(* ::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.                                                         *)
(************************************************************************)



SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\WKO4"];
<< WKO4.m


SeedRandom[0];
Subscript[\[Zeta], e]=Es[\[LeftAngleBracket]x->RandomLieSeries[{x,y}], y->RandomLieSeries[{x,y}]\[RightAngleBracket], RandomCWSeries[{x,y}]];
Subscript[\[Zeta], f]=Es[\[LeftAngleBracket]x->RandomLieSeries[{x,y}], y->RandomLieSeries[{x,y}]\[RightAngleBracket], RandomCWSeries[{x,y}]]


Subscript[\[Rho]\[Rho], 2][V_] := Rs[x,y]**(V//(-1)^deg);
(Subscript[\[Zeta], e]\[Congruent](Subscript[\[Zeta], e]//Subscript[\[Rho]\[Rho], 2]//Subscript[\[Rho]\[Rho], 2]))@{8}


Subscript[\[Rho], 3][\[Zeta]_Es] := \[Zeta] // dS[y] // d\[CapitalDelta][y,y,z] // dm[x,z,x] // d\[Sigma][{x,y}->{y,x}];
{Subscript[V, 0]@{2}, (Subscript[V, 0] // Subscript[\[Rho], 3])@{2}, (Subscript[V, 0] // Subscript[\[Rho], 3]// Subscript[\[Rho], 3]// Subscript[\[Rho], 3])@{2}}


\[Theta][x_,s_] := Module[{y}, \[CapitalTheta]s[x,y,-s] // dS[y] // dm[x,y,x]];
\[Theta][1,1]@{6}


w1=Es[\[LeftAngleBracket]x->LS@0, y->LS@0\[RightAngleBracket], CWS[CW[x]/12-CW[y]/12]-(2Cap[[2]]//t\[CapitalDelta][x,x,y])]


Subscript[\[Rho]\[Rho], 3][V_] := Subscript[\[Rho], 3][V**\[CapitalTheta]s[x,y,-1/4]**w1]**w1^-1**\[CapitalTheta]s[x,y,1/4]



