HDTenEightyP/NetNews huggingface dataset:
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math.symbolic
Subject: Re: an indefinite integral
Date: 26 Sep 1992 09:49:15 -0400
Organization: The Ohio State University, Dept. of Math.
NNTP-Posting-Host: function.mps.ohio-state.edu
Keywords: integral


"Not integrable"???  Of course it is integrable.  It is even continuous.
What you mean to ask is whether the integral is elementary.
-- 
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)
From: mstankus@oba.ucsd.edu (Mark Stankus)
Newsgroups: sci.math.symbolic
Subject: Teaching ODE w/ Mathematica?
Date: 26 Sep 92 04:54:13 GMT
Distribution: usa
Organization: Mathematics @ UCSD

What mathematica code is available for ODE at an undergraduate
level?  Also, are there any write-ups that anyone has
written to give to students to explain how to start
openwindows and start mathematica on a Sun Sparc 2?

Mark Stankus

-- 
mstankus
mstankus@oba
From: sl25@emu.pmms.cam.ac.uk (Steve Linton)
Newsgroups: sci.math.symbolic
Subject: Re: GROBNER BASIS
Date: 1 Oct 92 01:46:15 GMT
Organization: Cambridge University DPMMS

I have an algorithm that may provide an alternative to  Grobner methods in some circumstances. As Grobner basis, it has unbounded running time (this seems to be a feature of the problem) but I would expect it to do better fairly often. 

The principle limitation is that it cannot cope with the case of infintiely many solutions. On the other hand it can cope with non-commutative variables (solutions in this case are matrices).

I would be interested in some `real world' polynomials to test my program, both ones where you know how long Grobner basis code takes and ones you have not been able to do that way.

		Steve Linton
Newsgroups: sci.math.symbolic
From: hw@madvlsi.columbia.edu (Hongmo Wang)
Subject: Re: symbolic algebra and teaching math/sciences
Organization: Columbia University
Date: Mon, 5 Oct 1992 20:26:46 GMT
X-Posted-From: france.madvlsi.columbia.edu
NNTP-Posting-Host: sol.ctr.columbia.edu

In article <1992Oct3.103005.2192@drycas.club.cc.cmu.edu>, DORN@dirac.physics.jmu.edu (Dr. Dorn Peterson) writes:
|> It seems to me that Maple, Mathematica, etc. have one very great flaw when
|> they are used by students who are learning some branch of mathematics for
|> the first time.  That flaw is that they are too #@$% good.  They don't 
|> leave enough of the strategy part of problem solving to the student.  
 ...

But they also make BAD mistakes, for example, in Mma 1.2

If you 

Simplify[a + Sqrt[b] /. b -> (-1 + c)^2]

the answer is 

a - 1 + c 

but if you 

Simplify[a + Sqrt[b] /. b -> (1 - c)^2]

you will get

a + 1 - c

None gives the correct answer

a + Abs[-1 + c]

That is really BAD!

/hw
From: dan@math.uiuc.edu (Daniel R. Grayson)
Newsgroups: sci.math.symbolic
Subject: Re: Quick Question - Mathematica
Date: 29 Sep 92 22:31:57 GMT
Article-I.D.: news.BvD2LB.FoA
Reply-To: dan@math.uiuc.edu
Organization: University of Illinois at Urbana

dgenr8@leland.Stanford.EDU (Tom Harding) writes:

>Would someone be kind enough to tell me what conceptual shortcoming I am
>a victim of in expecting the following tidbit to work:
>
>   Plot3D[Abs[Complex[a, b]], {a, -Pi, Pi}, {b, -Pi, Pi}]
>
>...it is refusing to evaluate the function all the way down to a real number
>at each point.  However. it works for Abs[Plus[a, b]], which puzzles me all
>the more.  Any help would be greatly appreciated.
>
>   -Tom Harding

In older versions of mathematica, Complex is not a function which does
anything.  In newer versions, Complex returns an actual complex number
object.  To make your code work, replace Complex[a,b] by a + I b.
From: jstern@aris.ss.uci.edu (Jeff Stern)
Subject: Need package to display lattices (and labels) in mma
Newsgroups: sci.math.symbolic
Organization: University of California, Irvine
Date: 29 Sep 92 08:01:27 GMT


Does anyone know of one?  I am aware of Steven Skiena's package,
Combinatorica, but I need one to display the labels, as well.

