Pensieve header: A table of expanded MVA values for some small links. For a test of finite-typeness, see MultivariableAlexander-Testing.nb at AcademicPensieve/2009-03 and the bottom of this notebook.

<< KnotTheory`

Print[{
#, DrawMorseLink[#],
Expand[
Normal[Series[
MultivariableAlexander[#][t] /. t[i_] :> Exp[h (Subscript[x, i])],
{h, 0,3}
]] /. h -> 1
]
}]& /@ AllLinks[{2,8}];

Flip[X[i_,j_,k_,l_]] := If[l==j+1 || j-l>1, X[j,k,l,i], X[l,i,j,k]];
VCube[pd_, l_List] := Module[
{f},
Expand[pd*Times @@ ((1-f[#])& /@ l)] //. pd1_PD*f[i_] :> MapAt[Flip, pd1, i]
];

Print[# -> Series[VCube[PD[#], {5}] /. pd_PD :> MultivariableAlexander[pd][t] /. t[i_] -> E^(h x[i]), {h, 0, 0}]]& /@AllLinks[8];

Print[# -> Series[VCube[PD[#], {4,6}] /. pd_PD :> MultivariableAlexander[pd][t] /. t[i_] -> E^(h x[i]), {h, 0, 1}]]& /@AllLinks[8];