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Richard J. Fateman
science forum addict


Joined: 04 May 2005
Posts: 81

PostPosted: Mon May 01, 2006 6:31 pm    Post subject: Re: re-inventing the wheel... scope of assumptions. Reply with quote

Daniel Lichtblau wrote:
.... description of macsyma, then mathematica handling of assumptions
....
That seems to cover a good deal of the syntax and scope rules of
what might be plausible for assumptions, although why certain commands
like Simplify have extra arguments looks like a relic of a time when
Assumptions were not properly integrated into Mathematica.
Why not Assuming[.... , Simplify[...]]
instead of Simplify[..., Assumptions -> ...].

The details of what calculations are actually done with assumptions
are probably unstated and may vary from time to time, e.g. to what
extent are non-linear inequalities handled? Can one say Assume H is a
Hilbert Space ?

I indicated in my earlier note that assumptions HAVE been added
relatively recently to the post-1980 CAS. But designing them
in from the beginning might have resulted in a nicer system.

Are all issues now handled correctly? I doubt it. Is Macsyma's
design from 1978 or so superior to the more recent ad-hoc additions
to CAS? Not necessarily. Are the implementation details in Macsyma
(or Maxima) superior to those in other CAS? Probably not -- the details
are all pretty much undescribed in any case. But Macsyma has a good
excuse for not doing a great job on this topic: the design for the
simplifier was pretty much set up by 1968, running in an environment
that had the computing power of a cell phone.



Quote:

I don't know if this addresses all possible issues of points of
similarity or difference between current Mathematica assumptions usage
and that of Maxima.

One large set of issues is how good the assumption mechanism is in
actual use. Can collections of them be simplified, as one issue.

For example, both Macsyma and Mathematica
know that if n is an integer, then abs(sin((2*n+1)*pi/2)) is 1.
But given assumptions a<=0 && a>=0, it seems that Mathematica does
not know if a==0. Macsyma does, at least if asked is(a=0);


Quote:
I think it gives some idea, though. I'll get off
your feet now.

thanks.
RJF
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Daniel Lichtblau
science forum beginner


Joined: 12 May 2005
Posts: 48

PostPosted: Mon May 01, 2006 7:18 pm    Post subject: Re: re-inventing the wheel... scope of assumptions. Reply with quote

Richard J. Fateman wrote:
Quote:
Daniel Lichtblau wrote:
... description of macsyma, then mathematica handling of assumptions
...
That seems to cover a good deal of the syntax and scope rules of
what might be plausible for assumptions, although why certain commands
like Simplify have extra arguments looks like a relic of a time when
Assumptions were not properly integrated into Mathematica.
Why not Assuming[.... , Simplify[...]]
instead of Simplify[..., Assumptions -> ...].

Both are allowed and, to the best of my knowledge, they are equivalent
(except the latter might include further assumptions if it is inside a
construct such as the former).

Certainly the latter is, to an extent, in the artifact category. That
is to say, it is perfectly fine but I'm not sure it would be present
were Assuming[] constructs around before the Assumptions option was
implemented in Simplify and Integrate.


Quote:
The details of what calculations are actually done with assumptions
are probably unstated and may vary from time to time, e.g. to what
extent are non-linear inequalities handled?

They do vary in Mathematica. This provides room for improvement though
underspecification can also be viewed as a bad thing.

I will mention that nonlinear inequality assumption handling is, in
some functions, quite powerful. I'll say a little more below on this
topic.


Quote:
Can one say Assume H is a
Hilbert Space ?

Not at present, at least in any way I can think of.


Quote:
I indicated in my earlier note that assumptions HAVE been added
relatively recently to the post-1980 CAS. But designing them
in from the beginning might have resulted in a nicer system.

Are all issues now handled correctly? I doubt it. Is Macsyma's
design from 1978 or so superior to the more recent ad-hoc additions
to CAS? Not necessarily. Are the implementation details in Macsyma
(or Maxima) superior to those in other CAS? Probably not -- the details
are all pretty much undescribed in any case. But Macsyma has a good
excuse for not doing a great job on this topic: the design for the
simplifier was pretty much set up by 1968, running in an environment
that had the computing power of a cell phone.


