How to sort a list? NOT a newbie question.

[Michael James Barber]

All in Python 2.1.1:

>>> l1 = [1, '1j', [1,'1j']]
>>> l1.sort()
>>> print l1
[1, [1, '1j'], '1j']

>>> l2 = [1, 1j, [1,'1j']]
>>> l2.sort()
Traceback (most recent call last):
  File "<input>", line 1, in ?
TypeError: cannot compare complex numbers using <, <=, >, >=


This came up in the context of building the coefficients of polynomials 
from a list of roots.  If complex roots occur in complex conjugate pairs, 
then the resulting coefficients must be real, so I decided to cast the 
coefficients to floats in this case.  A straightforward test is to take 
the complex conjugate of each element of the list, then sort both lists 
and see if they are the same.  As is clear from the above, that definitely 
didn't work!  

For the particular problem I was working on, it was simple to find a 
workaround that was only slightly awkward.  I don't have any idea how to 
address the case shown above.  Admittedly, it is largely a rhetorical 
question, but what do people think is the "one obvious way" to sort such 
a list?  The goal is an "arbitrary but deterministic" sort, much like with 
other heterogeneous lists.


In a larger sense, this is a frustrating aspect of Python's numerical
model.  PEP 228 looks like a good start on treating all numbers just as
numbers, without the surprises that can arise now.  But where do
comparisons of complex numbers fit in?  Is it better to be mathematically
correct and raise an exception, or to have complex numbers respond in a
useful, but not really correct, fashion to all comparisons?

I've used Matlab extensively for about 8 years (although a lot less often
since discovering Python and Numeric about a year ago!).  In Matlab,
complex numbers are sorted based on their magnitudes, and then by phase
angle if the magnitudes are the same.  Comparing complex numbers using <,
<=, >, and >= always returns false.  I've known about the sorting for 
quite a while, but only learned about the behavior of the comparison 
operators after discovering Python's behavior yesterday.  While not 
strictly correct mathematically, I suspect that Matlab's approach is a 
good practical approach, since it took me so long to notice.  I don't know 
what Mathematica and others do.
-- 
					Michael J. Barber