- class property galois.FieldArray.units : FieldArray
All of the finite field’s units \(\{1, \dots, p^m-1\}\). A unit is an element with a multiplicative inverse.
Examples¶
All units of the prime field \(\mathrm{GF}(31)\) in increasing order.
In [1]: GF = galois.GF(31) In [2]: GF.units Out[2]: GF([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], order=31)
All units of the extension field \(\mathrm{GF}(5^2)\) in lexicographically-increasing order.
In [3]: GF = galois.GF(5**2, display="poly") In [4]: GF.units Out[4]: GF([ 1, 2, 3, 4, α, α + 1, α + 2, α + 3, α + 4, 2α, 2α + 1, 2α + 2, 2α + 3, 2α + 4, 3α, 3α + 1, 3α + 2, 3α + 3, 3α + 4, 4α, 4α + 1, 4α + 2, 4α + 3, 4α + 4], order=5^2)