HDTenEightyP/NetNews huggingface dataset:
From: martin@lyra.cis.umassd.edu (Gary Martin)
Subject: Re: Abel's proof of the insolubility of the quintic
Organization: University of Massachusetts Dartmouth
Date: Thu, 3 Sep 1992 02:27:31 GMT

In article <1992Sep2.204229.12330@news.cs.brandeis.edu> ruberman@binah.cc.brandeis.edu writes:

   Does anyone know a reference for a modern treatment of Abel's
   proof of the insolubility of the quintic?  A high-school student 
   recently came to me, having learnt the solutions to the lower degree
   equations, and hoping to understand the higher degree case as well.
   He tried to read Abel's memoir (translated into English in the venerable
   Source book in Mathematics).  Understandably, he didn't get too far
   since Abel's paper is rather dense and obscure to an untutored reader.
   (For instance he doesn't take any pains to explain what the meaning
   of `a solution in radicals to the general quintic' would actually mean.)

   One suggestion to this student is to read enough about groups and fields
   to learn the rudiments of Galois Theory.  There is a book of H. Edwards
   which more or less travels this route.  On the other hand, Abel's proof
   is quite elementary, and can in principle be explained to a high-school
   student.  (I said in principle!)  I am looking for a source for such an
   explanation; any pointers would be greatly appreciated.

I don't know a good reference, but as I recall, you need to know a
little bit about field extensions, how groups permute roots of
polynomials, the relation between solvability of groups and solvability
of equations, and the fact that the alternating group of degree 5 is
simple (and hence that the corresponding symmetric group is not
solvable).  I remember sketching the proof in about an hour for a
very sharp senior engineering major at Swarthmore about 7 years ago
using Fraliegh's algebra text as a guide.  The student was just about
to begin a first semester algebra course, so we had to go through the
necessary definitions.  I think we probably started with the chapter
in which the insolvability is proved and traced backwards through the
definitions and theorems as we discovered which ones we needed.  It
turned out not to be very much, and as I said, he was very sharp, so
it worked well.

--
Gary A. Martin, Assistant Professor of Mathematics, UMass Dartmouth
Martin@cis.umassd.edu
Newsgroups: sci.math
From: scavo@cie.uoregon.edu (Tom Scavo)
Subject: Re: Math Gods & lower Saints
Organization: University of Oregon Campus Information Exchange
Distribution: usa
Date: Sun, 23 Aug 92 18:51:13 GMT

In article <1992Aug22.080051.15169@ecst.csuchico.edu> madams@ecst.csuchico.edu (Michael E. Adams) writes:
>
>Question: given Monthly_Payment, Length_of_loan (in months), and the
>          Principal,  what is the interest rate (compounded monthly)? 

The solution may be obtained by iterating the formula

     f(r) = 12p/A (1 - (1 + r/12)^(-12n))

where  p  is the monthly payment,  A  is the amount of the loan,
n  is the number of years, and  r  is the unknown interest rate. 
This problem is discussed in J. Mathews and S.T. Tan (_Math Mag_
63(4), 263--269, Oct 1990).

-- 
Tom Scavo
scavo@cie.uoregon.edu
scavo@inferno.uoregon.edu
Newsgroups: sci.math
From: jchen@tomahawk.me.gu.edu.au (Jinghong CHEN)
Subject: Re: Proof of God's Existence
Organization: Griffith University, Brisbane, Australia
Date: Tue, 1 Sep 92 21:32:06 GMT

In article <Btw9nH.BIE@world.std.com> rsilver@world.std.com (Richard Silver) writes:
>In article <17ui6kINNsft@matt.ksu.ksu.edu> bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:
>>I was told by somebody that there is a mathematical proof of God's existence;
>>was wondering if somebody could shed some light on the same. 
>>Thanks. Looking forward to the response.
>

Proof of God's inexistence:

God can do anything.

So he can make a stone which he cannot lift.

