HDTenEightyP/NetNews huggingface dataset:
From: robertd@imsl.UUCP (Robert Daugherty)
Newsgroups: sci.math.symbolic
Subject: RE: Differential Equation Tables
Date: 13 Oct 92 13:11:24 GMT
Organization: IMSL, Inc., Houston

>The work that I have been doing recently seems to lead to nonlinear
>ordinary differential equations which I don't recognize.  What I 
>would like to find is something like an integral table but for 
>differential equations.  Generally I would be happy seeing a 
>solution in terms special functions.  I usually can write down
>some solutions to these equations and simply would like to verify
>that I have all of them.  Can someone suggest a possible reference?



A good reference book I found:
	Ordinary Differential Equations and their Solutions by
	George M. Murphy, published by D. Van Nostrand Company,
	copyright 1960.  Unfortunately the book is out of print.
	The publisher did grant permission to photcopy the book when
	I got my copy.
	
Newsgroups: sci.math.symbolic
From: katherle@daisy.uwaterloo.ca (Kate Atherley)
Subject: Re: MapleV - Log Plots
Keywords: Maple
Organization: University of Waterloo
Date: Fri, 16 Oct 1992 16:44:52 GMT

In article <hnatiw.718951944@ee.ualberta.ca> hnatiw@ee.ualberta.ca (Alan Hnatiw) writes:
> I have had MapleV for a month of so and I was trying to make 
> a frequency vs magnitude plot.  Since these plots are usaually
> in dB and log( freq. ) I look in my manuals to see if there was
> such and option.  I haven't found a solution yet, and I would be
> really appreciative if someone knows a way of makein log, log vs
> log plots.

In the current version of Maple there is no way to do log or log
vs log plots.  This shortcoming has been addressed for the next release
of Maple.

Kate
Waterloo Maple Software Technical Support
support@maplesoft.on.ca
Newsgroups: sci.math.symbolic
From: sherod@newton.Colorado.EDU (Scott Herod)
Subject: Differential Equations Tables
Organization: University of Colorado, Boulder
Date: Mon, 12 Oct 1992 03:34:54 GMT

The work that I have been doing recently seems to lead to nonlinear
ordinary differential equations which I don't recognize.  What I 
would like to find is something like an integral table but for 
differential equations.  Generally I would be happy seeing a 
solution in terms special functions.  I usually can write down
some solutions to these equations and simply would like to verify
that I have all of them.  Can someone suggest a possible reference?

Scott Herod
From: d3a132@pnl.gov (Carl P Baker)
Newsgroups: sci.math.symbolic
Subject: Re: mathematica
Date: 13 Oct 92 22:12:45 GMT
Reply-To: d3a132@pnl.gov
Organization: Battelle Pacific Northwest Laboratories

In article 39201@sdcc12.ucsd.edu, ee52fas@sdcc15.ucsd.edu (Anand Rao) writes:
>i need a software package that will let me write up lab reports,
>print
>mathematical symbols on my laser printer, do circuit diagrams, make
>tables and other things you do when writing up lab reports.  can
>anybody reccomend one to me? is mathematica anygood for this sort of
>thing? thanks.
>
>-anand


mathcad might work too.  There is a pretty reasonably priced educational version
of it too.  Or at least there was.

-- carl

Carl P Baker
cp_baker@pnl.gov
509-375-2724

Disclaimer: I am not the official spokesperson for anyone.  For which
organizations that use spokespersons are profoundly grateful.
From: jgk@osc.COM (Joe Keane)
Newsgroups: sci.math.symbolic
Subject: Re: Integral Tables
Summary: Mathematica sometimes works.
Keywords: branch
Date: 7 Oct 92 06:41:36 GMT
Reply-To: Joe Keane <jgk@osc.com>
Organization: Versant Object Technology, Menlo Park, CA
Weather: cloudy, high 73, low 57
Moon-Phase: waxing gibbous (82% of full)

In article <4355.Sep2919.43.3492@virtualnews.nyu.edu> brnstnd@nyu.edu (D. J.
Bernstein) writes:
>  Integrate[Sqrt[Cos[x]^2],{x,0,Pi/2}]
>  Integrate[Sqrt[Cos[x]^2],{x,0,Pi}]
>
>Both positive, obviously. Mathematica 1.2 gives 1 for the first and 0
>for the second. Mathematica 2.0 gives -1 for the first and 0 for the
>second.

