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 $xa=0$. 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)