Re: fundamental Integrate question
- To: mathgroup at smc.vnet.net
- Subject: [mg73068] Re: fundamental Integrate question
- From: "dimitris" <dimmechan at yahoo.com>
- Date: Thu, 1 Feb 2007 03:02:51 -0500 (EST)
- References: <200701301144.GAA14308@smc.vnet.net><epp6ju$d92$1@smc.vnet.net>
Yes I use 1/x but somehow failed to appear in the post. Thanks a lot for your response and bringing in my attention the setting: Unprotect[Limit]; Limit[a___] := Null /; (Print[InputForm[limit[a]]]; False) Best Regards Dimitris Anagnostou Ï/Ç Daniel Lichtblau Ýãñáøå: > dimitris wrote: > > Consider the classical example that incorrectly gave zero in a prior > > version of Mathematica > > (adopted from http://library.wolfram.com/infocenter/Conferences/5832/) > > > > In[345]:= > > Integrate[f[z], {z, 1 + I, -1 + I, -1 - I, 1 - I, 1 + I}] > > Chop[N[%]] > > Chop[NIntegrate[f[z], {z, 1 + I, -1 + I, -1 - I, 1 - I, 1 + I}]] > > > > Out[345]= > > 2*I*Pi > > > > Out[346]= > > 6.283185307179586*I > > > > Out[347]= > > 6.2831853071795685*I > > > > Of course the result is correct considering the pole at origin and the > > Residue theorem. > > > > Trying to understand how Mathematica applies the Newton-Leibniz > > formula I just want to know if > > I am right below: > > > > In[511]:= > > ((F[z] /. z -> 1 - I) - F[z] /. z -> -1 - I) + ((F[z] /. z -> 1 + I) - > > F[z] /. z -> 1 - I) + > > ((F[z] /. z -> -1 + I) - F[z] /. z -> 1 + I) + (Limit[F[z], z -> -1, > > Direction -> -I] - F[z] /. z -> -1 + I) + > > ((F[z] /. z -> -1 - I) - Limit[F[z], z -> -1, Direction -> I]) > > > > Out[511]= > > 2*I*Pi > > > > Thanks for any response! > > > > Dimitris > > Not clear what you use for f[x]. Maybe 1/x? Anyway, quoting the author > of that notebook: > > "It is important to assess whether an integration path crosses a branch > cut of an antiderivative (so that we might split the path into > segments)." So yes, I would imagine it does something along the lines > you suggest. > > To see explicitly what limits get computed you might first do > > Unprotect[Limit]; > Limit[a___] := Null /; (Print[InputForm[limit[a]]]; False) > > > Daniel Lichtblau > Wolfram Research