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

[Steven D'Aprano]

On Fri, Mar 14, 2014 at 11:24:26AM +0100, Antoine Pitrou wrote:

> > This PEP proposes two new binary operators dedicated to matrix
> > multiplication and matrix power, spelled ``@`` and ``@@``
> > respectively.  (Mnemonic: ``@`` is ``*`` for mATrices.)
> 
> That sounds like a strange choice to me. There's nothing in "@" or "@@"
> that suggests "matrices" or "multiplication".

The PEP even gives a mnemonic for it: @ is for mATrix multiplication.

There's nothing in @ that suggests "decorator", nor is there anything 
about * that suggests scalar multiplication.

Out of the common symbols used in Python, & is possibly the only 
operator symbol with a non-arbitrary connection to its meaning. & was 
originally a ligature of "et", the Latin word for "and". Everything else 
is pretty much arbitrary, and it's only habit and long use that makes 
them seem normal.


> 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". 

 
> That said, I'm rather sympathetic to the general idea, and if "@" is
> the least contentious option, then I'm ok with it too ("@@" doesn't
> sound like a good idea at all, though).

I don't see why. Since Python uses * and ** for scalar multiplication 
and exponentiation, and given that @ is accepted as matrix 
multiplication, then it is completely logical to follow the same 
pattern, which gives us @@ for matrix exponentiation. That's no sillier 
than using ** for exponentiation, instead of ^ as the Gods intended :-)





-- 
Steven