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Walter Roberson · Guest

Vladimir Bondarenko wrote:
[quote]On Oct 10, 5:35 pm, Pfenniger Daniel <daniel.pfenni...@unige.ch
wrote:
Vladimir Bondarenko wrote:
It took the VM machine less than 7 minutes to
identify the first defect in Matlab 2008b.

As is, without any evidence, it is pure slander, but
you don>t seem to bother about legal matters.
[/quote]
I didn>t time anything, but when I put together a simple testing
script and applied it against Matlab 2007a, it was a matter of
only about 15 minutes run time to crash Matlab R2007a completely.
R2008a is a bit tougher, but it didn>t take particularly long
(definitely less than half an hour) to find something that would crash it.

I have opened 10 "crashes" cases with Mathworks about my results, and
another 5 cases concerning situations where the Matlab code could be
improved. I have found about a dozen other combinations of circumstances that
will reliably crash R2008a, but which I have not yet written up for Mathworks
(they asked me to send the reports in batches.)

Specific evidence?

R2007a: movie(''); crashes Matlab (fixed in newer versions)

R2008a: movie(uint64(0)); crashes Matlab

The above are simple cases of obvious defects, unless you are willing to
define away a complete session crash as not being a "defect". Vladimir>s
tools are more refined, finding situations where products produce
dubious or decidedly incorrect answers. I don>t think it would have taken
very long to find such a case in Matlab 2008b: all one would have to do
is pull out some of the cases one had recorded against Maple, transpose
them into Matlab notation, and watch as the Maple-based Matlab Symbolic Toolbox
reproduced the existing Maple bug. For example, Maple 12:

[quote]log(exp(RootOf(_Z*exp(_Z)))); simplify(%);
Error, (in ln) numeric exception: division by zero[/quote]

but evalf(RootOf(_Z*exp(_Z))) is 0, and log(exp(0)) is 0 so there should
be no division by zero.

My saying that it was not much work to find ways to crash Matlab R2007a
or R2008a is not intended as a disparagement of the effort that Mathworks
has put into their products. Mathwork>s support has reacted admirably quickly
in verifying my reports, and I believe they will repair the serious defects
in the next release or the one after.

As a programmer myself, I know how hard it can be to think of all of the ways
that some fool (like me ;-) ) might abuse software; and as a programmer, I know
how easy it can be to read an algorithm dozens of times and never once see
the circumstances under which the algorithm Won>t Work. I>m not talking
about typos and off-by-one type errors: I>m referring to situations where
the circumstances that can break your algorithm just escape your attention. For example,
one might not happen to realize that the algorithm one is working on is only applicable
to topologies of orientable surfaces with even genus numbers if one>s attention
has been on linear algebra.

It is well established the bugs exist in nearly every serious programs. It used to be
thought that having two or three independent "tiger teams" that did not discuss
implementation with each other would be sufficient to produce the "right answer"
out of at least one of the implementations (for any situation that fell within the design
parameters), under the view that bugs were more or less just "accidents" -- but it has
been shown otherwise, that different groups tend to make the same -kinds- of errors.
Thus, it is valuable to have someone doing comparative testing of products -- to
discover the classes of defects in particular products, and to discover the
commonality of defect classes amongst the various products. Information about
what kinds of cases that multiple products tend to get wrong is of benefit to all
serious product designers so that they know what to pay special attention to; and
such information is also of strong interest to those who want to teach well.
Information about the commonality of class defects amongst multiple products
is also indicative of mathematics or technology that is not widely understood,
which is a hint that there is potentially room for others to re-examine that
particular field and find different expressions of it that might be easier to
understand or which might lead to new insights.

It is disappointing to see systematic analysis attacked as being of low value on
the basis that the analyzer does not provide "solutions" or does not debug
far enough to find the root cause for all of the difficulties encountered.
There is value in knowing the problems that exist. A person skilled in
finding the problems is not necessarily a person who is skilled in fault classification,
or in debugging, or in deep category theory, or in figuring out -why-
humans tend to have problems with certain kinds of knowledge: people with those
kinds of skills do exist, though, and if they had access to the fault information,
then they would have fertile grounds for investigation.

In regards to the matter of financial motive, I would point out this: everyone I work
with (in a government research facility) has the "financial motive" of doing a good job
so as to continue to be employed. For some of the people, it is perhaps mostly a nice
place to work, that pays tolerably well (but certainly not extravagantly), given that
the reality of the world is that one has to work *somewhere* -- but we have a high
concentration of people who believe firmly that the research we do is important for
public health, many of whom have turned down better-paying opportunities in order to
work there.

