On Sat, 28 Mar 2020, 12:06 Kwankyu Lee, <ekwan...@gmail.com> wrote:

>
>
> On Saturday, March 28, 2020 at 6:16:25 PM UTC+9, John Cremona wrote:
>>
>> Certainly this is not intentional. It just has not been done.
>
>
> Wrong. It was recently done for curves over finite fields in affine and
> projective spaces.
>

Sorry about that -- thanks for the correction.


> As we already have function fields over number fields, it would be a
> rather trivial task to connect the function fields with curves over number
> fields by refactoring the curve framework.
>

I hope you are right about this being easy. From an arithmetic geometry
perspective it seems to be a 2-dimensional rather than 1-dimensional
situation.



> Having this done well (and efficiently) would be a major step towards
>> bringing Sage closer to Magma's capabilities in this area.
>
>
> A major gap between Sage and Magma in this area is in performance speed.
>
>
>
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