I don't know if this addresses all possible issues of points of
similarity or difference between current Mathematica assumptions usage
and that of Maxima.

One large set of issues is how good the assumption mechanism is in
actual use. Can collections of them be simplified, as one issue.

For example, both Macsyma and Mathematica
know that if n is an integer, then abs(sin((2*n+1)*pi/2)) is 1.
But given assumptions a<=0 && a>=0, it seems that Mathematica does
not know if a==0. Macsyma does, at least if asked is(a=0);

Mathematica makes these inferences.

In[18]:= Refine[a==0, Assumptions->a<=0 && a>=0]
Out[18]= True

In[19]:= Simplify[a==0, Assumptions->a<=0 && a>=0]
Out[19]= True

This does not really scratch the surface of The Big Picture, that is to
say, how much can assumptions be used in practice to make deductions
that we might be able to make with same.

One area where one can go further with assumptions than by hand is in
using them in real inequality inferencing. This is because a computer
will generally be better at cylindrical decomposition than a human, and
often real inequality inferencing requires some aspects of a CAD
approach.

A drawback is that the machinery for this is expensive. So it cannot be
used blindly in all manner of functionality that might like to enjoy
the benefits, for example limit extraction or definite integration from
symbolic calculus. Mathematica will employ various devices in
attempting to derive the benefits of computationally difficult
inferencing without hanging on seemingly mundane computations. The
details of how this is done are reminiscent of quotes about making
sausage.

There are other issues for symbolic calculus as well, e.g. when to
regard inequalities as strict and when to do otherwise. This has to do
with the fact that, often, measure zero sets can be ignored (so work
with strict inequalities). But in some places e.g. at branch cuts or in
handling generalized functions this may be a bad idea. Certainly I do
not claim that all such issues have been resolved in Mathematica. About
all I can say is that I've stumbled over quite a large number of them.
Gives one an idea of how much symbolic calculus is the repository of
computational math voodoo.


Quote:
I think it gives some idea, though. I'll get off
your feet now.

thanks.
RJF

(Be glad I wasn't wearing pointy high heels.)

Daniel Lichtblau
Wolfram Research
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Craig Carey
science forum beginner


Joined: 18 Jun 2005
Posts: 41

PostPosted: Wed May 03, 2006 12:26 pm    Post subject: Re: Maple bugs: Downgrade to Maple V Release 3 of 1994 [assume/int/limit] Reply with quote

On Mon, 1 May 2006 16:26:00 +0000 (UTC), roberson@ibd.nrc-cnrc.gc.ca
(Walter Roberson) wrote:

Quote:
In article <1146471068.480178.183040@j33g2000cwa.googlegroups.com>,
Vladimir Bondarenko <vb@cybertester.com> wrote:
DESCRIPTION: Only Maple V Release 3 of 1994 can calculate this
trivial integral correctly.

TEST CASE: assume(z=0): int(sqrt(Pi*z), z);

EXPECTED: 2/3*(Pi*z~)^(3/2)/Pi

I don't see why you expect that value at all.

If one substitutes z=0 before attempting the integration, then
one is attempting to integrate the constant 0 with respect to the
variable 0, which is invalid.

To show "invalid" you might have to quote documentation.

If Maple's "assume (z = 0)" means
(1) z is constrained before the integration, and
(2) z starts off being free inside of -M to M, and that is
reduced until it becomes identical to the point 0,
then the answer is 0.

Ie. the answer is 0 in the 2 cases:
(a) z is constrained before the integration, and
(b) if F is the integral then the answer is F(0) - F(0).

The case ought be case (1).

Maple's documentation could change that; ie. permit a mathematically
wrong answer to be correct. Fairness would have Mr Bondarenko quote
the documentation, which never ever seems to occur.

--

If the 2nd parameter of the 2-argument int function was actually
0, then the software can convert that "0" into every symbol, eg.
r, s, t, u, v, w, x, y, ...

Then what is evaluated could be:

Integral wrt t, where 0<=t<=0, of f(x)

The answer is found to be 0 after noting that f (made to be the
function above) has a magnitude that is not too big, since its
value is zero, because of the fact that z = 0.