But the reward of knowing that one is benefiting humanity doesn>t pay the
heating bill, and I live in the coldest city in the world that has a population of over
600,000. Is it somehow improper or unethical for me to seek a living wage in return
for my work?

Axel Vogt · Guest

Walter Roberson wrote:
....
[quote]The above are simple cases of obvious defects, unless you are
willing to
define away a complete session crash as not being a "defect".
Vladimir>s
tools are more refined, finding situations where products produce
dubious or decidedly incorrect answers. I don>t think it would have
taken
very long to find such a case in Matlab 2008b: all one would have to do
is pull out some of the cases one had recorded against Maple, transpose
them into Matlab notation, and watch as the Maple-based Matlab
Symbolic
Toolbox
reproduced the existing Maple bug. For example, Maple 12:

log(exp(RootOf(_Z*exp(_Z)))); simplify(%);
Error, (in ln) numeric exception: division by zero

but evalf(RootOf(_Z*exp(_Z))) is 0, and log(exp(0)) is 0 so there
should
be no division by zero.
....[/quote]

This Maple bug steps in before log, already at
'simplify( exp(RootOf(exp(_Z))) )'.

Robert Israel · Guest

Axel Vogt <&noreply@axelvogt.de> writes:

[quote]Walter Roberson wrote:
...
The above are simple cases of obvious defects, unless you are
willing to
define away a complete session crash as not being a "defect".
Vladimir>s
tools are more refined, finding situations where products produce
dubious or decidedly incorrect answers. I don>t think it would have
taken
very long to find such a case in Matlab 2008b: all one would have to do
is pull out some of the cases one had recorded against Maple, transpose
them into Matlab notation, and watch as the Maple-based Matlab
Symbolic
Toolbox
reproduced the existing Maple bug. For example, Maple 12:

log(exp(RootOf(_Z*exp(_Z)))); simplify(%);
Error, (in ln) numeric exception: division by zero

but evalf(RootOf(_Z*exp(_Z))) is 0, and log(exp(0)) is 0 so there
should
be no division by zero.
...

This Maple bug steps in before log, already at
'simplify( exp(RootOf(exp(_Z))) )'.
[/quote]
That is a different bug, I think. Zeros of exp(_Z) do not exist, but Maple
does not know that, so it essentially applies the simplification rule
f(RootOf(f(_Z))) = 0.

I think what you mean is

[quote]simplify(exp(RootOf(_Z*exp(_Z))));
[/quote]
or more generally

[quote]simplify(f(RootOf(f(_Z)*g(_Z))));
[/quote]
0

If w is a zero of f(_Z)*g(_Z), we must have f(w) = 0 or g(w) = 0. I don>t
know why Maple jumps to the conclusion that f(w) = 0 here.
--
Robert Israel israel@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

Axel Vogt · Guest

Robert Israel wrote:
[quote]Axel Vogt <&noreply@axelvogt.de> writes:

Walter Roberson wrote:
...
The above are simple cases of obvious defects, unless you are
willing to
define away a complete session crash as not being a "defect".
Vladimir>s
tools are more refined, finding situations where products produce
dubious or decidedly incorrect answers. I don>t think it would have
taken
very long to find such a case in Matlab 2008b: all one would have to do
is pull out some of the cases one had recorded against Maple, transpose
them into Matlab notation, and watch as the Maple-based Matlab
Symbolic
Toolbox
reproduced the existing Maple bug. For example, Maple 12:

log(exp(RootOf(_Z*exp(_Z)))); simplify(%);
Error, (in ln) numeric exception: division by zero

but evalf(RootOf(_Z*exp(_Z))) is 0, and log(exp(0)) is 0 so there
should
be no division by zero.
...

This Maple bug steps in before log, already at
'simplify( exp(RootOf(exp(_Z))) )'.

That is a different bug, I think. Zeros of exp(_Z) do not exist, but Maple
does not know that, so it essentially applies the simplification rule
f(RootOf(f(_Z))) = 0.

I think what you mean is

simplify(exp(RootOf(_Z*exp(_Z))));

or more generally

simplify(f(RootOf(f(_Z)*g(_Z))));

0

If w is a zero of f(_Z)*g(_Z), we must have f(w) = 0 or g(w) = 0. I don>t
know why Maple jumps to the conclusion that f(w) = 0 here.
[/quote]
Thx, f(RootOf(f(_Z))) = 0 sounds like a reason to me.

