Pensieve header: Understanding Rot120 / Triality.

Rot120 / Triality

SetDirectory["C:\\drorbn\\AcademicPensieve\\2013-11\\DoubleTree"];
<< "../../2013-05/FreeLie.m"
<< "muCalculus.m"
<< "../../2013-10/WKOSolution8-1.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 = 6;
{V,C // dc[1]}

V // Rot120

V≡(V // Rot120 // Rot120 // Rot120)

quo=(V//dA[1,2])**(V // Rot120)

V**((SuperPlus[R])[1,2] // dP[12,3])

(((SuperPlus[R])[1,2] // dP[12,3])**V) ≡ (V**((SuperPlus[R])[1,2] // dP[12,3]))

(((SuperPlus[R])[1,2] // dP[12,3])**quo) ≡ (quo**((SuperPlus[R])[1,2] // dP[12,3]))

Θ[1,2,-1/2]

Θ[1,2,-1/2]//dm[1,2,2]

Vpp=(V**Θ[1,2,-1]**(dϵ[1]⋃(Θ[1,2,-1/2]//dm[1,2,2]))) // Rot120 // Rot120

$SeriesShowDegree=6; (V//dA[1,2])**Vpp

((V)//dA[1,2])**Vpp**((C**C)//dP[12])

C**C

{(48/32), (5760/3072), (362880/184320)}