So I guess everybody found this issue a non-issue. However, this for
example makes it possible to compute the genus of a function field
that is defined over a non-prime finite field
(genus currently uses singular)

I take the silence as a 'go ahead'. I'll add this to the patch of
http://trac.sagemath.org/sage_trac/ticket/12170

On 23 ינואר, 02:32, "syd.lavas...@gmail.com" <syd.lavas...@gmail.com>
wrote:
> In current version of sage you can not have a singular object for k(a)
> [x] when k is a non-prime finite field and a is transcendental. This
> is because singular does not support defining such rings explicitly,
> while if k was prime we had no problem.
>
> I don't know what the developers of singular were thinking, but
> probably the fundamental solution is to change the singular code. But
> meanwhile, one can define
> prime_field(k)(a)[t,x]
> and then quotient it with p(t) with minimal polynomial of the field
> extension.
>
> This helps the user to use lots of functions, as elementary as lcm,
> which are depending on Singular.
>
> I have written the code, if everybody is happy with this short-cut
> solution, I can go ahead an put the code on the trac
>
> Cheers,
> Syd

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