Hi Florent, On 17 Okt., 10:42, Florent Hivert <florent.hiv...@univ-rouen.fr> wrote: > On Sat, Oct 16, 2010 at 05:08:37PM -0400, David Roe wrote: > > You can either inherit from sage.rings.commutative_ring.CommutativeRing, or > > modify FreeModule to work better with the category framework. The first is > > probably the easier option. > > Just a note: Testing if some parent belong to a category is fairly trivial (as > it should):
I disagree. Of course, testing that a parent was DEFINED in a certain category is trivial. But there is a long way to go until the test results will be what a mathematician might mean by "it BELONGS to a certain category". For example: sage: P.<x,y,z> = GF(3)[] sage: P in Algebras(GF(3)) False Either (1) one should sytematically go through all parent classes in Sage and carefully choose the "right" category in the init method, or (2) one should introduce more elaborate tests for containment in categories, that would recognise "P in CommutativeAlgebras(GF(3))" even if P was just defined as being contained in Rings(). But what is the "right" category? Since there is Sage's coercion model: Wouldn't it be logical that "P in CommutativeAlgebras(ZZ)", because P is commutative and there is coercion from ZZ to GF(3)? Clearly those things can hardly be done when P is initialised. So, I believe that *if* we want to combine the category framework with Sage's coercion model than we have to opt for (2). I initiated a related discussion at http://groups.google.com/group/sage-algebra/browse_thread/thread/a937ffac63191edd, but perhaps it makes sense to discuss it on sage-devel? To summarise some of the arguments from the sage-algebra thread: * (1) would be the cleanest solution, but is likely to involve a lot of partially dull work. In the case of rings, it should always be tested if it is Rings() or CommutativeRings() or Algebras(R) or CommutativeAlgebras(R). Is this suitable for a student project? * (1) is fast, and we *want* that "X in Cat" is fast. * (1) is not so flexible - in the example above, one could hardly have "P in Algebras(ZZ)". * My suggestion for (2) is that, once "X in Cat" is establish, one would dynamically specialise the category of X by X._init_category_(Category.join([X.category(),Cat])). In that way, after the second call, (2) is as fast as (1). * Counterargument of Nicolas was that he knows cases in which (2) would be so slow that even doing it once is too much. So, if one opts for (2) (and I do) than one should introduce mechanisms to make things fast. For example, if the question is whether X is finite then I see four options/attitudes for the user. The user should be able to advice Sage: i) "I assert that X is finite. So, act on it, and don't try to verify that X is finite yourself", or ii) "I assert that X is not finite. So, act on it, and don't try to verify that X is infinite yourself", or iii) "I don't know whether X is finite, and I don't care. So, don't bother to test finiteness of X", or iv) "I don't know whether X is finite, but I am confident that you will find out by yourself". What should be the syntax in either case, and what should be the default? Besides, if one opts for (2) then it would also be reasonable to dynamically adapt parent and element classes. I think this could be done using ABCMeta from Python's abc module. I am not very experienced whith these things, but I hacked together an experimental version that somehow seems to work. More details are given in the thread on sage- algebra. Cheers, Simon -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
