gh-36122: Added hash function to elements of the fundamental group of an extended affine Weyl group
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.
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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})
```
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URL: https://github.com/sagemath/sage/pull/36122
Reported by: 65537
Reviewer(s): 65537, Travis Scrimshaw
