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Vladimir Bondarenko
science forum Guru
Joined: 23 Apr 2005
Posts: 601
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Vladimir Bondarenko
science forum Guru
Joined: 23 Apr 2005
Posts: 601
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 Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: An exact 1-D integration challenge - 2
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In article <310120050855541296%ed...@math.ohio-state.edu.invalid>, G.
A. Edgar <e...@math.ohio-state.edu.invalid> wrote:
| Quote: | In article <1107139609.684835.229...@c13g2000cwb.googlegroups.com>,
Vladimir Bondarenko <v...@cybertester.com> wrote:
int(ln(RootOf(-erf(_Z)+z)), z=0..1);
I get -gamma/2 - ln(2) [where gamma = Euler's constant]
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Bravo!
With minimalist means, you solved the task.
I like your instant approach much, it never
came to my mind.
With gratitude for joy and respect to your gift,
Vladimir Bondarenko |
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janos
science forum beginner
Joined: 24 Mar 2005
Posts: 3
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: Mathematica query
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Tony King wrote:
| Quote: | Does anyone know if it is possible for Mathematica to reverse or undo
a
generating function and recover the original recurrence relation?
Many thanks
Tony |
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Peter Luschny
science forum beginner
Joined: 13 May 2005
Posts: 36
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: euler(0,1) shows Maple bugs are really ubiquitous
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| Quote: | Vladimir Bondarenko" wrote:
Hi Maple customers all over the world,
After 10 years of its existent, in Maple 9.5.2 the bug with
euler(0,1) reported by Peter was fixed...
euler(0,1);
-------------------- (2004) Maple 9.5.2 ----------------------
1
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Hurrah, Maple quality improves! ;-)
PL> Well, I do not know how Maplesoft defines euler(s,z),
PL> s not an integer, therefore I will take my own approach.
PL> E := proc(s,z) z^s*(4^(s+1)*Zeta(0,-s,1/(4*z))
PL> - 2^(s+1)*Zeta(0,-s,1/(2*z))) end:
Just to explain a little bit, what this function does:
it is a generalization of the Euler numbers and gives
us a way to compute the Euler numbers with Maple without
using the Maple 'euler' function, which is known to be buggy
in almost all Maple releases, as your foregoing posting shows.
| Quote: | seq(E(i,1),i=0..10);
seq(euler(i),i=0..10);
1, 0, -1, 0, 5, 0, -61, 0, 1385, 0, -50521 |
1, 0, -1, 0, 5, 0, -61, 0, 1385, 0, -50521
| Quote: | seq(2^i*E(i,1/2)/i!,i=0..11);
seq(2^i*euler(i,1)/i!,i=0..11);
-17 62 -1382 |
1, 1, 0, -1/3, 0, 2/15, 0, ---, 0, ----, 0, ------
315 2835 155925
-17 62 -1382
-1, 1, 0, -1/3, 0, 2/15, 0, ---, 0, ----, 0, ------
315 2835 155925
| Quote: | series(1+tanh(x),x,12);
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3 5 17 7 62 9 1382 11
1 + x - 1/3 x + 2/15 x - --- x + ---- x - ------ x + ..
315 2835 155925
Note that the Maple coders did not even use such a well known relation
as the one given between the expansion of 1 + tanh(x) and the Euler
polynomials to check their code! 'Test Driven Development' does not
seem to be much appreciated in Waterloo.
In an test driven development Maple's 'Decadium Bug' would not
have even reached the beta build (sorry for you, Vladimir ;-)
However, a workaround for a Maple bug might again be buggy
because of another Maple bug, as we have seen:
Maple (VR5) computes E(0,1) = 1 and limit(E(s,1),s=0,real) = -2.
By the way, Mathematica 5.0 does it right:
In[1] = F[s_, z_] := z^s(4^(s+1)Zeta[-s,1/(4z)]- 2^(s+1)Zeta[-s,1/(2z)])
In[3] = F[0,1] Out[3]= 1
In[4] = Limit[F[s,1],s->0] Out[4]= 1
In[5] = Limit[F[s,1],s->0,Direction->-1] Out[5]= 1
In[6] = Limit[F[s,1],s->0,Direction->1] Out[6]= 1
Ok, this is the first part of the story. The second part
follows immediately. We have not looked at the Euler
polynomials yet.
