]+8 E^(2 y) y^3 Subscript[g, 5][y]+8 y^2 Subscript[g, 7][y]-8 E^y y^2 Subscript[g, 7][y]-y Subscript[h, 1][]-E^y y Subscript[h, 1][]),Subscript[f, 1][x_,z_]:>1/2 (-(1/((-1+E^x)^2))x (-2 (-1+E^x)^2 Subscript[f, 6][x,z]-2 x Subscript[f, 20][x,z]+(-1+E^x) (Subscript[g, 4][x]+4 (-1+E^x)^2 x Subscript[g, 5][x]))+Subscript[g, 8][z])};


(* ::Input::Initialization:: *)
ECAll=ECAllButOne\[Union]{ Subscript[f, 6][x_,z_]->(-((x Subscript[f, 7][x,z])/(-1+E^x))+Subscript[g, 9][x]+Subscript[g, 10][z])/x, Subscript[g, 10][y_]->1/(2 (-1+E^y)^2 y) (-1+E^y-y^2 Subscript[g, 4][y]+2 E^y y^2 Subscript[g, 4][y]-4 y^3 Subscript[g, 5][y]+8 E^y y^3 Subscript[g, 5][y]-4 E^(2 y) y^3 Subscript[g, 5][y]+2 E^y y Subscript[g, 6][y]-2 E^(2 y) y Subscript[g, 6][y]-y Subscript[g, 8][y]+E^y y Subscript[g, 8][y]-2 y Subscript[g, 9][y]+4 E^y y Subscript[g, 9][y]-2 E^(2 y) y Subscript[g, 9][y]-E^y y Subscript[h, 1][])};


(* ::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]](1+\[Epsilon] Subscript[c, i] Subscript[f, 1][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[c, j] Subscript[f, 2][Subscript[b, i],Subscript[b, j]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(c\), \(i\), \(2\)]\) Subscript[f, 3][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[c, i] Subscript[c, j] Subscript[f, 4][Subscript[b, i],Subscript[b, j]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(c\), \(j\), \(2\)]\) Subscript[f, 5][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[u, i] Subscript[w, i] Subscript[f, 6][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[u, i] Subscript[w, j] Subscript[f, 7][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[u, j] Subscript[w, i] Subscript[f, 8][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[u, j] Subscript[w, j] Subscript[f, 9][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[c, i] Subscript[u, i] Subscript[w, i] Subscript[f, 10][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[c, i] Subscript[u, i] Subscript[w, j] Subscript[f, 11][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[c, i] Subscript[u, j] Subscript[w, i] Subscript[f, 12][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[c, i] Subscript[u, j] Subscript[w, j] Subscript[f, 13][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[c, j] Subscript[u, i] Subscript[w, i] Subscript[f, 14][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[c, j] Subscript[u, i] Subscript[w, j] Subscript[f, 15][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[c, j] Subscript[u, j] Subscript[w, i] Subscript[f, 16][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[c, j] Subscript[u, j] Subscript[w, j] Subscript[f, 17][Subscript[b, i],Subscript[b, j]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(u\), \(i\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(w\), \(i\), \(2\)]\) Subscript[f, 18][Subscript[b, i],Subscript[b, j]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(u\), \(i\), \(2\)]\) Subscript[w, i] Subscript[w, j] Subscript[f, 19][Subscript[b, i],Subscript[b, j]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(u\), \(i\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(w\), \(j\), \(2\)]\) Subscript[f, 20][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[u, i] Subscript[u, j] 
\!\(\*SubsuperscriptBox[\(w\), \(i\), \(2\)]\) Subscript[f, 21][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[u, i] Subscript[u, j] Subscript[w, i] Subscript[w, j] Subscript[f, 22][Subscript[b, i],Subscript[b, j]]+\[Epsilon] Subscript[u, i] Subscript[u, j] 
\!\(\*SubsuperscriptBox[\(w\), \(j\), \(2\)]\) Subscript[f, 23][Subscript[b, i],Subscript[b, j]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(u\), \(j\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(w\), \(i\), \(2\)]\) Subscript[f, 24][Subscript[b, i],Subscript[b, j]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(u\), \(j\), \(2\)]\) Subscript[w, i] Subscript[w, j] Subscript[f, 25][Subscript[b, i],Subscript[b, j]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(u\), \(j\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(w\), \(j\), \(2\)]\) Subscript[f, 26][Subscript[b, i],Subscript[b, j]])


(* ::Input::Initialization:: *)
ur[i_]:=E^(Subscript[b, i]/4) \[DoubleStruckCapitalE][0](1+\[Epsilon] Subscript[c, i] Subscript[ur, 1][Subscript[b, i]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(c\), \(i\), \(2\)]\) Subscript[ur, 2][Subscript[b, i]]+\[Epsilon] Subscript[u, i] Subscript[w, i] Subscript[ur, 3][Subscript[b, i]]+\[Epsilon] Subscript[c, i] Subscript[u, i] Subscript[w, i] Subscript[ur, 4][Subscript[b, i]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(u\), \(i\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(w\), \(i\), \(2\)]\) Subscript[ur, 5][Subscript[b, i]]);
nr[i_]:=E^(-Subscript[b, i]/4) \[DoubleStruckCapitalE][0](1-\[Epsilon] Subscript[c, i] Subscript[ur, 1][Subscript[b, i]]-\[Epsilon] 
\!\(\*SubsuperscriptBox[\(c\), \(i\), \(2\)]\) Subscript[ur, 2][Subscript[b, i]]-\[Epsilon] Subscript[u, i] Subscript[w, i] Subscript[ur, 3][Subscript[b, i]]-\[Epsilon] Subscript[c, i] Subscript[u, i] Subscript[w, i] Subscript[ur, 4][Subscript[b, i]]-\[Epsilon] 
\!\(\*SubsuperscriptBox[\(u\), \(i\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(w\), \(i\), \(2\)]\) Subscript[ur, 5][Subscript[b, i]]);
ul[i_]:=E^(-Subscript[b, i]/4) \[DoubleStruckCapitalE][0](1+\[Epsilon] Subscript[c, i] Subscript[ul, 1][Subscript[b, i]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(c\), \(i\), \(2\)]\) Subscript[ul, 2][Subscript[b, i]]+\[Epsilon] Subscript[u, i] Subscript[w, i] Subscript[ul, 3][Subscript[b, i]]+\[Epsilon] Subscript[c, i] Subscript[u, i] Subscript[w, i] Subscript[ul, 4][Subscript[b, i]]+\[Epsilon] 
\!\(\*SubsuperscriptBox[\(u\), \(i\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(w\), \(i\), \(2\)]\) Subscript[ul, 5][Subscript[b, i]]);
nl[i_]:=E^(Subscript[b, i]/4) \[DoubleStruckCapitalE][0](1-\[Epsilon] Subscript[c, i] Subscript[ul, 1][Subscript[b, i]]-\[Epsilon] 
\!\(\*SubsuperscriptBox[\(c\), \(i\), \(2\)]\) Subscript[ul, 2][Subscript[b, i]]-\[Epsilon] Subscript[u, i] Subscript[w, i] Subscript[ul, 3][Subscript[b, i]]-\[Epsilon] Subscript[c, i] Subscript[u, i] Subscript[w, i] Subscript[ul, 4][Subscript[b, i]]-\[Epsilon] 
\!\(\*SubsuperscriptBox[\(u\), \(i\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(w\), \(i\), \(2\)]\) Subscript[ul, 5][Subscript[b, i]]);