Thanks in advance, Jeff Stern.  jstern@aris.ss.uci.edu
Newsgroups: sci.math.symbolic
From: twillis@top.cis.syr.edu (Thomas Willis)
Subject: Re: Quick Question - Mathematica
Organization: Syracuse University CIS Dept.
Date: Tue, 29 Sep 92 04:16:42 EDT

In article <1992Sep27.183825.19652@leland.Stanford.EDU>, dgenr8@leland.Stanford.EDU (Tom Harding) writes:
|> Would someone be kind enough to tell me what conceptual shortcoming I am
|> a victim of in expecting the following tidbit to work:
|> 
|>    Plot3D[Abs[Complex[a, b]], {a, -Pi, Pi}, {b, -Pi, Pi}]
|> 
|> ...it is refusing to evaluate the function all the way down to a real number
|> at each point.  However. it works for Abs[Plus[a, b]], which puzzles me all
|> the more.  Any help would be greatly appreciated.
|> 
|>    -Tom Harding

Strange, indeed. It worked for me.  I'm curious what platform your running
on?   One thing to try is wrapping a N[] around your function, i.e.
Plot3D[N[Abs[Complex[a, b]]]...

Session log follows:
=====================
Mathematica 2.1 for SPARC
Copyright 1988-92 Wolfram Research, Inc.
 -- Motif graphics initialized -- 
 In[1]:= a = b = 2
 Out[1]= 2
 In[2]:= Complex[a, b]
 Out[2]= 2 + 2 I
 In[3]:= Abs[Complex[a, b]]
    	 3/2
Out[3]= 2
In[4]:= Plot3D[Abs[Complex[a, b]], {a, -Pi, Pi}, {b, -Pi, Pi}]
Out[4]= -SurfaceGraphics-
In[5]:= Clear[a,b]
In[6]:= Plot3D[Abs[Complex[a, b]], {a, -Pi, Pi}, {b, -Pi, Pi}]
Out[6]= -SurfaceGraphics-

-----------------------------------------------------------------------------
o-----o     T.J. Willis
|\    |\                                                   Pressure(t)
| o---+-o   twillis@nova.npac.syr.edu              lim    -------------
o-+---o |   Research Assistant                     t->oo    Grace(t)
 \|    \|   Syracuse Center for Computational Science
  o-----o   Northeast Parallel Architectures Center          << Disclaimer.m
-----------------------------------------------------------------------------
From: murison@cfa203.HARVARD.EDU (Marc A. Murison, RG)
Newsgroups: sci.math.symbolic
Subject: Re: Maple on 386sx or 386
Date: 2 Oct 92 13:10:40 GMT
Organization: Smithsonian Astrophysical Observatory, Cambridge, MA,  USA

> In article <1992Sep30.203252.11747@samba.oit.unc.edu>
> Jim.Buddenhagen@bbs.oit.unc.edu (Jim Buddenhagen) writes:
>
>I have and IBM PC clone which is a 386sx with 4 meg of memory, running DOS 5.0,
>25 mhz.  Is there a version of Maple which will run in this environment?
>If so, how well would it run?  Does anyone have personal experience with this?

I've run Maple V both on a 386 DX 16MHz 8 megs and on a 486 25 MHz 
8 megs.  The 386 response seemed ok for a while.  But I've reached
the point where my 486 is severely constipated (I'm using
Maple to do analytical ray tracing).  I find the 386 unacceptably
slow these days.  I think that whatever system you have, you'll 
find bigger and better things to do on it until it bogs down. 
Depending on what you want to do with Maple, your 386 may be 
perfectly adequate.
--Marc Murison  murison@cfa.harvard.edu
Newsgroups: sci.math.symbolic
From: ara@zurich.ai.mit.edu (Allan Adler)
Subject: Re: symbolic algebra and teaching math/sciences
Organization: M.I.T. Artificial Intelligence Lab.
	<qmdbms.718281231@gsusgi1.gsu.edu>
Date: Mon, 5 Oct 1992 20:51:31 GMT

I think it is not productive to discuss this question without a clear
defintion of what use one wants to make of computers in teaching
algebra. Giving an example of their use is not really informative.
Why don't the people who say they have done it post copies of their
syllabi? That will at least give a context to the anecdotes.

