Re: Bug in Mathematica 6 - Integrate - 6 (Intermittent)

Daniel Lichtblau wrote:
On Jun 17, 3:09 am, Vladimir Bondarenko <v...@xxxxxxxxxxxxxxx> wrote:
Today, Daniel Lichtblau writes that Wolfram Research knows lots
about Mathematica defects... I believe him.

What I'd like is to learn from him, if this concrete defect is
known to WRI? (Any words like, It's a trade secret or I have not
enough time to get involved with your trifles would be a lame
excuse in the context...)

If it's a secret, we don't keep it very well. Replies have alrady more
or less explained it. Also, someone from WRI (me) discussed such
things at an axternal conference, ACA, in 2003.

http://www.math.unm.edu/ACA/2003/Sessions/T2.html


OK.

Here is an example of a Wolfram Research engineering nightmare.

This sort of phenomenon is a nightmare, of sorts. People who work on
these things either learn to live with them, improve on them, or find
other employment.


An intermittent bug discovered by the VM machine about an hour
ago.

Integrate[Exp[-z^2+z] Sin[z]/z, {z, 0, Infinity}]

Now Mathematica returns the integral unevaluated (very often)...
but if you or me have not enough math luck today you will have
a false answer

(-3*Pi*(-4 + Erf[1/2 - I/2] + Erf[1/2 + I/2]) - ((3 - 3*I)
*Sqrt[Pi]*(Erf[1/2 - I/2] + I*E^I*Erf[1/2 + I/2]))/E^(I/2)
+ HypergeometricPFQ[{1, 1}, {2, 5/2}, -I/2]
+ HypergeometricPFQ[{1, 1}, {2, 5/2}, I/2])/12

%//N

2.62117

NIntegrate[Exp[-z^2+z] Sin[z]/z, {z, 0, Infinity}]

1.49841

So that is the time of day.

Best wishes,

Vladimir Bondarenko
[...]

The fact that one can get an alternative result arises from a
combination of things that make it platform and state dependent. I'll
quote from the 2005 Wolfram Research Tech Conference notebook at the
URL below (leaving the incorrect grammar unchanged).

http://library.wolfram.com/infocenter/Conferences/5832

"We have use time constraints to prevent hangs. New set of problems:
Asynchronous interrupt handling, required by TimeConstrained, is
imperfect and in rare cases will cause a kernel crash.
Results now can be platform dependent."

This does not mention dependencies on rior computations and internal
cache states, but it's not a grteat leap to realise such dependencies
will exist.

As for the buggy second result, I've not looed into itbut I rather
suspect it is a problem in the cvolution approach. Probably a failure
of some sort to recognize an invalid application. Won't know until I
reproduce it so that's just a guess.


Daniel Lichtblau
Wolfram Research





Thanks for your explanations Mr Lichtblau.

At least we see that Mathematica people *do* care about bugs
(even on sundays... !!! )

Nothing is perfect in this world.

jacob
.

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