# Polynomial in $GF(p^2)$

Hello, I have a finite field $K=GF(p^2)$ and the polynomial ring $R=K[x,y]$. They are defined as such

```
p = 11;
K = GF(p^2,'t');
K.inject_variables();
R.<e1,e2> = K[];
f = (-4*t + 3)*e1*e2 + (2*t + 4)*e2^2 + (2*t - 4)*e1 + (-5*t + 3)
```

I would like to know if it is possible to group/order all the terms with respect to `t`

instead of `e1`

and `e2`

. That is, I would like to see

```
g = -4*e1*e2 + 2*e2^2 + 2*e1 - 5;
h = 3*e1*e2 + 4e2^2 + 4*e1 + 3;
```

such that

```
g*t + h == f
```

Thanks for your help!