Hi Maxime.

I would be very interested by the implementation of Montes algorithm


While Montes' algorithm is not implemented, there is an algorithm due to 
MacLane implemented that is to my knowledge essentially equivalent. You can 
find the implementation in the sage.rings.valuation namespace.

and OM representation of prime ideals in global function fields claimed 
> here 
> : https://wiki.sagemath.org/days86.5 
>

I think Jens Bauch had plans to work on this back then. But as far as I 
know, there is no real implementation for SageMath yet. I don't know much 
about these OM representations but I think that some of it can be done by 
the MacLane valuations implemented in SageMath. For global function fields, 
these are implemented in sage.rings.function_field.function_field_valuation.

If you are thinking on working on this, I would be very interested to 
discuss this further. Feel free to contact me directly if you want to 
schedule a call so I can give you a tour of the valuation code in SageMath. 
We could then try to at least create a ticket that lists what we have and 
what is missing.

Best,

julian

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