#18223: new categories for 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: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/ticket/18223 | b924b94bc2e1aa12021cc70b3a919532aa1e350a
Dependencies: | Stopgaps:
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Changes (by vdelecroix):
* status: needs_review => needs_work
Comment:
Hello Daniel,
1. There are tons of product orders that you can define on a cartesian
product of posets. You want to write a category for each of them? It is
not at all usable for people that wants to build a custom product. The aim
of categories is to factorize code not to expand the amount of work. I
think that you should seriously develop another strategy for providing an
order to a product of posets.
2. Moreover, this looks very unnatural to me:
{{{
sage: P = Poset((srange(10), lambda left, right: left <= right))
sage: Q = cartesian_product((P, P, P),
....: extra_category=Posets().CompareLexCartesianProduct())
}}}
IMHO, something like the following would be better
{{{
sage: posets.cartesian_product((P,P,P), order = my_order)
}}}
where order could also be a custom function or a string like 'lex',
'product', ... this second remark is just from the user point of view.
3. If there is one product, it should be the cartesian product (or the
coordinate wise product) which is the categorical one (when morphisms are
the monotone functions). Though as there is a lack of definitions, I am
not sure that `Hom` between two posets are the monotone functions. Would
be interesting to settle that.
4. Sided remark: this will not work with cython Element classes (as there
is no element_class)
{{{
self.element_class.__le__ = \
lambda left, right: left.parent().le(left, right)
}}}
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/18223#comment:9>
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