OM representation of ideals in function fields

[Maxime Bombar]

Hello everyone,

I would be very interested by the implementation of Montes algorithm and
OM representation of prime ideals in global function fields claimed here
: https://wiki.sagemath.org/days86.5

Do you know how far has it got ?

Best,

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Maxime Bombar

[julian...@gmail.com]

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

[Maxime Bombar]

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Hi Julian,

Happy new year. Thank you for your detailed answer. For sure, I would enjoy working on that in a foreseeable future, but I have other projects to deal with before. However, we can definitely schedule a call to talk deeper about that.

Best,

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Maxime