Thanks Dima. I certainly agree that there is a mathematical error with my
approach. I'm wondering if there is still a bug since the result of
compare(x,y) and P.islequal(x,y) differ. Shouldn't they be the same, even
if I am giving them bad input?
Best Regards,
Trevor Karn
On Thu, Jan 12, 2023 at 5:52 AM Dima Pasechnik <dimp...@gmail.com> wrote:
> 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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