Added hash function to elements of the fundamental group of an extended affine Weyl group

[65537]

This change allows users to compute the python hash function for elements of the (Borovoi) fundamental group of an extended affine Weyl group, and subsequently for elements of the extended Weyl group itself if using the FW realization. This, in turn, allows to use these mathematical objects as keys in dictionaries.

Fixes #36121 . It adds a __hash__ function to the class FundamentalGroupElement associated with FundamentalGroupOfExtendedAffineWeylGroup.

SAGE already associates to each element of the fundamental group an integer, accessible as its value() or _value. This integer is unique among other elements of the same fundamental group and thus suitable as a hash for hashmap applications (e.g. Python dictionaries). We return the hash of that integer, which is the integer itself for current python implementations.

W = ExtendedAffineWeylGroup('A4')
fun = W.fundamental_group().an_element()
w = W.FW().an_element()

hash(fun), {w: 0}

yields the following result:

(4, {pi[4] * S0*S1*S2*S3*S4: 0})

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

[github-actions]

Documentation preview for this PR (built with commit 8e9c87a; changes) is ready! 🎉

[tscrim]

Thank you for noticing and fixing this.

For next time, please be sure to add a doctest showing the issue is fixed (also, all methods need to have at least one doctest).

[65537]

Dear Travis,

thank you for reviewing and improving my pull request. I was following the (mathematically very similar) class WeylGroupElement whose hash function has neither a docstring nor a test, but I will make sure to always include them in future pull requests.

Best, Felix

[tscrim]

Indeed, that is generally a good idea. Unfortunately in this case that is some fairly old code that was included before we developed our modern practices. Thank you for adding it. LGTM.

[vbraun]

sage -t --long --warn-long 39.2 --random-seed=123 src/sage/combinat/root_system/fundamental_group.py
**********************************************************************
File "src/sage/combinat/root_system/fundamental_group.py", line 339, in sage.combinat.root_system.fundamental_group.FundamentalGroupElement.__hash__
Failed example:
    hash(w) == hash(w.value())
Exception raised:
    Traceback (most recent call last):
      File "/home/release/Sage/src/sage/doctest/forker.py", line 709, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/home/release/Sage/src/sage/doctest/forker.py", line 1144, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.combinat.root_system.fundamental_group.FundamentalGroupElement.__hash__[3]>", line 1, in <module>
        hash(w) == hash(w.value())
                        ^^^^^^^^^
    TypeError: 'tuple' object is not callable
**********************************************************************

[tscrim]

@65537 Sorry, I didn’t check the doctest carefully. Please change value() to value.

[65537]

Testing for value() is correct, as long as you are testing on FundamentalGroupElements, which was the main culprit here

[tscrim]

Ah, indeed.

[tscrim]

@vbraun Has this been merged? If so, should we close this?