(* ::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".                                               *)
(*                                                                      *)
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(* to using the Evaluate Initialization Cells menu command in the front *)
(* end.                                                                 *)
(*                                                                      *)
(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
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path="C:/drorbn/AcademicPensieve/";SetDirectory[path<>"2015-08/LesDiablerets-1508"];
Get[path<>"Projects/WKO4/FreeLie.m"];
Get[path<>"Projects/WKO4/AwCalculus.m"];
x=LW@"x"; y=LW@"y"; u=LW@"u";
$SeriesShowDegree = 6;


{F=LS[{x,y}, Fs], G=LS[{x,y}, Gs]}; Fs["y"]=1/2;
SeriesSolve[{F,G},
\[HBar]^-1 (LS[x+y]-BCH[y,x]\[Congruent]F-G-Ad[-x][F]+Ad[y][G])\[And]Subscript[div, x][F]+Subscript[div, y][G]\[Congruent]1/2 Subscript[tr, u][adSeries[ad/(E^ad-1), x][u]+adSeries[ad/(E^ad-1), y][u]-adSeries[ad/(E^ad-1), BCH[x,y]][u]]];
{F,G}  (* Can raise degree to 13 *)


\[CapitalPhi]s[2,1]=\[CapitalPhi]s[3,1]=\[CapitalPhi]s[3,2]=0;\[CapitalPhi]s[3,1,2]=1/24; \[CapitalPhi]=DKS[3, \[CapitalPhi]s];
SeriesSolve[\[CapitalPhi], (\[CapitalPhi]^\[Sigma][3,2,1]\[Congruent]-\[CapitalPhi])\[And](\[CapitalPhi]**\[CapitalPhi]^\[Sigma][1,23,4]**\[CapitalPhi]^\[Sigma][2,3,4]\[Congruent]\[CapitalPhi]^\[Sigma][12,3,4]**\[CapitalPhi]^\[Sigma][1,2,34])];
\[CapitalPhi] (* Can raise degree to 10 *)


R=DKS[t[1,2]/2];
Subscript[Z, B] = (-\[CapitalPhi])^\[Sigma][13,2,4]**\[CapitalPhi]^\[Sigma][1,3,2]**R^\[Sigma][2,3]**(-\[CapitalPhi])^\[Sigma][1,2,3]**\[CapitalPhi]^\[Sigma][12,3,4];
Subscript[Z, B]@{4}



