Dear all,
the current implementation of __hash__ for PermutationGroupElement returns
a hash that not only depends on the given permutation, but also on the
group the permutation lives in.
Thus the "same" permutation (when compared with __eq__) may have different
hash values, which is not in line with the Python documentation (
https://docs.python.org/3.5/reference/datamodel.html#object.__hash__) and
leads to unexpected situations as the following.
sage: G = SymmetricGroup(2)
sage: H = SymmetricGroup(1)
sage: d = {G.one() : "FooBaa"}
sage: H.one() in list(d.keys())
True
sage: H.one() in d
False
Best,
Johannes Schwab
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