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

[Ron Adam]

On 03/14/2014 07:32 AM, Steven D'Aprano wrote:
>> >AFAIK, other languages sometimes use ".*" for matrix multiplication (as
>> >opposed to element-wise multiplication). Why not re-use that
>> >convention? Would that lead to parsing difficulties?
> "Syntax should not look like grit on Tim Peters' monitor."
>
> .* is, in my opinion, pretty ugly, and leads to even ugly
> extensions:
>
> a .* b  # matrix multiplication
> a .*= b  # in place matrix multiplication
> a .** b  # matrix exponentiation
> a .**= b  # in-place matrix exponentiation
>
> And it suffers from exactly the same lack of connection to matrix
> multiplication as @ does: there is nothing about . that spells "matrix".
>
> It also has the problem that it could cause confusion with vector dot
> product. Read out A .* B aloud and you get something that sounds like it
> might mean dot product, "A dot times B".

The best I can come up with is to use '^' instead of dot.

    a ^* b  # matrix multiplication
    a ^^ b  # matrix exponentiation

Also two ^ together looks like a M.  It's not a strong association, but it 
may help some people remember what it's for.   Or the second one could be 
spelled... ^**, but I think the ^^ is cleaner.


Question?  Is it possible for python to tell these apart at compile time?

 >>> a = 6
 >>> b = 4
 >>> c = 8
 >>> a^b
2
 >>> a ^b c
   File "<stdin>", line 1
     a ^b c
          ^
SyntaxError: invalid syntax

So that this later example does...

      a.__use__(self, "b", c)


The ^b is unrelated to the name b in the second case.  Or is this just not 
possible?


If it could be done, then ...

      a ^* b    -->     a.__use__(self, "*", b)
      a ^^ b    -->     a.__use__(self, "^", b)


Where the __use__ method is defined on a module level object.  (and not 
defined on builtin's as a general rule.)

     def __use__(self, s, other):
        if s == "*":
           ...           # do matrix multiply
           return result
        elif s == "^":
           ...           # do matrix exponentiation
           return result
        raise TypeError



Anyway to make this work nicely?

Cheers,
    Ron