#16820: Implement ABCs for Lie algebras and finite dimensional given by
structure
cofficients
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.7
Component: algebra | Resolution:
Keywords: lie algebras, | Merged in:
days64, sd67 | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 09281457c8cf34a075be3b72ae88296a75c54d93
public/lie_algebras/fd_structure_coeff-16820| Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by tscrim):
* dependencies: #16819 =>
Comment:
Sorry for the delay in getting back to you; traveling plus clearing off my
built up work.
comment:29
I think the issue is that there isn't enough checking of coefficients and
maybe a default assumption somewhere that algebras are unital? Perhaps
it's also lifting up in some fashion? I'll take a look at that this week.
comment:31
I would say the set of 0x0 matrices is the empty set, not the set
containing a unique element, the empty matrix. As for the oddity, I think
we need a better/more uniform system for equality for things that behave
like 0. At the very least, this is an issue with
`CombinatorialFreeModuleElement` that deserves a separate ticket:
{{{
sage: C = CombinatorialFreeModule(ZZ, ['a','b'])
sage: C.zero() == 0
True
sage: C.zero() == QQ(0)
False
}}}
comment:34
Yes, that is definitely bad. I'm thinking we should have `lift` always
return an element of the UEA and state that explicitly. For the lifting to
the defining associative algebra, perhaps call that `lift_associative`?
--
Ticket URL: <http://trac.sagemath.org/ticket/16820#comment:37>
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