This is a start of an implementation of Jager' s state model for the Conway polynomial, following Chmutov' s talk in Oberwolfach

SetDirectory["C:/drorbn/projects/KnotTheory/svn/trunk/"]

<< KnotTheory`

pd=PD[Knot[5,2]]

List @@ Expand[Times @@ (pd /. x_X :> 1+x)]

s=X[3,8,4,9] X[5,10,6,1] X[9,6,10,7]

Union @@ s

Position[s, First[Union@@s]][[1,2]]

SetAttributes[p, Orderless]

(s /. X[i_,j_,k_,l_] :> If[PositiveQ[X[i,j,k,l]], p[i,l]p[j,k], -p[i,j]p[k,l]]) //. p[a_,b_]p[b_,c_] :> p[a,c]