- class property galois.FieldArray.primitive_element : FieldArray
A primitive element \(\alpha\) of the Galois field \(\mathrm{GF}(p^m)\). A primitive element is a multiplicative generator of the field, such that \(\mathrm{GF}(p^m) = \{0, 1, \alpha, \alpha^2, \dots, \alpha^{p^m - 2}\}\).
A primitive element is a root of the primitive polynomial \(f(x)\), such that \(f(\alpha) = 0\) over \(\mathrm{GF}(p^m)\).
Examples¶
In [1]: galois.GF(2).primitive_element Out[1]: GF(1, order=2) In [2]: galois.GF(2**8).primitive_element Out[2]: GF(2, order=2^8) In [3]: galois.GF(31).primitive_element Out[3]: GF(3, order=31) In [4]: galois.GF(7**5).primitive_element Out[4]: GF(7, order=7^5)