First the definition:
EP := proc(s,z) z^s*E(s,1/(2*z)) end;
The meaning is clear:
| Quote: | seq(EP(i,z),i=0..4);
2 2 3 3 4 |
1, z - 1/2, z - z, 1/4 - 3/2 z + z , z - 2 z + z ,
| Quote: | seq(euler(i,z),i=0..4);
2 2 3 3 4 |
1, z - 1/2, z - z, 1/4 - 3/2 z + z , z - 2 z + z ,
VB> Here is the bug, alive and kickin'!
VB> limit(euler(z,1), z=0); -> -1
But what does limit(euler(z,1), z=0) mean, exactly?
Now our version:
limit(EP(z,1), z=0); -> 1
It works! Even with good ol' buggy Maple! 
And we have assigned an exact meaning to the limit:
lim EP(z,1) = lim (2 - 4*2^z) Zeta(-z) = 1
z->0 z->0
Regards Peter |
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Sascha Bohnenkamp
science forum beginner
Joined: 24 Mar 2005
Posts: 1
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: [MuPad] SciLab Link doesn't work?
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I have the same problem here
I had a non-scilab version on the system before
I HAVE the right license
I HAVE the right installation package
I HAVE tcp/ip running
I did uninstall and reboot old versions before
but scilab does not work
maybe the uninstallaer should uninstall _everything_
(at least the sciface directory remains on the computer...)
| Quote: | r.e.s. <r.s@zzmindspring.com> wrote:
I'm hoping someone who uses MuPad Light 2.5.3 with the
"SciLab link" can help me ...
Hello,
please check the following:
1.) Do you really have a version with Scilab. This means can you find
a packages\scilab directory in your MuPAD installation _and_ inside this
directory there should be e.g. a directory Demo. If this is the case
you have the right setup. I just mentioned it, because in the Setup
for MuPAD Light 2.5.3 without Scilab there is a small mistake. Here
packages\scilab exist, but contains no valid Scilab installation.
If you have the right MuPAD version and a registration key, as you
mentioned and it still does not work, please let me know (PM).
I then will try together with you what's wrong.
Greetings,
Torsten |
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Guest
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: Steps towards writing a computer algebra system
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parisse@domain.invalid wrote:
| Quote: | The key question will be "is Axiom documented well enough so it can
be
modified, maintained, and extended by the next generation of
computational
mathematicians?". Hopefully the answer will be yes.
I believe that the answer (for axiom or other free CAS
systems) depends strongly on their interacting capabilities
with other systems. By interacting I mean in both
directions, not only being able to call alien CAS code
but also being callable by another CAS.
This will attract new users, and if a software doesn't attract new
users, it dies in the long term.
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Axiom can clearly communicate with other systems either thru the shell
or thru sockets. Axiom sends information to a separate C program (the
graphics code) and receives information from a separate C program (the
document browser) thru sockets. Mathaction interacts thru a shell.
And the library code is available thru Aldor. This is purely a
programming
issue.
I believe, however, that this point does go to the heart of the system
architecture. I used to distribute the Rosetta CDs which were a
collection
of about 100 different computer algebra systems. They fell into 3
categories:
library systems, engineering systems, and theory systems.
The library systems are by far the most common. They are usually
started
by the observation that language X (e.g. C++, haskall, etc) provide
inheritance and that this can easily be mapped onto the hierarchy of
groups, rings, fields, etc. The first effort is to build a polynomial
system. Later the code for various functions evolves. A large library
is created so that "anyone can call the code". It becomes obvious that
the API for the library is very complex (for instance, it is up to the
user to handle simplification issues) so an interpreter is provided
making the system interactive. They are usually special purpose.
The engineering systems are fewer. These are larger, general purpose
systems. Their focus is mainly on giving a "good, but not necessarily
correct in all domains" answer. It is often easy to get the system to
solve obvious problems like sqrt(x^2)=> x. These systems generally
revolve around a core engine which knows some mathematics, performs
heavy optimization, and provides a user interface for writing new
libraries in the interpreter language. There is rarely a compiled
language. They are generally viewed as easy to use.