Well, at least one version got one case right :-).

I've got some branch-cut-nightmare functions i can't get anything to deal
with.  The best i can do is graph the thing and stick in `+pi' by hand in
various intervals until it looks right.  Even Maple has a way to go.

--
Joe Keane, amateur mathematician
jgk@osc.com (uunet!amdcad!osc!jgk)
From: HEDDEN@ESDSDF.dnet.ge.com (Jerry D. Hedden)
Newsgroups: sci.math.symbolic
Subject: Computer Algebra in ML
Date: 15 Oct 1992 08:59:31 -0500
Organization: UTexas Mail-to-News Gateway
NNTP-Posting-Host: cs.utexas.edu

I am interested in exploring the development of a
computer algebra system using ML (CAML-Light actually).
The specific application will deal with tensors.

Has anyone done any work in this area?
Is there source code, grammars, etc. available?
Any literature on the subject?

Thank you,
Jerry D. Hedden
hedden@esdsdf.dnet.ge.com
From: edgar@function.mps.ohio-state.edu (Gerald Edgar)
Newsgroups: sci.math.symbolic
Subject: Re: Solving transcendental equations in MMA
Date: 14 Oct 1992 08:24:22 -0400
Organization: The Ohio State University, Dept. of Math.
Distribution: na
NNTP-Posting-Host: function.mps.ohio-state.edu

In article <1992Oct14.055350.24912@leland.Stanford.EDU> cchan@leland.Stanford.EDU (Chung Chan) writes:
>Does anyone know how I can possibly solve for:
>
>		1 + x = 2^x
>
>in MMA?
>

In Maple:

> eq := 1 + x = 2^x;

                                               x
                                eq := 1 + x = 2

> solve(eq,x);

                              W(- 1/2 ln(2)) + ln(2)
                            - ----------------------
                                       ln(2)


where:

    W         - the function satisfying  W(x) * exp(W(x)) = x


-- 
  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: es2j+@andrew.cmu.edu (Edward John Sabol)
Newsgroups: sci.math.symbolic
Subject: Some Mma tensor code wanted!
Date: 9 Oct 92 23:37:50 GMT
Article-I.D.: andrew.QepcVCi00VoG84CYhE
Organization: Doctoral student, Physics, Carnegie Mellon, Pittsburgh, PA

I'm wondering if someone has some code that will implement the following
tensor stuff in Mathematica. I would be eternally grateful.

1. The Levi-Civita tensor.

2. The wedge or exterior product in a given basis.

3. The cofactor of a matrix. Related problem: If I had a nxn matrix, how
would I construct a matrix that would be the same as the first except
for the given i-th row and j-th column deleted (resulting in an
(n-1)x(n-1) matrix)?

4. The symmetrizer and anti-symmetrizer tenor functions.

Feel free to give me pointers to ftp sites, etc, but DO NOT SUGGEST
MathTensor. It's out of my price range. If anyone has a public domain or
freeware implemenation similar to MathTensor, please let me know.
Anything would be of help.

Is there any chance that some future version of Mathematica will support
tensors more robustly?
Newsgroups: sci.math.symbolic
From: Hal.Varian@umich.edu
Subject: Re: How do you display a histogram in Mathematica
Reply-To: Hal.Varian@umich.edu
Organization: University of Michigan Math Dept
Distribution: usa
Date: Thu, 8 Oct 1992 14:56:55 GMT

In article <3067@news.cerf.net> jonesm@nic.cerf.net (Matthew Jones) writes:
> Subject about sayes it.
> How do you graph a histogram in Mathematica? I can't even find a 
> way to partition the set of points into bins and then do a ListPlot.
> Any help would be appreciated.
> 
> Matthew Jones
> jonesm@cerf.net

Here's the sampling distribution of a Mean, extracted from an elementary stat  
Notebook.

