> In retrospect, it appears that the OP should have asked the following 
> question:   From the perspective of Sage, if Python were to have 
> another arithmetic operator (denoted @) with identical precedence 
> rules to *, would we use it for anything?  Would we extend the 
> coercion model, etc.?   Are there any algebraic structures at all that 
> have two different "multiplications"? 
>
> If the answers are "yes!" and there are interesting examples, it would 
> provide support for his proposal. 
>
>  

>
> My personal answer to the above is:  no, no, no...   My reasoning is 
> that if the answer had been "YES!", then we most certainly would have 
> added such a thing via the preparser.  However, I can't remember even 
> once in 8 years when anybody ever brought up this as a proposed 
> addition to the preparser (both on lists or in person).     His actual 
> PEP had something claiming we had added something to the preparser, 
> but that was not a multiplication operator, but simply a backslash 
> shorthand for matrix inversion, like in Matlab, that nobody uses or 
> cares about  -- I just added it one day for fun in the early days -- 
> based on no demand. 


   I think of a tensor algebra of an algebra (I could probably come up with 
others with some thought that might be somewhat contrived but practical). 
Yet I don't want to modify the preparser to add (for example) # to denote 
something as specific as a tensor product, must less that we can't override 
it in subclasses. On a slightly related note, I would like a 
non-commutative and/or non-associative infix operator.

I had no idea such a shorthand was available in Sage. *Goes off to play 
with it*

Best,
Travis

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