Allan Adler
ara@altdorf.ai.mit.edu
Newsgroups: sci.math.symbolic
From: martin@math.rwth-aachen.de (  Martin Schoenert)
Subject: Re: My trouble with GAP (GROUP calculator).
Organization: Rechnerbetrieb Informatik  /  RWTH Aachen
Date:  2 Oct 92 12:21:04 GMT

mhiroshi@tansei.cc.u-tokyo.ac.jp (H. Murakami) writes:

    I ftped gap3r2p1 for the Unix source code
    and compiled it using /bin/cc or gcc2.2.2.

    The document writes that the system is interactive,
    I thought I will calculates the example in the document
    of determining the rubic cube's group.

    However, I found the system I created won't show what I
    typed in after the system prompt "gap>" and only the result is
    returned.

    Has anyone there overcome this difficulty or there is any
    nice way to change the mode of the system?
    I like the system show the user what user's input line is
    typed in as each stroke of the key. (since I am a poor typist.)

This is a well known problem.  Get 'pub/gap/upg3r1p2.dif.Z' via anonymous
'ftp'  from   'samson.math.rwth-aachen.de'.   This  upgrade   fixes  your
problem.

Martin.

--
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,  +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, D 51 Aachen, Germany
From: sg04@ploni.gte.com (Yechezkal Shimon Gutfreund)
Newsgroups: sci.math.symbolic
Subject: Mathematica Book (2nd ed)
Date: 5 Oct 92 15:12:12 GMT
Reply-To: sgutfreund@gte.com
Organization: GTE Laboratories, Waltham MA

My copy of the Mathematica Book (2nd edition) is beginning to
fall apart. This is unusual for me, since I am pretty careful
with texts.

What seems to be the problem is that the spine is glued together
but not sewn. Since I use the book constantly as a reference,
it has started to come apart between the color plates and the
rest of the pages (the mixed grades of paper seem to be a
real problem in a glued spine book).

The rest of the book is still in a pretty pristine form.

Suggestion: Make the next addison-wesley edition with
a sewn spine. (Yes, I have the spiral bound quick reference
guide, but sometimes it is not enough).

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Yechezkal Shimon Gutfreund		 		  sgutfreund@gte.com
GTE Laboratories, Waltham MA			    harvard!bunny!sgutfreund
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
From: jly@buc.edu.au
Newsgroups: sci.math.symbolic
Subject: CAS
Keywords: CAS
Date: 6 Oct 92 07:28:19 GMT
Reply-To: jly@buc.edu.au
Organization: BUC
NNTP-Posting-Host: 141.132.52.13


There is a program called ISETL
 (Interactive Set Language) which is not
 really a CAS but which is being used in teaching mathematics
at Purdue University . Ed Dubinsky is the person involved. We are
using DERIVE and Maple here and share some of your concerns.

John Yearwood
Newsgroups: sci.math.symbolic
From: cmumford@iat.holonet.net (Chris Mumford)
Subject: Solve[ a == Sin[b-c], b] ?????
Organization: HoloNet (BBS: 510-704-1058)
Date: Sun, 4 Oct 1992 19:06:40 GMT

Why is it that:

Solve[ a == Sin[b-c], b]

does not work, but:

Solve[ a == Sin[b+c], b] works?  It seems to work in version 1.2 of
Mathematica, but not 2.0.  Is this a bug?
From: gaylord@UX1.CSO.UIUC.EDU
Newsgroups: sci.math.symbolic
Subject: neural nets with Mathematica article
Date: 5 Oct 92 12:42:38 GMT

you might want to check out the article "Neural Networks in Mathematica" in
the November issur of "AI Expert"

richard j. gaylord, university of illinois, gaylord@ux1.cso.uiuc.edu

"if you're not programming functionally, then you must be programming
dysfunctionally"
From: 00s0davis@bsu-ucs.uucp
Newsgroups: sci.math.symbolic
Subject: symbmath to plotdata
Date: 28 Sep 92 15:41:00 GMT

dear netters,
	I've found a simple patch that gets around the incompatibility
of symbmath 2.1 and plotdata 1.1 (plotdata can't read the tables that 
symbmath creates). What needs to be done is this, create the table as 
outlined in the symbmath manual. Then edit the resulting file, adding 
a -> and a <cr> at the first line and replacing the done at the end
of the file with a -> and type end on the next line. that's all that 
needs to be done.
				just an dinosaur,
						Spencer
Newsgroups: sci.math.symbolic
From: knapp@spot.Colorado.EDU (David Knapp)
Subject: SphericalPlot in mma.
Organization: University of Colorado, Boulder
Date: Tue, 29 Sep 1992 21:07:22 GMT


