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gh-36057: `sage.arith`: Update `# needs` <!-- ^^^^^ Please provide a concise, informative and self-explanatory title. Don't put issue numbers in there, do this in the PR body below. For example, instead of "Fixes #1234" use "Introduce new method to calculate 1+1" --> <!-- Describe your changes here in detail --> <!-- Why is this change required? What problem does it solve? --> <!-- If this PR resolves an open issue, please link to it here. For example "Fixes #12345". --> - Part of: #29705 - Cherry-picked from: #35095 <!-- If your change requires a documentation PR, please link it appropriately. --> ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> <!-- If your change requires a documentation PR, please link it appropriately --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> <!-- Feel free to remove irrelevant items. --> - [x] The title is concise, informative, and self-explanatory. - [ ] The description explains in detail what this PR is about. - [x] I have linked a relevant issue or discussion. - [ ] I have created tests covering the changes. - [ ] I have updated the documentation accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on - #12345: short description why this is a dependency - #34567: ... --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: #36057 Reported by: Matthias Köppe Reviewer(s): David Coudert
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src/sage/arith/functions.pyx

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@@ -72,25 +72,25 @@ def lcm(a, b=None):
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Make sure we try `\QQ` and not merely `\ZZ` (:trac:`13014`)::
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sage: bool(lcm(2/5, 3/7) == lcm(SR(2/5), SR(3/7))) # optional - sage.symbolic
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sage: bool(lcm(2/5, 3/7) == lcm(SR(2/5), SR(3/7))) # needs sage.symbolic
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True
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Make sure that the lcm of Expressions stays symbolic::
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sage: parent(lcm(2, 4))
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Integer Ring
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sage: parent(lcm(SR(2), 4)) # optional - sage.symbolic
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sage: parent(lcm(SR(2), 4)) # needs sage.symbolic
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Symbolic Ring
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sage: parent(lcm(2, SR(4))) # optional - sage.symbolic
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sage: parent(lcm(2, SR(4))) # needs sage.symbolic
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Symbolic Ring
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sage: parent(lcm(SR(2), SR(4))) # optional - sage.symbolic
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sage: parent(lcm(SR(2), SR(4))) # needs sage.symbolic
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Symbolic Ring
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Verify that objects without lcm methods but which can't be
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coerced to `\ZZ` or `\QQ` raise an error::
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sage: F.<x,y> = FreeMonoid(2) # optional - sage.groups
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sage: lcm(x,y) # optional - sage.groups
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sage: F.<x,y> = FreeMonoid(2) # needs sage.groups
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sage: lcm(x,y) # needs sage.groups
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Traceback (most recent call last):
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...
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TypeError: unable to find lcm of x and y

src/sage/arith/long.pxd

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# sage.doctest: optional - sage.misc.cython
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# sage.doctest: needs sage.misc.cython
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r"""
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Fast conversion of Python objects to C long
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"""

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