Pensieve Header: A sample Lambda generated using TailScatteringTowardsTheHead.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2010-09"];
<< KnotTheory`
<< TailScatteringTowardsTheHead-Program.m

GD[Knot[10,165]]

gd = GD[Ar[3,1,+1], Ar[2,5,-1], Ar[6,4,+1]];
gd = GD[Ar[4,1,+1], Ar[7,2,-1], Ar[3, 6, +1], Ar[8,5,+1]];
gd=GD[Ar[6,1,-1],Ar[18,7,-1],Ar[8,3,1],Ar[2,17,1],Ar[14,5,1],Ar[16,9,1],Ar[10,15,1],Ar[4,11,1],Ar[13,20,1],Ar[19,12,1]];
{
gd,
n = Length[gd]
}

Draw[gd]

R[gd] // MatrixForm

Lambda[gd_] := Module[{arcs, r, n, j},
n = Length[gd];
arcs = Arcs[gd];
r = R[gd];
Table[
Inverse[Append[r, e[n+1, arcs[[gd[[j, 2]]]]]]].Append[x e[n, j], DR],
{j, n}
] // Transpose // Simplify
]

Inverse[Append[R[gd], e[n+1,1]]] // Simplify // MatrixForm

Lambda[gd] // MatrixForm

Inverse[Append[R[gd], e[n+1,1]]].Append[x IdentityMatrix[n], Table[DR, {n}]] // Simplify // MatrixForm

Append[R[gd], e[n+1,n+1]].Lambda[gd] // Simplify // MatrixForm