Dear Jerome,
On 1 Apr., 10:48, "[email protected]"
<[email protected]> wrote:
> G = SymmetricGroup(4)
> H = G.subgroup([G((1,2,3))])
> K = G.subgroup([G((2,3,1))])
You can see how subgroups are compared: type 'K.__cmp__??' and you'll
see the source code. It is:
def __cmp__(self, other):
if self is other:
return 0
if not isinstance(other, PermutationGroup_generic):
return -1
c = cmp(self.ambient_group(), other.ambient_group())
if c: return c
if self.is_subgroup(other):
return -1
else:
return 1
'K==H' just tests whether 'K.__cmp__(H)' returns zero. As you can see
from the code, this is the case if and *only* if K is the same object
(in computer's memory) as H.
Unfortunately, the output of G.subgroup(...) is not cached. Hence,
even though G((1,2,3))==G((2,3,1)), the two subgroups are not
considered being equal.
I think this is a bug. Before returning -1 if self.is_subgroup(other),
it should be tested whether other.is_subgroup(self), in which case 0
should be returned. Do people agree?
Yours,
Simon
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