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Re: computing residues


On Fri, 4 Mar 2005 10:29:00 +0000 (UTC), Andrzej Kozlowski  
<akoz at mimuw.edu.pl> wrote:

> I have to admit Mathematica is smarter than I had thought and in fact:
>
>
> Residue[1/Sin[x],{x,Root[8*#1^3-6*#1-1&,3]-Cos[Pi/9]}]
>
> 1
>
> I made a mistake by using Root[8*#1^3-6*#1-1&,1] instead of
> Root[8*#1^3-6*#1-1&,3] in the first part of my example below. In fact
> Residue deals with this case impressively well. This certainly seems to
> reduce the strength  of my argument, though I still would prefer to get
> an unevaluated input in the non-numerical case.
>
> Andrzej
>

This is simply a case where Mathematica assumes sufficiently close values  
to be equal:

In[1]:=
Residue[Csc[x],
   {x, Root[8*#^3 - 6*# - 1&, 3] - Cos[Pi/9] + 10^-75}]

Out[1]=
1

which is incorrect. Series and Limit make the same 'error of the second  
kind'.

Maxim Rytin
m.r at inbox.ru


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