galois.FieldArray.irreducible_poly

class property galois.FieldArray.irreducible_poly : Poly

The irreducible polynomial \(f(x)\) of the Galois field \(\mathrm{GF}(p^m)\).

Notes¶

The irreducible polynomial is of degree \(m\) over \(\mathrm{GF}(p)\).

Examples¶

In [1]: galois.GF(2).irreducible_poly
Out[1]: Poly(x + 1, GF(2))

In [2]: galois.GF(2**8).irreducible_poly
Out[2]: Poly(x^8 + x^4 + x^3 + x^2 + 1, GF(2))

In [3]: galois.GF(31).irreducible_poly
Out[3]: Poly(x + 28, GF(31))

In [4]: galois.GF(7**5).irreducible_poly
Out[4]: Poly(x^5 + x + 4, GF(7))