#18223: cartesian products with orders
-------------------------------------+-------------------------------------
Reporter: dkrenn | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.7
Component: categories | Resolution:
Keywords: sd67 | Merged in:
Authors: Daniel Krenn | Reviewers: Benjamin Hackl
Report Upstream: N/A | Work issues:
Branch: u/dkrenn/cat | Commit:
/cartesian-product-posets | e87db1a0f635bb81e3510dfa7ca1617e31462380
Dependencies: #18586 | Stopgaps:
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Comment (by dkrenn):
Replying to [comment:18 vdelecroix]:
> 1. I think that the class `CartesianProductPosets` would better be
somewhere in `combinat/posets` rather in `sets/cartesian_product`. It is
always better to split files.
Ok, split and moved to sage.combinat.posets
> 2. Why is the following not a poset
> {{{
> sage: P = Poset((srange(3), lambda left, right: left <= right))
> sage: cartesian_product([P,P]).category()
> Category of Cartesian products of finite enumerated sets
> }}}
It now is. (I've used the solution Benjamin suggested above).
> 3. The argument `order` in the class `CartesianProductPosets` is
mandatory. While the following just works
> {{{
> sage: C = cartesian_product([ZZ, ZZ], extra_category=Posets())
> }}}
> actually not
> {{{
> sage: TestSuite(C).run()
> Failure in _test_not_implemented_methods:
> Traceback (most recent call last):
> ...
> AssertionError: Not implemented method: le
> ------------------------------------------------------------
> The following tests failed: _test_not_implemented_methods
> }}}
The problem is that `ZZ` (and `QQ` as well) is not a in the category of
`Posets`. (#19269 will change this).
> 4. As I already said, it would make sense to have the product order as a
default since it is '''the''' cartesian product (in a categorical sense
when morphisms are increasing functions).
Default argument: done.
--
Ticket URL: <http://trac.sagemath.org/ticket/18223#comment:25>
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