Hello.
I have to work with a simplicial complex whose vertices are frozenset.
and found that is_connected() is wrong.
Version and OS:
SageMath version 9.5
WSL (Ubuntu) on Windows 10
To Reproduce (inside sage command):
sage: V = SimplicialComplex([[1, 2, 3]])
sage: V.is_connected()
True
sage: W = SimplicialComplex([[frozenset({1}), frozenset({2}),
frozenset({3})]])
sage: W.is_connected()
False
I think this is because SimplicialComplex.is_graph() is wrong:
sage: V.graph()
Graph on 3 vertices
sage: W.graph()
Looped multi-graph on 2 vertices
This is probably because in topology/simplicial_complex.py, the dictionary
of edges in SimplicialComplex.graph()
is constructed by using min and max of the endpoints:
for e in edges:
try:
v = min(e)
max_e = max(e)
and in python, min([frozenset({1}), frozenset({2})]) and
max([frozenset({1}), frozenset({2})]) are both frozenset({1}), so graph()
yields (wrong) loops.
Best,
Haruhisa
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