Greetings to all.

With the following matter I am betting on there being a simple mistake on my part due to fatigue owing to a challenging session of intense computing. The following link at Math.Stackexchange.Com points to a computation involving complex residues. Consult the link for additional details.

I usually verify my computations with Maple, I did the same this time. Thereby I happened on a curious phenomenon which I have documented below. Please study the session data provided, I believe it speaks for itself.

user@host:~$ math
Mathematica 10.0 for Linux x86 (64-bit)
Copyright 1988-2014 Wolfram Research, Inc.
In[1]:= Residue[z^2/(z^4 + 2*z^2 + 2)^2, {z, 2^(1/4)*Exp[3*Pi*I/8]}]
1/8 1/4
(-1) ((-1) + Sqrt[2])
Out[1]= ----------------------------
1/4 1/4 3
16 2 ((-1) - Sqrt[2])
In[2]:= N[%]
Out[2]= 0.117223 - 0.0083308 I
In[3]:=
user@host:~$ maple
|\^/| Maple 18 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> residue(z^2/(z^4 + 2*z^2 + 2)^2, z=2^(1/4)*exp(3*Pi*I/8));
0
> quit
memory used=0.9MB, alloc=8.3MB, time=0.07
user@host:~$

I am looking forward to learning what the correct syntax is to get the residue in this case and I hope I can assist other users who might have run into the same problem. I will cancel the question should it turn out to be trivial and of little potential use to the community.

Best regards,

Marko Riedel

**Post Scriptum. **Being a programmer myself I would be curious to learn more about the algorithms that are deployed here and how and why they did not succeed.