The theory systems are designed from scratch to attack the mathematical
issues. These are large, general purpose systems (e.g. Docon, Axiom)
which have very steep learning curves. They are hard for the user to
learn. They provide large libraries. They have an interpreter and a
compiler. The focus is on correctness and generality.
All of the above observations are based on "hasty generalization" and
personal observation so take them with their obvious biases.
An ultimate issue, in my opinion, is how scalable these systems are.
Axiom currently has approximately 1100 domains, categories, and
packages.
If we project out 30 years to systems with 1Thz cpu, 1Petabyte disk,
and
1Terabyte of memory and assume the algebra systems are 100 times larger
the scaling question becomes central.
A library system becomes harder to use as now the API consists of
1Million
different functions each of which give subtle variations of answers. We
can see this in the NAG library code where there are a dozen routines
for
doing numeric integration.
An engineering system with a million packages will have dozens of
packages
for doing symbolic manipulation of differential equations all written
in
isolation and "contributed".
A theory system will have 1million domains, categories, and packages
but
there is a theoretic skeleton to place new routines categorically. This
allows code to be written "in its most general setting" and ensures
that
the code fulfills categorical requirements.
It is hardly a surprise that I feel that systems based on category
theory
can continue to scale by a factor of 100 where I believe (and it is
only
a biased belief) that the other two kinds of systems cannot.
The "grand challenges" for computational mathematics include issues of
scaling. They include issues of correctness (hence I believe that
systems
like ACL2 need to be integrated so that we can attempt to prove the
algorithms correct). There is also the issue, discussed above, of
documenting a system to the point where it becomes its own textbook
in mathematics.
In fact, we ought to consider building a
"grand challenges" list for computational mathematics. It would
generate
some truly entertaining discussion :-)
Tim Daly |
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Guest
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: Steps towards writing a computer algebra system
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| Quote: | Axiom can clearly communicate with other systems either thru the shell
or thru sockets. Axiom sends information to a separate C program (the
graphics code) and receives information from a separate C program (the
document browser) thru sockets. Mathaction interacts thru a shell.
And the library code is available thru Aldor. This is purely a
programming
issue.
|
I would prefer a full connection to a standard programming
language, e.g. a dynamic (or static) library with header files
for calls from C/C++ (or optionnaly any language that can call the
libraries you find on a Unix-like system).
So that we would not have to learn yet another language (an
effort that few will do anyway) and we could work with 100% efficiency
on the exchanged data. |
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Allan Adler
science forum beginner
Joined: 25 Mar 2005
Posts: 30
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: Steps towards writing a computer algebra system
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daly@rio.sci.ccny.cuny.edu writes:
| Quote: | So as part of the effort to open source the Axiom code every file in
the system has been rewritten into a literate program. There are no longer
any Makefiles, C, Lisp, Spad, Boot, etc. files. Everything is a document.
We used Norman Ramsey's NOWEB, a language-independent version of Knuth's
WEB (which only worked for Pascal).
Work is underway to fully document the system including both the algebra
and the underlying interpreter/compiler, the graphics, and the document
browser. Every file both generates code and generates a .dvi file.
For an example of a literate form look at the file called
src/algebra/dhmatrix.spad.pamphlet. In a fully built system you can
find the generated .dvi file in $AXIOM/doc/src/algebra/dhmatrix.spad.dvi
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I'm glad to learn of this development. I'm downloading the book and
the source now.
| Quote: | People fail to realize how hard it is to build such a large, general
purpose system. I have about 100 systems that have been constructed.
Almost all of them disappeared because the funding ran out. Axiom,
Maple, Reduce, Mathematica, and a few others exist only because sustained,
long term funding was available.
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I hope that Macsyma (at least the free version), GAP, Pari-gp and other
free computer algebra systems that I know about also become available in
literate forms. In the case of the commercial systems, the commercial basis
for their continued existence seems to be one of the obstacles to their
literate documentation, at least in a publicly available form.
| Quote: | And commercial systems disappear. Macsyma is gone and Axiom would have
disappeared but for the efforts and good graces of NAG (The Numerical
Algorithms Group).
|
Why isn't NAG pursuing a literate version of Macsyma and its substrata?
