#17367: Classes of combinatorial structures
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Reporter: elixyre | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.9
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: Jean-Baptiste | Reviewers:
Priez | Work issues:
Report Upstream: N/A | Commit:
Branch: | c13301a1fe97f639089a691bd0f75d78cc8aa6a0
u/elixyre/class_of_combinatorial_structures| Stopgaps:
Dependencies: |
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Comment (by elixyre):
Hi Vincent,
Thank you about your comments.
Replying to [comment:17 vdelecroix]:
> I strongly think that creating this category is useless
This seems '''not''' totally useless to create a new category or I don't
know how to do that easily using the category framework of sage.
Let me ask you how to that in the following...
> '''and''' I certainly understand that it is needed. What I propose is to
not create a new category but make this featured sets with NN grading and
finite slices available. What I would rather implement is:
> - making the grading set a parameter of the category `SetsWithGrading`
(in your case it would be `NN`)
The parameter ''grading set'' is already provided in the `SetsWithGrading`
category.
> - adding an axiom `FiniteSlice` to `SetsWithGrading`
I also wish to provide a category `GradedComponent` (or `Subset`) with
methods `ambient` (which return the set with grading) and `grade` (why
not). Where put this class:
{{{#!python
class SetsWithGrading(Category):
....
class GradedComponent(Category):
def super_category(self):
return .???.
class ParentMethods:
def ambient(self):
pass
def grade(self):
pass
}}}
It seems natural to have `GradedComponent` as a nested class of
`SetWithGrading`, right? (There is no reason that it appears elsewhere.)
At this point, if I use `FiniteSlice` as an axiom, ''a priori'' this
class `GradedComponent` should have `FiniteSets` (or better
`FiniteEnumeratedSets`) as super category but without the axiom this only
should have `Sets`. How do that (easily and properly)?
So my opinion is `FiniteSlice` is not an axiom and the code of
`GradedComponent` should be duplicate, one using `Sets` as super category
and the other using `FiniteSets`.
> That way, what you are trying to define would simply be
> {{{
> sage: SetsWithGrading(NN).FiniteSlices() & EnumeratedSets()
> Join of Category of sets with grading Non negative integer semiring with
finite slices
> and Category of enumerated sets
> }}}
> (.. the names are awful, but I hope that the plan is clear ...).
If we have a finite sets (in sage), could we assume that it is an
enumerated sets? (I suppose the answer is '''no''' but...)
--
Ticket URL: <http://trac.sagemath.org/ticket/17367#comment:19>
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