On Fri, Jun 12, 2015 at 07:27:51AM -0400, Mark Shimozono wrote:
> I'm implementing smash products of AlgebrasWithBasis,
> which are tensor products of algebras with not-necessarily-componentwise
> product. When the tensor factors are themselves tensor products,
> I don't want to use the default tensor product construction, which flattens
> tensors (good for linear operations but disastrous for the above purpose).
Yup.
> My solution was to allow the tensor product construction to admit a
> category suggestion, which is then used to choose a new grouped tensor
> implementation or the usual flattened one.
>
> The smash product only makes sense when the algebras are over the
> same base ring.
>
> Sometimes I want to choose the flattened tensor even when the factors
> are all algebras and sometimes of course I want the grouped tensor product.
Ok, thanks for the description.
We encountered something similar when playing with cartesian products
with Vincent. When A and B are modules over different base rings RA
and RB (but same base ring category),
cartesian_product(A,B)
should not be in Modules(Rings()). Currently, the category for the
cartesian product is obtained by starting from the meet of the
category of A and the category of B; this should be refined to take
into account the base rings of A and B. So probably we want some
method
meet_category_of([A,B,...])
which implements this logic, starting from the parents and not only
from their categories.
I am not sure:
- Where to put such a method (and what its name should be). As a
starter, let's take sage.categories.category.meet_category_of.
- How to implement it; I guess we can start by doing the usual meet,
and then hardcoding the special rule for modules; maybe later we
will have other use cases guiding us toward something more general.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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