<<Statistics`DescriptiveStatistics`
<<Statistics`DataManipulation`
<<Graphics`Graphics`

sampleList=Table[Mean[Table[Random[],{25}]],{50}]
BarChart[BinCounts[sampleList,{.25,.75,.025}]]
--
Hal.Varian@umich.edu    Hal Varian
voice: 313-764-2364     Dept of Economics
fax:   313-764-2364     Univ of Michigan
                        Ann Arbor, MI 48109-1220
From: sg04@ploni.gte.com (Yechezkal Shimon Gutfreund)
Newsgroups: sci.math.symbolic
Subject: Mma catching a kill signal
Date: 16 Oct 92 15:36:29 GMT
Reply-To: sgutfreund@gte.com
Organization: GTE Laboratories, Waltham MA

I have a mathematica process running in batch mode -batchinput
-batchoutput. I would like it to catch a kill signal and do
some clean up. Can I do this? 

Part of the cleanup is to close down a mathlink connection
to a C program. Is it better to send the kill signal there
and then signal the mathematica parent?

BTW: where does -batchinput, -batchoutput put the results?
-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Yechezkal Shimon Gutfreund		 		  sgutfreund@gte.com
GTE Laboratories, Waltham MA			    harvard!bunny!sgutfreund
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Newsgroups: sci.math.symbolic
From: lee@math.washington.edu (John M. Lee)
Subject: Re: Some Mma tensor code wanted!
Organization: Mathematics Dept., U. of Washington
Date: Sat, 10 Oct 1992 21:23:50 GMT

In article <QepcVCi00VoG84CYhE@andrew.cmu.edu> es2j+@andrew.cmu.edu 
  (Edward John Sabol) writes:

> I'm wondering if someone has some code that will implement the following
> tensor stuff in Mathematica. I would be eternally grateful.

> 1. The Levi-Civita tensor.

> 2. The wedge or exterior product in a given basis.

> 3. The cofactor of a matrix. Related problem: If I had a nxn matrix, how
> would I construct a matrix that would be the same as the first except
> for the given i-th row and j-th column deleted (resulting in an
> (n-1)x(n-1) matrix)?

> 4. The symmetrizer and anti-symmetrizer tenor functions.


I've recently announced the release of a Mathematica Package called Ricci
that does some, but not all, of the things you suggest.  I'll e-mail the
full announcement to you; if anyone else is interested, send e-mail to me. 


--
Jack Lee
Dept. of Mathematics
University of Washington
Seattle, WA
Newsgroups: sci.math.symbolic
From: ent3c@fermi.clas.Virginia.EDU (Eric  Turkheimer)
Subject: n,k permutations in Mma
Organization: University of Virginia
Date: Mon, 12 Oct 1992 14:10:03 GMT


I know this is a little elementary, but can someone help me with a
function to generate the permutations of n objects taken k at a time?
The only way I can manage it is via the Permutations function, but
this is very inefficient because it first generates _all_ the
permutations, then trims them down those with k length.

While I'm asking, is there an easy way to add a row to a matrix?  That
is

rowadd[{1,2},{{3,4},{5,6}}] would give {{1,2},{3,4},{5,6}}.

Thanks
Eric Turkheimer
ent3c@virginia.edu
Newsgroups: sci.math.symbolic
From: wmcb@math.appstate.edu (Bill Bauldry)
Newsgroups: sci.math.symbolic
Subject: Re: Simple (?) Maple question and Thermodynamics
Followup-To: sci.math.symbolic
Date: 14 Oct 1992 19:38:02 GMT
Organization: Appalachian State Univ, Math Sciences
Distribution: world
NNTP-Posting-Host: lynx.math.appstate.edu

In article <1992Oct14.131733.3263@news.clarkson.edu>,
taylor@sun.soe.clarkson.edu (Ross Taylor,Peyt312,6652,2655436) wrote:
> 
> Here is a portion of a Maple session that takes a pressure 
> explicit equation of state and gets to the dimensionless 
> Helmholtz free energy ( Fr(T,V,n) ).
> 
> P := (n * R * T) / (V - B) - D / (V * (V + B));
> Ar(T,V,n) := int( (P - (n*R*T)/V),V=V0..infinity);
> Ar(T,V,n) := subs(V0=V,Ar(T,V,n));
[deleted]
> Fr(T,V,n) := collect(Fr(T,V,n),T);
> 
> Here is what Maple gives me for Fr(T,V,n);
>                                                   (ln(V) - ln(V + B)) D
>          Fr(T, v, n) := (- ln(V - B) + ln(V)) n + ---------------------
>                                                           B R T
> 
> This is, of course, correct.  However, I want to get the answer 
> in a form that has terms like this:
> 
>             V                V + B
>       ln (-----)         ln (-----)
>           V - B                V
>
> So far I have been unable to get Maple to do this.  The function
> collect  (...,ln) does not give answers in the right form. 