What is done is to compute the area under a curve when the width
of the region (ie. 0<=x<=0) is zero.


On 1 May 2006 10:19:07 -0700, "Vladimir Bondarenko"
<vb@cybertester.com> wrote:

Quote:
Walter Roberson writes...

WR> I don't see why you expect that value at all.

I agree with you about the indefinite integral here.


I doubt that that a single member of sci.math.symbolic would
wish to fairly defend Mr Bondarenko. Did Mr Bonarenko imply
that he held an opinion?. He does seem interested in quoting
anything.

Even his output from Maple doubtles lacks the trait of being a
quoted except of a message that was actually sent to Maplesoft.


Quote:
And this shows again, how _human_ testers are fallible!


Mr Bondarenko original statement

| DESCRIPTION: Only Maple V Release 3 of 1994 can calculate this
| trivial integral correctly.

; is incorrec ...

or is that untrustable ?.

Mr Bondarekno seems to be unable to shake off the habit of

being elsewhere.

Ukraine or his home town, Simferopol, probably does contribute to
Google's running costs.



Craig Carey, research@ijs.co.nz
New Zealand.
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Roman Pearce
science forum beginner


Joined: 03 May 2005
Posts: 37

PostPosted: Fri May 05, 2006 12:58 am    Post subject: Re: Waste your days with Maple, over and over again [Maple 9.5 - MacOSX 10.4.4 - No Interface!] Reply with quote

Quote:
My message is that with Maplesoft, even installation -
TRADITIONALLY - does not work smoothly, and the
gentleman in question was forced to wait for 2 DAYS
before being able to make the upgrade running.

To WASTE his time!

He has paid his money and has his full right to enjoy
the acquired stuff - this is the gist of my message.

The reason it didn't work is that Sun broke compatibility between Java
1.4 (which Maple uses) and Java 1.5. They left out a whole component
that Maple uses. Normally this wouldn't be a problem - Maple ships
with a complete copy of Java 1.4 on Windows, Linux, and Unix platforms.
However, on Mac OS X Java is provided by Apple, and it is included as
part of the operating system. You can't get a standalone version to
distribute with your program. So when Apple upgraded systems to use
Java 1.5 by default it broke a bunch of programs, and there was nothing
the developers could do other than to tell users to revert to Java 1.4
as the default, or install missing components for Java 1.5. The
relevant tech support article is here:
http://maplesoft.com/support/faqs/Maple95/Installation/4.aspx
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Vladimir Bondarenko
science forum Guru


Joined: 23 Apr 2005
Posts: 601

PostPosted: Fri May 05, 2006 1:38 am    Post subject: Re: Waste your days with Maple, over and over again [Maple 9.5 - MacOSX 10.4.4 - No Interface!] Reply with quote

Roman Pierce writes...

http://groups.google.com/group/sci.math.symbolic/msg/82fb78579b351812

RP> The reason it didn't work is that Sun broke compatibility
RP> between Java 1.4 (which Maple uses) and Java 1.5.
[ ... skipped ...]


Thanks for your detailed explanation.

Unlike the mass of other Maple bugs, this
concrete bug is not introduced by Maplesoft.
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rjf
science forum beginner


Joined: 05 May 2006
Posts: 5

PostPosted: Fri May 05, 2006 3:26 pm    Post subject: Re: Waste your days with Maple, over and over again [Maple 9.5 - MacOSX 10.4.4 - No Interface!] Reply with quote

Vladimir Bondarenko wrote:
Quote:
Roman Pierce writes...

http://groups.google.com/group/sci.math.symbolic/msg/82fb78579b351812

RP> The reason it didn't work is that Sun broke compatibility
RP> between Java 1.4 (which Maple uses) and Java 1.5.
[ ... skipped ...]


Thanks for your detailed explanation.

Unlike the mass of other Maple bugs, this
concrete bug is not introduced by Maplesoft.

