How can I construct matrices over the octonions?

asked 2024-01-19 06:18:53 +0200

TD gravatar image

Using QuaternionAlgebra, I can make and multiply matrices with quaternionic entries without difficulty. Using OctonionAlgebra, if I try to make a matrix I get a type error telling me that my algebra is not a ring. So far as I can track it down, Matrix_Spaces runs a test asking whether the algebra is in Rings. QuaternionAlgebras are; OctonionAlgebras are not.

Is there a reasonable way to work around this issue? Manually add my octonion algebra to Rings? Disable the type check in Matrix_Spaces?? Something else?

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I suggest to report this issue at https://github.com/sagemath/sage/issues

Max Alekseyev gravatar imageMax Alekseyev ( 2024-01-19 16:09:54 +0200 )edit

Octonions not being associative, matrices make no sense.

FrédéricC gravatar imageFrédéricC ( 2024-01-19 20:18:20 +0200 )edit

Which operations are needed for these matrices over the octonions? Just make an own class if the wanted mathematical application is a short (or not involved) project...

dan_fulea gravatar imagedan_fulea ( 2024-01-23 14:39:21 +0200 )edit

@FrédéricC & @dan_fulea: Matrix multiplication requires only multiplication and addition, which are already defined. But I don't know enough Sage/Python to bypass the test in Matrix_Spaces which is preventing matrix computations using existing operations. @Max Alekseyev: Will do; thanks for the suggestion.

TD gravatar imageTD ( 2024-01-28 05:00:25 +0200 )edit
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