# Extension field arithmetic

code:

```
p=(2^3) ; extension field over(2^3)
F.<a>=GF(2^3);F.modulus();#F third degree irreducible polynomial (x^3+x+1)
R.<x>=F[];#R generate extension field (2^3)^2
K.<b>=F.extension(x^2+(a^2+a+1)*x+a^2); second degree irreducible polynomial over (2^3)^2
R.<z>=PolynomialRing(K) ;
f3= z + (a^2 + 1)*b + a + 1; polynomial obtained after execution of program
from the above polynomial i want to separate out terms (a^2+1) which is attached with b and (a+1)
as i want my result in following manner ***(a+1 , a^2+1)***.
```

Thanks