Pensieve header: Formula testing for the future double-tree paper; continued pensieve://2013-11/.

Double-Tree Formula Testing

SetDirectory["C:\\drorbn\\AcademicPensieve\\2013-10"];
<< "../2013-05/FreeLie.m"
<< "../2013-05/muCalculus.m"
<< "WKOSolution8-0.m"

α=MakeLieSeries[{"1","2"},αs]; β=MakeLieSeries[{"1","2"},βs];
γ=MakeCWSeries[{"1","2"},γs];
V=M[{1->α, 2->β}, γ];
κs[d_, 1] := If[OddQ[d], 0, κs[d]]; κ=MakeCWSeries[{"1"},κs];
Unprotect[C]; C=M[{1->MakeLieSeries[0]}, κ];
$SeriesShowDegree=5; $SeriesCompareDegree = 8;

{V,C // dc[1]}

The Hard R4 Equation

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

The Twist Equation

V**Θ[1,2] ≡ (SuperPlus[R])[1,2]**(V // dσ[{1,2}->{2,1}])

The Unitarity Equation

V**(V // dA[1] // dA[2]) ≡ dϵ[1]⋃dϵ[2]

The Cap Equation

(V**(C // dΔ[1,1,2])  // dc[1] // dc[2]) ≡ (C⋃(C//dσ[1,2])// dc[1] // dc[2])

The Vertical Flip Equation

V**(V // dS[1] // dS[2]) ≡ (SuperPlus[R])[1,2]