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Maybe You are right, so I'll write it more clearly (I hope).

Let GF(2^4)={0, 1, a, a+1, a^2, a^2+1, a^2+a, a^2+a+1, a^3, a^3+1, a^3+a, a^3+a+1, a^3+a^2, a^3+a^2+1, a^3+a^2+a, a^3+a^2+a+1} and a^4+a+1=0.

Let T:= x*([c^2((y/x)^4+(y/x))+c^2(1+c+c^2)((y/x)^3+(y/x))]/[(y/x)^4+c(y/x)^2+1])+(xy)^(1/2),

where c is constant in GF(16) (for example c=a^2+a). Convention: if x=0 then y/x=0 (custom_divide).

Now I want to calculate all values of the function T:

x=0            y=0            T=...
x=0            y=1            T=...
x=0            y=a            T=...
...
x=a^3+a^2+a+1  y=a^3+a^2+1    T=...
x=a^3+a^2+a+1  y=a^3+a^2+a    T=...
x=a^3+a^2+a+1  y=a^3+a^2+a+1  T=...

I've to define this function T with this constant c.