--
Ignorantly,
Allan Adler <ara@zurich.csail.mit.edu>
* Disclaimer: I am a guest and *not* a member of the MIT CSAIL. My actions and
* comments do not reflect in any way on MIT. Also, I am nowhere near Boston. |
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Richard J. Fateman
science forum addict
Joined: 04 May 2005
Posts: 81
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: Steps towards writing a computer algebra system
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parisse@domain.invalid wrote:
| Quote: | Axiom can clearly communicate with other systems either thru the shell
or thru sockets. Axiom sends information to a separate C program (the
graphics code) and receives information from a separate C program (the
document browser) thru sockets. Mathaction interacts thru a shell.
And the library code is available thru Aldor. This is purely a
programming
issue.
I would prefer a full connection to a standard programming
language, e.g. a dynamic (or static) library with header files
for calls from C/C++ (or optionnaly any language that can call the
libraries you find on a Unix-like system).
So that we would not have to learn yet another language (an
effort that few will do anyway) and we could work with 100% efficiency
on the exchanged data.
|
This (essentially functional) approach does not work so well
if the axiom system maintains state, allocates memory, can produce
error messages, etc. While I generally prefer a functional
approach to decomposing programming problems, I think you are
making the assumption that a C or C++ programmer would find it
easy to produce Axiom data structures that could be passed into
Axiom routines, and that using the returned results in C or C++
would also be easy. I don't know enough about the equivalence
of C and Aldor, but my guess is that you would have to learn
a lot about Aldor to make this work. In which case maybe you
should be writing in Aldor. I don't know what the support
situation looks like for Aldor.
I have observed that the command, in Axiom,
)lisp
evaluates a lisp expression, so my guess is that Axiom could
(for example), gobble down all of Maxima's lisp code, using
it as a library. How about it, Tim?
RJF |
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J. Horta
science forum beginner
Joined: 15 Jun 2005
Posts: 46
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: Historical CAS question
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On Mon, 31 Jan 2005 06:53:43 -0800, daly wrote:
| Quote: | J. Horta wrote:
On Tue, 25 Jan 2005 09:04:35 -0800, daly wrote:
J. Horta wrote:
On Mon, 24 Jan 2005 09:18:03 +0000, Fabio wrote:
Thanks, I think. Don't care to be famous and I don't
really want to do anything for mathematicians. What
I do want to do is some non-commutative associative
algebra.
Have you tried Axiom?
http://axiom.axiom-developer.org
Fabio
Yes, I've attempted to compile axiom twice now and failed.
There is something squirly about one of the system headers
on SuSE 9.2. If I recall the bfd.h or bfdlink.h header has
a structure that doesn't agree with the usage in axiom. Some
structure is missing a _raw_size data member. I attempted
to replace the references with a size member but somehow
the source is generated by the make files so my changes kept
getting written over. I've given up on axiom for the time
being.
This is a known problem and there is a fix for it.
Check with the axiom-developer@nongnu.org mailing list
and we'd be happy to help you. --Tim Daly
Okay, Googled on axiom _raw_size and found the issue with
binutils. Down grading binutils sounds risky so I attempted
to change _raw_size reference in the cvs image I check out.
No luck there since no file appears to contain said variable.
Undaunted I changed my bdf.h which seemed to work but the
build gaged. So, how does one change _raw_size (or even find
for that matter and oh by the way 'grep -l -R _raw_size *'
won't do it) in a local copy of the source?
This has been fixed in the February 2005 release which is
available in the CVS at http://savannah.nongnu.org/projects/axiom,
http://sourceforge.net/projects/axiom, or on the developer site
http://arch.axiom-developer.org
Basically you need to set the AXIOM shell variable correctly.
The ./configure script will recognize a Fedora Core 3 system.
If you have the source tree in "/tmp/axiom" you would type:
export AXIOM=/tmp/axiom/mnt/fedora3
export PATH=$AXIOM/bin:$PATH
make
axiom
I build a Fedora Core 3 system over the weekend and built axiom
on it. It builds cleanly.
Tim Daly
Axiom Lead Developer.
