> I hope other people respond, too.  I would suggest looking at
>
> <http://www.sagemath.org/doc/reference/coercion.html>
>
> and the code in sage/algebras/quatalg (for quaternion algebras): use
> this as one model for how to implement a noncommutative algebra.

Another place to look is algebras/iwahori_hecke_algebra.py,
showing how to an algebra as a subclass of CombinatorialFreeModule.

Dan

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