Re: [sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
On Saturday, July 9, 2016 at 12:37:15 PM UTC-4, Jakob Kroeker wrote: > > I think backward compatibility is a strong argument to keep returning True. >> > > well, there is also the option to deprecate the is_connected() function > for the empty graph > and then change the behaviour after a year. > > By the way, what about defining that the empty graph is connected AND > disconnected. > ( I'm joking :-) ) > Why not? A set can be open and closed :-) which is a perfect occasion to recall the hilarious (if not quite SFW): https://www.youtube.com/watch?v=SyD4p8_y8Kw -- 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] Re: Is the glass half-full or half-empty ? Pick a standard.
> > I think backward compatibility is a strong argument to keep returning True. > well, there is also the option to deprecate the is_connected() function for the empty graph and then change the behaviour after a year. By the way, what about defining that the empty graph is connected AND disconnected. ( I'm joking :-) ) But seriously, I just thought, what about dropping the definition for graph connectedness at all. and introduce three different cases instead: - a graph has 0 components - a graph has exactly 1 component - a graph has 2 or more components At least we are able to count ;-) I think If we cannot handle special cases consistently even in theory, we will never ever be able to implement it without getting tons of worms... Jakob Am Donnerstag, 22. August 2013 23:29:45 UTC+2 schrieb Stefan: > > I think backward compatibility is a strong argument to keep returning True. > > I also have an answer based on "my favorite definition is ...", namely the > analogue with matroid connectivity, where any matroid that is too small to > have a k-separation, is automatically k-connected. Extending this to > graphs, the empty graph should be infinitely connected. > -- 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] Re: Is the glass half-full or half-empty ? Pick a standard.
On 2013-08-20 23:21, Andrew Gainer-Dewar wrote: How about extending the input signature of Graph.is_connected() to include an option empty_graph_is_connected = False -1 for needless complication. -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
Hi, On Tuesday, 20 August 2013 23:21:43 UTC+2, Andrew Gainer-Dewar wrote: How about extending the input signature of Graph.is_connected() to include an option empty_graph_is_connected = False ? The problem with such a global variable is that is_connected() is used not just by humans, but also by other methods. The authors of those methods don't always know about the global variables affecting the computation; this is what caused the characteristic symmetric function mess in http://trac.sagemath.org/ticket/14885 . And even if they do, it is hard to work around this to obtain reliable behavior; one would have to change the global variable within the computation and then change it back at the end. Best regards, Darij -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
+1 On Thursday, August 22, 2013 6:04:22 AM UTC+1, Robert Bradshaw wrote: Is anyone arguing for returning True? If not, let's return False and put a note about it in the docs. -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
I will argue against False. We've had the convention that Graph().is_connected() is True for the last n years. This was an arbitrary (if heedless) choice at the boundary of several definitions. It doesn't seem to be an undue source of bugs, so the only impact of changing this arbitrary choice to another arbitrary choice will be to subtly break backwards-compatibility and add warning noise. I just consulted NetworkX, and I am convinced that their solution is the only reasonable change we could make: if len(G)==0: raise nx.NetworkXPointlessConcept( Connectivity is undefined for the null graph.) -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
I think backward compatibility is a strong argument to keep returning True. I also have an answer based on my favorite definition is ..., namely the analogue with matroid connectivity, where any matroid that is too small to have a k-separation, is automatically k-connected. Extending this to graphs, the empty graph should be infinitely connected. -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
Darij Grinberg darijgrinb...@gmail.com writes: Hi, On Tuesday, 20 August 2013 23:21:43 UTC+2, Andrew Gainer-Dewar wrote: How about extending the input signature of Graph.is_connected() to include an option empty_graph_is_connected = False ? The problem with such a global variable is that is_connected() is used not just by humans, but also by other methods. The authors of those methods don't always know about the global variables affecting the computation; this is what caused the characteristic symmetric function mess in http://trac.sagemath.org/ticket/14885 . And even if they do, it is hard to work around this to obtain reliable behavior; one would have to change the global variable within the computation and then change it back at the end. I don't think anyone was suggesting a global variable. empty_graph_is_connected would be a keyword option to is_connected(). -Keshav -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
How about extending the input signature of Graph.is_connected() to include an option empty_graph_is_connected = False ? (It could, of course, default to True instead, but I'm an enumeration guy and think this is nonsense.) Advantages, as I see them: * True-ists and False-ists both get their way. * Novice users of Graph.is_connected() are forced to confront the problem by the semantics of the method itself. * Can be configured to not break existing code (although this requires using the obviously wrong True). * Reflects the essentially definitional/philosophical nature of the problem. Disadvantages, as I see them: * Complicates the semantics of the method. * Adds a bit of logic. * Fails to end the philosophical debate—we'd still need to decide what to set to default! --Andrew signature.asc Description: OpenPGP digital signature
Re: [sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
