Addition and multiplication puzzle

[Bruce Wolk]

Mark Dickinson wrote:
> Can anyone either reproduce or explain the following
> apparently inconsistent behaviours of __add__ and
> __mul__?  The class Gaussian provides a sub-bare-bones
> implementation of Gaussian integers (a Gaussian
> integer is a complex number x+yi for which both x and
> y are
> integers):
> 
> class Gaussian(object):
>     """class representing Gaussian integers"""
> 
>     def __init__(self, x, y = 0):
>         self.real, self.imag = x, y
> 
>     def __repr__(self):
>         return repr(self.real) + "+" + repr(self.imag)
> + "*i"
> 
>     def __add__(self, other):
>         if type(other) != Gaussian:
>             other = Gaussian(other)
>         return Gaussian(self.real + other.real,
> self.imag + other.imag)
> 
>     def __mul__(self, other):
>         if type(other) != Gaussian:
>             other = Gaussian(other)
>         return Gaussian(self.real * other.real -
> self.imag * other.imag, \
>                           self.real * other.imag +
> self.imag * other.real)
> 
> Under Python 2.3.2 I get:
> 
> 
>>>>i = Gaussian(0, 1)
>>>>i * 3
> 
> 0+3*i
> 
>>>>3 * i   # surprise!
> 
> 0+3*i
> 
>>>>i + 3
> 
> 3+1*i
> 
>>>>3 + i
> 
> Traceback (most recent call last):
>   File "<stdin>", line 1, in ?
> TypeError: unsupported operand type(s) for +: 'int'
> and 'Gaussian'
> 
> In other words, I can *multiply* an int by a Gaussian
> in either order, but I can only *add* a Gaussian to an
> int, not the other way around.  The surprise is that
> multiplying an int by a Gaussian works---I'd expect it
> to complain since there's no __rmul__ method defined,
> in just the same way that 3+i produced an exception
> above.  Why do addition and multiplication behave
> differently?
> 
> Yours hoping for enlightenment,
> 
> Mark
> 
> 
> __________________________________
> Do you Yahoo!?
> The New Yahoo! Shopping - with improved product search
> http://shopping.yahoo.com
> 
3*i gives the expected error under Python 2.2.2.  Curious indeed.