I have the errors for 'exp(RootOf(exp(f(T)))); simplify(%);' as well
and dito with a factor exp(RootOf(f*exp(_Z))) or for f a function

Vladimir Bondarenko · Guest

On Oct 12, 10:55 am, Walter Roberson <rober...@hushmail.com> writes:

[quote]VladimirBondarenko wrote:
On Oct 10, 5:35 pm, Pfenniger Daniel <daniel.pfenni...@unige.ch
wrote:
VladimirBondarenko wrote:
It took the VM machine less than 7 minutes to
identify the first defect in Matlab 2008b.
As is, without any evidence, it is pure slander, but
you don>t seem to bother about legal matters.

I didn>t time anything, but when I put together a simple testing
script and applied it against Matlab 2007a, it was a matter of
only about 15 minutes run time to crash Matlab R2007a completely.
R2008a is a bit tougher, but it didn>t take particularly long
(definitely less than half an hour) to find something that would crash it.

I have opened 10 "crashes" cases with Mathworks about my results, and
another 5 cases concerning situations where the Matlab code could be
improved. I have found about a dozen other combinations of circumstances that
will reliably crash R2008a, but which I have not yet written up for Mathworks
(they asked me to send the reports in batches.)

Specific evidence?

R2007a: movie(''); crashes Matlab (fixed in newer versions)

R2008a: movie(uint64(0)); crashes Matlab

The above are simple cases of obvious defects, unless you are willing to
define away a complete session crash as not being a "defect".Vladimir>s
tools are more refined, finding situations where products produce
dubious or decidedly incorrect answers. I don>t think it would have taken
very long to find such a case in Matlab 2008b: all one would have to do
is pull out some of the cases one had recorded against Maple, transpose
them into Matlab notation, and watch as the Maple-based Matlab Symbolic Toolbox
reproduced the existing Maple bug. For example, Maple 12:

log(exp(RootOf(_Z*exp(_Z)))); simplify(%);

Error, (in ln) numeric exception: division by zero

but evalf(RootOf(_Z*exp(_Z))) is 0, and log(exp(0)) is 0 so there should
be no division by zero.

My saying that it was not much work to find ways to crash Matlab R2007a
or R2008a is not intended as a disparagement of the effort that Mathworks
has put into their products. Mathwork>s support has reacted admirably quickly
in verifying my reports, and I believe they will repair the serious defects
in the next release or the one after.

As a programmer myself, I know how hard it can be to think of all of the ways
that some fool (like me ;-) ) might abuse software; and as a programmer, I know
how easy it can be to read an algorithm dozens of times and never once see
the circumstances under which the algorithm Won>t Work. I>m not talking
about typos and off-by-one type errors: I>m referring to situations where
the circumstances that can break your algorithm just escape your attention. For example,
one might not happen to realize that the algorithm one is working on is only applicable
to topologies of orientable surfaces with even genus numbers if one>s attention
has been on linear algebra.

It is well established the bugs exist in nearly every serious programs. It used to be
thought that having two or three independent "tiger teams" that did not discuss
implementation with each other would be sufficient to produce the "right answer"
out of at least one of the implementations (for any situation that fell within the design
parameters), under the view that bugs were more or less just "accidents" -- but it has
been shown otherwise, that different groups tend to make the same -kinds- of errors.
Thus, it is valuable to have someone doing comparative testing of products -- to
discover the classes of defects in particular products, and to discover the
commonality of defect classes amongst the various products. Information about
what kinds of cases that multiple products tend to get wrong is of benefit to all
serious product designers so that they know what to pay special attention to; and
such information is also of strong interest to those who want to teach well.
Information about the commonality of class defects amongst multiple products
is also indicative of mathematics or technology that is not widely understood,
which is a hint that there is potentially room for others to re-examine that
particular field and find different expressions of it that might be easier to
understand or which might lead to new insights.

It is disappointing to see systematic analysis attacked as being of low value on
the basis that the analyzer does not provide "solutions" or does not debug
far enough to find the root cause for all of the difficulties encountered.
There is value in knowing the problems that exist. A person skilled in
finding the problems is not necessarily a person who is skilled in fault classification,
or in debugging, or in deep category theory, or in figuring out -why-
humans tend to have problems with certain kinds of knowledge: people with those
kinds of skills do exist, though, and if they had access to the fault information,
then they would have fertile grounds for investigation.

