Help:=proc(): print(`GF2(x,y,t), GF2p(x,t,p), GF2pMoa(x,y,t,p)`):end:


#GF2(x,y,t): the weight-enumerator of the set
#of all words in {[1,0],[-1,0],[0,-1],[0,1]} where the weight of
#a word is t^lenght(w)*x^(current nubmber of #)*y^(#of E's)
GF2:=proc(x,y,t) local fD,fmD,fE,fmE,sol:

#F=1+(x+1/x+y+1/y)*t*F


sol:=
solve({
fD=t*x+ fD*t*x+ fmD*t*x+fE*t*x+fmE*t*x,
fmD=t/x+ fD*t/x+ fmD*t/x+fE*t/x+fmE*t/x,
fE=t*y+ fD*t*y+ fmD*t*y+fE*t*y+fmE*t*y,
fmE=t/y+ fD*t/y+ fmD*t/y+fE*t/y+fmE*t/y
},
{fD,fmD,fE,fmE});

factor(normal(1+subs(sol,fD)+subs(sol,fmD)+
subs(sol,fE)+subs(sol, fmE)
));

end:

#GF2p(x,y,t,p): the weight-enumerator of the set
#of all words in {[1,0],[-1,0],[0,-1],[0,1]} where the weight of
#a word is t^lenght(w)*x^(current nubmber of #)*y^(#of E's)
GF2p:=proc(x,y,t,p) local fD,fmD,fE,fmE,sol:

#F=1+(x+1/x+y+1/y)*t*F


sol:=
solve({
fD=t*x*p[1]+ fD*t*x*p[1]+ fmD*t*x*p[1]+fE*t*x*p[1]+fmE*t*x*p[1],
fmD=t/x*p[-1]+ fD*t/x*p[-1]+ fmD*t/x*p[-1]+fE*t/x*p[-1]+fmE*t/x*p[-1],
fE=t*y*p[2]+ fD*t*y*p[2]+ fmD*t*y*p[2]+fE*t*y*p[2]+fmE*t*y*p[2],
fmE=t/y*p[-2]+ fD*t/y*p[-2]+ fmD*t/y*p[-2]+fE*t/y*p[-2]+fmE*t/y*p[-2]
},
{fD,fmD,fE,fmE});

factor(normal(1+subs(sol,fD)+subs(sol,fmD)+
subs(sol,fE)+subs(sol, fmE)
));

end:

#GF2pMoa(x,y,t,p): the weight-enumerator of the set
#of all words in {[1,0],[-1,0],[0,-1],[0,1]} where the weight of
#a word is t^lenght(w)*x^(current nubmber of #)*y^(#of E's)
#Moa's hopeful  colleague's way
GF2pMoa:=proc(x,y,t,p) local fD,fmD,fE,fmE,sol,q:
q:=(1-p)/3;




sol:=
solve({
fD=t*x*p+ fD*t*x*p+ fmD*t*x*q+fE*t*x*q+fmE*t*x*q,
fmD=t/x*q+ fD*t/x*q+ fmD*t/x*p+fE*t/x*q+fmE*t/x*q,
fE=t*y*q+ fD*t*y*q+ fmD*t*y*q+fE*t*y*p+fmE*t*y*q,
fmE=t/y*q+ fD*t/y*q+ fmD*t/y*q+fE*t/y*q+fmE*t/y*p
},
{fD,fmD,fE,fmE});

factor(normal(1+subs(sol,fD)+subs(sol,fmD)+
subs(sol,fE)+subs(sol, fmE)
));

end: