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sagemathgh-37784: Speed up symmetric group simple_module_rank()
<!-- ^ Please provide a concise and informative title. --> <!-- ^ Don't put issue numbers in the title, do this in the PR description below. --> <!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method to calculate 1 + 2". --> <!-- v Describe your changes below in detail. --> <!-- v Why is this change required? What problem does it solve? --> <!-- v If this PR resolves an open issue, please link to it here. For example, "Fixes sagemath#12345". --> Since we are going to work with a matrix $f^{\lambda} \times f^{\lambda}$ (recall $f^{\lambda}$ is the number of standard Young tableaux of shape $\lambda$), then we should just store the list of standard tableaux rather than iterating over them repeatedly. This results in a major speedup: ``` sage: from sage.combinat.specht_module import simple_module_rank sage: %time simple_module_rank([5,3,2], GF(2)) CPU times: user 1.34 s, sys: 35.7 ms, total: 1.38 s Wall time: 1.38 s 200 ``` versus before ``` sage: %time simple_module_rank([5,3,2], GF(2)) CPU times: user 4.97 s, sys: 65 ms, total: 5.03 s Wall time: 5.06 s 200 ``` ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> - [x] The title is concise and informative. - [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. For example, --> <!-- - sagemath#12345: short description why this is a dependency --> <!-- - sagemath#34567: ... --> URL: sagemath#37784 Reported by: Travis Scrimshaw Reviewer(s): Darij Grinberg
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