Hey Jori, > > OK. I have used to using html docs, but this of course varies. >
Of course (although I should be a little more honest and state that my viewpoint comes primarily from people who I've told to use the `?`). > > Neither way, at least .show() function for poset does not tell about > figsize-option etc. > Well, I've never really been able to understand the graph plotting. IIRC most of the doc is in the header of some module... just use view(P, tightpage=True), it uses dot2tex if you install the optional spkg (with sage -i dot2tex). IMO the output is much prettier. > > Trying to understand... mathematically there is kind of diamond inclusion > of classes: > > finite lattices \subset lattices > finite lattices \subset finite posets > lattices \subset posets > finite posets \subset posets > > Which means that, for example, every function for finite lattice is > available for finite poset, but not necessarily other way. On C++ > this could be modelled with multiple inheritance. > Otherway around, any methods for finite posets is also for finite lattices, but you're right, it's basically multiple inheritance. > > But how come categories to this picture? > As I stated, they can act like ABC's (abstract base classes), but can be set at runtime based on inputs (see MatrixSpace(R, m, n) with m = n and with m != n). Here's also a nice tutorial on the subject <http://www.sagemath.org/doc/thematic_tutorials/coercion_and_categories.html>. Although they carry more information with them which is used for the morphisms. > > This is still quite confusing (or I am dumb, or both). To get posets of > size 5 one can say > > Posets(5) > > which internally does something like > > [x for x in GenerateAllDirectedGrapsh(5) if x.is_poset()] > > To get lattices of size 5 one says > > [sage.combinat.posets.lattices.FiniteLatticePoset(x) for x in Posets(5) if > x.is_lattice()] > > Because a) FiniteLatticePoset is not available on global namespace and b) > there is no ready method to get lattices of given size. > > Am I right on this? > `Posets` is special; it's not the actual category object, like say Groups is. It's somewhat of an abuse here IMO, but it's minor. Although I don't think we have methods to get all lattices of a given rank yet in Sage...IDK off-hand for sure. Best, Travis -- 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/d/optout.
