dft for symmetric group algebra when p|n! #37748
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The DFT for the SGA throws a ZeroDivisionError p|n. Uses the idempotents as computed in [Murphy '83] to build the Pierce decomposition of the group algebra over a finite field. The "modular" Fourier transform is the homomorphic projection onto each block via v |--> v*e_i. This change of basis matrix is the modular Fourier transform, and works even when p|n.
attempting to get through lint
remove helper functions in favor of lambda functions
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doctest is currently failing. I think that has something to do with the preloaded examples in the comments. I am attempting to build sage locally for the first time to run doctest with the changed |
use p=2, n=3 for a small example.
lowercase m in matrix
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the output in the example I had was wrong. that's been corrected. now test modularized distributions is failing with: [sagemath_objects-10.4.beta1] ERROR: Could not find a version that satisfies the requirement cysignals>=1.10.2 (from versions: none) |
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Admittedly I don't know enough about modular representation theory to check this code mathematically, but here are some programming comments.
Also, the documentation for the .dft-method should be rewritten a bit to explain the form argument, to make the explanation of mult dependent on form = "seminormal", and to also explain the different approaches used depending on form. For the explanation of the modular approach, you can also refer to [Murphy '83], which needs to be formatted as [Mur1983]_ in the docstring to give a hyperlink in the documentation.
| if form == "seminormal": | ||
| return self._dft_seminormal(mult=mult) |
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It might be a good idea to catch the error in the case form and choose it depending on whether the characteristic divides ._dft_seminormal always fails in the modular case)
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I agree, at the very least the failing cases p|n should at least be handled with a clear error message. I believe it only fails when p | n! (n was a type - it's the order of the symmetric group, so n!). I've chosen to just remove the standard argument for form and return the modular DFT in that case.
remove the self-reference to .dft(). just state that it's computing the DFT when the characteristic divides the order of the group. Co-authored-by: Sebastian A. Spindler <153911337+S17A05@users.noreply.github.com>
Co-authored-by: Sebastian A. Spindler <153911337+S17A05@users.noreply.github.com>
remove form from argument
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Documentation preview for this PR (built with commit 2fa1ab6; changes) is ready! 🎉 |
jacksonwalters
changed the title
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Accidentally closed this PR when I deleted the fork on my end. Should be reopened. |
The DFT for the SGA throws a ZeroDivisionError when p|n. Uses the idempotents as computed in [Murphy '83] to build the Pierce decomposition of the symmetric group algebra over a finite field. There is a homomorphic projection onto each block via v |--> v*e_i. The change of basis matrix is the modular Fourier transform, and works even when p|n.
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