Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Re: computing residues


Maxim wrote:
> 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


To clarify a bit, I will point out that all the above go through common 
code for zero testing.

In[6]:= Developer`ZeroQ[Root[8*#^3 - 6*# - 1&, 3] - Cos[Pi/9] + 10^-75]
Out[6]= True

In our development kernel this can be influenced by a system option.

In[9]:= Developer`SetSystemOptions[ZeroTestNumericalPrecision->200];

In[10]:= Developer`ZeroQ[Root[8*#^3 - 6*# - 1&, 3] - Cos[Pi/9] + 10^-75]
Out[10]= False


Daniel Lichtblau
Wolfram Research





  • Prev by Date: Re: Help on iteration
  • Next by Date: SQLSelect
  • Previous by thread: Re: computing residues
  • Next by thread: Re: computing residues