- galois.FieldArray.additive_order() integer | ndarray
Computes the additive order of each element in \(x\).
- Returns¶
An integer array of the additive order of each element in \(x\). The return value is a single integer if the input array \(x\) is a scalar.
Notes¶
The additive order \(a\) of \(x\) in \(\mathrm{GF}(p^m)\) is the smallest integer \(a\) such that \(x a = 0\). With the exception of 0, the additive order of every element is the finite field’s characteristic.
Examples¶
Compute the additive order of each element of \(\mathrm{GF}(3^2)\).
In [1]: GF = galois.GF(3**2, display="poly") In [2]: x = GF.elements; x Out[2]: GF([ 0, 1, 2, α, α + 1, α + 2, 2α, 2α + 1, 2α + 2], order=3^2) In [3]: order = x.additive_order(); order Out[3]: array([1, 3, 3, 3, 3, 3, 3, 3, 3]) In [4]: x * order Out[4]: GF([0, 0, 0, 0, 0, 0, 0, 0, 0], order=3^2)