Re: [sage-devel] Re: Bug in poset
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 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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[sage-devel] Re: Bug in poset
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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[sage-devel] Re: Bug in poset
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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[sage-devel] Re: Bug in poset
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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[sage-devel] Re: Bug in poset
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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[sage-devel] Re: Bug in poset
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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