On Wednesday, July 11, 2018 at 10:35:28 AM UTC+9, Nils Bruin wrote:
 

> Note that most parts of the function field infrastructure doesn't make use 
> of the fact that residue fields as finite (if you do it right, basically 
> only the part that computes divisor class groups), so with a bit of care 
> the same code should work in characteristic 0 for most computations.
>

I agree.
 

> It would be great if you could include that case in your code as well. 
>

That would not happen. See below.
 

> I think this is also how the function field code in magma was developed 
> (start with global function fields, retool the code to also work for 
> characteristic 0 (or non-finite positive characteristic base field) where 
> it makes sense). 
>

So we should follow the same path: focus on global function fields first, 
and then extend to over other fields.

The ticket #22982 is only for global function fields. This already seems to 
take a long time to be merged to Sage. I do not have a reviewer for its 
subticket #25435 yet. Perhaps the subticket should be further split to 
subsubtickets, as no one seems to want to review the lengthy code. 

After this ticket, I expect someone else (perhaps not me) would come up to 
extend my code to function fields to over other fields. Some algorithms 
that I implemented assume essentially finite base field. A prominent one is 
the Leonard-Pellikaan-Singh-Swanson algorithm computing the maximal order.  

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