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dft for symmetric group algebra when p|n! #37748

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dft for symmetric group algebra when p|n! #37748

wants to merge 15 commits into from

Commits on Apr 4, 2024

  1. dft for symmetric group algebra when p|n 

    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.
    @jacksonwalters
    jacksonwalters committed Apr 4, 2024
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  2. Update symmetric_group_algebra.py

    @jacksonwalters
    jacksonwalters committed Apr 4, 2024
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  3. remove trailing whitespace 

    attempting to get through lint
    @jacksonwalters
    jacksonwalters committed Apr 4, 2024
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  4. finish adapting from Jupyter notebook

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    jacksonwalters committed Apr 4, 2024
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  5. put all code into single lines 

    remove helper functions in favor of lambda functions
    @jacksonwalters
    jacksonwalters committed Apr 4, 2024
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  6. Update symmetric_group_algebra.py

    @jacksonwalters
    jacksonwalters committed Apr 4, 2024
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  7. Update symmetric_group_algebra.py

    @jacksonwalters
    jacksonwalters committed Apr 4, 2024
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Commits on Apr 5, 2024

  1. try formatting matrix

    @jacksonwalters
    jacksonwalters committed Apr 5, 2024
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  2. example was wrong 

    use p=2, n=3 for a small example.
    @jacksonwalters
    jacksonwalters committed Apr 5, 2024
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  3. matrix is misspelled 

    lowercase m in matrix
    @jacksonwalters
    jacksonwalters committed Apr 5, 2024
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  4. use transpose to get matrix of coordinate vectors

    @jacksonwalters
    jacksonwalters committed Apr 5, 2024
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  5. Update src/sage/combinat/symmetric_group_algebra.py 

    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>
    @jacksonwalters @S17A05
    jacksonwalters and S17A05 committed Apr 5, 2024
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  6. Update src/sage/combinat/symmetric_group_algebra.py 

    Co-authored-by: Sebastian A. Spindler <153911337+S17A05@users.noreply.github.com>
    @jacksonwalters @S17A05
    jacksonwalters and S17A05 committed Apr 5, 2024
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Commits on Apr 6, 2024

  1. Update symmetric_group_algebra.py

    @jacksonwalters
    jacksonwalters committed Apr 6, 2024
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  2. add commentary explaining the DFT in this case 

    remove form from argument
    @jacksonwalters
    jacksonwalters committed Apr 6, 2024
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