Lets define a field F.<t> = GF(2^n)
now i want to define a variable points of the form x1+x2*t+...+xn*t^(n-1) and then solving equation with this by comparing coefficients of t^i.

Now I am defining R= PolynomialRing(ZZ,'x',n) c=R.gens() R=R.quotient_ring([c[i]^2-c[i] for i in range(0,n)]) then i get n variables but if I write x= sum(c[i]*t^i for i in (0,n)) I get the parent of x is R. and I am unable to collect the coefficients of t^i. after defining y and z in the same way. if I do X=x+y+z then I am getting the value as a Ring element with monomials in xi's and coefficients in F as X in a Ring element.

Can anyone suggest any way to get the results as f1+f2*t+f3*t^2+...+fn*t^(n-1) and then collect fi's where fi's are functions in the variables xi's.