I agree the situation with zn_poly is a mess, but I think it would be good 
to do some actual benchmarks to check if the NTL code is faster or 
comparable to the zn_poly version, I don't see any data in the ticket but 
you do say "The one thing it does is done better by NTL" so maybe you 
already did some?
Computing zeta functions of hyperelliptic curves is pretty fundamental 
thing to do for many applications in arithmetic geometry, and performance 
is important there, so it would really be a shame if those applications got 
significantly slower.
The decision of whether its worth the maintainence burden should be done 
with full knowledge of what we are losing, if it turns out its nothing, 
thats great!
I also this the claim that it's only used in one place undersells it a 
little bit, the wrapped function `interval_products` is used both in the 
hyperelliptic_curves and cyclic_covers modules (since 2018) 
(https://github.com/sagemath/sage/search?q=interval_products), though they 
are admittedly very related applications, there are a range of parameters 
with which this code may be called.

On Tuesday, November 9, 2021 at 2:25:59 PM UTC+1 Michael Orlitzky wrote:

> Trac: https://trac.sagemath.org/ticket/32841
>
> In short, zn_poly is one of "those" packages. Abandoned in 2008, and
> kept on life support by sage developers ever since. Despite our
> efforts, the build system remains crazy and it would take a good bit of
> time to re-do the whole thing using autotools or cmake or whatever to
> make it reliable and easy to package.
>
> And it turns out, the sage library doesn't really need it any more. The
> one thing it does is done better by NTL.
>
> I'm posting here because it's a standard SPKG, but I think removal is a
> clear win in this case. Smaller tarballs, faster build times, easier on
> packagers, and no more time wasted updating zn_poly for new compilers
> and operating systems.
>
> But if any number theorists think I've overlooked something, please
> speak up.
>
>
>

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