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gh-35269: Implement characteristic polynomial computation for Drinfeld modules of any Rank <!-- ^^^^^ Please provide a concise, informative and self-explanatory title. Don't put issue numbers in there, do this in the PR body below. For example, instead of "Fixes #1234" use "Introduce new method to calculate 1+1" --> ### 📚 Description The goal of this PR is to implement methods for computing the characteristic polynomial (of the Frobenius endomorphism) of a Drinfeld Fq[t]-module. This largely closes #35028, though opportunities to implement other algorithms, as well as the question of computing characteristic polynomials for arbitrary morphisms, remain open. Some further reading on characteristic polynomials of Drinfeld modules: Gekeler, E.-U. (2008). Frobenius Distributions of Drinfeld Modules over Finite Fields. Transactions of the American Mathematical Society, 360(4), 1695–1721. http://www.jstor.org/stable/20161942 Angles, B. On some characteristic polynomials attached to finite Drinfeld modules. Manuscripta Math 93, 369–379 (1997). https://doi.org/10.1007/BF02677478 @kryzar @xcaruso @DavidAyotte @schost ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> <!-- If your change requires a documentation PR, please link it appropriately --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> - [x] I have made sure that the title is self-explanatory and the description concisely explains the PR. - [x] I have linked an issue or discussion. - [x] I have created tests covering the changes. - [x] I have updated the documentation accordingly. ### ⌛ Dependencies None as it only requires the base implementation of Drinfeld modules which has been merged. URL: #35269 Reported by: ymusleh Reviewer(s): Antoine Leudière, David Ayotte, DocTrivial, Xavier Caruso, ymusleh
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src/doc/en/reference/references/index.rst

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@@ -246,6 +246,10 @@ REFERENCES:
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Symposium, Volume 51, page 20.
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Australian Computer Society, Inc. 2006.
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.. [Ang1997] B. Anglès. 1997. *On some characteristic polynomials attached to
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finite Drinfeld modules.* manuscripta mathematica 93, 1 (01 Aug 1997),
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369–379. https://doi.org/10.1007/BF02677478
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.. [AP1986] \S. Arnborg, A. Proskurowski,
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*Characterization and Recognition of Partial 3-Trees*,
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SIAM Journal of Alg. and Discrete Methods,
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Int. Math. Res. Not. (2015).
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:doi:`10.1093/imrn/rnv194`, :arxiv:`1408.0320`.
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.. [MS2019] \Y. Musleh and \'E. Schost. Computing the characteristic polynomial
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of a finite rank two Drinfeld module. In Proceedings of the 2019
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.. [MS2019] \Y. Musleh and \'E. Schost. *Computing the characteristic polynomial
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of a finite rank two Drinfeld module*. In Proceedings of the 2019
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ACM on International Symposium on Symbolic and Algebraic
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Computation, pages 307–314. ACM, 2019.
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.. [MS2023] \Y. Musleh and \'E. Schost. *Computing the Characteristic Polynomial
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of Endomorphisms of a finite Drinfeld Module using Crystalline
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Cohomology*. In Proceedings of the 2023 ACM on International
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Symposium on Symbolic and Algebraic Computation, pages 461–469.
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ACM, 2023.
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.. [MSSY2001] Mateescu, A., Salomaa, A., Salomaa, K. and Yu, S., *A
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sharpening of the Parikh mapping*. Theoret. Informatics Appl. 35
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(2001) 551-564.

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