#15300: Weyl and Clifford Algebras
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.13
Component: algebra | Resolution:
Keywords: days54 | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/algebras/weyl_clifford-15300| 760de0bd03f0b251215ecdaf981759fb37362aeb
Dependencies: | Stopgaps:
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Comment (by tscrim):
Replying to [comment:16 darij]:
> Is there an established class for bilinear forms (not necessarily
symmetric!) on free modules? I'd need one to get anywhere towards the
Clifford-exterior iso.
I don't think so. I think this is usually worked (hacked) around using
dedicated methods.
> The `scalar` function as it stands is rather useless, since on the
exterior algebra it just returns the product of the constant coefficients
of `self` and `other`. What should be made (I can do that) is the lift of
a bilinear (not quadratic) form on `V` to the exterior algebra of `V`
(using the Gram matrix). But that requires bilinear forms, too, so I'd
love to hear whether they exist before doing any changes.
I'd just have a function `Element.scalar(other)` (or some other name)
which projects down `self` and `other` to the exterior algebra and does
the computation there via some (predefined) `scalar()` method.
--
Ticket URL: <http://trac.sagemath.org/ticket/15300#comment:18>
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