Question about completeness of cubic number field data

[Randy Yee]

Hi LMFDB support team,

I had a quick question about the completeness of data concerning cubic number fields. The relevant page on the website https://www.lmfdb.org/NumberField/Completeness
notes that tables are complete for degree 3 fields up to an absolute discriminant bound of 3,375,000.

However, data is available for much larger discriminant bounds than this.

Since there is a way to compute cubic fields up to a chosen discriminant bound rather quickly, I had thought that it would be relatively easy to check if any of the invariant data was missing for much larger discriminant than this. 

I was hoping to double-check 1) That the info on the webpage is up-to-date, and 2) whether or not I'm overlooking some reason why the data is only considered complete up to this bound.

Thanks for your help!

Randy Yee 

[John Jones]

Hi,

There are different sorts of completeness results listed on that page.  For example, it also has all cubic fields where the largest ramified prime is < 30.  Also, fields may have been added because of connections to other parts of the LMFDB.  That is why there are more fields.

You are right that the data could be extended further.  There is a question of whether or not it is worth the storage space to add more fields of a given type compared with how much interest people might have for that data.  Adding more data may also slow down searches.  The number fields section is more likely to have timeouts for slow searches alreaddy.  There are multiple places where we could have easily extended the number field data but thought it was not worth it.  I am open to suggestions if there is a particular reason to add more in some area.

For fields we do have, I would definitely want to fill in any missing data.  When something is missing it is because it seemed like it would take to long to compute, but methods improve so maybe more could be added.  If you are going to try to compute some of this data, note that we keep track of when the computation assumes GRH, so that needs to be tracked.

Let me know if you have other questions (or I misunderstood your questions).

John Jones

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[Randy Yee]

Hi John,

Thanks for the very quick and thorough response!

A subset of the research group I am in is interested in tabulation for low-degree fields, and your answer helps to clarify the current situation greatly.

Cheers,

Randy Yee

---

From: John Jones <j...@asu.edu>
Sent: Monday, May 5, 2025 10:00
To: Randy Yee <randy...@ucalgary.ca>
Cc: lmfdb-...@googlegroups.com <lmfdb-...@googlegroups.com>
Subject: Re: Question about completeness of cubic number field data

 

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