Pensieve header: Analysis of k=2 invariants in QU.

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\SL2Portfolio"];
<< KnotTheory`
<< "SL2PortfolioProgram.m"

OverbayP2Data=Get["C:\\drorbn\\AcademicPensieve\\People\\Overbay\\OverbayP2Data.m"];

$p=5; $k=2; $U=QU;

SCθ[p_]:=Collect[ Cθ@(Subscript[𝕆, CU])[{y,a,x} ,p]/. {CU->Times, γ|ℏ->1}, ϵ, Simplify];
SQθ[p_]:=Collect[ Qθ@(Subscript[𝕆, QU])[{y,a,x} ,p]/. {QU->Times, γ|ℏ->1}, ϵ, Simplify];

(Subscript[𝔼[L_,Q_,P_], $k_]):=𝔼[L,Q,Series[Normal@P,{ϵ,0,$k}]];
(Subscript[(Subscript[𝔼, d_->r_])[L_,Q_,P_], $k_]):=(Subscript[𝔼, d->r])@@(Subscript[𝔼[L,Q,P], $k]);
𝔼3@𝔼[ω_,L_,Q_,Ps_]:=CF/@(Subscript[𝔼[L,(ω^(-1)) Q,(ω^(-1))((((ω^(-4))ϵ))^(-1+Range@Length@Ps)).Ps], $k]);
𝔼4@𝔼[L_,Q_,P_]:=Module[
{ω=((Normal[P])^(-1))/.ϵ->0,Ps=CoefficientList[P,ϵ]},
CF/@𝔼[ω,L,ω Q,(ω^(-3+4Range@Length@Ps))Ps]];
𝔼3@(Subscript[𝔼, sp___])[as___]:=𝔼3@𝔼[as]/.𝔼->(Subscript[𝔼, sp]);
𝔼4@(Subscript[𝔼, sp___])[as___]:=𝔼4@𝔼[as]/.𝔼->(Subscript[𝔼, sp]);

P[Knot[n_,k_]] := P[Knot[n,k]]=Module[{fname},
fname="../SL2Invariant/k=2/Data/"<>ToString[n]<>"_"<>ToString[k]<>".m";
Collect[𝔼3[Get[fname][[2,2]]][[3]] // Normal, ϵ, Simplify]
];
QP[K_Knot]:=QP[K]=CF@P[K];

H[p_]:=If[TrueQ@Simplify[p==(p/.T->1/T)],σ@@CoefficientList[Expand@Together[p]/.(T^(n_))/;n<0:>0,T], p];

MatrixForm[AllKnots[{3,7}] /. K_Knot :> {K,
ω=Factor[(((QP@K/.ϵ->0))^(-1))]; H@ω,
qp=Collect[QP@K/.{y->0},{ϵ,a},Factor]; CoefficientRules[Together[-1+ω qp/.{ϵ->(ω^2)ϵ, a->a/ω}], {ϵ,a}] /.{({1,0}->p_):>({1,0}->T p/(T-1))}/. ({k_,d_}->p_):>({k,d}->H@Factor[p]),
P1=Factor@Expand@Together[(*((T )/(((T-1))^2))*)(ω^3)Coefficient[qp/.a->-1/2,ϵ]]; H@P1,
OP2=K/.OverbayP2Data/.T->(T^(1/2)); H@OP2}]