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Okay, I just downloaded the cvs image and tried a configure
and build. Same error same place. I am running SuSE 9.2 and
have no real interest in switching to fedora3 at the moment.
Does it compile in fedora because they use _raw_size as a
variable name instead of rawSize in SuSE?? This sounds like
an utter triviality to me and I mystified why I'm unable to
to simply repair the problem by changing variable names. No
complaint, just asking. |
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Max Goldfarb
science forum beginner
Joined: 24 Mar 2005
Posts: 1
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: new system
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vasil_stanev wrote:
| Quote: | is it possible to invent a new binary system with two digits: /1/ and
/infinity/?Could it be used in computers?
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Would this new binary system be functionally distinguishable from what
we have now? What benefits would this give to us?
Just wondering.
-Max G |
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Gabriel Dos Reis
science forum beginner
Joined: 24 Mar 2005
Posts: 4
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: GPL vs LGPL vs CAS
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Bernard Parisse <parisse@domain.invalid.fr> writes:
[...]
| The problem of funding in EU is probably similar to the US one,
| it's that people having an academic position do not consider
| that software developement is part of their research work.
That is kinda chicken-egg problem; software development is hardly
considered in academic evaluation. So, it is hard to blame people for
not doing something not considered for getting tenure or promotion.
-- Gaby |
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Gabriel Dos Reis
science forum beginner
Joined: 24 Mar 2005
Posts: 4
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: GPL vs LGPL vs CAS
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Bernard Parisse <parisse@domain.invalid.fr> writes:
[...]
| >> There are however most probably academic positions in the corresponding
| >> fields of maths or computer science, and I don't see why contributing
| >> to an open CAS could not be seen as a research publication,
| >> therefore the number is $0 only because people in these academic
| >> positions do not see software development as research.
| > Because the US funding agencies do not see system building
| > as research, professors who do CAS-related work must propose
| > something else to get funding from NSF, DARPA, DOE, ONR,
| > NSA, in the United States.
| >
|
| Humm, I wonder who decides in the US funding agencies? I mean
The situation is hardly different from what used to be in France.
At several occasions, I've heard first hand comments that building
system software (part of academic work) is engineering work, not
research. The relatively recent move at INRIA is kind of exception,
but still.
-- Gaby |
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Richard Fateman
science forum Guru Wannabe
Joined: 03 May 2005
Posts: 181
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: GPL vs LGPL vs CAS
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Gabriel Dos Reis wrote:
| Quote: | Bernard Parisse <parisse@domain.invalid.fr> writes:
[...]
| The problem of funding in EU is probably similar to the US one,
| it's that people having an academic position do not consider
| that software developement is part of their research work.
That is kinda chicken-egg problem; software development is hardly
considered in academic evaluation. So, it is hard to blame people for
not doing something not considered for getting tenure or promotion.
-- Gaby
|
There is a point for academics to get something to work, once.
There is not much of a point to get it to work on 3 different
operating systems, 5 kinds of hardware, .... . And there
is also not much of a point in having graduate students
answering questions from users who were too lazy to read
the manual. This is not responsible training. Thus you
need to hire staff to do such things, if it is to be
done at all.
It is a difficult call to make, where to draw the line.
I think that EU researchers tend to be more theoretical.
In my university, computer science is in a college of
engineering.
RJF |
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Guest
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| Posted: Thu Mar 24, 2005 7:46 pm Post subject:
Re: Steps towards writing a computer algebra system
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| Quote: | This (essentially functional) approach does not work so well
if the axiom system maintains state, allocates memory, can produce
error messages, etc. While I generally prefer a functional
approach to decomposing programming problems, I think you are
making the assumption that a C or C++ programmer would find it
easy to produce Axiom data structures that could be passed into
Axiom routines, and that using the returned results in C or C++
would also be easy.
|
There are probably different levels of possible interactions,
and probably the most efficiency you want, the more you
have to learn of the internals of Axiom. I hope
it should be possible to have a not too complex C or C++ interface
with at least the axiom commandline functionnalities, and
maybe the possibility to build/unbuild the main data
structures (like symbolics, vectors and matrices).
The question is more if Axiom people are interested in
developping such an interface or not. |
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