(* ::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\\Talks\\Beijing-2407"];
Once[<<IType.m];


(* ::Input::Initialization:: *)
Subscript[T, 3]=Subscript[T, 1] Subscript[T, 2];  SuperPlus[i_]:=i+1;
$\[Pi]=(CF@Normal[#+O[\[Epsilon]]^2]/. {Subscript[\[Pi], is__]:>B^-1 Subscript[\[Pi], is],Subscript[x, is__]:>B^-1 Subscript[x, is],Subscript[p, is__]:>B Subscript[p, is]}/.\[Epsilon] B^b_/;b<0->0/.B->1)&;


(* ::Input::Initialization:: *)
\[ScriptCapitalL][Subscript[X, i_,j_][1]]:=Subscript[T, 3]\[DoubleStruckCapitalE][Plus[
\!\(
\*SubsuperscriptBox[\(\[Sum]\), \(\[Nu] = 1\), \(3\)]\((
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]i\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(i\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]i\)])\) + 
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]j\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(j\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]j\)])\) + \((
\*SubscriptBox[\(T\), \(\[Nu]\)] - 1)\) 
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]i\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(i\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(j\), \(+\)]\)])\))\)\),
Subscript[p, 3\[InvisibleComma]j] Subscript[x, 2\[InvisibleComma]i](Subscript[T, 1] Subscript[x, 1\[InvisibleComma]i]-Subscript[x, 1\[InvisibleComma]j]),
\[Epsilon](Subscript[T, 3]-1)Subscript[p, 1\[InvisibleComma]j] Subscript[x, 3\[InvisibleComma]i](Subscript[p, 2\[InvisibleComma]j]-Subscript[p, 2\[InvisibleComma]i]),
\[Epsilon](1/2-Subscript[p, 3\[InvisibleComma]i] Subscript[x, 3\[InvisibleComma]i]-Subscript[T, 3] Subscript[p, 1\[InvisibleComma]j] Subscript[p, 2\[InvisibleComma]j] Subscript[x, 1\[InvisibleComma]i] Subscript[x, 2\[InvisibleComma]i]+Subscript[p, 2\[InvisibleComma]j] Subscript[p, 3\[InvisibleComma]i] Subscript[x, 2\[InvisibleComma]j] Subscript[x, 3\[InvisibleComma]i]-Subscript[T, 2] Subscript[p, 2\[InvisibleComma]j] Subscript[p, 3\[InvisibleComma]j] Subscript[x, 2\[InvisibleComma]i] Subscript[x, 3\[InvisibleComma]j]+(Subscript[T, 3]-1)Subscript[p, 3\[InvisibleComma]j] Subscript[x, 3\[InvisibleComma]i](Subscript[T, 1] Subscript[p, 1\[InvisibleComma]j] Subscript[x, 1\[InvisibleComma]i]+Subscript[T, 2] Subscript[p, 2\[InvisibleComma]j] Subscript[x, 2\[InvisibleComma]i])+(Subscript[p, 1\[InvisibleComma]j] Subscript[x, 1\[InvisibleComma]j](Subscript[p, 2\[InvisibleComma]i] Subscript[x, 2\[InvisibleComma]i]-Subscript[p, 3\[InvisibleComma]i] Subscript[x, 3\[InvisibleComma]i])+Subscript[T, 1] Subscript[p, 1\[InvisibleComma]i] Subscript[x, 1\[InvisibleComma]i](Subscript[p, 3\[InvisibleComma]j] Subscript[x, 3\[InvisibleComma]j]-Subscript[p, 2\[InvisibleComma]j] Subscript[x, 2\[InvisibleComma]j])+(Subscript[T, 3]-1)Subscript[p, 1\[InvisibleComma]j] Subscript[x, 1\[InvisibleComma]j](Subscript[p, 2\[InvisibleComma]j] Subscript[x, 2\[InvisibleComma]i]-Subscript[T, 1] Subscript[p, 3\[InvisibleComma]j] Subscript[x, 3\[InvisibleComma]i]))/(Subscript[T, 1]-1)) ]]


