make use of the b-file

[mantepse]

fixes #41005

When requesting more terms, we check whether the b-file of the oeis provides them.

[maxale]

I'd suggest to separate number= from a request to get terms from b-file. For example, b-file may contain 10,000 terms while the user may like to get only 1,000 of them.

[github-actions]

Documentation preview for this PR (built with commit 9ed0b41; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

[mantepse]

I'd suggest to separate number= from a request to get terms from b-file. For example, b-file may contain 10,000 terms while the user may like to get only 1,000 of them.

Do you think it's possible/ worthwhile to download only a part? How many mb could it be?

[maxale]

@mantepse My concern is not about the size of b-files. Most of them have at most a few thousand terms and are not that large. So, it's fine to download b-file as a whole. My point is that the user may still want just some particular number of terms even if a larger number of terms is available. Also, value number=True is quite counterintuitive. I think it better to have another parameter for fetching bfile (e.g., download=True, online=True, or alike) and allow it be specified alongside with number=.

[mantepse]

Ah, but that's exactly what it does. If they want 100 terms and Oeis knows 100 terms, then s.first_terms(100) will return 100 terms. If necessary, the b file will then be fetched.

[maxale]

Oh, I do not see that from reading the description:

       - ``number`` -- integer, ``True`` or ``None`` (default); the
          number of terms returned (if less than the number of
          available terms).  When set to ``True``, fetches the
          b-file.  When set to ``None``, returns all the known terms.

There are two things: whether or not we want to fetch the b-file, and the number of terms to return. They seem to be intermixed in an unobvious way here. To my view we should either

• always get terms from the b-file, and then not even mention that; or
• get them from b-file only by an explicit request, and this request should be spelled differently from the number of terms (number=) we want.

Also, you mention "number of available terms" - what is that? The number of terms in the OEIS entry, or the number of terms in the b-file?

[mantepse]

Also, you mention "number of available terms" - what is that? The number of terms in the OEIS entry, or the number of terms in the b-file?

I meant the latter. What I had in mind was the following: as a user, if I want to check or make a conjecture from the first few terms, I don't care how they are obtained. So, in most cases I will want to get all of them. So, the two proposals amount to

sage: s.first_terms(True)

or, with the other proposal

sage: s.first_terms(fetch_all=True)

If for some reason I want 50 terms if at all possible, I would do

sage: s.first_terms(50)

and probably

sage: s.first_terms(50, fetch_all=True)

I guess one reason not to download the b-file, but other than that getting as many terms as possible is if I run through very many sequences. In this case downloading could be too expensive. (I checked, it does make a difference even if only checking 20 sequences.) So, this would be

sage: s.first_terms()[:50]

versus

sage: s.first_terms(50, fetch_all=False)

However, in this case one possibly should download the database anyway.

I'm not completely decided what's really better. I must say that, generally, the number argument does not make much sense to me.

[maxale]

I never used number= myself either. But allowing it to have value True somehow defeats its purpose. I would rather always (by default) get terms from b-file, but provided an option for getting a short version version of just displayed terms. If we don't want to introduce an additional parameter, should we use special value number=0 for that purpose?

That is,

• s.first_terms() gives all terms (from b-file)
• s.first_terms(0) gives all terms that are displayed in the OEIS entry (not from b-file)
• s.first_terms(50) gives 50 terms (from whatever source)

[mantepse]

How about using infinity oo instead of True?

[mantepse]

Note that currently the full entry of the sequence is obtained at once. Getting the b file takes additional time, and actually quite a bit.

[maxale]

So, we proposed two possibilities:

• number=None (default) for terms from b-file, number=0 for displayed terms;
• number=None (default) for displayed terms, number=oo for terms from b-file.

I'm fine with either, but a big question remains - do we fetch b-file by default?

[mantepse]

No, fetching the b-file by default is not a good idea. The initial terms are in the same download as the description, so we cannot be lazy here. But the b-file is an additional download and should be avoided if possible.

[maxale]

Ok, please proceed with your last suggestion then.

[maxale]

Thanks! It just came to me that it'd be beneficial to have an interface global parameter controlling the default behavior for fetching b-file. E.g., I run once oeis.allow_bfiles(True) and then .fist_terms() for every sequence gets all the terms from b-file. Can this feature be implemented as well?

[mantepse]

I would rather not. In what way would it be easier than calling first_terms(oo)?

[maxale]

For some yes, for other - not. It's an alternative approach to handling things, which I personally prefer more.

Here is analogy with next_prime() function - we can call it each time with next_prime(n, proof=False), but instead we can call once proof.arithmetic(False) and then just call next_prime(n) without setting proof=False explicitly.

[mantepse]

done, please check! (oeis.options is your friend)