[Python-Dev] Re: the "3*x works w/o __rmul__" bug

[Fernando Perez]

Alex Martelli wrote:
> On Tuesday 28 October 2003 08:24 pm, Fernando Perez wrote:
>> I just wanted to add a small comment on this discussion, which I'd been 
>> following via the newsgroup mirror.
> 
> 
> Thanks for your comments!  I didn't even know we HAD an ng mirror...

Via gmane news, it works quite well in fact.  I typically follow python-dev
there, and only subscribe occasionally if I need to say something.

> Yes, of course, you're right.  However, the most specific problem is: do 
> you know of ANY use cases where A*x and x*A should give different results,
> or the former should succeed and the latter should fail, *when x is an
> integer*?
> 
> If you can find any use case for that, even in an obscure branch of maths,
> then clearly the urgency of fixing this bug goes WAY up.

Well, I'm not a mathematician myself, but I did ask two friends and neither of
them could think of such a case quickly (they're applied people, though, we
need to ask someone doing abstract algebra :)

But I think I can see a 'semi-reasonable' usage case.  Bear with me for a
moment, please.  Suppose A is a member of a class representing a non-linear
operator which acts on functions f, such that in particular:

A(x*f) != x*A(f)

for x an integer.

Now, if for some reason I decide to implement the 'application of A', which in
the above I represented with (), with '*', the bug you mention does surface,
because then:

A*x*f != x*A*f

Or does it?  The left-right order of associativity plays a role here also, and
I don't know exactly how python treats these.

Granted, this example is somewhat contrived.  Here, using __call__ for
application would be more sensible, and the associativity rules may still hide
  the bug.  Using '*' for application is not totally absurd, because if you are
using finite matrix representations of your operators and functions, then in
fact operator-function application _does_ become multiplication in the
finite-dimensional vector space.

But it _suggests_ a possibility for the bug to surface.  At the same time, it
also shows that 'really reasonable' uses will probably not easily expose this one.

The one idea which I think matters, though, is the following: since in python
we can't define new operators, in specific problem domains the existing ones
(such as '*') may end up being reused in very unconventional ways.  So while I
can't think now of a non-commutative integer*THING multiplication, I don't see
why someone might not build a THING where '*' isn't really what we think of as
'multiplication', and then the bug matters.

In the end, I'd argue that it would be _nice_ to have it fixed, but I
understand that with finite developer resources available, this one may have
to take a back seat until someone can show a truly compelling case.  Perhaps
I'm just not imaginative enough to see one quickly :)

> Thanks again for your help -- we DO need to hear from users!!!

No problem, thanks for being receptive :)

Best,

f