In regards to the matter of financial motive, I would point out this: everyone I work
with (in a government research facility) has the "financial motive" of doing a good job
so as to continue to be employed. For some of the people, it is perhaps mostly a nice
place to work, that pays tolerably well (but certainly not extravagantly), given that
the reality of the world is that one has to work *somewhere* -- but we have a high
concentration of people who believe firmly that the research we do is important for
public health, many of whom have turned down better-paying opportunities in order to
work there.

But the reward of knowing that one is benefiting humanity doesn>t pay the
heating bill, and I live in the coldest city in the world that has a population of over
600,000. Is it somehow improper or unethical for me to seek a living wage in return
for my work?
[/quote]
WR> I don>t think it would have taken very long to find such
WR> a case in Matlab 2008b: all one would have to do is pull
WR> out some of the cases one had recorded against Maple,
WR> transpose them into Matlab notation, and watch as the
WR> Maple-based Matlab Symbolic Toolbox reproduced
WR> the existing Maple bug.

Actually, Matlab 2008b>s default symbolic engine is MuPAD 5.1.

It did inherit quite a number of defects detected by the VM
machine (VMM) in MuPAD 4.0.6 and, in a (small) part posted
here

http://groups.google.com/groups/search?q=%22mupad+bugs%22&start=0&scoring=d&hl=en&ie=UTF-8&

many of them, but far from all, have been fixed in MuPAD 5.1,
though.

But, unfortunately, new numerous defects have been identified
by the VMM throughout all the MuPAD solvers, - and more.

Best wishes,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester Ltd.

--------------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

--------------------------------------------------------------

sashap · Guest

On Oct 23, 3:00 am, Vladimir Bondarenko <v...@cybertester.com> wrote:
[quote]Hello,

MeijerG[{{1}, {5/4, 7/4}}, {{1/2, 1, 1}, {}}, 1]

?
[/quote]
In[137]:= FullSimplify[
RootReduce[
Limit[FunctionExpand[
MeijerG[{{1}, {5/4, 7/4}}, {{1/2, 1, 1}, {}}, x]], x -> 1]]]

Out[137]= (2*2^(3/4)*(Sqrt[2 + Sqrt[2]]*
ArcTan[Sqrt[2*(1 + Sqrt[2])]] -
Sqrt[2 - Sqrt[2]]*Log[1 + Sqrt[2] + Sqrt[2*(1 + Sqrt[2])]]))/
Sqrt[Pi]

Cheers,
Oleksandr
[quote]
Best wishes,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester Ltd.

------------------------------------------------

"We must understand that technologies
like these are the way of the future."

------------------------------------------------[/quote]

Guest

sashap schrieb:
[quote]
In[137]:= FullSimplify[
RootReduce[
Limit[FunctionExpand[
MeijerG[{{1}, {5/4, 7/4}}, {{1/2, 1, 1}, {}}, x]], x -> 1]]]

Out[137]= (2*2^(3/4)*(Sqrt[2 + Sqrt[2]]*
ArcTan[Sqrt[2*(1 + Sqrt[2])]] -
Sqrt[2 - Sqrt[2]]*Log[1 + Sqrt[2] + Sqrt[2*(1 + Sqrt[2])]]))/
Sqrt[Pi]

[/quote]
The simplifier might have pulled out the factor 2^(1/4) from the
nested roots and written this as

4*(Sqrt[Sqrt[2]+1]*A - Sqrt[Sqrt[2]-1]*L)/Sqrt[Pi].

Martin.

Vladimir Bondarenko · Guest

On Oct 26, 3:21 pm, "Joerg J. Buchholz" <jjbuchh...@gmail.com> wrote:
[quote]In R2008b, solve seems to return strange results:

solve ('x^(5/2) + x^(1/2) = 42')

ans
0
[/quote]
We also acquired MATLAB 2008b + Symbolic Toolbox.

Your example is just a specific case of the hundreds MATLAB 2008b
bugs discovered by our VM machine without any human intervention.
But this is just the beginning of the story.

To make a long story short, on Oct 15, 2008 we sent a message to
the MathWorks owners but had a communication problem; Mr. Lord
kindly promised "to determine the correct course of action for
the issue" we raised.

So, hopefully, thanks to Mr. Lord>s effort, soon we will be able
to sent an email message to Mr. Little and Dr. Moler in the way
it reaches them.

Best wishes,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester Ltd.

