Wishlist: search option "disjoint from" a set of primes for bad primes

[AurelPage]

It would often be useful to be able to specify a list of primes that you don't want to be bad. This probably applies to many objects, but I am mainly thinking about classical modular forms ("Bad p" field); note that it could also be a separate search field like for global number fields ("Unramified primes" field).

The automatic "similar issues" feature of github suggests #3160, which makes me realise that specifying the number of bad primes also makes sense and could also be useful for modular forms.

[edgarcosta]

Would be enough to have an option of "exclude" as in https://www.lmfdb.org/EllipticCurve/Q/ ?

On Wed, 25 Mar 2020 at 09:49, AurelPage notifications@github.com wrote:

It would often be useful to be able to specify a list of primes that you don't want to be bad. This probably applies to many objects, but I am mainly thinking about classical modular forms ("Bad p" field); note that it could also be a separate search field like for global number fields ("Unramified primes" field).

The automatic "similar issues" feature of github suggests #3160 https://github.com/LMFDB/lmfdb/issues/3160, which makes me realise that specifying the number of bad primes also makes sense and could also be useful for modular forms.

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[AurelPage]

Yes, "exclude" is the same as "disjoint from".

[edgarcosta]

I'm aware that "exclude" = "disjoint from", but the question would it be enough to have a single box, or are you asking for two boxes, as in number fields https://www.lmfdb.org/NumberField/?

[AurelPage]

Either would be fine, but of course two boxes allow for finer searches. This could also be an opportunity to uniformise the way it is done in various objects: several search fields vs only one, formulation ("include" vs "superset") etc.

[edgarcosta]

We have been trying to uniformize the search. Take a look at: https://olive.lmfdb.xyz/NumberField/ At the moment, seems that only place we are missing the exclude option is classical modular forms.

[AurelPage]

I see, thanks! It seems that only number fields has a separate search box, so maybe simply adding an "exclude" option to the "Bad p" box of modular forms is reasonable.

[JohnCremona]

I think we should be consistent across all objects we have which have a notion of bad or ramified primes, which is a lot of them. We should have the same search options for all these using as similar wording as possible

[rbommel]

See also PR #3776.

[roed314]

And PR #3779.

[rbommel]

Is this issue resolved now?

[AndrewVSutherland]

None of HMF, BMF, ECNF provide an option to constrain primes dividing the conductor norm. Just adding a bad primes search option should automatically provide include/exclude/exactly/subset options.

[JohnCremona]

What these three have in common is that the primes in question are number field primes so it is not at all clear how a user might input them. Easier, though less good, would be for the database to include a list of prime numbers dividing the norm of the level / conductor. Then one could easily constrain these in a search.

[AndrewVSutherland]

@JohnCremona we discussed this at today's "LMFDB Friday" meeting I think the plan is to add options to constrain the primes dividing the level/conductor norm and the primes dividing the discriminant of the number field separately; both are integers, and the primes dividing the conductor of the L-function (also an integer) are the primes that divide the product of these, but we thought it would be more useful/flexible to let users constrain the level/conductor norm and field discriminant separately.

I believe @rbommel is working on this.

[rbommel]

Yes, after David finished checking my code to put the lists of bad primes in the tables, I will continue on this.

[JohnCremona]

Understood ! Please tell me the new column names and types so I can update my scripts for ECNF and BMF.

[rbommel]

My current idea was to have the columns 'field_bad_primes' and 'level_bad_primes' for BMF and HMF, and 'conductor_norm_factors' for ECNF. All of them are 'integer[]'. But nothing has been done so far, so feel free to make other suggestions for the names.

[JohnCremona]

For ECNF: there are columns 'n_bad_primes' (number of bad p), 'bad_primes' (list of strings only useful for display), and 'local_data' which is a list of dicts, one per bad prime, of which one key is 'normp'. So if C is an ECNF record then [ld['np'] for ld in C['local_data']] gives you the norms of the bad primes. I suppose that just factoring 'conductor_norm' is easier.

[JohnCremona]

For BMFs: there is only 'level_norm' in the databse. The script to display one BMF actually constructs the number field and the level as an ideal and factors it. Sorry about that. HMFs also (in hmf_forms) only has 'level_norm', and a text column for 'level_ideal'.

[rbommel]

See also pull request #4527.

[JohnCremona]

I see that ec_nfcurves has a new column 'conductor_norm_factors': 'integer[]'. I will revise my upload scripts so that new data uploaded fills this correctly. (Referring to #610 which mentions 55 missing curves over sextic fields, I now have 42 of them and so hop to fill those gaps before too long.)

[rbommel]

That is great, @JohnCremona, thank you very much!