I cannot seem to get SphericalPlot[r,{theta range},{phi range}] to work
in either our unix mma or our NeXT mma. I don't expect the latter to 
work because it is on a Next, but I should think that it would work in unix.
Also, a friend has told me it doesn't work on IBMs either.

Is there a trick to this is or is this just coincidence? Do I have to load
special libraries to run that function? Is there a command line that someone
could send me that works for them?

Any help would be appreciated.




-- 
David Knapp                                      University of Colorado, Boulder
Perpetual Student                                   knapp@spot.colorado.edu
Newsgroups: sci.math.symbolic
From: stanly@crunch.unm.edu (Stanly Steinberg)
Subject: Mathematica: Help Simplifying an Infinite Sum
Date: Mon, 28 Sep 92 04:04:51 GMT
Organization: University of New Mexico, Albuquerque NM

In the following, ans is obviously zero:

f[x_,y_] := Sum[a[n]*Sin[n*Pi*x]*Sinh[n*Pi*y],{n,1,Infinity}]

ans = D[f[x,y],{x,2}] + D[f[x,y],{y,2}]

How can I force mathematica to see this??
How about f[1,y] = 0??


--
Professor Stanly Steinberg, Department of Mathematics and Statistics
University of New Mexico, Albuquerque, NM 87131-1141, 505-277-5323
stanly@math.unm.edu    stanly@unmb.bitnet
FAX 505-277-5505 (or at Ecodynamics 505-843-9641)
Newsgroups: sci.math.symbolic
From: Richard J. Gaylord <gaylord@ux1.cso.uiuc.edu>
Subject: Re: symbolic algebra and teaching math/sciences
X-Xxdate: Tue, 6 Oct 92 02:32:06 GMT
X-Useragent: Nuntius v1.1.1d11
Organization: University of Illinois
Date: Tue, 6 Oct 1992 07:30:01 GMT
X-Xxmessage-Id: <A6F6AB269F029B13@mm-mac19.mse.uiuc.edu>

jaffer@zurich.ai.mit.edu (Aubrey Jaffer)

In article <JAFFER.92Oct5214709@camelot.ai.mit.edu> Aubrey Jaffer,
jaffer@zurich.ai.mit.edu writes:
>In article <1aqe9eINN3g4@agate.berkeley.edu>
fateman@peoplesparc.Berkeley.EDU 
>(Richard Fateman) writes:
>
>   Some people seem to think that because you can do some symbolic
>   (indefinite) integration that these programs would be especially
>   useful to courses that teach humans how to do symbolic indefinite
>   integration.  This is not at all obvious to me.

==============================================

obviously just because a program can do math doesn't mean that its at all
helpful for teaching people how to do the same math; especially if you
don't know how the program is doing its math.
Newsgroups: sci.math.symbolic,sci.math
From: ilya@kronecker.mit.edu (Ilya Zakharevich)
Subject: Vector spaces in symbolic calculations - Query
Summary: How to code a vector space in computer
Organization: MIT Department of Mathematics
Date: Fri, 2 Oct 92 03:16:44 GMT

Hi, netters,

Did anyone managed to find a feasible way to work "directly" with vector spaces
with some symbolic algebra package? Well, the simple idea what does it mean is

	Calculations of homology

It looks a little bit dull to work with basises if you consider sub-quotients.
From the other side, let call a subquotient of a coordinate vector space
"an abstract vector space." 

It looks like any standard operation over such objects is again an
object of the same nature. 

Therefore the first idea that comes to my mind is to consider a vector
space as a pair of matrices NxM and NxK such that there concatenation
has the same rank as the second. (So their column spaces are subspaces of
each other, so the abstract vector space is the quotient of these two 
subspaces).

Did anyone invent  something better?