-----------------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

-----------------------------------------------------------------

rio · Guest

"Peter Pein" <petsie@dordos.net> ha scritto nel messaggio
news:ga12ff$7gq$1@online.de...
[quote]Nasser Abbasi schrieb:
"Vladimir Bondarenko" <vb@cybertester.com> wrote in message
news:ed8d2d31-de34-4524-ade1-681924e6a1b8@m44g2000hsc.googlegroups.com...
Being not humans, we do not know what fatigue is.

Last minute fantastic piece of news from the VM machine:

(* Mathematica 6.0.3 *)

NIntegrate[Sin[z], {z, 5, 1}]
NIntegrate[Sin[z], {z, 1, 5}]

0.25664 <------------- BUG
0.25664
[/quote]
with Axiom

(69) -> a123:=integrate(sin(x), x=5..1)

(69) cos(5) - cos(1)
(70) -> a123::Float

Cannot convert from type OrderedCompletion Expression Integer to
Float for value
cos(5) - cos(1)

(70) -> a123+0.0

(70) - 0.2566401204 0491345293
here with Axiom seems ok, but i don>t know how convert a123 to Float

Nasser Abbasi · Guest

"Scott Seidman" <namdiesttocs@mindspring.com> wrote in message
[quote]
If the bug report looks like your usenet post, I>m not surprised it was
deleted. You would think someone in the business of finding and
cataloging bugs would be able to throw together a cogent bug report.

[/quote]
Hello Scott;

Let me make sure I understand the above.

Are you saying that, to make a post about a software bug, the posting must
adhere to some protocol and format, which is unspecified as what that should
be, but it is implied that the posting must be of some high quality in the
opinion of the readers,or otherwise, this posting can legally and morally be
deleted by anyone who has the power to do so?

If my understanding is wrong, please clarify.

If my understand is close enough to what you meant, then do you have a link
as what such a bug report should look like for those who might want to make
posting regarding other bugs found in the future to avoid their post being
deleted?

regards,
Nasser

Daniel Lichtblau · Guest

On Nov 17, 5:08 pm, Vladimir Bondarenko <v...@cybertester.com> wrote:
[quote]Hello,

MeijerG[{{1}, {5/4, 7/4}}, {{1, 1, 1/2}, {}}, 1]

?

-----------------------------------------------------------

On the nature and goal of Cyber Tester>s challenges

http://groups.google.com/group/sci.math.symbolic/msg/ea861b72145e02aa...

-----------------------------------------------------------

The Cyber Tester>s challenges, as I wrote repeatedly is not
about finding concrete answers (I know all of them because
it is me who designs them) but about a way the human beings
use to get to this answer.

So is there a Simplifier who can show how using a string of
CAS commands one can "elementarize" this MeijerG instance?

Best wishes,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester Ltd.

-----------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

-----------------------------------------------------------
[/quote]
No idea what is a simplest form, but this one is at least elementary.

In[1]:= InputForm[mg FullSimplify[Limit[MeijerG[{{1}, {5/4,7/4}}, {{1,1,1/2}, {}},x], x-
[quote]1]]]
[/quote]
Out[1]//InputForm((2 - 2*I)*(-1)^(1/8)*2^(1/4)*
(2*(1 + (-1)^(1/4))*ArcSin[Sqrt[1 - 1/Sqrt[2]]] +
(-I + (-1)^(3/4))*Log[1 + Sqrt[2] + Sqrt[2*(1 + Sqrt[2])]]))/Sqrt
[Pi]

Daniel Lichtblau
Wolfram Research

Vladimir Bondarenko · Guest

On Nov 18, 2:33 am, Daniel Lichtblau <d...@wolfram.com> wrote:
[quote]On Nov 17, 5:08 pm, Vladimir Bondarenko <v...@cybertester.com> wrote:

Hello,

MeijerG[{{1}, {5/4, 7/4}}, {{1, 1, 1/2}, {}}, 1]

?

-----------------------------------------------------------

On the nature and goal of Cyber Tester>s challenges

http://groups.google.com/group/sci.math.symbolic/msg/ea861b72145e02aa...

-----------------------------------------------------------

The Cyber Tester>s challenges, as I wrote repeatedly is not
about finding concrete answers (I know all of them because
it is me who designs them) but about a way the human beings
use to get to this answer.

So is there a Simplifier who can show how using a string of
CAS commands one can "elementarize" this MeijerG instance?

Best wishes,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester Ltd.

-----------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

-----------------------------------------------------------

No idea what is a simplest form, but this one is at least elementary.

