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
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