galois.FieldArray.prime_subfield

class property galois.FieldArray.prime_subfield : type[FieldArray]

The prime subfield \(\mathrm{GF}(p)\) of the extension field \(\mathrm{GF}(p^m)\).

Notes

For the prime field \(\mathrm{GF}(p)\), the prime subfield is itself.

Examples

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

In [2]: galois.GF(2**8).prime_subfield
Out[2]: <class 'galois.GF(2, primitive_element='1', irreducible_poly='x + 1')'>

In [3]: galois.GF(31).prime_subfield
Out[3]: <class 'galois.GF(31, primitive_element='3', irreducible_poly='x + 28')'>

In [4]: galois.GF(7**5).prime_subfield
Out[4]: <class 'galois.GF(7, primitive_element='3', irreducible_poly='x + 4')'>