- 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)