It could be a bug in maple if the reason it occurs is

that maple relies on behavior of Java that is non-standard
and just happens to work in Java 1.4. That is, the change
from Java 1.4 is that Sun fixed a bug. It is an error to
write a program that relies on someone else's bug, no?
RJF
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Vladimir Bondarenko
science forum Guru


Joined: 23 Apr 2005
Posts: 601

PostPosted: Mon May 08, 2006 9:23 pm    Post subject: Re: An exact 1-D integration challenge - 21 Reply with quote

C W <sylvest...@ns.sympatico.ca> writes...

http://groups.google.com/group/sci.math.symbolic/msg/d0734942a2286095

CW> If You believe You are able to identify this kind of
CW> integrals readily


Readily? I did not claim that this task is simple. My words
were "nice stuff"...


CW> Int(exp(x*Pi)*x/(1+exp(x*Pi)^2)/(1+x^2),x = 0 .. infinity);


As for your integral, obviously, it is equal to

sum((-1)^n*Ci(Pi*(2*n+1)), n= 0..infinity);

but I have a vague feeling that it could be simplified further...
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C W
science forum addict


Joined: 25 May 2005
Posts: 64

PostPosted: Sun May 14, 2006 9:17 pm    Post subject: Re: An exact 1-D integration challenge - 22 - for tough guys and gals only ;) Reply with quote

igor.kh@gmail.com wrote:
Quote:

Igor Khavkine wrote:
Vladimir Bondarenko wrote:
Hello the computer algebra tough guys and gals, ;)

Is there a person who can show how using a computer algebra
system's commands, pls accompanied with as little verbiage
as possible, to calculate the exact value of this integral

int(ln(z)*exp(-z)/(1 + z^2), z= 0..infinity);

?

By popular request, here's an outline of the integral's evaluation.

Maple 9.5:

-Im(1/(z+I)) assuming z,real;
1
------
2
z + 1

limit(diff(z^s,s),s=0);
ln(z)

int(z^s*exp(-z)/(z+I),z=0..infinity);
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Maple V R4 would not integrate this. What other code would generate this result
?

Chris

Quote:
/
(s/2) | (- s/2)
-I (-1) |-Pi csc(Pi s) exp(I) I + GAMMA(s) (-1) s
\

(- s/2) (s + 1)
(-1) I exp(I) Pi
+ ------------------------------
sin(Pi s)

\
(- s/2) (s + 1) |
- GAMMA(s) (-1) s (s + 1) I exp(I) GAMMA(-1 - s, I)|
/

limit(diff(%,s),s=0);
-exp(I) Ei(2, I) gamma I

+ exp(I) MeijerG([[], [1, 1]], [[0, 0, -1], []], I)

+ gamma I + exp(I) Ei(2, I) I

simplify(%);
2
-exp(I) Ei(2, I) gamma I - exp(I) - exp(I) I + 1/24 exp(I) Pi

+ 1/2 I exp(I) Pi - 1/2 I exp(I) Pi gamma + exp(I) gamma

2
- 1/2 exp(I) gamma

+ 1/2 I exp(I) hypergeom([1, 1, 1], [2, 2, 3], -I)

+ gamma I + exp(I) Ei(2, I) I

-Im(%%);
-gamma + Im(exp(I) Ei(2, I) gamma I

- exp(I) MeijerG([[], [1, 1]], [[0, 0, -1], []], I)

- exp(I) Ei(2, I) I)

evalf(%);
-0.7081853242

evalf(Int(ln(z)*exp(-z)/(1+z^2),z=0..infinity));
-0.7081853240

Have a nice day.

Igor
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alex-math@mail.ru
science forum beginner


Joined: 03 May 2006
Posts: 15

PostPosted: Thu May 18, 2006 12:26 pm    Post subject: Re: Eigenvalues for tridiagonal symmetric matrix Reply with quote

http://www.math.niu.edu/~ammar/cortona/cortona.html

I found nice web page about fast inversion of Toeplitz Matrices
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Peter Luschny
science forum beginner


Joined: 13 May 2005
Posts: 36

PostPosted: Sun Jun 04, 2006 1:34 pm    Post subject: [OT] "Now summer is gone." Reply with quote

Vladimir Bondarenko schrieb:

Quote:
Arseniy Tarkovsky .

I love him!

Quote:
Now summer is gone. .
And might never have been. .
In the sunshine it's warm. .
But there has to be more. .

