Pensieve header: Computing Θ on random rotational virtual knots.

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\Theta"];
Once[<<Theta.m]

RandomVK[n_]:={Prepend[#,2RandomInteger[1]-1]&/@Partition[PermutationList[RandomPermutation[2n],2n],2],
Table[RandomInteger[{-2,2}],2n+1]};

RandomVK[3]

(PolyPlot[Θ[#],ImageSize->Tiny])&/@Table[RandomVK[10],20]

Rev[{X_,φ_}]:=Module[{n=Length@X}, {Replace[{s_,i_,j_}:>{s,2n+1-i,2n+1-j}]/@X,Reverse[PadRight[-φ,2n+1]]}]

K=Rot@Knot[10,100]
Rev@K
{PolyPlot@Θ@K,PolyPlot@Θ@Rev@K}

Union@Table[Θ@Rot@K==Θ@Rev@Rot@K, {K, AllKnots[{3,10}]}]

K=RandomVK[10]
Rev@K
{PolyPlot@Θ@K,PolyPlot@Θ@Rev@K}