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gh-37013: Implement the center of a universal enveloping algebra in the PBW basis <!-- ^^^^^ 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" --> <!-- Describe your changes here in detail --> We provide an implementation of the center of the universal enveloping algebra in the PBW basis of a finite dimensional Lie algebra with basis. We provide a few other fixes along the way: - Add an option to return all Casimir elements, not just the first obtained (in particular, see type $D_{2n}$). - Add some latex output options for some Lie algebras. - Improving compatibility with the `plural` g-algebras. <!-- Why is this change required? What problem does it solve? --> <!-- If this PR resolves an open issue, please link to it here. For example "Fixes #12345". --> <!-- If your change requires a documentation PR, please link it appropriately. --> ### 📝 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! --> <!-- Feel free to remove irrelevant items. --> - [x] The title is concise, informative, and self-explanatory. - [x] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [x] I have created tests covering the changes. - [x] I have updated the documentation accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on - #12345: short description why this is a dependency - #34567: ... --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: #37013 Reported by: Travis Scrimshaw Reviewer(s): Frédéric Chapoton
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src/doc/en/reference/algebras/lie_algebras.rst

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sage/algebras/lie_algebras/abelian
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sage/algebras/lie_algebras/affine_lie_algebra
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sage/algebras/lie_algebras/bch
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sage/algebras/lie_algebras/center_uea
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sage/algebras/lie_algebras/classical_lie_algebra
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sage/algebras/lie_algebras/examples
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sage/algebras/lie_algebras/free_lie_algebra

src/doc/en/reference/references/index.rst

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.. [MoPa1994] \P. Morton and P. Patel. The Galois theory of periodic points
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of polynomial maps. Proc. London Math. Soc., 68 (1994), 225-263.
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.. [Motsak2006] Olekasandr Motsak. *Computation of the central elements and
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centralizers of sets of elements in non-commutative polynomial
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algebras*. PhD Thesis, 2006.
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https://kluedo.ub.rptu.de/frontdoor/deliver/index/docId/2308/file/Thesis.pdf
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.. [MP2019] \M. Montes, D. Penazzi
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"Yarara and Coral v1"
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https://csrc.nist.gov/CSRC/media/Projects/Lightweight-Cryptography/documents/round-1/spec-doc/yarara_and_coral-spec.pdf

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