#19473: FiniteDimensionalAlgebra.is_unitary is not sufficient
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Reporter: darij | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.10
Component: algebra | Resolution:
Keywords: finite- | Merged in:
dimensional algebra, linear | Reviewers: Travis Scrimshaw
algebra | Work issues: clear up
Authors: Darij Grinberg, | associativity requirement; if
Travis Scrimshaw | necessary, change superclass and
Report Upstream: N/A | is_unitary method
Branch: | Commit:
public/algebra/finite_dim_algebra_fixes-19473|
0cfe0366fc527d2f692c835be3d40f60aa61c471
Dependencies: | Stopgaps:
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Comment (by pbruin):
Replying to [comment:15 tscrim]:
> Replying to [comment:13 pbruin]:
> > Replying to [comment:5 tscrim]:
> > > I would get rid of the `copy` attribute, instead make this a
`UniqueRepresentation` (or perhaps a `UniqueFactory` so we can better
control the cache key), and make the table a tuple of immutable matrices
that gets set by the `__classcall_private__`.
> > How does introducing `UniqueRepresentation` help in solving this
ticket? Wouldn't it be better to do that on a separate ticket?
>
> We can separate off the table issues into a separate ticket, that is
okay with me. Want me to do that?
> > > We also need to fix the category, which is wrong for non-
associative, non-unital cases.
> > I agree. It is unfortunate that refining the category after
initialisation is possibly problematic.
>
> The other option would be to add boolean parameters that do checks in
the initialization (which would require some minor refactoring if we
wanted to go the `UniqueRepresentaion` route and would mean we do that on
this ticket).
It seems to me that there are four mostly independent issues:
1. the wrong `is_unitary()` method;
2. the fact that the multiplication table is mutable;
3. determining the correct category;
4. implementing unique representation.
We could possibly fix issue 2 on this ticket (assuming it just takes a few
lines), but also doing 3 and 4 on this ticket would be way too much in my
opinion. I would prefer just solving issue 1 on this ticket and opening
separate tickets (possibly with dependencies) for issues 2, 3 and 4.
--
Ticket URL: <http://trac.sagemath.org/ticket/19473#comment:16>
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