(* pu6.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,
   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,
   x1^(n1_)*x5^(n5_) :> x1^n5*x5^n1 /; n5 > n1,
   x2^(n2_)*x5^(n5_) :> x2^n5*x5^n2 /; n5 > n2,
   x3^(n3_)*x5^(n5_) :> x3^n5*x5^n3 /; n5 > n3,
   x4^(n4_)*x5^(n5_) :> x4^n5*x5^n4 /; n5 > n4,
   x1^(n1_)*x6^(n6_) :> x1^n6*x6^n1 /; n6 > n1,
   x2^(n2_)*x6^(n6_) :> x2^n6*x6^n2 /; n6 > n2,
   x3^(n3_)*x6^(n6_) :> x3^n6*x6^n3 /; n6 > n3,
   x4^(n4_)*x6^(n6_) :> x4^n6*x6^n4 /; n6 > n4,
   x5^(n5_)*x6^(n6_) :> x5^n6*x6^n5 /; n6 > n5
   };

qmax = 5  
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;
link15 = link12 /. x2->x5;
link25 = link15 /. x1->x2;
link35 = link15 /. x1->x3;
link45 = link15 /. x1->x4;
link16 = link12 /. x2->x6;
link26 = link16 /. x1->x2;
link36 = link16 /. x1->x3;
link46 = link16 /. x1->x4;
link56 = link16 /. x1->x5;
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;
point5 = point1 /. x1 -> x5;
point6 = point1 /. x1 -> x6; 
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};
pointpair56 = pointpair12 //. {x1 -> x5, x2 -> x6};
pointpair45 = pointpair34 /. x3 -> x5;
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;
angle51 = angle3 /. x3 -> x5;
angle53 = angle51 //. {x1 -> x3, x2 -> x4};
angle61 = angle51 /. x5 -> x6;
angle63 = angle53 /. x5 -> x6;
angle64 = angle61 //. {x1 -> x4, x2 -> x5};
pointtriple = Sum[t^(6j) c[j]^3 x1^(2j) x2^(2j) x3^(2j), 
                                     {j, 0, Floor[qmax/3]}] + O[t]^max
linktriple = pointtriple;
newpointtriple = pointtriple //. {x1 -> x4, x2 -> x5, x3 -> x6};
newlinktriple = newpointtriple;
biglinktriple = Sum[t^(6j) c[j]^3 x1^j x2^j x3^j x4^j x5^j x6^j, 
                                     {j, 0, Floor[qmax/3]}] + O[t]^max
pyramid4 = Sum[t^(6j) c[j]^3 x1^j x2^j x3^j x4^(3j), 
                                     {j, 0, Floor[qmax/3]}] + O[t]^max
pyramid5 = pyramid4 /. x4 -> x5;
pyramid6 = pyramid4 /. x4 -> x6;
linkpair13 = Sum[t^(4j) c[j]^2 x1^j x2^j x3^j x4^j, 
                                     {j, 0, Floor[qmax/2]}] + O[t]^max
linkpair15 = linkpair13 //. {x3 -> x5, x4 -> x6};
linkpair35 = linkpair15 //. {x1 -> x3, x2 -> x4};
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;
quadpyr5 = Sum[t^(8j) c[j]^4 x1^j x2^j x3^j x4^j x5^(4j), 
                                     {j, 0, Floor[qmax/4]}] + O[t]^max
quadpyr6 = quadpyr5 /. x5 -> x6;
pyrpair = Sum[t^(12j) c[j]^6 x1^(2j) x2^(2j) x3^(2j) x4^(3j) x5^(3j), 
                                     {j, 0, Floor[qmax/6]}] + O[t]^max
pointquint = Sum[t^(10j) c[j]^5 x1^(2j) x2^(2j) x3^(2j) x4^(2j) x5^(2j), 
                                     {j, 0, Floor[qmax/5]}] + O[t]^max
linkquint = pointquint; 
quintpyr = Sum[t^(10j) c[j]^5 x1^j x2^j x3^j x4^j x5^j x6^(5j), 
                                     {j, 0, Floor[qmax/5]}] + O[t]^max
quadpyrpair = Sum[t^(8j) c[j]^4 x1^j x2^j x3^j x4^j x5^(2j) x6^(2j), 
                                     {j, 0, Floor[qmax/4]}] + O[t]^max
pointsex = Sum[t^(12j) c[j]^6 x1^(2j) x2^(2j) x3^(2j) x4^(2j) x5^(2j) x6^(2j), 
                                     {j, 0, Floor[qmax/6]}] + O[t]^max
linksex = pointsex; 

identity = link12*link13*link23*link14*link24*link34*link15*link25*link35*
     link45*link16*link26*link36*link46*link56*
     point1*point2*point3*point4*point5*point6;
transpos = link12*link34*link35*link45*link36*link46*link56*
     angle3*angle4*angle51*angle61*pointpair12*point3*point4*point5*point6;
threecycles = linktriple*pyramid4*pyramid5*pyramid6*link45*link46*link56*
     pointtriple*point4*point5*point6;
transposprs = link12*link34*linkpair13^2*angle51*angle53*angle61*angle63*
     link56*pointpair12*pointpair34*point5*point6;
fourcycles = linkquad*linkpair13*quadpyr5*quadpyr6*link56*
     pointquad*point5*point6;
transpthreecyc = linktriple*link45*pyrpair*pyramid6*angle64*
     pointtriple*pointpair45*point6;
fivecycles = linkquint^2*pointquint*quintpyr*point6;
transpostrip = link12*link34*link56*linkpair13^2*linkpair15^2*linkpair35^2*
     pointpair12*pointpair34*pointpair56;
transpfourcyc = linkquad*linkpair13*quadpyrpair^2*link56*
     pointquad*pointpair56;
threecycprs = linktriple*newlinktriple*biglinktriple^3*
     pointtriple*newpointtriple;
cyclics = linksex^2*biglinktriple*pointsex;

pu6series = (1/720)(identity + 15*transpos + 40*threecycles + 
     45*transposprs + 90*fourcycles + 120*transpthreecyc + 
     144*fivecycles + 15*transpostrip + 90*transpfourcyc + 
     40*threecycprs + 120*cyclics);
pu6temp = (Expand[Normal[pu6series] * x1^2 x2^2 x3^2 x4^2 x5^2 x6^2] //.
     orderRules)/(x1^2 x2^2 x3^2 x4^2 x5^2 x6^2);
pu6 = Collect[pu6temp, Prepend[Table[c[qmax-i], {i,0,qmax}], t]]

pu6point = pu6 //. c[n_] -> 1
pu6line = pu6 //. {x1->1, x2->1, x3->1, x4->1, x5->1, x6->1}
pu6total = pu6line //. c[n_] -> 1

Save["pu6.out", pu6, pu6point, pu6line, pu6total]
Quit[]