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oscar-system / Oscar.jl

A comprehensive open source computer algebra system for computations in algebra, geometry, and number theory.
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`clifford_algebra` #2312

Open fingolfin opened 1 year ago

fingolfin commented 1 year ago

It would be nice to have a convenient constructor for Clifford algebras, which either takes a quadratic form, or a field (ring?) F plus a dimension n (and then chooses a "standard" quadratic form on a suitable n-dimensional vector space).

Since we have PBW-algebras, it shouldn't be too hard to implement this, I think?

thofma commented 1 year ago

I think it would be more efficient to implement them as a special case of finite dimensional associative algebras. Or maybe I am mistaken. Depends also a bit on what one wants to do with them.

wdecker commented 1 year ago

Should be possible!

Am 24.04.2023 um 17:57 schrieb Max Horn @.***>:

It would be nice to have a convenient constructor for Clifford algebras, which either takes a quadratic form, or a field (ring?) F plus a dimension n (and then chooses a "standard" quadratic form on a suitable n-dimensional vector space).

Since we have PBW-algebras, it shouldn't be too hard to implement this, I think?

— Reply to this email directly, view it on GitHub https://github.com/oscar-system/Oscar.jl/issues/2312, or unsubscribe https://github.com/notifications/unsubscribe-auth/AASSXESMBFJW24RIBRQIM5DXC2PHBANCNFSM6AAAAAAXJZDUH4. You are receiving this because you are subscribed to this thread.

fieker commented 1 year ago

On Mon, Apr 24, 2023 at 08:57:37AM -0700, Max Horn wrote:

It would be nice to have a convenient constructor for Clifford algebras, which either takes a quadratic form, or a field (ring?) F plus a dimension n (and then chooses a "standard" quadratic form on a suitable n-dimensional vector space).

Since we have PBW-algebras, it shouldn't be too hard to implement this, I think?

What do you want to do with them? I think Gabi also was once interested in them... -- Reply to this email directly or view it on GitHub: https://github.com/oscar-system/Oscar.jl/issues/2312 You are receiving this because you are subscribed to this thread.

Message ID: @.***>

fingolfin commented 1 year ago

So maybe I can ask Gabi what she needs exactly. I can also dig out who was the other person who asked me about this, and ask them what they exactly need...

But for my purposes, I'd just want to be able to get a generating set, and then compute some products and sums and get normal forms for the resulting elements. I.e. a glorified pocket calculator.