(**This function computes the symbolic bound on the
     6th derivatives of the pair functions.  This is the bound
     used in chapter 9 of the paper.**)

<<derivatives2

PolyNorm[f_]:=(
ff1=Table[f[[j]],{j,1,Length[f]}];
{x1,y1,x2,y2}={1,1,1,1};
g2=Abs[ff1];
g3=Sum[g2[[j]],{j,1,Length[g2]}];
Clear[x1,y1,x2,y2];
g3)

UpperBound[L_]:=(
f1=SymbolicDerivativeG[L];
f2=Expand[Numerator[f1]];
PolyNorm[f2])

aa6:={
{1,1,1,1,1,1},
{1,1,1,1,1,2},
{1,1,1,1,1,3},
{1,1,1,1,1,4},
{1,1,1,1,2,2},
{1,1,1,1,3,3},
{1,1,1,1,4,4},
{1,1,1,2,2,2},
{1,1,1,3,3,3},
{1,1,1,4,4,4},
{1,1,1,1,2,3},
{1,1,1,1,2,4},
{1,1,1,1,3,4},
{1,1,1,2,2,3},
{1,1,1,2,2,4},
{1,1,1,3,3,4},
{1,1,1,2,3,4},
{1,1,2,2,3,3},
{1,1,2,2,3,4}}

UpperBound[aa6[[2]]]