#16055: Implement Jordan algebras
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: algebra | Resolution:
Keywords: jordan algebra | Merged in:
Authors: Travis Scrimshaw | Reviewers: Darij Grinberg
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/algebras/jordan-16055 | 4404242dbb01346805cbdce258053636356f71b6
Dependencies: | Stopgaps:
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Changes (by tscrim):
* reviewer: => Darij Grinberg
Comment:
Replying to [comment:21 darij]:
> Does this mean that this will break again when the base ring coercion is
reintroduced?
This isn't a coercion for non-commutative base rings. The commutativity of
the associative algebra actually suppresses the non-associativity of the
Jordan algebra since
{{{
(xy + yx)/2 = xy = yx
(yz + zy)/2 = yz = zy
(xyz + zyx)/2 = xyz = yxz = ... = zyx
}}}
Perhaps we could add extra checks for the base ring being commutative and
adding such a coercion if there is a need, but for now I think we have the
conversion and left/right actions.
> Also, I've finished reviewing this, but there is a TODO in the latest
commit.
Fixed; sign error. So can I consider this as a positive review?
--
Ticket URL: <http://trac.sagemath.org/ticket/16055#comment:23>
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