Adding an implementation of the Abreu-Nigro symmetric functions #39988
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@darijgr You might be interested in this. However, when writing doctests for my code, I came across a counterexample to Conjecture 1.5 in the Huh et al. paper mentioned above and contradicts the results in that paper. So I think there is a bug in my implementation somewhere, but I don't see where right now. If you have time, please take a look. |
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Documentation preview for this PR (built with commit 104b42b; changes) is ready! 🎉 |
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Okay, fixed. I forgot/missed that Hessenberg functions need to be weakly increasing. |
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@darijgr Can you approve the PR? (I am rerunning parts of the bots, but they only failed for unrelated reasons.) |
darijgr
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Thank you both. |
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sagemathgh-39988: Adding an implementation of the Abreu-Nigro symmetric functions <!-- ^ Please provide a concise and informative title. --> <!-- ^ Don't put issue numbers in the title, do this in the PR description below. --> <!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method to calculate 1 + 2". --> <!-- v Describe your changes below in detail. --> <!-- v Why is this change required? What problem does it solve? --> <!-- v If this PR resolves an open issue, please link to it here. For example, "Fixes sagemath#12345". --> Following the definition given in (2.2) of https://arxiv.org/abs/2504.09123, we implement the Abreu-Nigro symmetric functions $g_{H,k}(x; q)$, where $H$ is a Hessenberg function. To do so, we also implement their $\rho$ basis. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - sagemath#12345: short description why this is a dependency --> <!-- - sagemath#34567: ... --> URL: sagemath#39988 Reported by: Travis Scrimshaw Reviewer(s): Darij Grinberg, Frédéric Chapoton
vbraun
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sagemathgh-39988: Adding an implementation of the Abreu-Nigro symmetric functions <!-- ^ Please provide a concise and informative title. --> <!-- ^ Don't put issue numbers in the title, do this in the PR description below. --> <!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method to calculate 1 + 2". --> <!-- v Describe your changes below in detail. --> <!-- v Why is this change required? What problem does it solve? --> <!-- v If this PR resolves an open issue, please link to it here. For example, "Fixes sagemath#12345". --> Following the definition given in (2.2) of https://arxiv.org/abs/2504.09123, we implement the Abreu-Nigro symmetric functions $g_{H,k}(x; q)$, where $H$ is a Hessenberg function. To do so, we also implement their $\rho$ basis. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - sagemath#12345: short description why this is a dependency --> <!-- - sagemath#34567: ... --> URL: sagemath#39988 Reported by: Travis Scrimshaw Reviewer(s): Darij Grinberg, Frédéric Chapoton
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Following the definition given in (2.2) of https://arxiv.org/abs/2504.09123, we implement the Abreu-Nigro symmetric functions$g_{H,k}(x; q)$ , where $H$ is a Hessenberg function. To do so, we also implement their $\rho$ basis.
⌛ Dependencies