I think that, at some point, the framework should be aware of the internal operations in the corresponding parent. I mean: if we are talking about algebras, the expression of an element in terms of the generators will include products, sums, and multiplication by scalars. If we are talking about a group, it will involve only products and inverses, and so on. So the procedures you mention should return (or accept as entry) something that represents that kind of "tree of operations". But it definitely sounds like a nice way to go.
On 5 nov, 11:18, 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. > > Only problem: Someone needs to implement it. There could be general > implementations on the category level, though. > > Efficiency is a different question... > > Best regards, > Simon -- 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.
