#17160: Finitely generated axiom for (mutiplicative) magmas, semigroups,
monoids,
groups
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Reporter: nthiery | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: categories | Resolution:
Keywords: | Merged in:
Authors: Nicolas M. Thiéry | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/nthiery/categories/finitely- | f027ce2b5e1abe22d49bcdc96f2cfeebced8fc16
generated-magmas-17160 | Stopgaps:
Dependencies: #10668 |
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Comment (by tscrim):
Replying to [comment:10 nthiery]:
> I considered this and I agree that this would have the advantage of
> being consistent with the basis things. However I don't see what I
> would put in the categories with axiom for `FinitelyGenerated` axiom
> besides the subcategories with axioms for `WithGeneratingSet`, so this
> looks like overkill. Besides,
>
> Categories of finitely generated group with generating set
>
> is not great. I am torn.
I have things that have infinite (enumerable) distinguished generating
sets (ex. free group/monoid with generators indexed by `NN` or Yangians
#15484), so separating these axioms will be useful. In fact, the
enumeration could be done in for the general `WithGeneratingSet` category
and would (at least should) error out if the generating set is not
enumerable. Although I only know of 1 thing which will be finite
dimensional but doesn't come with a distinguished basis. Plus I think we
could do an extra case in `_repr_object_names_static` to change the repr
into:
{{{
Category of groups with finite generating set
}}}
Here's another thought, what about we look at the cardinality of the
generating set? So we only have `WithGeneratingSet` which calls
`is_finitely_generated`, whose default is to look at the cardinality of
the generating set to determine the output of repr. At least that's the
only place where I could see us (currently) using the fact that the
generating set is finite. For the enumeration, all we really need is the
generating set is enumerable. Although I guess we really want to add
`EnumeratedSets` to the category heirachy, so this probably is not so
useful of an idea...
> Opinions anyone else?
Darij, Aladin, or anyone else, your thoughts?
--
Ticket URL: <http://trac.sagemath.org/ticket/17160#comment:11>
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