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gh-36128: Compute the characteristic varieties of a finitely presented group <!-- Describe your changes here in detail --> Let $G$ be a finitely presented group. For a field $\mathbb{k}$, let $\Lambda:=\mathbb{k}[G]$ be its group algebra and let $\mathbb{T}$ be its maximal spec, which is a torus. An element $\xi\in\mathbb{T}$ determines a local system of coefficients and the characteristic varieties of $G$ are defined as $$V_k(G):=\\{\xi\in\mathbb{T}\mid \dim H^1(G;\xi)\geq k\\}.$$ Except for the neutral element these are the reduced varieties of the Fitting ideals of the Alexander matrix of the presentation. The function `char_var` gives systems of generators of these ideals. A `groebner` option is given to give Groebner basis; it is set as an option since the computations may be quite long. ### 📝 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. - [ ] 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: #36128 Reported by: Enrique Manuel Artal Bartolo Reviewer(s): Enrique Manuel Artal Bartolo, miguelmarco, Travis Scrimshaw
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src/doc/en/reference/references/index.rst

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@@ -1388,6 +1388,10 @@ REFERENCES:
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20(1.6):1-18, 2015. :doi:`10.1145/2780652` or
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[`<https://hal.inria.fr/hal-01182890>`_].
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.. [CS1999a] \D. Cohen and A. Suciu. *Characteristic varieties of arrangements*.
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Math. Proc. Cambridge Philos. Soc.127 (1999), no.1, 33–-53.
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:doi:`10.1017/S0305004199003576`.
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.. [CCLSV2005] \M. Chudnovsky, G. Cornuejols, X. Liu, P. Seymour, K. Vuskovic.
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*Recognizing berge graphs*.
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Combinatorica vol 25 (2005), n 2, pages 143--186.

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