RuchitJagodara
commented
7 months ago If we are creating a new function specifically for non-associative matrices (matrices based on non-associative structures), we should not implement functions whose definitions are not properly defined. Perhaps we can ask the user how they want to define it, but I am not sure if this is possible. However, we can still create a new class with all the properties that are properly defined (e.g., trace, transpose, conjugate). So I am working on this to make a new class and if I find some method to implement functions like determinant then I will let you know.
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Steps To Reproduce
O=OctonionAlgebra(SR) M=MatrixSpace(O,2,2)
Expected Behavior
Matrices are defined so long as multiplication and addition make sense.
Actual Behavior
Running the above code results in the TypeError base_ring (=Octonion algebra over Symbolic Ring) must be a ring
Additional Information
This is somewhere between a bug report and a feature request. Matrix multiplication is well defined so long as addition and multiplication are defined; an associative ring is not required. So are many other operations (e.g. trace, transpose, conjugate) but not all (e.g. determinant). Having Matrix_Spaces test for an (associative) ring prevents access to those operations that are defined. Ideally, there should probably be a separate matrix class for the nonassociative case. But I'd rather have to deal with unreliable results of poorly-defined operations (e.g. determinant) than be blocked from multiplying nonassociative matrices altogether.
As a workaround, is there a reasonably simple way to disable the test in Matrix_Spaces? Perhaps by manually adding my instance of an octonion algebra to Rings? Something else?
Environment
Checklist