class property galois.FieldArray.primitive_elements : FieldArray

All primitive elements \(\alpha\) of the Galois field \(\mathrm{GF}(p^m)\). A primitive element is a multiplicative generator of the field, such that \(\mathrm{GF}(p^m) = \{0, 1, \alpha, \alpha^2, \dots, \alpha^{p^m - 2}\}\).

Examples

In [1]: galois.GF(2).primitive_elements
Out[1]: GF([1], order=2)

In [2]: galois.GF(2**8).primitive_elements
Out[2]: 
GF([  2,   4,   6,   9,  13,  14,  16,  18,  19,  20,  22,  24,  25,  27,
     29,  30,  31,  34,  35,  40,  42,  43,  48,  49,  50,  52,  57,  60,
     63,  65,  66,  67,  71,  72,  73,  74,  75,  76,  81,  82,  83,  84,
     88,  90,  91,  92,  93,  95,  98,  99, 104, 105, 109, 111, 112, 113,
    118, 119, 121, 122, 123, 126, 128, 129, 131, 133, 135, 136, 137, 140,
    141, 142, 144, 148, 149, 151, 154, 155, 157, 158, 159, 162, 163, 164,
    165, 170, 171, 175, 176, 177, 178, 183, 187, 188, 189, 192, 194, 198,
    199, 200, 201, 202, 203, 204, 209, 210, 211, 212, 213, 216, 218, 222,
    224, 225, 227, 229, 232, 234, 236, 238, 240, 243, 246, 247, 248, 249,
    250, 254], order=2^8)

In [3]: galois.GF(31).primitive_elements
Out[3]: GF([ 3, 11, 12, 13, 17, 21, 22, 24], order=31)

In [4]: galois.GF(7**5).primitive_elements
Out[4]: GF([    7,     8,    14, ..., 16797, 16798, 16803], order=7^5)
Last update: Jul 28, 2022