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Implement Goss polynomials of Drinfeld modules #35991

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merged 10 commits into from Aug 27, 2023
Merged

Implement Goss polynomials of Drinfeld modules #35991

merged 10 commits into from Aug 27, 2023

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DavidAyotte
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@DavidAyotte DavidAyotte commented Jul 26, 2023 •
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This PR implements Goss polynomials of Drinfeld modules. The interested PR reviewer should read section 3 of this paper. In particular, the recurrence relation (ii) of Proposition 3.4 of op. cit. is used in order to compute the $n$-th Goss polynomial of a Drinfeld module.

CC: @xcaruso @ymusleh @kryzar

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  • The title is concise, informative, and self-explanatory.
  • The description explains in detail what this PR is about.
  • I have linked a relevant issue or discussion.
  • I have created tests covering the changes.
  • I have updated the documentation accordingly.

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@DavidAyotte
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Thanks for the comments, I think I have addressed all of them.

xcaruso
xcaruso reviewed Jul 27, 2023
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Just a small suggestion. Otherwise, LGTM.

src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py Outdated Show resolved Hide resolved
@DavidAyotte @xcaruso
Update src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py
3cfab68 
Co-authored-by: Xavier Caruso <xcaruso@users.noreply.github.com>
kryzar
kryzar approved these changes Jul 27, 2023
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Thanks for this contribution @DavidAyotte. I approve the changes.

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xcaruso commented Jul 29, 2023

It seems that they are currently problems with automatic checkings.

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xcaruso commented Aug 1, 2023

Cc @vbraun
I'd like to give a positive review to this ticket but the build test fails for some reason that I did not understand and which is most likely unrelated to this ticket. What should I do?

@fchapoton
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I have re-launched the checks on top of 10.1. The branch has been re-based.

@DavidAyotte
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I have re-launched the checks on top of 10.1. The branch has been re-based.

Thanks Frédéric! The failing doctest does not seem to be related to this branch.

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Indeed, it is unrelated. Feel free to set to positive if you think this is ready.

@fchapoton
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but note that the added raise is not correctly doctested

@xcaruso
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xcaruso commented Aug 21, 2023

Good point, Frédéric.
Maybe you could fix this by adding a doctest, David.

@DavidAyotte
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Thanks for pointing this out. I added the desired doctest.

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Documentation preview for this PR (built with commit 09fbdfa; changes) is ready! 🎉

vbraun pushed a commit to vbraun/sage that referenced this pull request Aug 23, 2023
sagemathgh-35991: Implement Goss polynomials of Drinfeld modules
8cf6e03 
    
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This PR implements Goss polynomials of Drinfeld modules. The interested
PR reviewer should read section 3 of [this
paper](https://link.springer.com/article/10.1007/BF01410204). In
particular, the recurrence relation (ii) of Proposition 3.4 of op. cit.
is used in order to compute the $n$-th Goss polynomial of a Drinfeld
module.

CC: @xcaruso @ymusleh @kryzar

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### ⌛ Dependencies

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URL: sagemath#35991
Reported by: David Ayotte
Reviewer(s): Antoine Leudière, Xavier Caruso
@vbraun vbraun merged commit a102fbd into sagemath:develop Aug 27, 2023
12 of 13 checks passed
@mkoeppe mkoeppe added this to the sage-10.2 milestone Aug 27, 2023
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