Pensieve header: Simplifying the WKO equations written in MGA language.

Simplifying the Equations

SetDirectory["C:\\drorbn\\AcademicPensieve\\2013-05"];
<< FreeLie.m
$SeriesShowDegree=3; $SeriesCompareDegree = 6;
<< muCalculus.m

α=RandomLieSeries[{"1","2"}];
β=RandomLieSeries[{"1","2"}];
γ=RandomCWSeries[{"1","2"}];
V=M[{1->α, 2->β}, γ];
κ=RandomCWSeries[{"1"}];
Unprotect[C]; C=M[{1->MakeLieSeries[0]}, κ];
{V,C}

HardR4[d_, V_] := Module[{lhs=(SuperPlus[R])[2,3]**(SuperPlus[R])[1,3]**V,rhs = V**((SuperPlus[R])[1,3] // dΔ[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**Θ[1,2],rhs = (SuperPlus[R])[1,2]**(V // dσ[{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 = dϵ[1]⋃dϵ[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 // dΔ[1,1,2])  // dc[1] // dc[2],rhs = C⋃(C//dσ[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}
];

l1=(SuperPlus[R])[2,3]**(SuperPlus[R])[1,3]**V

L1=(SuperPlus[ρ])[2,3]⋃(SuperPlus[ρ])[1,4]⋃(V//tσ[1,5]//tσ[2,6]) // hm[3,4,3] // tha[1,1] // tm[1,5,1] // tha[2,2] // tm[2,6,2]

l1≡L1

r1=V**((SuperPlus[R])[1,3] // dΔ[1,1,2])

R1=V⋃((SuperPlus[ρ])[4,3] // tΔ[4,4,5]) // tm[1,4,1] // tm[2,5,2]

r1≡R1