Compare:

So summer is gone,
Leaving no epitaph.
It's still warm in the sun.
Only that's not enough.

Peter
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Chip Eastham
science forum Guru


Joined: 01 May 2005
Posts: 412

PostPosted: Mon Jun 19, 2006 10:50 pm    Post subject: Re: Vladimir Bondarenko: The #1 world's CAS human tester Reply with quote

Vladimir Bondarenko wrote:

[snip; follow-ups limited to sci.math.symbolic as most germane]

Quote:
A few selected opinions about quality of my work
are placed here

http://www.cas-testing.org/index.php?list=7

these opinions belong, respectively, to


COMMENT 1 Albert D. Rich http://www.derive.com

COMMENT 2 Prof Dr Oleg Marichev, WRI www.functions.wolfram.com

COMMENT 3 Dr Anwar Shiekh, WRI, Test Dev Group Supervisor

COMMENT 4 Prof Dr Walter Oevel, SciFace GmbH
http://www.math.uni-paderborn.de/~walter/

COMMENT 5 Dr Anwar Shiekh, WRI, Test Dev Group Supervisor

COMMENT 6 Dr Anwar Shiekh, WRI, Test Dev Group Supervisor

COMMENT 7 Dr Anwar Shiekh, WRI, Test Dev Group Supervisor

COMMENT 8 Dr Michael Wester www.math.unm.edu/~wester

COMMENT 9 Dr Anwar Shiekh, WRI, Test Dev Group Supervisor

COMMENT 10 Dr Anwar Shiekh, WRI, Test Dev Group Supervisor

COMMENT 11 Dr Stefan Wehmeier, SciFace GmbH
http://www-math.uni-paderborn.de/~stefanw/

COMMENT 12 Dr Anwar Shiekh, WRI, Test Dev Group Supervisor

COMMENT 13 Kelly Roach http://www.kellyroach.com/

COMMENT 14 Dr Anwar Shiekh, WRI, Test Dev Group Supervisor

Re, your subject taking the title "The #1 world's CAS human tester",
I admit relief that you do not give only your word for this. However,
although I'm not a professional statistician, the repetition of the
same authority nine times in a sample of fourteen comments about
"quality of my work" (your description) suggests selection bias.

Repetition is a powerful psychological reinforcer, but make sure
that what you reinforce is congenial to your ends.

I suspect you have done a great deal of useful work with the range
of CAS's mentioned. Unfortunately your endless self-promotion in
overly frequent newsgroup posts undermines (in my view) what
credibility this effort should have earned you.

Remember Gauss's dicta: Few but ripe. Not that he did not try
many different ways of doing things, but he was selective in what
out of his corpus he chose to make public. Arguably this was in
some cases out of a fear of tarnishing his reputation, but still the
rule is commendable to those who would promote themselves as
"experts from afar".


sympathetically, chip
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Craig Carey
science forum beginner


Joined: 18 Jun 2005
Posts: 41

PostPosted: Tue Jun 20, 2006 10:31 am    Post subject: Re: Vladimir Bondarenko: A short bio sketch Reply with quote

On 19 Jun 2006 21:59:23 -0700, "Vladimir Bondarenko" wrote:

Quote:
I fully agree with you.

Maybe. It is almost certainly not a credible comment, eg. for
containing 5 words and no more.

Also "Ionnis" has an anonymous [junk] e-mail address, olympus.mons.
Apparently the named is in Greece, since a header says:

NNTP-Posting-Host: athnrd02.forthnet.gr

There is an astrology program here, to process Mr Vladimir Bondarenko's
birth time:
http://www.zaytsev.com/

This project here, of posting so many messages, could be attributed
(put under) Pluto 29 Leo 16 square Saturn 26 Scorpio 16.

Such mismatches with the topic implied by 'sci math & symbolic'; it
might be better for a science group.

Rather than process (or enhance) my information request, above,
then: why don't you (or perhaps a higher fraction in Ukraine)listen to
the music of Ludwig van Beethoven ?.

