Thanks, John.  Allowable syntax is  residue(z)  or  residue(z == 0).  The 
former defaults to using 0, so they should be equivalent and both forms 
give the same result.

LIke I said, my complex analysis is rusty.  And I am really asking for 
somebody else.  Is the chunk of code that produces 2 (above) not following 
the definition of the residue?

On Thursday, November 5, 2015 at 4:30:52 AM UTC-8, John Cremona wrote:
>
> Why are you giving the argument z to the residue function ?  If you wanted 
> the residue at 0 put that.  But exp (2/z)  is not meromorphic at 0 so the 
> residue there is surely undefined ?
> On Nov 5, 2015 3:53 AM, "Rob Beezer" <goo...@beezer.cotse.net 
> <javascript:>> wrote:
>
>>
>>
>> On Wednesday, November 4, 2015 at 7:37:58 PM UTC-8, vdelecroix wrote:
>>>
>>> z/2 vs 2/z 
>>>
>>
>> Ouch!  Sorry.  Wrong input, same output.
>>
>> z = var('z')
>> f = e^(2/z)
>> f.residue(z)
>>
>> Result: 0
>>
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