Implementation of monomial divisibility diagrams for efficient membership tests

[ThTer11]

This draft pull request implements monomial divisibility diagrams (MDDs) in AlgebraicSolving.jl, following the ideas from our paper A data structure for monomial ideals with applications to signature Gröbner bases (Pierre Lairez, Rafael Mohr, Théo Ternier, link: https://arxiv.org/abs/2601.05026).

The goal is to speed up membership tests in monomial ideals, which are used in the signature Gröbner basis implementation.

[RafaelDavidMohr]

@ThTer11 I did some small changes, for me the main code looks good now. So if you think it's good as well, you can remove the Draft status.

The one bigger thing I did was to integrate the Hilbert series computation via MDD's into the already present functionality for computing Hilbert series. In the user function hilbert_series there is now a keyword use_mdd which enables computing the HS via MDD's, I changed the documentation accordingly. @rprebet @ederc @mohabsafey is this change okay for you as well?

[mohabsafey]

Many thanks for this. It looks like the tests are not successful. Can you have a look?

[RafaelDavidMohr]

Many thanks for this. It looks like the tests are not successful. Can you have a look?

Fixed!

[codecov-commenter]

⚠️ Please install the to ensure uploads and comments are reliably processed by Codecov.

Codecov Report

❌ Patch coverage is 73.78277% with 70 lines in your changes missing coverage. Please review.
✅ Project coverage is 82.70%. Comparing base (91d7230) to head (29d66ba).
⚠️ Report is 4 commits behind head on main.

Files with missing lines	Patch %	Lines
src/siggb/monomial_diagram.jl	68.13%	65 Missing ⚠️
src/algorithms/hilbert.jl	75.00%	3 Missing ⚠️
src/siggb/helpers.jl	66.66%	2 Missing ⚠️
❗ Your organization needs to install the Codecov GitHub app to enable full functionality.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #129      +/-   ##
==========================================
- Coverage   83.62%   82.70%   -0.93%     
==========================================
  Files          32       33       +1     
  Lines        3188     3544     +356     
==========================================
+ Hits         2666     2931     +265     
- Misses        522      613      +91     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.