#18223: cartesian products with orders
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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/behackl/cat | Commit:
/cartesian-product-posets | 0a74ff134169bd9e1fa9d50eb061f69c19fe351e
Dependencies: #18586 | Stopgaps:
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Comment (by behackl):
Thanks for having a look at the code Vincent! I'd like to add some more
comments as well.
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.
Currently, I like the idea that both "types" of cartesian products can be
found in the same file; I'm not quite sure if it would really be more
clean to move this code to some other file. In any case, I don't really
have any arguments for or against moving the code, I'll leave this
decision to those with more experience.
> 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
> }}}
This is the same behavior as we had before; this ticket did not change
that. However, it probably should.
My suggestion would be to add the line
{{{
CartesianProduct = CartesianProductPosets
}}}
to the `ParentMethods`-class in `categories/posets.py`, together with an
appropriate (lazy) import. If I understood correctly, this would make all
parents with a subcategory of `Posets()` use the
`CartesianProductPosets`-class for constructing the cartesian product.
This change would also suggest using a default argument for the order
(otherwise, this change is potentially backwards-incompatible)---and as
Vincent has pointed out in 4., this would be somehow natural.
> 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
> }}}
>
As far as I can see, this comes from
{{{
return parents[0].CartesianProduct(...)
}}}
in the last line of `cartesian_product` in `categories/sets_cat.py`. If
the category of `parents[0]` isn't a subcategory of `Posets()`, the non-
poset cartesian product is constructed. In any case, I think it is easy to
take care of that case.
I agree completely with 4, 5, 7; and I know too little about
`_refine_category_` to comment on 6. It seems like a good idea to follow
#18305 and implement `_richcmp_` in the `Element`-class.
Finally, I pushed another small commit with some documentation-related
changes.
I'd suggest taking care of setting `Parent.CartesianProduct` automatically
for subcategories of `Posets()`, as well as adapting `cartesian_product`
such that in case `extra_category` is a subcategory of `Posets()`, the
class `CartesianProductPosets` is used for the construction of the
cartesian product.
Other than that, this would be `positive_review` from my side.
Benjamin
--
Ticket URL: <http://trac.sagemath.org/ticket/18223#comment:21>
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