(* ::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:: *)
\[Delta] /: Subscript[\[Delta], i_,j_]:=If[i==j,1,0];


(* ::Input::Initialization:: *)
Subscript[\[Tau], i_,j_][\[Zeta]_] := (\[Zeta] /. {Subscript[z_, k_]:>Subscript[z, k/.{i->j,j->i}],Subscript[z_, l_,k_]:>Subscript[z, l/.{i->j,j->i},k/.{i->j,j->i}]})
(* Non-linear over \[DoubleStruckCapitalQ](Subsuperscript[t, i, \[PlusMinus]1])! *)


(* ::Input::Initialization:: *)
Subscript[B, i_,j_][\[Xi]_]:=\[Xi]/.Subscript[v, k_]:>Subscript[v, k]+Subscript[\[Delta], k,j](t-1)(Subscript[v, j]-Subscript[v, i])//Expand


(* ::Input::Initialization:: *)
Subscript[G, i_,j_][\[Xi]_]:=\[Xi]/.Subscript[v, k_]:>Subscript[v, k]+Subscript[\[Delta], k,j](Subscript[t, i]-1)(Subscript[v, j]-Subscript[v, i])//Expand


(* ::Input::Initialization:: *)
Subscript[TG, i_,j_][\[Xi]_] := \[Xi] /. {
Subscript[v, k_]:>Subscript[v, k]+Subscript[\[Delta], k,j]((Subscript[t, i]-1)(Subscript[v, j]-Subscript[v, i])+Subscript[v, i,j]-Subscript[v, i,i])+Subscript[\[Delta], k,i](Subscript[u, j]-Subscript[u, i])Subscript[u, i] Subscript[w, j],
Subscript[v, l_,k_]:>Subscript[v, l,k]+(Subscript[t, i]-1)
(Subscript[\[Delta], k,j](Subscript[v, l,j]-Subscript[v, l,i])+(Subscript[\[Delta], l,i]-Subscript[\[Delta], l,j] \!\(\*SubsuperscriptBox[\(t\), \(i\), \(-1\)]\) Subscript[t, j])(Subscript[u, k]+Subscript[\[Delta], k,j](Subscript[t, i]-1)(Subscript[u, j]-Subscript[u, i]))Subscript[u, i] Subscript[w, j]),
Subscript[u, k_]:>Subscript[u, k]+Subscript[\[Delta], k,j](Subscript[t, i]-1)(Subscript[u, j]-Subscript[u, i]),
Subscript[w, k_]:>Subscript[w, k]+(Subscript[\[Delta], k,j]-Subscript[\[Delta], k,i])(\!\(
\*SubsuperscriptBox[\(t\), \(i\), \(-1\)] - 1\)) Subscript[w, j]}//Expand



