#19613: Implement basic representations of semigroups
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.1
Component: group theory | Resolution:
Keywords: representation, | Merged in:
semigroups, | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 38529351ae5581559a6a33a6fc6fe825b974ef81
public/representations/basic_implementation-19613| Stopgaps:
Dependencies: |
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Comment (by darij):
Replying to [comment:16 tscrim]:
> Replying to [comment:15 darij]:
> > Replying to [comment:14 tscrim]:
> > > Replying to [comment:13 darij]:
> > > > Wait, what? `TrivialRepresentation` does not inherit from
`Representation`? This I really don't like. Particularly if you don't
expose `self._module`, there should be no reason to keep the trivial one
out of it.
> > >
> > > Why should it? They are completely different implementations.
> >
> > Implementations yes, but the underlying concepts should be of the same
type. One of the next steps will be a direct sum of two representations,
for example. You do want to be able to add a regular and a trivial
representation, I assume?
>
> That is more about having a common API. Anyways, `Representation` and
`TrivialRepresentation` will have a common ABC, so I think this issue is
moot.
Ah, perfect.
> > > > S4. In the `_acted_upon_` of `TrivialRepresentation`, does
`_from_dict(d)` do the right thing when `d == 0` ?
> > >
> > > This will never happen as `monomial_coefficients` returns a `dict`.
However, I do see a potential when acting on the zero element. I will
check/doctest this.
> >
> > You multiply all the entries of that `dict` with
`sum(scalar.coefficients())`. If this sum is 0, then it's suddenly a
`dict` full of zeroes.
>
> `_from_dict` has an optional argument to check for removing zeros (whose
default is `True`). So this isn't an issue.
Oh! I forgot the semantics of `_from_dict`; so it's not as low-level as I
expected. You are right!
--
Ticket URL: <http://trac.sagemath.org/ticket/19613#comment:17>
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