#19613: Implement basic representations of semigroups
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: group theory | Resolution:
Keywords: representation | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/representations/basic_implementation-19613|
9f2ff6e14f3376d420dbe87715a0bd112e0ccdb7
Dependencies: | Stopgaps:
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Comment (by tscrim):
Replying to [comment:2 darij]:
> Can you document the `left_repr` keyword in the `regular_representation`
method in `semigroups.py`?
Added.
> In the `_acted_upon_` of `TrivialRepresentation`, I would use a `sum`
method instead of the `sum` function (I hope it would involve less
indirection/ducktyping).
That isn't ducktyping (it's the python `sum` not the symbolic `sum` that
is at the top-level interface). Also, all `self.base_ring().sum(elts)`
does is call `sum(elts, self.zero())` so it involves one further level of
indirection.
> Does the `RegularRepresentation` allow both multiplying by elements of
the semigroup and multiplying by elements of the semigroup algebra? (And
if so, please doctest both.)
Yes, and I added some doctests about this. I also caught a few bugs with
these doctests.
> I have recently wrotten some really sloppy code to build a finite
semigroup out of a multiplication table (I hoped to use it on #19892, but
then I found that semigroups lack the support for that, so I ended up
avoiding it). I'm wondering -- would this be useful for this patch? At the
very least it could give us a way to doctest the methods. I could polish
the code and submit it here; I just want to make sure it won't be in vain,
as I have a hard time believing that there is no such thing in Sage
already...
There is code in `algebras/finite_dimensional_algebras` which essentially
does that. We probably could separate that code into the semigroup part
and the algebra part (and combine it with your code). However, I think
that is better for a separate ticket because it won't directly apply to
this (could be good for extensive testing of this, but I think that could
be overkill).
--
Ticket URL: <http://trac.sagemath.org/ticket/19613#comment:4>
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