(* pu4.m:  S. A. Fulling, Nov. 1995 (first version summer 1994) *)

Off[General::spell1]
Share[];
orderRules = {
   x1^(n1_)*x2^(n2_) :> x1^n2*x2^n1 /; n2 > n1,
   x1^(n1_)*x3^(n3_) :> x1^n3*x3^n1 /; n3 > n1,
   x2^(n2_)*x3^(n3_) :> x2^n3*x3^n2 /; n3 > n2,
   x1^(n1_)*x4^(n4_) :> x1^n4*x4^n1 /; n4 > n1,
   x2^(n2_)*x4^(n4_) :> x2^n4*x4^n2 /; n4 > n2,
   x3^(n3_)*x4^(n4_) :> x3^n4*x4^n3 /; n4 > n3
   };

qmax = 7  
max = 2(qmax+1)

link12 = Sum[t^(2j) c[j] x1^j x2^j, {j, 0, qmax}] +O[t]^max
link13 = link12 /. x2->x3;
link23 = link13 /. x1->x2;
link14 = link12 /. x2->x4;
link24 = link14 /. x1->x2;
link34 = link14 /. x1->x3;
point1 = Sum[t^(2j) c[j] x1^(2j), {j, 0, qmax}] + O[t]^max
point2 = point1 /. x1 -> x2;
point3 = point1 /. x1 -> x3;
point4 = point1 /. x1 -> x4;
pointpair12 = Sum[t^(4j) c[j]^2 x1^(2j) x2^(2j), 
                                  {j, 0, Floor[qmax/2]}] + O[t]^max
pointpair34 = pointpair12 //. {x1 -> x3, x2 -> x4};
angle3 = Sum[t^(4j) c[j]^2 x1^j x2^j x3^(2j),
                                  {j, 0, Floor[qmax/2]}] + O[t]^max
angle4 = angle3 /. x3 -> x4;
pointtriple = Sum[t^(6j) c[j]^3 x1^(2j) x2^(2j) x3^(2j), 
                                  {j, 0, Floor[qmax/3]}] + O[t]^max
linktriple = pointtriple;
pyramid = Sum[t^(6j) c[j]^3 x1^j x2^j x3^j x4^(3j), 
                                  {j, 0, Floor[qmax/3]}] + O[t]^max
linkpair = Sum[t^(4j) c[j]^2 x1^j x2^j x3^j x4^j, 
                                  {j, 0, Floor[qmax/2]}] + O[t]^max
pointquad = Sum[t^(8j) c[j]^4 x1^(2j) x2^(2j) x3^(2j) x4^(2j), 
                                  {j, 0, Floor[qmax/4]}] + O[t]^max
linkquad = pointquad; 

identity = link12*link13*link23*link14*link24*link34*
                                  point1*point2*point3*point4;
transpos = link12*link34*angle3*angle4*pointpair12*point3*point4;
threecycles = linktriple*pyramid*pointtriple*point4;
transposprs = link12*link34*linkpair^2*pointpair12*pointpair34;
cyclics = linkquad*linkpair*pointquad;

pu4series = (1/24)(identity + 6*transpos + 8*threecycles + 
                                  3*transposprs + 6*cyclics);
pu4temp = (Expand[Normal[pu4series] * x1^2 x2^2 x3^2 x4^2] //. 
                                 orderRules) / (x1^2 x2^2 x3^2 x4^2);
pu4 = Collect[pu4temp, Prepend[Table[c[qmax-i], {i,0,qmax}], t]]

pu4point = pu4 //. c[n_] -> 1
pu4line = pu4 //. {x1->1, x2->1, x3->1, x4->1}
pu4total = pu4line //. c[n_] -> 1

Save["pu4.out", pu4, pu4point, pu4line, pu4total]
Quit[]