Cheers, Ilya Zakharevich
From: gaylord@UX1.CSO.UIUC.EDU
Newsgroups: sci.math.symbolic
Subject: neural nets in mathematica follow-up.
Date: 5 Oct 92 13:56:45 GMT

sorry, i should have said the article on neural nets with mathematica is by
james a. freeman.  

his book ""Exploring Neural Networks with Mathemtica" by A-W is due out in
March according to the publisher.

richard j. gaylord, university of illinois, gaylord@ux1.cso.uiuc.edu

"if you're not programming functionally, then you must be programming
dysfunctionally"



Newsgroups: sci.math.symbolic
From: WKWINKEL@ibm.rz.uni-passau.de
Subject: Re: Maple on 386sx or 386
Organization: University of Passau - Germany
Date: Thu, 1 Oct 1992 08:17:56 GMT

In article <1992Sep30.203252.11747@samba.oit.unc.edu>
Jim.Buddenhagen@bbs.oit.unc.edu (Jim Buddenhagen) writes:
 
>
>I have and IBM PC clone which is a 386sx with 4 meg of memory, running DOS 5.0,
>25 mhz.  Is there a version of Maple which will run in this environment?
>If so, how well would it run?  Does anyone have personal experience with this?
>
>Same question for the  386 33mhz, 8meg ram.
>
>Please respond to       jb1556@swuts.sbc.com       or   post.
>
>I will summarize if there is general interest.
>--
>   The opinions expressed are not necessarily those of the University of
>     North Carolina at Chapel Hill, the Campus Office for Information
>        Technology, or the Experimental Bulletin Board Service.
>           internet:  bbs.oit.unc.edu or 152.2.22.80
 
Jim,
We have maple V running at a 386/33 with 8 MB and a 387 coprocessor.
I didn't use it much yet, but the things I tried out worked at an
acceptable speed. I don't know of the speed of any other similar
programs though.
The 387 speeded up the system 600% using a turbo pascal program with
mainly REAL variables. If the enhancement is somewhat similar with
maple (as you may understand I don't want to plug it out again to try out :)
I'd think a 386 DX would be the minimum.
But - try it out yourself. There is a demo version of maple V available.
It's ought to be at
daisy.waterloo.edu 129.97.140.58 or
neptune.inf.ethz.ch 129.132.101.33
If it's not it surely is on our ftp server: ftp.fmi.uni-passau.de
(forgot the internet number ...)
Regards,
Olaf Winkelhake
University of Passau, Germany
Newsgroups: sci.math.symbolic
From: WKWINKEL@ibm.rz.uni-passau.de
Subject: Re:maple V ftp sites?
Organization: University of Passau - Germany
Date: Mon, 28 Sep 1992 07:57:55 GMT

The book "Maple, first leaves" mentiones
daisy.waterloo.edu 129.97.140.58  and
neptune.inf.ethz.ch 129.132.101.33
as ftp sites for maple V
Regards,
Olaf Winkelhake
University of Passau, Germany
Newsgroups: sci.math,sci.logic
From: frank@Cookie.secapl.com (Frank Adams)
Subject: Re: ZFC etc. (was Re: Report on Philosophies of Physicists)
Date: Thu, 01 Oct 1992 20:45:46 GMT
Organization: Security APL, Inc.

One last time:

A hypothetical proof of the inconsistency of the propositional calculus is
a problem ALL BY ITSELF, because we believe that the propositional calculus
is consistent even BEFORE we prove it, because it represents a formalization
of part of our reasoning process.

By contrast, a proof of the impossibility of generally finding a conjunctive
normal form is a problem ONLY IN CONJUNCTION WITH THE PROOF THAT SUCH A FORM
ALWAYS EXISTS.

