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1 year ago
gh-37733: Bell polynomials univariate variable fix, complete and ordinary variants <!-- ^ 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 #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 #12345". --> I've changed the implementation of `bell_polynomial` so that `bell_polynomial(n,n) == x0^n` instead of `x^n` because when `k < n`, `bell_polynomial(n,k)` is a polynomial in variables `x0, ..., xn-k`. I added a relevant example to illustrate the new behaviour (there were none for the old behaviour) and tests for the degenerate examples. This is based upon my suggestion proposed in issue #37727. After [suggestions](https://github.com/sagemath/sage/issues/37727#issuec omment-2036002403) from @tscrim, I changed `k` to be an optional argument with default value `None`. If `k is None`, complete Bell polynomials is returned instead. Also, support for ordinary analogues was added. Documentation, examples and tests were subsequently updated. ### :memo: 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. ### :hourglass: Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - #12345: short description why this is a dependency --> <!-- - #34567: ... --> URL: https://github.com/sagemath/sage/pull/37733 Reported by: Nolord Reviewer(s): Nolord, Travis Scrimshaw
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