In [1]: a = galois.Poly.Random(5); a
Out[1]: Poly(x^5 + x^2, GF(2))

In [2]: a.field
Out[2]: <class 'galois.GF(2, primitive_element='1', irreducible_poly='x + 1')'>

In [3]: GF = galois.GF(2**8)

In [4]: b = galois.Poly.Random(5, field=GF); b
Out[4]: Poly(101x^5 + 80x^4 + 239x^3 + 22x^2 + 35x + 108, GF(2^8))

In [5]: b.field
Out[5]: <class 'galois.GF(2^8, primitive_element='x', irreducible_poly='x^8 + x^4 + x^3 + x^2 + 1')'>