Try:
   combine( Fr(T,V,n), ln );
                                            /  D  \
                                            |-----|
                            /  V  \n /  V  \\B R T/
                         ln(|-----|  |-----|       )
                            \V - B/  \V + B/

See also the help screen for combine for other variants.

Regards,
Bill
----

+=======================+===============================+
     Bill Bauldry       |   wmcb@math.appstate.edu
    Math. Sciences      | wmcb@lynx.math.appstate.edu
  Appalachian State U   |  BauldryWC@appstate.bitnet
   Boone, NC   28608    |       (704) 262-2355
+=======================+===============================+
When judging a mathematician you should only integrate f_+
- A Zygmund
Newsgroups: sci.math.symbolic
From: renggli@masg1.epfl.ch (loris renggli)
Newsgroups: sci.math.symbolic
Subject: MMA 2.0 ComplexExpand bug
Date: 15 Oct 92 11:24:11 GMT
Organization: Math. Dept., Swiss Institute of Technology

Someone did probably notice this bug of ComplexExpand :

In[1]:= Simplify[ ComplexExpand[ z^2 * Conjugate[z^2] ,{z}] ]

Out[1]= (I Im[z] + Re[z])

So my question is : Is there a patch for this ?

------------------------------------------------------------------------
Loris RENGGLI
Swiss Federal Institute of Technology
Math. Dept                             e-mail : renggli@masg1.epfl.ch
CH-1015 Lausanne (Switzerland)               or renggli@dma.epfl.ch
--
From: storch@draper.com (Joel Storch)
Newsgroups: sci.math.symbolic
Subject: Generalized Eigenvalue Problem
Keywords: eigenvalues
Date: 8 Oct 92 23:06:49 GMT
Reply-To: storch@draper.com (Joel Storch)
Organization: Draper Lab


Does anyone have a  Mathematica package to solve the generalized eigenvalue 
problem            

                       A x = lambda B x

where A is real-symmetric and B is real-symmetric and positive definite ?
From: gaylord@UX1.CSO.UIUC.EDU
Newsgroups: sci.math.symbolic
Subject: Re: >=0
Date: 15 Oct 92 14:24:18 GMT


a additional note on the question:

you must have made an error because
 

using the rewrite rule g[x_] := If[x>=0,True,False]

and inputting
g[2 y^2]
     
returns

If[2 y >= 0, True, False]

it does not return False (you probably got a false  with a rewrite rule you
forgot to clear).

the reason is that since y is undefined mathematica can't decide if it is
true or false and so it returns the input unevaluated.


the rest of my discussion is, i believe, okay.



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

"if you're not programming functionally, then you must be programming
dysfunctionally"
From: kim@uful07.phys.ufl.edu (Jaewan Kim)
Newsgroups: sci.math.symbolic
Subject: maple initialization file
Keywords: maple, .mapleinit
Date: 9 Oct 92 15:43:53 GMT
Article-I.D.: eng.1992Oct9.154353.10364
Distribution: usa
Organization: University of Florida, Gainesville


-- 
Jaewan Kim at the University of Florida Physics department
internet address: kim@uful07.phys.ufl.edu
Newsgroups: sci.math.symbolic
From: lepard@mayo.edu (Kevin O. Lepard)
Newsgroups: sci.math.symbolic
Subject: 2D convolution, 2D fourier w/ Mma
Keywords: 2D, convolution, fourier, mathematica
Date: 13 Oct 92 17:50:39 GMT
Reply-To: lepard@mayo.edu
Organization: Mayo Foundation


---
I am starting to use Mathematica in a 2D DSP class I'm taking, and I am trying
to do a 2D convolution.  The Mma book discusses doing this by multiplying the
fourier transforms of the 2 data sets then taking the inverse fourier
transform of that.  I understand that.  However, I can't get an answer that
matches any of the examples in the book (the answers aren't even close to
each other).

