I agree with others in that Vladimir is doing a great job. Keep up the
great work!
I hate Mathematica 6. The help files are so bad I cancelled my 3 year
premier service for this reason alone. Heck...If I have to keep reading
help in 5.2, why pay for 6.0?
Entering College students that I know of are not going to use 6.0 cause
they
can't learn from the help file by doing 50+ clicks for each keyword, with
no
structure.
There are many bugs in 6.0 as Vladimir has pointed out, as well as code
that
crashes the system.
Anyway, here is something one may find interesting. This makes it so hard
to use MM 6.0
AllMethods = {CartesianRule, ClenshawCurtisRule,
GaussBerntsenEspelidRule, GaussKronrodRule,
LobattoKronrodRule, LobattoPeanoRule, MultiPanelRule,
NewtonCotesRule, TrapezoidalRule, AdaptiveMonteCarlo,
AdaptiveQuasiMonteCarlo, DoubleExponential,
DuffyCoordinates, ExtrapolatingOscillatory, MonteCarlo,
QuasiMonteCarlo, Trapezoidal, EvenOddSubdivision,
SymbolicPiecewiseSubdivision, OscillatorySelection,
UnitCubeRescaling}
TableForm[Table[{m = AllMethods[[j]];
m,
NIntegrate[Sin[z]*(BesselJ[1, z]/Sqrt[z + z^2]),
{z, 0, Infinity}, Method -> m]}, {j, 21}]]
{CartesianRule, 0.8000354262780739},
{ClenshawCurtisRule, 0.75798428807618},
{GaussBerntsenEspelidRule, 0.75798428807618},
{GaussKronrodRule, 0.75798428807618},
{LobattoKronrodRule, 0.75798428807618},
{LobattoPeanoRule, 0.75798428807618},
{MultiPanelRule, 0.75798428807618},
{NewtonCotesRule, 0.75798428807618},
{TrapezoidalRule, 0.75798428807618},
{AdaptiveMonteCarlo, 0.8004524848776702},
{AdaptiveQuasiMonteCarlo, 0.7981365243033698},
{DoubleExponential, 0.75798428807618},
{DuffyCoordinates, 0.75798428807618},
{ExtrapolatingOscillatory, 0.7694525127979034},
{MonteCarlo, 0.7970124128688676},
{QuasiMonteCarlo, 0.7977051437229787},
{Trapezoidal, 0.75798428807618},
{EvenOddSubdivision, 0.8000354262780739},
{SymbolicPiecewiseSubdivision, 0.8000354262780739},
{OscillatorySelection, 0.75798428807618},
{UnitCubeRescaling, 0.8000354262780739}
Reading the Error outputs are "interesting." (I left them out)
As you can see, a few "Methods" give 0.8000035, but not many.
So, which one is more accurate? I do not know.
If I increase MaxPoints, and MaxRecursion,etc... then the answer gets
further away from .800035, so my guess would have been that it's closer to
0.757 after doing all the above work.
I do not like Wolfram Research always-keeping bugs/crashes a "secret."
They
should post informative articles on what the real issues are. Once we
know
what the current limitations are, the more we all benefit. We probably
would be more tolerant also.
PS. Wolfram Research, please update you help files.
Keep up the great work.
--
Dana DeLouis
Mathematica 6
Having to use 5.2 Help
Having to read/study Books for 4.0
"Vladimir Bondarenko" <vb@[EMAIL PROTECTED]
> wrote in message
news:1bfb8c3a-ebab-4ddc-9bac-85017cf7292b@[EMAIL PROTECTED]
> ----------------------------------------------------------------
>
> Our little demo continues..... Hello again from the VM machine
> which hopefully soon will not be ignored by CAS manufacturers.
>
> ----------------------------------------------------------------
>
> N[Integrate[Sin[z] BesselJ[1, z]/Sqrt[z + z^2], {z,0,Infinity}]]
>
> 0.800192
>
> ----------------------------------------------------------------
>
> Mathematica 6, unlike the previous versions, returns an invalid
> result 0.757984 without any warning implying that the result
> may be false, -- as it is.
>
> ----------------------------------------------------------------
>
> NIntegrate[Sin[z] BesselJ[1, z]/Sqrt[z + z^2], {z, 0, Infinity}]
>
> ----------------------------------------------------------------
> VERSION OUTPUT RESOLUTION
> ----------------------------------------------------------------
>
> Mathematica 6.0 0.757984 <------------------------------ BUG
>
> Mathematica 5.2 0.800035 OK
>
> Mathematica 4.2 0.800035 OK
>
> Mathematica 3.0 0.800035 OK
>
> ----------------------------------------------------------------
>
> Best wishes,
>
> Vladimir Bondarenko
>
> VM and GEMM architect
> Co-founder, CEO, Mathematical Director
>
> http://www.cybertester.com/
Cyber Tester, LLC
> http://maple.bug-list.org/
Maple Bugs Encyclopaedia
> http://www.CAS-testing.org/
CAS Testing
>
> ----------------------------------------------------------------
|
