Any reason not to just test r.multiplicative_order() ?

John Cremona

On 20 April 2014 20:11, Jan Medina <[email protected]> wrote:
> I did this algorithm to find a primitive element of a multiplicative group
> on a finite field. This is a basic algorithm
> def random_primitive(p,h):
>     F.<x>=GF(p^h)
>     s=p^h-1
>     r=F.random_element()
>     j=0
>     if r!=0:
>         for t in prime_factors(s):
>             if r^(s/t)==1:
>                 j=j+1
>         if j==0:
>             return r
>         else:
>             return random_primitive(p,h)
>     else:
>         return random_primitive(p,h)
>
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