Re: [sage-devel] Problems with posets
Victor, a kind of followup: https://trac.sagemath.org/ticket/24584 I think we should add is_extension() to posets, and then maybe functions to list "minimal extensions" and "minimal un-extensions" (right term for that?) of a poset. I think that the last one is just a way to remove a covering relation. With those we could have principal upper and lower sets of a power poset, i.e. an extensions poset you asked. -- Jori Mäntysalo
Re: [sage-devel] Problems with posets
On Mon, 15 Jan 2018, Victor Porton wrote:
Are you sure? I think I need non-automorphism permutations. Automorphism
by definition maps a Hasse diagram into itself, while I need to map it
into other diagrams, not into itself.
True, but I think that the converse should be doable by automorphism
group ("permutations divided by automorphism").
I say that a poset A is greater than the poset B if and only if:
For every x, y: if x<=y in B-order then if x<=y in A-order.
This is called 'extension' of a poset, see
http://planetmath.org/extensionofaposet . Mostly linear extensions are
studied, and I think there is not (yet) a program in Sage to list
extensions of a poset.
Actually listing all extensions of an antichain would be exactly all
labeled posets. Maybe I should think about implementing this.
By the way, can anyone give me CPU power of a supercomputer for free?
Try to make a paper together with someone in Finland... 1000 CPU hours
is automatically available here for any researcher in any university,
more by asking.
(There was error, 1 CPU hours is the right value.)
I am an amateur researcher. It is hard for me to find a research partner.
OK. For that I don't have good suggestions.
However I saved money on an UPS, so in the case if electricity
disconnects or something happens with my Linux I would need start anew.
If you don't want to make a code that can save temporary results you can
just install some virtualization software (VirtualBox is my favorite in
desktop), install Sage inside the virtual machine, and then make snapshots
of the virtual machine sometimes. You can even make it automatic, see
https://www.techrepublic.com/article/how-to-automate-virtualbox-snapshots-with-the-vboxmanage-command/
--
Jori Mäntysalo
Re: [sage-devel] Problems with posets
On Monday, January 15, 2018 at 9:51:05 AM UTC+2, Jori Mäntysalo wrote: > > On Mon, 15 Jan 2018, Victor Porton wrote: > > > So I have no tool to enumerate not up-to-isomorphism :-( > > At least you can re-compute OEIS serie A001035 by > > [sum(sum(factorial(i)/P.hasse_diagram().automorphism_group(return_group=False, > > > order=True)) for P in Posets(i)) for i in range(6)] > > so I guess the right direction is to use automorphism group of the Hasse > diagram. A digraph d can be translated to poset just by Poset(d). Are you sure? I think I need non-automorphism permutations. Automorphism by definition maps a Hasse diagram into itself, while I need to map it into other diagrams, not into itself. > > Another issue: I need only posets greater than a certain fixed poset > > Please give an example. What would be a poset "greater" than, say, > posets.DiamondPoset(5)? > I say that a poset A is greater than the poset B if and only if: For every x, y: if x<=y in B-order then if x<=y in A-order. posets.DiamondPoset(5) is no different. > By the way, can anyone give me CPU power of a supercomputer for free? > > Try to make a paper together with someone in Finland... 1000 CPU hours is > automatically available here for any researcher in any university, more by > asking. I am an amateur researcher. It is hard for me to find a research partner. I may try to publish the result of this research in a peer reviewed journal, but it may be rejected with high probability. Anyway I am calculating this not to publish, but for writing an applied software. 1000 hours. It is 41.7 days. Or it is 5.2 days if I will manage to run it on all 8 threads of my 4-core CPU. I can well wait 5 days or even a month. However I saved money on an UPS, so in the case if electricity disconnects or something happens with my Linux I would need start anew. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
Re: [sage-devel] Problems with posets
On Mon, 15 Jan 2018, Victor Porton wrote: So I have no tool to enumerate not up-to-isomorphism :-( At least you can re-compute OEIS serie A001035 by [sum(sum(factorial(i)/P.hasse_diagram().automorphism_group(return_group=False, order=True)) for P in Posets(i)) for i in range(6)] so I guess the right direction is to use automorphism group of the Hasse diagram. A digraph d can be translated to poset just by Poset(d). Another issue: I need only posets greater than a certain fixed poset Please give an example. What would be a poset "greater" than, say, posets.DiamondPoset(5)? By the way, can anyone give me CPU power of a supercomputer for free? Try to make a paper together with someone in Finland... 1000 CPU hours is automatically available here for any researcher in any university, more by asking. -- Jori Mäntysalo
[sage-devel] Problems with posets
I want to check a graph theoretic conjecture appeared during an applied software research. I am going to conduct a numeric experiment involving three posets of the size N (for small N). (I hope N=4 or 5 will suffice, but it is entirely unknown for me.) I can take one of the three up-to-isomorphism, but the other two cannot be taken up-to-isomorphism, because this way its relations with the other two posets would be "erased". So I have three posets: one up-to-isomorphism and the other two not up- to-isomorphism. To my frustration I found that we have sage.combinat.posets.posets.FinitePosets_n(n) but not sage.combinat.posets.posets.FinitePosets(n). So I have no tool to enumerate not up-to-isomorphism :-( Could you help me to solve this problem? I am not strong in graph theory. If somebody provides an algorithm to enumerate all posets on a set, this may help considerably. Another issue: I need only posets greater than a certain fixed poset (one of the three posets mentioned above, actually). Filtering out posets which are not greater than the given one would rule out many variants and speed up the search. So I wish that they would be ruled out on the stage of enumeration, rather than enumerating all of them and filtering out these which are not greater than it. By the way, can anyone give me CPU power of a supercomputer for free? My problem may be important for development of XML technologies in the World. Don't hesitate to write me. Well, my actual problem: https://math.stackexchange.com/q/2601651/4876 -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
