Once[<< KnotTheory`]
SetDirectory["C:\\drorbn\\AcademicPensieve\\Talks\\MoscowByWeb-2104"];
<< Alpha.m
<< Gamma.m

MultivariableAlexander[PD[X[1,12,2,13], X[13,2,6,3], X[8,4,9,3], X[4,10,1,9],X[6,17,7,16],X[15,8,16,7],X[14,10,15,11],X[11,17,12,14]]/. j_Integer/;j>5:>j-1][T]/.T[j_]:>(Subscript[T, j])

𝒜[pd_PD]:=𝒜[List@@(pd/.X[i_,j_,k_,l_]:>If[PositiveQ[X[i,j,k,l]], (Subscript[X, i,j/.{1->0},k/.{1->0},l]),(Subscript[(OverBar[X]), i,j,k/.{1->0},l/.{1->0}])])];
𝒜[L_Knot|L_Link]:=𝒜[PD@L];
𝒜P[L_Knot|L_Link|L_PD]:=Coefficient[𝒜[L][[4]], Wedge[]]/.Thread[
(Subscript[τ, #])&/@(Skeleton@L/.Loop->Alternatives)->Table[t[i],{i,Length@Skeleton@L}]
]

𝒜[Knot[3,1]]

𝒜P[Knot[3,1]]

Table[Simplify[((𝒜P[L]/(1-t[1]))/(MultivariableAlexander[L][t]))],{L,AllLinks[{2,9}]}]

Γ[pd_PD]:=Γ[List@@(pd/.X[i_,j_,k_,l_]:>If[PositiveQ[X[i,j,k,l]], (Subscript[X, i,j/.{1->0},k/.{1->0},l]),(Subscript[(OverBar[X]), i,j,k/.{1->0},l/.{1->0}])])];
Γ[L_Knot|L_Link]:=Γ[PD@L];
ΓP[L_Knot|L_Link|L_PD]:=Γ[L][[4]]/.Thread[
(Subscript[τ, #])&/@(Skeleton@L/.Loop->Alternatives)->Table[t[i],{i,Length@Skeleton@L}]
]

Γ[Knot[3,1]]

ΓP[Knot[3,1]]

Table[Simplify[((ΓP[L]/(1-t[1]))/(MultivariableAlexander[L][t]))],{L,AllLinks[{2,9}]}]

Γ@Link[9,NonAlternating,27]

𝒜@Link[9,NonAlternating,27]