#16001: Make the tensor functorial construction work for crystals
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: categories | Resolution:
Keywords: tensor products | Merged in:
construction | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 25f4a43d3daef82fc79421a2485b626f91d77816
public/combinat/crystals/tensor_construction-16001| Stopgaps:
Dependencies: |
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Comment (by nthiery):
Hi Travis!
Thanks for the feature, we want it!
I know the math tradition of calling this a tensor, and see the point of
being kind to the user there, but it's still an abuse: in term of
functorial construction, it's a cartesian product and I believe it should
really be *implemented* as such for consistency with the rest of the
infrastructure. For example, this would have the following desirable
consequences:
- Inheriting features from cartesian products (counting, enumeration, ...)
- When we will start working more intensively on the linear span of
cristals, the tensor product thereof will call the cartesian product on
the basis, not the tensor product, so you would not get the crystal
structure on the basis
- For someone not knowing crystals, that's more informative
- ...
Also we might want some day to endow a vector space with a crystal
structure, in which case there would be an ambiguity about the meaning of
the tensor product. But I don't have a serious use case.
So, to accomodate the user, it's probably possible to introduce a little
trick so that calling {{{tensor}}} on a bunch of crystals automatically
builds their cartesian product.
Cheers,
Nicolas
PS: It's not exactly the same situation, but it's a bit like direct sums
of vector spaces that are actually implemented as what they are in terms
of construction on sets, namely cartesian products.
--
Ticket URL: <http://trac.sagemath.org/ticket/16001#comment:2>
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