       Re: bugs in Mathematica 5.1

• To: mathgroup at smc.vnet.net
• Subject: [mg54085] Re: bugs in Mathematica 5.1
• From: "Gennady Stupakov" <stupakov at yahoo.com>
• Date: Thu, 10 Feb 2005 02:46:21 -0500 (EST)
• References: <cud70l\$2s4\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Thanks everbody who replied to my post.

It turns out that in my setup I have the option GenerateConditions->False by
default. If I do it now with this option on and off, here is what I get (to
avoid formatting problems I did computation in the kernel without invoking
FrontEnd notebook interface):

Mathematica 5.1 for Microsoft Windows

<--stuff deleted here-->

In:= Integrate[Exp[I x^2],{x,0,Infinity},GenerateConditions->True]

2
I x
Integrate::idiv: Integral of E     does not converge on {0, Infinity}.

2
I x
Out= Integrate[E    , {x, 0, Infinity}, GenerateConditions -> True]

In:= Integrate[Exp[I x^2],{x,0,Infinity},GenerateConditions->False]

Out= 0

I still consider this result as a bug.

"yehuda ben-shimol" <bsyehuda at gmail.com> wrote in message
news:cud70l\$2s4\$1 at smc.vnet.net...
> 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 in your post however is correct for the Sine and Cosine
> rpresentation.
>
> Note that in In 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:={\$System, \$Version, \$MachineType, \$ProcessorType}
> > Out={"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:={Integrate[E^(I*x^2), {x, 0, Infinity}], Integrate[Cos[x^2] +
> > I*Sin[x^2], {x, 0,
> > Infinity}]}
> > Out={0, (1/2 + I/2)*Sqrt[Pi/2]}
> >
> > Second is a more complicated integral that I recently encounted in my
> > research.
> >
> > In:=Integrate[E^(a*Cos[x] - b*Cos[2*x]), {x, 0, 2*Pi},
> > GenerateConditions -> True]
> > Out=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:=
> > 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={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.
> >