[Python-ideas] Fwd: [RFC] draft PEP: Dedicated infix operators for matrix multiplication and matrix power

[Robert Kern]

On 2014-03-18 08:02, Nick Coghlan wrote:
>
> On 18 Mar 2014 09:08, "Nathaniel Smith"
> <njs at pobox.com
> <mailto:njs at pobox.com>> wrote:
>  >
>  > On Fri, Mar 14, 2014 at 8:15 PM, Nick Coghlan
> <ncoghlan at gmail.com
> <mailto:ncoghlan at gmail.com>> wrote:
>  > > A few other miscellaneous comments:
>  > >
>  > > - nice work on the PEP Nathaniel!
>  >
>  > Thanks!
>  >
>  > > - as with others, "@" as the operator doesn't thrill me, but I also think it
>  > > crosses the threshold of "good enough given the constraints"
>  > > - the PEP should probably recommend adding an "operator.matmul" function, a
>  > > "PyObject_MatrixMultiply" C API and consider whether or not the new special
>  > > method should be given a C level type slot.
>  >
>  > operator.matmul and PyObject_MatrixMultiply are obvious enough, but
>  > I'm afraid I'm not too clear on the tradeoffs about adding a C level
>  > type slot, or even entirely sure what the alternative is. (I guess I
>  > just assumed that all special methods used C level type slots and
>  > there was nothing to think about.) Do you (or anyone) have any
>  > thoughts?
>
> I suspect you're going to want one, as without it, the implementation method
> ends up in the class dict instead (the context management protocol works that way).
>
> I suspect the design we will want is a new struct for Py_Matrix slots (akin to
> those for numbers, etc). The alternative would be to just add more "Number"
> slots, but that isn't really accurate.

Would it be more palatable if the name were something like __altmul__ or 
__auxmul__ rather than __matmul__? Really, it's just a second 
multiplication-like operator. The leading use case for a second 
multiplication-like operator happens to be matrix multiplication, but I strongly 
suspect it will get used for other mathematical things like symbolic function 
composition or operator application (as in "linear operator", not +-*/) and 
maybe some secondary multiplication types in the weirder groups and fields (you 
can bet I will resurrect my Clifford algebra module to use this operator for one 
of the several types of multiplication they support). Granted, there is still 
some awkwardness in that *none* of the builtin number types will support it.

And hey, look! It makes the @ux or @lt multiplication operator makes a sensible, 
language-independent mnemonic! (not that "auxiliary" or "alternate" work in all 
languages, but at least the 'a' is baked into the special method name)

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
  that is made terrible by our own mad attempt to interpret it as though it had
  an underlying truth."
   -- Umberto Eco