(* pl3.m:  S. A. Fulling, Nov. 1995 (first version summer 1994) *)

Off[General::spell1]
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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
   }

qmax = 8
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
point1 = Sum[t^(2j) c[j] x1^(2j), {j, 0, qmax}] + O[t]^max
point2 = point1 /. x1 -> x2
point3 = point1 /. x1 -> x3

identity = link12*link13*link23*point1*point2*point3
pl3temp = (Expand[Normal[identity] * x1^2 x2^2 x3^2] //.  
                                   orderRules) / (x1^2 x2^2 x3^2)
pl3 = Collect[pl3temp, Prepend[Table[c[qmax-i], {i,0,qmax}], t]]

pl3point = pl3 //. c[n_] -> 1
pl3line = pl3 //. {x1->1, x2->1, x3->1}
pl3total = pl3line //. c[n_] -> 1

Save["pl3.out", pl3, pl3point, pl3line, pl3total]
Quit[]