Pensieve header: HOMFLYPT studies following arXiv://1707.07733.

<< KnotTheory`

?HOMFLYPT

H[K_] :=  HOMFLYPT[K][a,z]; H /@ AllKnots[7]

Factor /@ H /@ AllKnots[7] /. z->0

n=12;
Ks=AllKnots[n];
M=Table[
D[
Coefficient[HOMFLYPT[K][a,z], z,0],
{a,j}
] /. a->1,


{j,0,2n}, {K,Ks}];
MatrixRank[M]

n=11;
Ks=AllKnots[{0,n}];
Hs=Table[
Coefficient[HOMFLYPT[K][a,z], z,0],
{K,Ks}];
{Length[Ks], Length[Union[Hs]]}