Take a look at sage/categories/pushout.py. You will need to define
construction() methods on both A and B, which return pairs (F_A, X_A) and
(F_B, X_B), where the F are ConstructionFunctors with F_A(X_A) = A and
F_B(X_B) = B. You then need to tell Sage how to merge F_A and F_B. See
pushout.py for details and examples.
David
On Fri, Jan 2, 2015 at 1:36 PM, Daniel Krenn <kr...@aon.at> wrote:
> I've tried to reduce my problem to the following set-up and question:
>
> Say we have algebraic structures A and B (think of groups) constructed
> like this:
>
> A = CreateGroup('alpha')
> B = CreateGroup('beta')
>
> Elements are then
>
> a = A.an_element()
> b = B.an_element()
>
> Now I want to perform a binary operation on a and b, e.g.
>
> c = a * b
>
> Thus, the coercion model has to find a parent where both live in (there
> is no coercion from A to B or vice versa).
>
> I have a common parent C which can be created from A and B:
>
> C = PlugTogether(A, B)
>
> (think here of something similar to a cartesian product). This parent C
> is what we want to find, but how can the coercion model do this? How can
> it discover this PlugTogether construction?
>
> I've read about functorial constructions, but are these here the key? If
> yes, how does this work (since there are two groups involved)?
>
> Best wishes
>
> Daniel
>
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