On Sun, Jun 11, 2017 at 11:30 AM, John H Palmieri
<[email protected]> wrote:
>
>
> On Saturday, June 10, 2017 at 7:05:49 PM UTC-7, David Joyner wrote:
>>
>> On Thu, Jun 8, 2017 at 10:49 PM, John H Palmieri <[email protected]>
>> wrote:
>> >
>> >
>> > On Thursday, June 8, 2017 at 5:16:15 PM UTC-7, David Joyner wrote:
>> >>
>> >> Hi all:
>> >>
>> >> This is kind of a newbie question, as I'm not an expert on simplicial
>> >> complexes. It's also a minor technical issue on the documentation, not
>> >> the code.
>> >>
>> >> I'm trying to debug some code of mine and, on reading the
>> >> documentation for chain_complex on
>> >>
>> >>
>> >> http://doc.sagemath.org/html/en/reference/homology/sage/homology/simplicial_complex.html,
>> >> found this: "The rows and columns of the boundary matrices are indexed
>> >> by the lists given by the n_cells() method, which by default are
>> >> sorted." On the other hand, the documentation for n_cells has this
>> >> statement: "Sort the list if the argument sort is True. If sort is
>> >> None (the default), then sort depending on the value of the
>> >> sort_facets parameter (from the initialization of the simplicial
>> >> complex)." However, the sort_facets parameter (unless I'm mistaken)
>> >> does not sort the individual faces but rather sorts the vertices in
>> >> each facet.
>> >
>> >
>> > The documentation means that if "sort_facets" was True originally, then
>> > n_cells will also sort its result before returning it. ("then sort
>> > depending
>> > on the value of the sort_facets parameter": so if sort_facets was True,
>> > then
>> > n_cells should also sort. It doesn't mean "sort using the effect of the
>> > sort_facets parameter", but sort depending on its value, which is True
>> > or
>> > False. This could be made clearer, I guess.)
>> >
>>
>>
>> To be clear, I am getting different computations using the same sage
>> computations on different machines. One (recent, but used, linux)
>> machine consistently gives ones result, the other gives (randomly?)
>> several others. The "other" (a 8 yr old, a mac with possibly memory
>> issues) machine gives different results. I'm not saying your methods
>> are machine dependent, just that *for me* they seem to be.
>>
>> To be clear, these "inconsistent" computations take at least one day.
>> The "toy" (consistent) examples are okay.
>
>
> That's strange. Are you just getting different orders when you sort, or
> different answers for homology? Are the answers consistent on each machine?
> What type of object are the vertices?
>
The example which gives strange output is the bipyramid complex:
S = SimplicialComplex(maximal_faces=[(1,2,3), (1,2,4),\
(1,2,5), (1,3,4),(1,3,5),(2,3,4),(2,3,5)])
which has 9 1-faces. I'm computing the list of all stable configurations,
namely vectors c in ZZ^9 having non-negative components which cannot
fire (in the sense of chip-firing - see Duval, Klivans, Martin
https://arxiv.org/pdf/1101.3981.pdf) with respect to the 1-dimls simplicial
spanning tree given by the 1-faces (1, 4), (1,5), (2,5), (3,4). On an old
mac running OS 10.11.6 and sage 7.2.b0, the output is usually 268125,
after about a day, but once I also got 137500. On a linux machine running
ubuntu and sage 7.3, I always get 395625. These computations use
the S.chain_complex.differential method to compute the 1-diml
combinatorial up Laplacian, Q, then does a time-consuming search.
(Basically, I check that no column vector q of Q, except possibly one
corresponding to a face in the spanning tree, has the property that
all components of c-q remain non-negative, except possibly those
corresponding to a face in the spanning tree.)
A similar computation using the 3-simplex is relatively quick and
always produces
2500 stable configurations for both machines.
>>
>>
>> > I don't know if there is ever a good reason to specify
>> > sort_facets=False.
>> > Maybe we should deprecate it?
>> >
>> >>
>> >> In my code, I expected the faces of a fixed dimension to
>> >> be returned as a deterministic sorted list not a set whose ordering
>> >> could be random. Now, it *does* seem as though the faces are sorted.
>> >> It's just that, to me, the documentation of n_cells doesn't make that
>> >> clear.
>> >>
>> >> I'm asking if I'm mis-understanding something here or not.
>> >>
>> >> - David Joyner
>> >
>> >
>> > --
>> > John
>> >
>> >
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