(* ::Input::Initialization:: *)
\[ScriptCapitalL][Subscript[X, i_,j_][-1]]:=\!\(
\*SubsuperscriptBox[\(T\), \(3\), \(-1\)] \(\[DoubleStruckCapitalE][Plus[\[IndentingNewLine]
\*SubsuperscriptBox[\(\[Sum]\), \(\[Nu] = 1\), \(3\)]\((
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]i\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(i\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]i\)])\) + 
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]j\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(j\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]j\)])\) + \((
\*SubsuperscriptBox[\(T\), \(\[Nu]\), \(-1\)] - 1)\) 
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]i\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(i\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(j\), \(+\)]\)])\))\), \[IndentingNewLine]
\*SubsuperscriptBox[\(T\), \(2\), \(-1\)] \((
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] - 
\*SubsuperscriptBox[\(T\), \(1\), \(-1\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)])\), \[IndentingNewLine]\[Epsilon]\ 
\*SubsuperscriptBox[\(T\), \(1\), \(-1\)] \((\((
\*SubscriptBox[\(T\), \(3\)] - 1)\) 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] - \((
\*SubscriptBox[\(T\), \(3\)] - 1)\) 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)])\), \[IndentingNewLine]\[Epsilon] \((\(-1\)/2 + 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] - 
\*SubsuperscriptBox[\(T\), \(1\), \(-1\)] 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] - \((1 - 
\*SubsuperscriptBox[\(T\), \(1\), \(-1\)] - 
\*SubsuperscriptBox[\(T\), \(2\), \(-1\)])\) 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] - 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] - 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]j\)] + 
\*SubsuperscriptBox[\(T\), \(1\), \(-1\)] 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] - \((1 - 
\*SubsuperscriptBox[\(T\), \(2\), \(-1\)])\) 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] - 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] + 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]j\)] + 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]j\)] + \((1 - 
\*SubsuperscriptBox[\(T\), \(3\), \(-1\)])\) 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] \((
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]j\)] + 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] - 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] + \((2 - 
\*SubsuperscriptBox[\(T\), \(2\), \(-1\)])\) 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)])\) + \((
\*SubscriptBox[\(T\), \(1\)] \((1 - 
\*SubsuperscriptBox[\(T\), \(2\), \(-1\)])\) 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] - 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]i\)] + 
\*SubscriptBox[\(T\), \(1\)] 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(p\), \(2\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(2\[InvisibleComma]j\)] - 
\*SubsuperscriptBox[\(T\), \(2\), \(-1\)] \((
\*SubscriptBox[\(T\), \(3\)] - 1)\) 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] + 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]i\)] - 
\*SubscriptBox[\(T\), \(1\)] 
\*SubscriptBox[\(p\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(p\), \(3\[InvisibleComma]j\)] 
\*SubscriptBox[\(x\), \(1\[InvisibleComma]i\)] 
\*SubscriptBox[\(x\), \(3\[InvisibleComma]j\)])\)/\((
\*SubscriptBox[\(T\), \(1\)] - 1)\))\)\ ]]\)\)


(* ::Input::Initialization:: *)
\[ScriptCapitalL][Subscript[C, i_][\[CurlyPhi]_]]:=\!\(
\*SubsuperscriptBox[\(T\), \(3\), \(\[CurlyPhi]\)] \(\[DoubleStruckCapitalE][
\*SubsuperscriptBox[\(\[Sum]\), \(\[Nu] = 1\), \(3\)]
\*SubscriptBox[\(x\), \(\[Nu]\[InvisibleComma]i\)] \((
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]
\*SuperscriptBox[\(i\), \(+\)]\)] - 
\*SubscriptBox[\(p\), \(\[Nu]\[InvisibleComma]i\)])\) + \[Epsilon]\ \[CurlyPhi] \((
\*SubscriptBox[\(p\), \(3, i\)]\ 
\*SubscriptBox[\(x\), \(3, i\)] - 1/2)\)]\)\)


(* ::Input::Initialization:: *)
Subscript[vs, i_]:=Sequence[Subscript[p, 1,i],Subscript[p, 2,i],Subscript[p, 3,i],Subscript[x, 1,i],Subscript[x, 2,i],Subscript[x, 3,i]];
\[ScriptCapitalF][is__]:=\[DoubleStruckCapitalE][Sum[Subscript[\[Pi], \[Nu],i] Subscript[p, \[Nu],i],{i,{is}}, {\[Nu],3}]];
\[ScriptCapitalL][K_]:=CF[\[ScriptCapitalL]/@Features[K][[2]]];
vs[K_] := Union@@Table[{Subscript[vs, i]},{i,Features[K][[1]]}]