Is anyone arguing for returning True? If not, let's return False and put a note about it in the docs. On Tue, Aug 20, 2013 at 2:21 PM, Andrew Gainer-Dewar andrew.gainer.de...@gmail.com wrote: How about extending the input signature of Graph.is_connected() to include an option empty_graph_is_connected = False ? (It could, of course, default to True instead, but I'm an enumeration guy and think this is nonsense.) Advantages, as I see them: * True-ists and False-ists both get their way. * Novice users of Graph.is_connected() are forced to confront the problem by the semantics of the method itself. * Can be configured to not break existing code (although this requires using the obviously wrong True). * Reflects the essentially definitional/philosophical nature of the problem. Disadvantages, as I see them: * Complicates the semantics of the method. * Adds a bit of logic. * Fails to end the philosophical debate—we'd still need to decide what to set to default! --Andrew -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
Yo !! As you can check here http://mathoverflow.net/questions/120536/is-the-empty-graph-a-tree the big shot guys agree that the empty graph is to be considered disconnected. So YES in general, mathematicians appear to be depressed persons. Come on. It's not funny at all ! Let's just say that we don't know, and refuse this sterile discussion ! It will be nice to admit that we don't know what we don't know, for once ! :-P Nathann -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
[sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
Hello! As you can check here http://mathoverflow.net/questions/120536/is-the-empty-graph-a-tree the big shot guys agree that the empty graph is to be considered disconnected. So YES in general, mathematicians appear to be depressed persons. On Mon, Aug 19, 2013 at 5:51 PM, Nathann Cohen nathann.co...@gmail.comwrote: Hell everybody !! There is a discussion on theology going on at #15060, about whether we should consider whether the empty graph is connected or not. We already had one about deciding whether the empty graph is a tree or not, and Karl-Dieter supposed that other discussions of this kind already happened in Sage. Here's the thing : we have two definitions which conflict on a trivial case only, and we have functions that are expected to answer whether -- yes or no -- the property holds. I personally voted for not answering anything, and raising a We Have No Idea And We Don't Want To Be Forced To Give An Answer Exception in this case, for there is no way to give an answer that would not lead anybody to very weird bugs. What do you think ? Darij agreed with this idea, and Karl-Dieter believes that we should make a decision and answer something :-) Help us ! :-P Nathann -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
PS Note that if you ever did decide to have a method G.is_disconnected() then I would want that to be False also for the emtpy graph, just as 1 is not composite. On 19 August 2013 17:07, Jernej Azarija azi.std...@gmail.com wrote: Hello! As you can check here http://mathoverflow.net/questions/120536/is-the-empty-graph-a-tree the big shot guys agree that the empty graph is to be considered disconnected. So YES in general, mathematicians appear to be depressed persons. On Mon, Aug 19, 2013 at 5:51 PM, Nathann Cohen nathann.co...@gmail.com wrote: Hell everybody !! There is a discussion on theology going on at #15060, about whether we should consider whether the empty graph is connected or not. We already had one about deciding whether the empty graph is a tree or not, and Karl-Dieter supposed that other discussions of this kind already happened in Sage. Here's the thing : we have two definitions which conflict on a trivial case only, and we have functions that are expected to answer whether -- yes or no -- the property holds. I personally voted for not answering anything, and raising a We Have No Idea And We Don't Want To Be Forced To Give An Answer Exception in this case, for there is no way to give an answer that would not lead anybody to very weird bugs. What do you think ? Darij agreed with this idea, and Karl-Dieter believes that we should make a decision and answer something :-) Help us ! :-P Nathann -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-devel] Re: Is the glass half-full or half-empty ? Pick a standard.
On 19 August 2013 19:26, Keshav Kini keshav.k...@gmail.com wrote: John Cremona john.crem...@gmail.com writes: [...] and then you will not have the silly situation that (in 5.11) sage: G = Graph([]); G Graph on 0 vertices sage: G.is_connected() True sage: G.connected_components() [] as to me it seems contradictory to have a graph claiming to be connected but having no connected components. Why? A graph is connected iff every pair of vertices is connected, which is to say that every connected component is the same as every other connected component (i.e. a uniqueness property). The existence of a connected component seems to me to be independent from the uniqueness of a connected component, and so either 0 or 1 connected components should be admitted. I was trying to argue against any position based on my favourite definition is ... and it satisfies that definition since the whole point is that there are many different defintions which agree on nontrivial cases but give different result for the trivial cases. If you define a prime number to be an integer with precisely 2 prime divisors, itself and 1, then you find that the only prime number is -1. It seems (to me) much better to decide on an important property which you want to be true -- such as uniqueness of primes factorizations, or decompositions into connected components, and use the definition for trivial objects which is consistent with that. John Anyway, I'm not trying to argue that the empty graph should be considered connected. Maybe it is more useful to define connectedness by existence *and uniqueness* of connected components, after all. I like the nLab wiki link that darij provided in the ticket description [1]. I'm especially tickled by the example, False is not true :) -Keshav [1] http://ncatlab.org/nlab/show/too+simple+to+be+simple -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
