I confirm the error: P.maximal_elements() contains S5 and A5.
As a possibly minimal example, it suffices to use only the last 3 groups: I
also see the error with
P = Poset(data=(groups[16:], compare), element_labels=strs[16:]).
Please open a ticket.
On Wednesday, January 11, 2023 at 9:58:32 AM UTC-7 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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