Pensieve header: Computation with Huan Vo regarding Stavros’ “Planar Limit”.

<<KnotTheory`

PlanarLimit[knot_][a_]:=HOMFLYPT[knot][a,0]
(* the planar limit of a knot *)
PL[P_,Q_,a_]:=PlanarLimit[Mirror[TorusKnot[P,Q]]][a]

HOMFLYPT[PD[Loop[1],Loop[2]]][a,z]

HOMFLYPT[Link[2,Alternating,1]][a,z]

HOMFLYPT[#][a,z]& /@ AllKnots[{3,5}]

PlanarLimit[#][a]& /@ AllKnots[{3,10}] // Union // Length

Conway[#][a]& /@ AllKnots[{3,10}] // Union // Length

D[Conway[#][a], a, a,a]& /@ AllKnots[{3,10}] // Union // Length

D[Conway[#][a], a, a,a]& /@ AllKnots[{3,10}]

CE=GatherBy[AllKnots[{3,10}], Conway[#][z]&]

CE /. K_Knot :> PlanarLimit[K][a]