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] (Proposed feature) Enumerate all labeled posets
On Mon, 2018-01-15 at 23:28 +0200, Jori Mäntysalo wrote: > On Mon, 15 Jan 2018, Victor Porton wrote: > > > I need to enumerate all labeled (that is NOT up-to-isomorphism) > posets of N > > elements. > > The algorithm is here: https://stackoverflow.com/a/48270680/856090 > > No, that paper gives "method to construct pairwise non-isomorphic > posets", > i.e. up-to-isomorphism. > > Btw, just extending poset by adding a new maximal element covering > all > possible subsets of maximal elements will give you all posets having > 1, 2, > ..., n as a linear extension. That is not enought? Yes, you are right, that algorithm generated not all posets (not up- to-isomorphism). I have deleted the wrong answer at StackOverflow. So as for now, the best solution I have is to enumerate posets up to isomorphism and compose them with all permutations of the set of N elements. It may generate duplicates however and thus isn't very efficient. I confess that I am not ready to write this code into Sage core. I will write my own function which will use permutations to enumerate all posets of N elements, to use in my own endeavor. > -- > Jori Mäntysalo -- 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] (Proposed feature) Enumerate all labeled posets
On Mon, 15 Jan 2018, Victor Porton wrote: I need to enumerate all labeled (that is NOT up-to-isomorphism) posets of N elements. The algorithm is here: https://stackoverflow.com/a/48270680/856090 No, that paper gives "method to construct pairwise non-isomorphic posets", i.e. up-to-isomorphism. Btw, just extending poset by adding a new maximal element covering all possible subsets of maximal elements will give you all posets having 1, 2, ..., n as a linear extension. That is not enought? -- Jori Mäntysalo
[sage-devel] (Proposed feature) Enumerate all labeled posets
I need to enumerate all labeled (that is NOT up-to-isomorphism) posets of N elements. The algorithm is here: https://stackoverflow.com/a/48270680/856090 I would like to write a patch to include this algorithm into Sage. But Posets(3) is already taken to mean unlabeled (up-to-isomorphism) posets. Please advice how to name the new enumerator to avoid confusion. After receiving your advice I am glad to work to make a patch for Sage. -- 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 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.
[sage-devel] Re: Bug report: Could not import nbconvert: No module named base
Le lundi 15 janvier 2018 03:13:53 UTC+1, Victor Porton a écrit : > > > http://localhost:/nbconvert/script/home/porton/math/namespaces/Comparison%20of%20counter-example%20algorithms.ipynb?download=true > > 500 : Internal Server Error > The error was: > > Could not import nbconvert: No module named base > This is a known issue, see https://groups.google.com/d/msg/sage-devel/Qsf9Gb4pDt4/vIORrWIABwAJ A fix is under preparation at https://trac.sagemath.org/ticket/24484 Eric. -- 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.
