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: bugs in Mathematica 5.1

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54045] Re: [mg54032] bugs in Mathematica 5.1
  • From: yehuda ben-shimol <bsyehuda at gmail.com>
  • Date: Wed, 9 Feb 2005 09:27:17 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
I use the same system AND,
for  Integrate[E^( I*x^2),{x,0,Infinity}] I just got a complaint from
Mathematica that the analytic integral cannot converge, so How exactly
did you get 0???

The line In[1] in your post however is correct for the Sine and Cosine
rpresentation.

Note that in In[3] the integrand of the NIntegrate is not identical to
the integrand of the analytical Integrate (you changed the - sign into
+ sign).

I changed the (+) to (-) and reevaluated. 
After evaluation I got the following result:
Analytic -> 7.95493
NIntegrate -> 15.4442
This is surprsing since the function is smooth, always positive and
always stays under 8, so the result I got from the NIntegrate is the
wrong one.
I played a little bit with AccuracyGoal, Method and other parameters
of NIntegrate, with no success.
Does anyone else has an idea??
yehuda






On Tue, 8 Feb 2005 05:31:09 -0500 (EST), Gennady Stupakov
<stupakov at yahoo.com> wrote:
> I tried to post this a few days ago, but it looks like it did not make it.
> 
> Here is a couple of bugs that I found recently in Mathematica 5.1.
> 
> In[13]:={$System, $Version, $MachineType, $ProcessorType}
> Out[13]={"Microsoft Windows","5.1 for Microsoft Windows (October 25, 2004)",
> "PC", "x86"}
> 
> First, I integrate E^(I*x^2),  from 0 to Infinity and get zero, which, of
> course, is wrong.
> 
> In[1]:={Integrate[E^(I*x^2), {x, 0, Infinity}], Integrate[Cos[x^2] +
> I*Sin[x^2], {x, 0,
> Infinity}]}
> Out[1]={0, (1/2 + I/2)*Sqrt[Pi/2]}
> 
> Second is a more complicated integral that I recently encounted in my
> research.
> 
> In[2]:=Integrate[E^(a*Cos[x] - b*Cos[2*x]), {x, 0, 2*Pi},
> GenerateConditions -> True]
> Out[2]=If[Re[a] < Re[b], 2*Pi*BesselI[0, -a + b], Integrate[E^(a*Cos[x] -
> b*Cos[2*x]), {x, 0,
> 2*Pi},Assumptions -> Re[a] >= Re[b]]]
> 
> Let us check this result comparing it with numerical integration for, say,
> b=2 and a=1:
> 
> In[3]:=
> b = 2.;
> a = 1.;
> {Integrate[E^(a*Cos[x] - b*Cos[2*x]), {x, 0, 2*Pi}], NIntegrate[E^(a*Cos[x]
> + b*Cos[2*x]),
> {x, 0, 2*Pi}]}
> Out[5]={7.95493, 20.8711}
> 
> Again, the analytical result is wrong.
> 
> It would be interesting if those bugs are reproduced on other OS and/or
> versions of Mathematica.
> 
> Gennady.
> 
>


  • Prev by Date: Re: Summary: Which[] as Textbook Input, Plot[] Questions
  • Next by Date: Re: Summary: Whichas Textbook Input, PlotQuestions
  • Previous by thread: Re: bugs in Mathematica 5.1
  • Next by thread: Re: bugs in Mathematica 5.1