(* ::Package:: *)

(************************************************************************)\012(* This file was generated automatically by the Mathematica front end.  *)\012(* It contains Initialization cells from a Notebook file, which         *)\012(* typically will have the same name as this file except ending in      *)\012(* ".nb" instead of ".m".                                               *)\012(*                                                                      *)\012(* This file is intended to be loaded into the Mathematica kernel using *)\012(* the package loading commands Get or Needs.  Doing so is equivalent   *)\012(* to using the Evaluate Initialization Cells menu command in the front *)\012(* end.                                                                 *)\012(*                                                                      *)\012(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)\012(* automatically each time the parent Notebook file is saved in the     *)\012(* Mathematica front end.  Any changes you make to this file will be    *)\012(* overwritten.                                                         *)\012(************************************************************************)\012\012

(* ::Input::Initialization:: *)
CF[\[Omega]_. \[ScriptCapitalE]_\[DoubleStruckCapitalE],specs___]:=CF[\[Omega],specs]CF[#,specs]&/@\[ScriptCapitalE];
CF[\[ScriptCapitalE]_List]:=CF/@\[ScriptCapitalE];
CF[q_,vp_,h_]:= Module[{H},Expand@Collect[q,vp,H]/.H->h];
CF[q_,vp_]:=CF[q,vp,Factor];
CF[q_]:=CF[q,\[Epsilon]|Subscript[(p|x|\[Pi]|\[Xi]), _]|SubPlus[(p|x|\[Pi]|\[Xi])]|SubMinus[(p|x|\[Pi]|\[Xi])]];


(* ::Input::Initialization:: *)
\[DoubleStruckCapitalE]/:\[DoubleStruckCapitalE][A_]\[DoubleStruckCapitalE][B_]:=\[DoubleStruckCapitalE][A+B];


(* ::Input::Initialization:: *)
$\[Pi]=Identity; 


(* ::Input::Initialization:: *)
Unprotect[Integrate]; 
\[Integral]\[Omega]_. \[DoubleStruckCapitalE][L_]\[DifferentialD](vs_List):=Module[{n,L0,Q,\[CapitalDelta],G,Z0,Z,\[Lambda],DZ,DDZ,FZ,a,b},
n=Length@vs; L0=L/.\[Epsilon]->0;
Q=Table[(-\!\(
\*SubscriptBox[\(\[PartialD]\), \(vs[[\(a\)\(]\)], vs[[\(b\)\(]\)]\)]L0\))/.Thread[vs->0]/.Subscript[(p|x), __]->0,{a,n},{b,n}];
If[(\[CapitalDelta]=Det[Q])==0,Return@"\!\(\*
StyleBox[\"Degenerate\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\" \",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"Q\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
StyleBox[\"!\",\nFontColor->RGBColor[1, 0, 0]]\)"];
Z=Z0=CF@$\[Pi][L+vs . Q . vs/2]; G=Inverse[Q];
FixedPoint[(DZ=Table[\!\(
\*SubscriptBox[\(\[PartialD]\), \(v\)]Z\),{v,vs}];
DDZ=Table[\!\(
\*SubscriptBox[\(\[PartialD]\), \(u\)]DZ\),{u,vs}];
FZ=Sum[G[[a,b]](DDZ[[a,b]]+DZ[[a]]DZ[[b]]),{a,n},{b,n}]/2;
Z=CF[Z0+\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Lambda]\)]\($\[Pi][FZ]\ \[DifferentialD]\[Lambda]\)\)])&,Z];
PowerExpand@Factor[\[Omega] \[CapitalDelta]^(-1/2)]\[DoubleStruckCapitalE][CF[Z/.\[Lambda]->1/.Thread[vs->0]]]];
Protect[Integrate];


(* ::Input::Initialization:: *)
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   "], "Byte", ColorSpace -> "RGB", ImageResolution -> {168., 168.}, ImageSize -> {64.2857142857141, Automatic}, Interleaving -> True], ({
   {M=\!\(\*
      TagBox[
       RowBox[{"(", "", GridBox[{
          {
           RowBox[{"-", "1"}], 
           RowBox[{"-", "1"}], "2", "0"},
          {"0", "0", "0", "0"},
          {"0", "1", 
           RowBox[{"-", "1"}], "0"},
          {"1", "0", 
           RowBox[{"-", "1"}], "0"}
         },
         GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
         GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}}], "", ")"}],
       Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\)},
   {\!\(\*OverscriptBox[\(M\), \(_\)]\)=\!\(\*
      TagBox[
       TagBox[
        RowBox[{"(", "", GridBox[{
           {"1", 
            RowBox[{"-", "1"}], "0", "0"},
           {"0", "0", "0", "0"},
           {
            RowBox[{"-", "2"}], "1", "1", "0"},
           {"1", "0", 
            RowBox[{"-", "1"}], "0"}
          },
          GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
          GridBoxSpacings->{"Columns" -> {Offset[0.27999999999999997`], {Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> {Offset[0.2], {Offset[0.4]}, Offset[0.2]}}], "", ")"}],
        Function[BoxForm`e$, MatrixForm[BoxForm`e$]]],
       Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]\)}
  })}
};


(* ::Input::Initialization:: *)
Subscript[Q, i_,j_,k_,l_]:={Subscript[p, i],Subscript[p, j],Subscript[p, k],Subscript[p, l]} . (t M-t^-1 M\[Transpose]) . {Subscript[x, i],Subscript[x, j],Subscript[x, k],Subscript[x, l]};
Subscript[\!\(\*OverscriptBox[\(Q\), \(_\)]\), i_,j_,k_,l_]:={Subscript[p, i],Subscript[p, j],Subscript[p, k],Subscript[p, l]} . (t \!\(\*OverscriptBox[\(M\), \(_\)]\)-t^-1 \!\(\*OverscriptBox[\(M\), \(_\)]\)\[Transpose]) . {Subscript[x, i],Subscript[x, j],Subscript[x, k],Subscript[x, l]};


(* ::Input::Initialization:: *)
Subscript[px, i_]:=Sequence[Subscript[p, i],Subscript[x, i]];



