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implement combinatorial logarithm and connected graphs - #42626

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mantepse wants to merge 2 commits into
sagemath:developfrom
mantepse:species/connectedgraphs
Open

implement combinatorial logarithm and connected graphs#42626
mantepse wants to merge 2 commits into
sagemath:developfrom
mantepse:species/connectedgraphs

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@mantepse

@mantepse mantepse commented Aug 4, 2026

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We port the fast version of the combinatorial logarithm of symmetric functions from the old species framework to the new lazy symmetric function framework.

We use it to implement a faster version of connected graphs.

@mantepse

mantepse commented Aug 4, 2026

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@parthchvn, if you have comments, I am all ears :-)

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github-actions Bot commented Aug 4, 2026

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Documentation preview for this PR (built with commit eab5337; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

@parthchvn

parthchvn commented Aug 5, 2026

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Hello Martin!

I tried using the explicit formula

$$\text{coefficient}(n) = \frac{1}{n}\sum_{d \mid n}\mu(d)(-1)^{n/d-1}p_d^{n/d}. $$

During the initial computation LazySymmetricFunctions(p)(coefficient).truncate(N) I saw a noticable speedup (~ 4x for N=20,40,80) as compared to current implementation that invokes plethysm. Do you think we should switch to the formula?

cf. https://dmtcs.episciences.org/12818/pdf , eq 2.42

@mantepse

mantepse commented Aug 5, 2026

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Excellent! Could you post the patch as a suggestion, for example, so I can apply it?

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