++Carey
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Craig Carey
science forum beginner


Joined: 18 Jun 2005
Posts: 41

PostPosted: Tue Jun 20, 2006 3:05 pm    Post subject: Re: Vladimir Bondarenko: The #1 world's CAS human tester Reply with quote

On 19 Jun 2006 15:50:42 -0700, "Chip Eastham" wrote:
[re-inserted]---
Quote:
I strongly support the idea of having a site listing Maple
bugs as posted by Vladimir Bondarenko and commented on by
Bertfried Fauser

-- Prof Dr R. Ablamowicz http://www.math.tntech.edu/rafal/
[end]---

It is not what Mr Bonarenko writes, but only the subset approved
by Mr B. Fauser ( http://clifford.physik.uni-konstanz.de/~fauser/ )

So extra e-mailing would be required before Mr Ablamowicz text can
back the hypothesis that the first author was the world's best
tester of symbolic algebra computer programs.

....
Quote:
COMMENT 14 Dr Anwar Shiekh, WRI, Test Dev Group Supervisor
....
although I'm not a professional statistician, the repetition of the
same authority nine times in a sample of fourteen comments about
"quality of my work" (your description) suggests selection bias.

Would suggest unreliability (I suppose); since when data is
hierarchical:
* groups of names > names of individuals > treatises [ > ideas ]
then bias can be simultaneously absent and present. Names can lack
importance whereas concurrently the attribute can be atributed to
material issues of fact, and findings, statements, policies, etc.

Quote:
Remember Gauss's dicta:

One further clipping removing "'s dicta:" can lead to an irreducible
catch-phrase or cliche.
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Chip Eastham
science forum Guru


Joined: 01 May 2005
Posts: 412

PostPosted: Tue Jun 20, 2006 4:29 pm    Post subject: Re: Vladimir Bondarenko: The #1 world's CAS human tester Reply with quote

Craig Carey wrote:
Quote:
On 19 Jun 2006 15:50:42 -0700, "Chip Eastham" wrote:
[re-inserted]---
I strongly support the idea of having a site listing Maple
bugs as posted by Vladimir Bondarenko and commented on by
Bertfried Fauser

-- Prof Dr R. Ablamowicz http://www.math.tntech.edu/rafal/
[end]---
It is not what Mr Bonarenko writes, but only the subset approved
by Mr B. Fauser ( http://clifford.physik.uni-konstanz.de/~fauser/ )

So extra e-mailing would be required before Mr Ablamowicz text can
back the hypothesis that the first author was the world's best
tester of symbolic algebra computer programs.

...
COMMENT 14 Dr Anwar Shiekh, WRI, Test Dev Group Supervisor
...
although I'm not a professional statistician, the repetition of the
same authority nine times in a sample of fourteen comments about
"quality of my work" (your description) suggests selection bias.

Would suggest unreliability (I suppose); since when data is
hierarchical:
* groups of names > names of individuals > treatises [ > ideas ]
then bias can be simultaneously absent and present. Names can lack
importance whereas concurrently the attribute can be atributed to
material issues of fact, and findings, statements, policies, etc.

Well, in plainer words, I suspect here self-selection among
commenters yields unrepresentative sampling, not that
Vladimir did any "cherry-picking" of the comments.

Quote:
Remember Gauss's dicta:

One further clipping removing "'s dicta:" can lead to an irreducible
catch-phrase or cliche.

I take your point! Like this:

"Remember Strunk: Omit needless words."

http://www.bartleby.com/141/strunk5.html#13

Benjamin Franklin had an amusing if cautionary riff on this
topic, his anecdote about composing a solicitation that
began as:

"John Thompson, Hatter, makes and sells Hats for ready
Money", with a figure of a hat subjoined.

http://www.ushistory.org/franklin/biography/chap09.htm

regards, chip
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Peter Luschny
science forum beginner


Joined: 13 May 2005
Posts: 36

PostPosted: Tue Jun 20, 2006 10:46 pm    Post subject: Re: Maple experts, who are they? Reply with quote

Maarten van Reeuwijk wrote:

Thank you for you interest. But maybe it is not clear:
The whole text in my posting is a quotation from:

E.W. Dijkstra: On the cruelty of really teaching computing science,
Communications of the ACM 32,12 (1989), 1398-1404.

http://www.smaldone.com.ar/documentos/ewd/EWD1036_pretty.pdf
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