(*inverse stereographic projection*)
s[x_, y_] := {(2*x)/(1 + x*x + y*y), (2*y)/(1 + x*x + y*y), 1 - 2/(1 + x*x + y*y)};

(*Here is the basic 2-point interaction function.
  We are using R2*)

f[x1_,y1_,x2_,y2_]:=Power[1- s[x1,y1].s[x2,y2],-1]

Clear[a,b,c,d,e];


(*Omega'_12 matches Java *)

a1=432/512 (1-a) + 416/512 a;
b1=16/512 b;
c1=-32/512 (1-c) + 16/512 c
d1=-348/512 (1-d) + -465/512 d;
e1=64/512 e

(*Omega'_11: matches Java*)

a1=+27/32 a + 498/512 (1-a);
b1=16/512 b;
c1=-32/512 (1-c) + 16/512 c
d1=-348/512 (1-d) + -465/512 d;
e1=64/512 e

(*Omega'_32: matches Java*)

a1=432/512 (1-a) + 416/512 a;
b1=16/512 b;
c1=-16/512 (1-c) + 32/512 c;
d1=-348/512 (1-d) + -465/512 d;
e1=64/512 e

(*Omega'_31: matches Java*)

a1=+27/32 a + 498/512 (1-a);
b1=16/512 b;
c1=-16/512 (1-c) + 32/512 c
d1=-348/512 (1-d) + -465/512 d;
e1=64 e/512;


P=Numerator[Together[f[a1+e1,b1,c1,d1] + f[-a1+e1, b1, c1, d1] - 
 f[a1, b1, 0, d1] - f[-a1, b1, 0, d1]]];

MonoSeq[u_]:=(
aa1=u Power[a b c d e,100];
aa2=Table[aa1[[j,2]],{j,1,5}];
aa2-100)

P20=D[P,{c,2}];
P02=D[P,{e,2}];
P11=D[D[P,c],e];
Q=Expand[P20 P02-P11 P11]

Q=Expand[zzz Q];
LQ=Table[{
Q[[j]]/Q[[j,1]],
MonoSeq[Q[[j]]/Q[[j,1]]],Q[[j,1]]},{j,1,Length[Q]}];
Q=Expand[Q/zzz];
LQ=Sort[LQ];
LQ=Table[{LQ[[j,2]],LQ[[j,3]]},{j,1,Length[LQ]}];