Implement cocharacter and primitive Eulerian polynomials for hyperplane arrangements

[tscrim]

📚 Description

As defined in a recent paper https://arxiv.org/abs/2306.15556.

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

[tscrim]

@saliola I implemented this following your paper, but I don't get the positivity for simplicial arrangements you claim:

sage: H = hyperplane_arrangements.braid(4)
sage: H.is_simplicial()
True
sage: H.primitive_eulerian_polynomial()
6*z^3 - 7*z^2 + 2*z

Did I make a mistake my implementation?

[saliola]

Check the minimal element. We use the intersection of all the hyperplanes as the minimal element, which I think this is opposite to Sage's convention (inclusion vs reverse inclusion).

[tscrim]

I had thought of that. Sage is also using the 0 dimensional subspace as the minimal element. (Edit, adding example:)

sage: H.intersection_poset("subspace").minimal_elements()[0]
Affine space p + W where:
  p = (0, 0, 0)
  W = Vector space of dimension 3 over Rational Field

Do you have a nonsymmteric poset on hand to check?

[Bastidas-Jose]

It seems that in the example, the minimal element is the ambient space--expressed as the sum of p (the origin) and W (the ambient space itself).

[tscrim]

Ah, you’re right, I misread it. I will fix it on Monday. Thank you.

[tscrim]

Thank you. I have fixed it and added a lot more examples.

[Bastidas-Jose]

That's great, thank you!

[tscrim]

Thank you. @josebastidasolaya I will interpret that as a positive review. Although we now need @saliola to approve the PR request since permissions are now much more restrictive in this new workflow...

[fchapoton]

doc does not build

[sagemath_doc_html-none] OSError: /sage/src/sage/geometry/hyperplane_arrangement/arrangement.py:docstring of sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement.primitive_eulerian_polynomial:3: WARNING: citation not found: BHS2023

[vbraun]

pdf docs don't build

[tscrim]

@fchapoton Thank you for fixing it. Sorry I couldn't get to it sooner; I was traveling to the US (for FPSAC this week).

[vbraun]

[sagemath_doc_pdf-none] ! Undefined control sequence.
[sagemath_doc_pdf-none] <argument> ... \in L} |\mu (B,X)| (z - 1)^{\codim 
[sagemath_doc_pdf-none]                                                   X},\end {split}
[sagemath_doc_pdf-none] l.2887 ...\mu(B,X)| (z - 1)^{\codim X},\end{split}

[tscrim]

Sorry about that. This will fix that issue. I also added one additional parenthetical comment to the documentation specifying that the minimal element is the 0 dimensional subspace (which is opposite of Sage’s convention of being the entire space).

[tscrim]

@saliola, @kwankyu, @fchapoton Could someone approve the PR since it is a positive review?

[kwankyu]

LGTM.

[kwankyu]

Thank you. @josebastidasolaya I will interpret that as a positive review.

I don't know what "that" is, which was enough for you to "interpret that" as a positive review. I think you should have requested it explicitly from him.

As he did not express objection to your interpretation and now I approved this PR, I would not bother about it anymore.

[kwankyu]

Though this PR has no problem code-wise, I have a little concern about its content:

The PR implements two concepts defined in a paper published in arXiv very recently (June 2023?). First I admit that I know nothing about the research field of hyperplane arrangements. But it seems to me that the two concepts, as defined in a very recent paper, have not yet been known widely in the field. Then it seems too early to get their implementations into sage. I think that what is implemented in sage should be something of general interest in the field, not only by a few readers and authors of a paper kept in arXiv for a few months.

I may be wrong as I don't know the field. Then please correct me.

[tscrim]

Though this PR has no problem code-wise, I have a little concern about its content:

The PR implements two concepts defined in a paper published in arXiv very recently (June 2023?). First I admit that I know nothing about the research field of hyperplane arrangements. But it seems to me that the two concepts, as defined in a very recent paper, have not yet been known widely in the field. Then it seems too early to get their implementations into sage. I think that what is implemented in sage should be something of general interest in the field, not only by a few readers and authors of a paper kept in arXiv for a few months.

IMO, that is a very arbitrary/ill-defined standard (I would also say it has already been a few months too) and it is contrary to Sage's goal of being a computational tool for experimental mathematics through sharing code. I don't see an argument in your post for why we should not include new and/or not-widely-known (in some definition) algorithms/computations/objects/etc. Yes, it can be difficult to change nomenclature (such as if a conflict arises), but we can still change method names if a need arises later.

[github-actions]

Documentation preview for this PR (built with commit e466d94; changes) is ready! 🎉

[kwankyu]

I did not attempt to define a standard of what can or cannot be included into Sage. I doubt anyone could.

In practice, it is all judged by the authors and reviewers of a PR. As a reviewer, I made my judgement based on the circumstances, which is not of much weight of course as I don't know the field. If another reviewer who knows the field think different and accepts the PR, I would not object.

For my judgement, I would not accept implementations of concepts not of general interest in the field.

[fchapoton]

ok