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Implementation of monomial divisibility diagrams for efficient membership tests#129

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ThTer11 wants to merge 22 commits intoalgebraic-solving:mainfrom
ThTer11:withmdd
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Implementation of monomial divisibility diagrams for efficient membership tests#129
ThTer11 wants to merge 22 commits intoalgebraic-solving:mainfrom
ThTer11:withmdd

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@ThTer11
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@ThTer11 ThTer11 commented Mar 13, 2026

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.

@ThTer11 ThTer11 changed the title Withmdd Implementation of monomial divisibility diagrams for efficient membership tests Mar 13, 2026
@RafaelDavidMohr
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@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?

@ThTer11 ThTer11 marked this pull request as ready for review March 16, 2026 08:47
@mohabsafey
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Many thanks for this. It looks like the tests are not successful. Can you have a look?

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

Fixed!

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3 participants