#15300: Weyl and Clifford Algebras
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.2
Component: algebra | Resolution:
Keywords: days54 | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/algebras/weyl_clifford-15300| a6a7206f3de8240b9783b8464c55f1ccb1d6cb4b
Dependencies: #16037 | Stopgaps:
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Comment (by tscrim):
Replying to [comment:52 jhpalmieri]:
> Note that when you're using `CombinatorialFreeModule`, you shouldn't
need both `_repr_term` and `_repr_` for elements: just use `_repr_term`.
You should also delete the `_latex_` method for elements.
If I didn't override `_repr_`, it wouldn't redirect to
`repr_from_monomials` (it goes to `repr_lincomb`).
> For the function `repr_from_monomials`, I wonder if `repr_lincomb`
(defined in `sage.misc.latex`) does kind of the same thing?
As I recall, `repr_lincomb` doesn't have as nice of printing (IMO) as
`repr_from_monomials` with regard to spacing with the base ring being a
polynomial ring.
> By the way, can you compute the centers of any of these algebras? If so,
having a method which returns it would be very nice.
A counter question, do you want the honest center or the supercenter of
the Clifford/exterior algebra?
For the honest center, it should be trivial (given there is an even and
odd element) since given an odd `x` and even `y`, we have `xy = -yx +
LOT`. The exterior algebra is supercommutative, so its supercenter is the
entire algebra. For general Clifford algebras, my first thought is it
would correspond to rows of 0 in the quadratic form, but IDK off the top
of my head for certain.
--
Ticket URL: <http://trac.sagemath.org/ticket/15300#comment:53>
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