No, no bug (yet).
The problem is that you are not careful constructing the correct subgroups
to use.
E.g. if you want groups[2] to be a subgroup of groups[5]=<(1,2,3,4)>
you must take groups[2]=<(1,3)(2,4)>, not groups[2]=<(1,2)(3,4)>.
You can start with the maximal subgroups of S_5, and intersect them, then
intersect the intersections, etc.
Or you can rewrite your compare(a,b) in terms of "an element of the
conjugacy class of subgroups with `b`
a representative contained in `a`"
E.g. using libgap:
sage:
groups[-1]._libgap_().ConjugacyClassSubgroups(groups[1]._libgap_()).Elements()
[ Group([ (4,5) ]), Group([ (3,4) ]), Group([ (3,5) ]), Group([ (2,3) ]),
Group([ (2,4) ]), Group([ (2,5) ]), Group([ (1,2) ]), Group([ (1,3) ]),
Group([ (1,4) ]), Group([ (1,5) ]) ]
But this might well be a different poset, as once you fixed just one
maximal subgroup H_1, the conjugacy class of the 2nd maximal subgroup H_2
might already be splitting into different orbits w.r.t. conjugaction by
H_1, so potentially different choices, etc...
HTH
Dima
On Wednesday, January 11, 2023 at 6:30:32 PM UTC dmo...@deductivepress.ca
wrote:
> P erroneously thinks that GA(1,5) is less than A5. I have no idea what's
> causing that either.
>
> On Wednesday, January 11, 2023 at 11:21:39 AM UTC-7 Trevor Karn wrote:
>
>> Thanks for the confirmation. I'll double check this is not a logic bug
>> before I open a ticket.
>>
>> On Wednesday, January 11, 2023 at 1:20:09 PM UTC-5 Trevor Karn wrote:
>>
>>> At least part of the problem is that I gave bad generators for GA(1,5).
>>> It should be [[(1,2,3,4,5)],[(2,3,5,4)]].
>>>
>>> On Wednesday, January 11, 2023 at 11:58:32 AM UTC-5 Trevor Karn wrote:
>>>
>>>> Hi all,
>>>>
>>>> I was wondering if anyone can reproduce this bug with Poset creation. I
>>>> create a Poset by passing the elements and the comparison function as a
>>>> tuple (elements, func) and a pair of elements for which func(x,y) returns
>>>> True has P.lequal(x,y) returning False
>>>>
>>>> I'm trying to create the subgroup lattice up to conjugacy of S5.
>>>>
>>>> sage: load('s5-subgroup.sage') # builds poset, see below
>>>> sage: groups[-2]
>>>> Permutation Group with generators [(1,2,3), (1,2,3,4,5)]
>>>> sage: groups[-1]
>>>> Permutation Group with generators [(1,2), (1,2,3,4,5)]
>>>> sage: compare(groups[-2], groups[-1])
>>>> True
>>>> sage: P.is_lequal('A5','S5')
>>>> False
>>>>
>>>> The content of 's5-subgroup.sage' is below.
>>>>
>>>> gens = [
>>>> [[]], # trivial
>>>> [[(1,2)]], # S2
>>>> [[(1,2),(3,4)]], #z/2
>>>> [[(1,2)],[(3,4)]], # disjoint V4
>>>> [[(1,2),(3,4)],[(1,3),(2,4)]], # double transp V4
>>>> [[(1,2,3,4)]], # z/4
>>>> [[(1,2,3,4)],[(1,3)]], # D8 (D4 in GAP notation)
>>>> [[(1,2,3)]], # z/3
>>>> [[(1,2,3)],[(4,5)]], # z/6
>>>> [[(1,2,3)],[(1,2)]], # S3
>>>> [[(1,2,3)],[(1,2),(4,5)]], # twisted S3
>>>> [[(1,2,3)],[(1,2)],[(4,5)]], # S3 x S2
>>>> [[(1,2),(3,4)],[(1,2,3)]], # A4
>>>> [[(1,2,3,4)],[(1,2)]], # S4
>>>> [[(1,2,3,4,5)]], # z/5
>>>> [[(1,2,3,4,5)],[(2,5),(3,4)]], # D10
>>>> [[(1,2,3,4,5)],[(2,3,4,5)]], # GA(1,5)
>>>> [[(1,2,3,4,5)],[(1,2,3)]], # A5
>>>> [[(1,2,3,4,5)],[(1,2)]] # S5
>>>> ];
>>>>
>>>> strs = ['1', 'S2', 'Z/2', 'V4', 'V4 (dbl)', 'Z/4', 'D8',
>>>> 'Z/3', 'Z/6', 'S3', 'S3 (twist)', 'S3xS2',
>>>> 'A4', 'S4', 'Z/5', 'D10', 'GA(1,5)', 'A5',
>>>> 'S5']
>>>>
>>>> to_group = lambda x: PermutationGroup(gens=x);
>>>> groups = list(map(to_group, gens));
>>>> compare = lambda x, y: x.is_subgroup(y);
>>>> P = Poset(data=(groups, compare), element_labels=strs)
>>>>
>>>>
>>>>
>>>>
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