(* ::Package:: *)

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SetDirectory["C:\\drorbn\\AcademicPensieve\\2013-10"];
<< "../2013-05/FreeLie.m"
$SeriesShowDegree=3; $SeriesCompareDegree = 5;
<< "../2013-05/muCalculus.m"


\[Mu]Coefficients[expr_] := Flatten[Last[Reap[Collect[expr, _LW|_CW, Sow[#]&]]]];
\[Mu]Coefficients[l_List] := \[Mu]Coefficients /@ l;


\[Alpha]=MakeLieSeries[{"1","2"},\[Alpha]s];
\[Beta]=MakeLieSeries[{"1","2"},\[Beta]s];
\[Gamma]=MakeCWSeries[{"1","2"},\[Gamma]s];
V=M[{1->\[Alpha], 2->\[Beta]}, \[Gamma]];
\[Kappa]s[d_, 1] := If[OddQ[d], 0, \[Kappa]s[d]];
\[Kappa]=MakeCWSeries[{"1"},\[Kappa]s];
Unprotect[C]; C=M[{1->MakeLieSeries[0]}, \[Kappa]];


HardR4[d_, V_] := Module[{lhs=SuperPlus[R][2,3]**SuperPlus[R][1,3]**V,rhs = V**(SuperPlus[R][1,3] // d\[CapitalDelta][1,1,2])},
{lhs[1]@d-rhs[1]@d, lhs[2]@d-rhs[2]@d, lhs[3]@d-rhs[3]@d, lhs[W]@d-rhs[W]@d}
];
TwistEq[d_, V_] := Module[{lhs=V**\[CapitalTheta][1,2],rhs = SuperPlus[R][1,2]**(V // d\[Sigma][{1,2}->{2,1}])},
{lhs[1]@d-rhs[1]@d, lhs[2]@d-rhs[2]@d, lhs[W]@d-rhs[W]@d}
];
UnitarityEq[d_, V_] := Module[{lhs=V**(V // dA[1] // dA[2]),rhs = d\[Epsilon][1]\[Union]d\[Epsilon][2]},
{lhs[1]@d-rhs[1]@d, lhs[2]@d-rhs[2]@d, lhs[W]@d-rhs[W]@d}
];
CapEq[d_, V_, C_] := Module[{lhs=V**(C // d\[CapitalDelta][1,1,2])  // dc[1] // dc[2],rhs = C\[Union](C//d\[Sigma][1,2])},
{lhs[W]@d-rhs[W]@d}
];
VerticalFlipEq[d_, V_] := Module[{lhs=V**(V // dS[1] // dS[2]),rhs = SuperPlus[R][1,2]},
{lhs[1]@d-rhs[1]@d, lhs[2]@d-rhs[2]@d, lhs[W]@d-rhs[W]@d}
];



