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Re: The year of Cyber Tester
Posted:
Aug 31, 2008 5:48 AM
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On Aug 31, 12:14 pm, cliclic...@freenet.de wrote:
> Vladimir Bondarenko schrieb:
>
> > On Aug 31, 2:14?am, cliclic...@freenet.de wrote:
> > > Vladimir Bondarenko schrieb:
>
> > > > The last minute piece of news from the VM machine:
>
> > > > (* ? ? ? ? ? ?Mathematica 6.0.3 ? ? ? ? ? ? ? ? *)
>
> > > > LaplaceTransform[BesselI[1/2, z], z, s]
>
> > > > -1/(Sqrt[2] Sqrt[1 + s])
>
> > > > (* ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?*)
>
> > > ... the correct result being 1 / (Sqrt[s^2 - 1] Sqrt[Sqrt[s^2 - 1] +
> > > s]), according to Gradshteyn-Ryzhik. Again, this integral is probably
> > > attacked by viewing it as a Mellin convolution of Meijer-G functions,
> > > and Mathematica is obviously having problems in this area. In fact,
> > > the bug could be the "same" as that reported for Sqrt[z] Cosh[x]: note
> > > that BesselI[1/2,z] = Sqrt[2/(Pi z)] Sinh[z].
>
> > Right you are!
>
> > This just reflects the fact the VM machine is still not
> > implemented to the extent we'd like it; our programmers
> > will fix the bug some fine day. We need more workforce.
>
> > So this time we decided, as a compensation for you, to
> > post two catches :)
>
> > -------------------------------------------------------
>
> > The last minute pieces of news from the VM machine:
>
> > (* Mathematica 6.0.3 *)
>
> > Integrate[ArcTan[z] Log[z]/(1+z^2)^2, {z, 0, Infinity}]
>
> > 0
>
> > while it is (7 Zeta[3] - Pi^2)/16 = -0.09095037994.
>
> > (* Mathematica 6.0.3 *)
>
> > LaplaceTransform[Log[z] Sinh[z], z, s]
>
> > EulerGamma/(1 - s^2)
>
> > while a correct answer is
>
> > ((EulerGamma + Log[s - 1])/(1 - s) +
> > (EulerGamma + Log[s + 1])/(1 + s))/2
>
> All of those point to Meijer-G convolution problems. I suppose this
> means that Mathematica failures in this area are widespread, perhaps
> you are making public what Wolfram Research would call a large-scale
> breakage. Do you think a free download of a replacement kernel would
> be in order for customers who paid for these bugs?
>
> Martin.
M> Do you think a free download of a replacement kernel would
M> be in order for customers who paid for these bugs?
Humm... as for me, a very interesting question...
M> perhaps you are making public what Wolfram Research would
M> call a large-scale breakage.
Actually, what we report here in selected droplets are taken
by an eyedropper out of our internal stream. Usually, we try
to select the defects by the beauty criterium.
We have some other solid stuff which does not boil down to
the reported by the Cyber Tester over the years. I mean the
stuff about the current commercial systems (Mathematica,
Maple, MuPAD, TI-Nspire) and our favourite Derive.
Best wishes,
Vladimir
--
Vladimir Bondarenko
Co-founder, CEO, Mathematical Director
http://www.cybertester.com/ Cyber Tester, LLC
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"We must understand that technologies
like these are the way of the future."
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