As an example, let's say I want to convolve

7 8 9
4 5 6	(where 1 is located at coordinates (n1,n2) = (0,0), 2 is at (1,0),
1 2 3	 5 is at (1,1), etc.)

with

-1 -1
 1  1 	(where the lower left hand corner is (n1=0, n2=0))

The answer in the book (Two-Dimensional Signal and Image Processing, by J.S. Lim)
is:

-7 -15 -17 -9
 3   6   6  3
 3   6   6  3
 1   3   5  3

If anyone can help me understand how to do this, I'd be grateful.  I've read
what it has to say in _Mathematica_A_System_for_doing_Mathematics_by_Computer_
(several times) but am apparently too dense to understand it.

I don't have a notebook front end, so if someone could include the syntax
required to do this from the command line, that would really help a lot.

Thanks in advance.

Kevin
-----------------------------------------------------------------------------
Kevin O. Lepard
Internet:  lepard@mayo.edu

Disclaimer:  These opinions are mine alone and do not necessarily represent
those of the Mayo Foundation, Mayo Clinic, or any other person or institution.
From: t68@nikhefh.nikhef.nl (Jos Vermaseren)
Newsgroups: sci.math.symbolic
Subject: Re: Schoonship
Date: 9 Oct 92 09:52:33 GMT
Reply-To: t68@nikhefh.nikhef.nl (Jos Vermaseren)
Organization: Nikhef-H, Amsterdam (the Netherlands).

The question whether schoonschip has a version for PC should be easy
to answer once you realize that it is written in assembler language.
The very earliest version was written for an IBM mainframe, but that
was soon replaced by a version written in compass (the assembler language
of the CDC mainframes). We are talking about the 60's here.
In the 80's the CDC mainframes were rapidly disappearing, so around
1985 Veltman rewrote schoonschip for the motorola 68000 series (after
first writing a very nice assembler). Hence nowadays it will run on
most machines that contain a 680x0 chip. Occasionally people start rumors
that it is in state of being ported to another assembler language, but
these rumors are all wrong.

Jos Vermaseren

Disclamor:
1: Veltman is a good friend of mine and he doesn't even earn anything
himself from schoonschip these days.
2: He says I am his competitor
From: murison@cfa.harvard.edu (Marc A. Murison)
Newsgroups: sci.math.symbolic
Subject: Re: Q: Easy way to integrate a matrix in MAPLE?
Date: 13 Oct 92 13:30:47 GMT
Organization: Smithsonian Astrophysical Observatory

In article <1992Oct12.235905.18944@eng.cam.ac.uk> dscy@eng.cam.ac.uk (D.S.C. Yap) writes:
>How does one get maple to integrate a matrix?  That is, I would like
>to integrate a matrix in an element by element manner.  For example,
>if Q is a matrix, I would like
>   int(Q,x=0..l);
>to return a matrix of the same size as Q, where the elements of this
>resultant matrix are the result of integrating the elements of Q wrt x
>between 0 and l.

This will do what you want:  newQ := map(int,Q,x=0..l);
---------------------------------------------------------------------
Marc A. Murison                            Precision Astronomy Group
Smithsonian Astrophysical Observatory      murison@cfa.harvard.edu
Cambridge, MA                              (617) 495-7079
---------------------------------------------------------------------
From: jmborwei@orion.uwaterloo.ca (Jonathan Borwein)
Subject: Centre for experimental and constructive mathematics
Summary: We exist
Keywords: jobs,fellowships, new centre, experimental mathematics
Organization: Simon Fraser University, University of Waterloo
Date: Thu, 15 Oct 1992 19:37:38 GMT


\documentstyle[12pt]{article}
\parskip=0.5ex

\begin{document}
\begin{center}{\Large \bf Simon Fraser Centre for Experimental and
Constructive Mathematics} \end{center}

	This Centre located in Burnaby, British Columbia (Greater Vancouver)
is intended to further research and graduate education in Computation in
the Mathematical Sciences. The Centre aims to provide a sophisticated
environment for Mathematical research on topics that require a substantial
mix of computation, experimentation and mathematics. Of interest are
questions on how one uses the computer:
	 To build intuition?  To generate hypotheses?
To validate conjectures or prove theorems? To discover nontrivial examples
and counter-examples?

