On Mon, Nov 5, 2012 at 2:18 AM, Simon King <simon.k...@uni-jena.de> wrote: > Hi Marco, > > On 2012-11-04, mmarco <mma...@unizar.es> wrote: >> I don't know if this is the right place and time to ask this: what >> about morphisms for Parent with generators? I mean, in some cases, you >> can define a morphism just by passing a list with the images of the >> generators to .hom() But apparentñy, it has to be done by hand for >> each case. Would it be possible to implement it in Parent? > > Theoretically it may be possible. Consider, for example, a ZZ[x] > module M. You know the images of the generators of M, and you know that > you want to have a morphism in the category of ZZ[x]-modules. Hence, > from the images of the generators of M, you can construct the images of > any elements x of M, provided that either M or x has a method that > expresses x in terms of the generators, and provided that there is > another method that understands the output of the first method. > > So, if you want a general framework, I could imagine that the following > could work. Provide Parent with a method, say, > def to_generator_data(self,x) > which by default raises a NotImplementedError. > And then, there could be a method > def from_generator_data(self, data, gens=None) > that constructs an element out of the data returned by to_generator_data, > but with an optional argument `gens` that defaults to the list of > generators. > > The specification is: > self.from_generator_data(self.to_generator_data(x))==x > for all x in self. Such a method could be useful anyway, because it > provides copying and pickling of elements. > > And if R, S are parents and the generators of R are > mapped to a list gens_images, then > S.from_generator_data(R.from_generator_data(x), gens_images) > should return the image of an element x of R under a morphism from R to > S given by gens_images.
Yes, I that sounds like a reasonable proposal. However, there's still the question as to which category you're considering the generators over--we'd probably have to make that explicit. > Only problem: Someone needs to implement it. There could be general > implementations on the category level, though. > > Efficiency is a different question... The morphism itself, once detected, could be made very efficient, even if it was implemented in the category. - Robert -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To post to this group, send email to sage-devel@googlegroups.com. To unsubscribe from this group, send email to sage-devel+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en.
