#18265: Axioms for semigroups: L,R,J,H-trivial, aperiodic
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Reporter: nthiery | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.2
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: Nicolas M. Thiéry | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/nthiery/semigroups/axioms-18265 | d09fe3b47c5d755661ae0053702829985bdf13fc
Dependencies: | Stopgaps:
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Comment (by nthiery):
Hi Travis,
Thanks for the review.
Replying to [comment:13 tscrim]:
> - Do we want these to be axioms since these properties for subcategories
do not make as much sense (e.g., for groups, L-trivial = R-trivial =
J-trivial = category consisting only of the trivial group, correct?)
We want them to be axioms to interact nicely with each other: there
will be many interesting combinations between the Finite / X-trivial /
Unital axioms (and more will come, like Regular, ...). In fact
implementing those was one of my original motivation for implementing
axioms in Sage :-)
Indeed `Groups().XTrivial()` is, well, trivial, so that's boring. But
this is only polluting the namespace of the Groups() category, not the
groups themselves, so that's a minimal annoyance.
> - Typo "preoder".
Thanks for catching. Fixed!
> - Do we want to spend some time trying to beautiful axiom printing
> (i.e., "J-trivial" instead of "jtrivial")?
This would be cute, indeed. I'll have a quick look if it's trivial to
do. Otherwise, we can leave it for later; that will be easy to change
anyway.
> - I would like to see the defining properties to the category level
> documentation, not only in the subcategory methods.
I agree that documentation at the category level would be highly
desirable. But I don't want to duplicate manually the documentation.
That's a general problem that requires a general solution by having a
nice automatically generated default documentation for categories with
axioms. See also the related:
http://trac.sagemath.org/ticket/16363
In the mean time the subcategory methods are the most appropriate
location for the doc, since this makes it accessible for all
subcategories by `XXX.Jtrivial?`
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New commits:
||[http://git.sagemath.org/sage.git/commit/?id=d09fe3b47c5d755661ae0053702829985bdf13fc
d09fe3b]||{{{18265: typo: preoder -> preorder}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/18265#comment:15>
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