	The centre will commence full operation July 1, 1993. Activities will
include the following.

(i)  Provision for and sponsorship of Post-Doctoral Fellowships in areas
related to Experimental and Constructive Mathematics.

(ii)  Sponsorship of regular short-term and longer-term research visitors
to the Centre.

(iii) Organization of regular Colloquia and occasional Conferences on
advances in Experimental and Constructive  Mathematics.

(iv) Participation in the training of graduate students in Experimental and
Constructive  Mathematics.

(v) Establishment, development and maintenance of accessible software
archives.

(vi) Collaboration with similar centres and appropriate individuals at
other Canadian and foreign Universities and Institutes.

	The initial steering committee consists of J. Borwein (Director), P.
Borwein and R. Russell. Enquiries can be directed to jborwein@math.sfu.ca .

The Centre  is soliciting applications for {\bf two Post-Doctoral Fellows}
commencing after July 1, 1993, in any areas compatible with the interests
of the centre.  The stipend will be set on the NSERC PDF scale.  These are
primarily research positions though some teaching may be involved.
Potential Post-Doctoral Fellows should send a curriculum vitae and arrange
for three letters of reference to be sent to Dr. J.M. Borwein,
Department of Combinatorics and Optimization,University of Waterloo, N2L
3G1, Ontario preferably by December 15, 1992.


The Centre will be soon be soliciting applications for the position of
 {\bf Computer System Administrator} commencing April 1, 1993.  Salary
range is \$42,846-\$54,955. This person will be responsible for the
installation and operation of the CECM computing facility and will be
expected to provide technical leadership for this and related projects.  A post
graduate degree in Computing Science or Electrical/Electronic Engineering and 
five years' experience (or an equivalent combination of experience and training) are required.


\end{document}
~
From: hibrown@sarah.albany.edu (Herb Brown)
Subject: Re: schoonship manual
Organization: State University of New York at Albany
Date: Wed, 7 Oct 92 13:19:58 GMT

In article <1992Oct6.222503.7804@news.cs.brandeis.edu> fell@binah.cc.brandeis.edu writes:
>Does anyone know how to obtain a copy of the scoonship manual. Thanks.


I believe the original distribution (on a FISH disk) contained an lharced
version of the manual called SchipAMIdocs.lzh. 

Herb


-- 
Herb Brown  Math Dept  The Univ at Albany  Albany, NY 12222  (518) 442-4640
Director,                                          hibrown@math.albany.edu  
Computer Assisted Instruction in Mathematics       hibrown@csc.albany.edu
--------------------------------------------------------------------------
From: ee52fas@sdcc15.ucsd.edu (Anand Rao)
Newsgroups: sci.math.symbolic
Subject: mathematica
Date: 8 Oct 92 23:09:59 GMT

i need a software package that will let me write up lab reports,
print
mathematical symbols on my laser printer, do circuit diagrams, make
tables and other things you do when writing up lab reports.  can
anybody reccomend one to me? is mathematica anygood for this sort of
thing? thanks.

-anand
Newsgroups: sci.math.symbolic
From: rao@tree.egr.uh.edu (Jagannatha  Rao)
Subject: Do you also get this Mathematica bug?
Organization: University of Houston
Distribution: usa
Date: Mon, 12 Oct 1992 22:49:29 GMT


My mathematica (version 2.0 on Next) crashes every time I do the following:

	1. Plot anything
	2. Select the output graph cell and select the Graph menu "Convert to  
bitmap"
	3. Then, select the same graph (now a bitmap) and select the menu  
"convert to postscript". 

	No errors, nothing. Simply quits. I know these steps are not useful for  
anything, but I thought I would find out if other versions also have this  
effect. 

--
Jagannatha Rao				E-mail:rao@tree.egr.uh.edu
Department of Mechanical Engineering    Tel   :(713) 743-4535
University of Houston                   Fax   :(713) 743-4503
Houston, TX 77204-4792

Newsgroups: sci.math.symbolic