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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### ⌛ Dependencies

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URL: #36122
Reported by: 65537
Reviewer(s): 65537, Travis Scrimshaw

Author: Release Manager

src/sage/combinat/root_system/fundamental_group.py

@@ -325,6 +325,21 @@ def act_on_affine_lattice(self, wt):
         """
         return wt.map_support(self.parent().action(self.value()))
 
+    def __hash__(self):
+        r"""
+        Return the hash of ``self``.
+
+        TESTS:
+
+        Check that :issue:`36121` is fixed::
+
+            sage: W = ExtendedAffineWeylGroup('A4')
+            sage: fun = W.fundamental_group().an_element()
+            sage: hash(fun) == hash(fun.value())
+            True
+        """
+        return hash(self.value())
+
 
 class FundamentalGroupOfExtendedAffineWeylGroup_Class(UniqueRepresentation,
                                                       Parent):