Re: computing residues

*To*: mathgroup at smc.vnet.net*Subject*: [mg54902] Re: computing residues*From*: Maxim <ab_def at prontomail.com>*Date*: Sat, 5 Mar 2005 01:34:48 -0500 (EST)*References*: <200503010658.BAA25262@smc.vnet.net> <200503030329.WAA21091@smc.vnet.net> <4a6a68e0a91addc250bf47ab9ab03e74@mimuw.edu.pl> <d09d9c$d4c$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: Re: computing residues***From:*Daniel Lichtblau <danl@wolfram.com>

**References**:**computing residues***From:*mjumbo <mjumbo@nm.ru>

**Re: computing residues***From:*Daniel Lichtblau <danl@wolfram.com>