In[1]:= InputForm[mg > FullSimplify[Limit[MeijerG[{{1}, {5/4,7/4}}, {{1,1,1/2}, {}},x], x-

1]]]

Out[1]//InputForm> ((2 - 2*I)*(-1)^(1/8)*2^(1/4)*
(2*(1 + (-1)^(1/4))*ArcSin[Sqrt[1 - 1/Sqrt[2]]] +
(-I + (-1)^(3/4))*Log[1 + Sqrt[2] + Sqrt[2*(1 + Sqrt[2])]]))/Sqrt
[Pi]

Daniel Lichtblau
Wolfram Research
[/quote]
Great.

You are right, one can put it in a shorter way,

8*Sqrt[(1+Sqrt[2])/Pi]*ArcTan[Sqrt[Sqrt[2]-1]] -
4*Sqrt[(Sqrt[2]-1)/Pi]*Log[1+Sqrt[2]+Sqrt[2*(1+Sqrt[2])]]

But what about Mathematica 7, can it express the original
MeijerG instance using just FunctionExpand or FullSimplify?

Thanks in advance for your answer.

Vladimir Bondarenko
Cyber Tester Ltd.

sashap · Guest

The answer is 2*Pi^(3/2)*(1+I).

Oleksandr Pavlyk

In[154]:= NIntegrate[
MeijerG[{{1/2, 1}, {}}, {{1/2, 1}, {}}, -1/
x] MeijerG[{{1}, {}}, {{1/2}, {}}, x]/x, {x, 0, Infinity}]

Out[154]= 11.1367 + 11.1367 I

In[155]:= N[MeijerG[{{1/2, 1, 1}, {}}, {{1/2, 1/2, 1}, {}}, I , 1/2]]

Out[155]= 11.1367 + 11.1367 I

In[156]:MeijerG[{{1/2, 1}, {}}, {{1/2, 1}, {}}, -1/
x] MeijerG[{{1}, {}}, {{1/2}, {}}, x]/x // FunctionExpand //
FullSimplify[#, x > 0] &

Out[156]= (\[Pi]^(3/2) (1 + I Sqrt[x]))/(Sqrt[x] (1 + x)^(3/2))

In[157]:= Integrate[%, {x, 0, Infinity}]

Out[157]= (2 + 2 I) \[Pi]^(3/2)

On Nov 18, 1:26 am, Vladimir Bondarenko <v...@cybertester.com> wrote:
[quote]Hello,

MeijerG[{{1/2, 1, 1}, {}}, {{1/2, 1/2, 1}, {}}, I, 1/2]

?

The generalized MeijerG definition is herehttp://documents.wolfram.com/mathematica/functions/MeijerG

Best wishes,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester Ltd.

-----------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

-----------------------------------------------------------[/quote]

Chip Eastham · Guest

On Nov 18, 7:33 pm, Vladimir Bondarenko <v...@cybertester.com> wrote:
[quote]http://www.wolfram.com/products/mathematica/index.html

If you>re doing anything technical, think Mathematica -- not just for
computation, but for modeling, simulation, visualization, development,
documentation, and deployment.

Why Mathematica? Because this one integrated system delivers
unprecedented workflow, coherence, reliability, and innovation. Rather
than different toolkits for different jobs, Mathematica has been built
ground-up over nearly 20 years to deliver one vision: the ultimate
technical application and environment.

http://www.wolfram.com/products/mathematica/experience/request.cgi

Please use this form to request a free 15-day, save-disabled trial
version of Mathematica. Your request will be processed by Wolfram
Research, and you can expect an email response within three business
days.

Linux x86/x86-64bit
IBM AIX
Linux Itanium
Solaris UltraSparc
Solaris x86
[/quote]
[most newsgroups removed from reply]

I like it better when you make unattributed quotes
from Renaissance poetry.

chip

Vladimir Bondarenko · Guest

On Nov 19, 3:25 am, Chip Eastham <hardm...@gmail.com> wrote:
[quote]On Nov 18, 7:33 pm, Vladimir Bondarenko <v...@cybertester.com> wrote:

http://www.wolfram.com/products/mathematica/index.html

If you>re doing anything technical, think Mathematica -- not just for
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Linux x86/x86-64bit
IBM AIX
Linux Itanium
Solaris UltraSparc
Solaris x86

[most newsgroups removed from reply]

I like it better when you make unattributed quotes
from Renaissance poetry.

chip
[/quote]
Thanks for the feedback.

You might like even better when you see new
and novel results from the VM machine.


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