KnotTheoryPath = "~/projects/KnotTheory/trunk/";
AppendTo[$Path, KnotTheoryPath];

<<KnotTheory`

CheckIdentity1[nn_][KK_]:=Chop[N[QuantumKnotInvariant[A1,Irrep[A1][{2nn-2}]][KK][Exp[(2π I)/(8nn-4)]]-2 (-1)^(1+Ceiling[nn/2]) QuantumKnotInvariant[(Subscript[D, nn-1]),Irrep[(Subscript[D, nn-1])][UnitVector[nn-1,nn-1]]][KK][-Exp[-((2π I)/(4nn-2))]]]]

CheckIdentity1[5]/@{Knot[0,1],Knot[3,1],Knot[5,1]}

Table[CheckIdentity1[n][Knot[5,2]],{n,5,6}]

CheckIdentity1[7][Knot[3,1]]

CheckIdentity2[nn_][KK_]:=Chop[N[QuantumKnotInvariant[A1,Irrep[A1][{2}]][KK][Exp[(2π I)/(8nn-4)]]-QuantumKnotInvariant[(Subscript[D, nn-1]),Irrep[(Subscript[D, nn-1])][UnitVector[nn-1,1]]][KK][-Exp[-((2π I)/(4nn-2))]]]]

CheckIdentity2[5][Knot[0,1]]

CheckIdentity2[5]/@{Knot[0,1],Knot[3,1],Knot[3,1]}

Table[CheckIdentity2[n][Knot[5,2]],{n,5,6}]