One is a direct assault on our reasoning processes, one is more indirect.
That's all there is to it.
From: jwa@math.rice.edu (James Anderson)
Newsgroups: sci.math
Subject: Re: INTERESTING TOPOLOGY QUESTION
Keywords: Dense sets
Date: 6 Oct 92 13:42:23 GMT
Distribution: usa
Organization: Dept. of Mathematics, Rice University

In article <1992Oct6.020715.19878@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:
>In article <4frzz5=@rpi.edu> sassoj@rs6412.ecs.rpi.edu (John J. Sasso Jr.) writes:
>>QUESTION:  Given the interval [0,1], does there exist two sets A and B such
>>           that A is dense in [0,1], B is dense in [0,1], and the Lebesgue
>>           outer measure of A and B is |A| = |B| = 1/2 ? 
>
>Nice question.  Simply take the interval [0,1] and, starting at the left
>endpoint, color the first point red, the second point black, the third
>point red, and so on; call all the red points A and all the black points
>B.  :-)  
>
>I suppose you want A and B disjoint?  As phrased, the answer to your
>question is clearly yes, take A to be [0,1/2] union the rational numbers
>in [0,1], and take B = A.  But I bet that's not what you MEANT.
>
>In any event, here's what I know, which was enough to answer my own
>questions along these lines.  Given a Lebesgue measurable set S of
>positive measure, it has a "point of density," that is, a point x
>such that as e -> 0 (from above), 
>
>measure([x-e,x+e] intersect S)/2e -> 1.
>
>This settled my question, which was: is there a measurable set S
>such that the measure of S intersect any interval [a,b] is, say,
>half the length of [a,b]?  I.e., is there a set of "uniform density
>1/2"?  No.  Any measurable set must be "lumpy".


John Baez's response does contain the seed to an answer to the original question, though.
Let A be the set containing the rationals in (0,1/2) and the irrationals in (1/2,1), and let 
B be the set containing the rationals in (1/2,1) and the irrationals in (0,1/2).
Then, both A and B are dense in [0,1] and the outer measure of both is 1/2.

Jim Anderson
From: loeb@greco-prog.fr (Daniel LOEB)
Newsgroups: sci.math
Subject: Re: A proposal for a variant of chess
Date: 30 Sep 92 08:40:14 GMT
Organization: GRECO Programmation du CNRS - Bordeaux,France

Newsgroups: sci.math
Subject: Re: A proposal for a variant of chess
Reply-to: loeb@geocub.greco-prog.fr

In article <1992Sep22.033321.14102@galois.mit.edu> you write:
>In article <1992Sep21.152035.12341@newstand.syr.edu> hgraber@lynx.cat.syr.edu (Harry Graber) writes:
>>     We wonder if this has been proposed before, and would like to hear
>>your opinions of this game. Suppose chess were played with three people
>>instead of two. The two who actually play the game decide upon the moves
>>they wish to make and submit them to the third person, who moves both
>>white's and black's men simultaneously. That is the only difference
>>between this game and the way chess is played now: white does not go
>>first.
>>
>>     There are two questions that come to mind right away...
>
>Most fundamentally, the game as described is not well-defined.  What
>if both players say that they want to move their piece to the same
>square?  What happens?

I noticed that the game is not completely defined. 
In my posting I ask for further information.
However, one could adopt some sort of simple conflict resolution.
(eg: the pieces "bounce" or both pieces are removed with no effect on
the square in question.) Some people might also like to prohibit
pieces (except the knights?) from moving through each other.  

>I have trouble seeing a way to resolve this without breaking the
>symmetry or introducing a very different element into the game.

These solutions are all symmetric, and they don't introduce any
fundamentally new elements into the game. 

>This is perhaps an interesting philosophical point: since real life goes on
>"concurrently" rather than players taking turns, in real life one
>will expect people's plans to "bump into each other" as I have described
>above.

"Concurrent" games are often called "matricial" games. There is a
great amount of literature on the subject.

Yours, Daniel Loeb				loeb@geocub.greco-prog.fr
HOME 	150, cours Victor-Hugo; Appt D45; 33000 Bordeaux France
WORK	LABRI; Universite de Bordeaux I; 33405 Talence Cedex France
PHONE(H)+(33) 56 31 48 26, (W)+(33) 56 84 69 05, (FAX) +(33) 56 84 66 69
-------------
Mankind faces a crossroads.  One path leads to despair and utter hopelessness,
the other to extinction.  Let us pray we choose correctly.  -- Woody Allen

-- 

Yours, Daniel Loeb				loeb@geocub.greco-prog.fr
HOME 	150, cours Victor-Hugo; Appt D45; 33000 Bordeaux France
WORK	LABRI; Universite de Bordeaux I; 33405 Talence Cedex France
Newsgroups: sci.math