So he cannot lift that stone.

So "God can do anything" is wrong.

---------------------------------------------------------------------------
J.CHEN                               |E-MAIL: jchen@tomahawk.me.gu.edu.au
School of Microelectronic Engineering| Phone: +61-7-8755050
Faculty of Science and Technology    |   Fax: +61-7-8755198
Griffith University                  |   Fax: +61-7-8755050
Nathan, QLD 4111, Australia          | 
---------------------------------------------------------------------------
From: rcollins@cs.umass.edu (Bob Collins)
Newsgroups: sci.math
Subject: polynomial roots and zero divisors
Date: 27 Aug 92 16:45:00 GMT
Reply-To: RCollins@cs.umass.edu
Organization: CS Dept, UMass at Amherst
News-Software: VAX/VMS VNEWS 1.41


  I would like to find the eigenvalues/vectors of a square 
matrix.  Unfortunately, the elements of the matrix are not 
members of a field.  In particular, they are "dual numbers",
defined in Yaglom's "Complex Numbers in Geometry" as a type of
complex number (a + b E), a and b being reals, and E being a
nilpotent imaginary unit; so E^2 = 0.  Dual numbers form a
commutative ring, but they are not a field since any number 
of the form (0 + a E) is a zero divisor.

Question: Can I find the eigenvalues of a matrix (roots of a
characteristic polynomial) whose elements (coefficients) are 
from a commutative ring, but not a field?

In the textbook "Contemporary Abstract Algebra" by J.A.Gallian
there is an example of finding all solutions to x^2 - 4 x + 3 = 0
over Z(12).  There are four solutions: x = 1, 3, 7, 9.  Gallian
says the "easiest" way to find these solutions is to try every
element!  OK for a finite group, I guess, but not for my problem.
Are there any other approaches that will work for infinite groups?

I know there is a vast literature on commutative rings out there.
Unfortunately, this isn't my field (no pun intended), so I have no 
idea where to start looking.  Does anyone have any advice, or 
pointers to relevant papers?  


  --Bob Collins
  --RCollins@cs.umass.edu
Newsgroups: sci.math
From: niall@nmsu.edu (Niall Graham)
Subject: Re: Einstein's Erdos number
Organization: Computing Research Lab
Date: Thu, 3 Sep 1992 05:00:55 GMT


>Just a guess, but Ernst Straus was an assistant to Einstein in the late 40s, 
>and surely a co-author of Erdos'. 

Correct.   Einstein's co-authors were 
Ehrenfest, Lorentz, Minkowski, Somerfeld, Straus, Weyl.
Straus' co-authors include Erdos and Cantor.
Source: From Figure 1 of "On properties of a well-known graph or
what is your ramsey number?"  Annals of the New York Academy of
Sciences, Vol. 328. The author calls himself Tom Odda of Xanadu University.

Niall Graham
Los Alamos
From: dens@flammulated.owlnet.rice.edu (Dennis Allen Schmitz)
Newsgroups: sci.math
Subject: Re: Problematic smurfs!
Date: 1 Sep 1992 06:26:34 GMT
Followup-To: sci.math
Organization: Rice University, Houston, Texas


     There is a bit of commotion in the crowd, but no one stands up.
     The mayor requests the same demand a bit more sternly.
     Again, commotion, but no one stands up.
     The mayor, irate, demands the red hatted smurfs to stand up.
     Then, a certain amount of smurfs rise.

During the third commotion each smurf asks his neighbor if he should stand.

All the smurfs with red hats stand up.

(Why not? -- smurfs have no prior knowledge of own hat color, no
constraint in problem about finding out later.)

Later,
den

(What is this, some psychology experiment to see how an audience reacts
to unsolvable problems? <yawn>)
Newsgroups: sci.math.num-analysis
From: mihai@nada.kth.se (Mihai Dorobantu)
Subject: Re: Oscillatory Integration?
Organization: Royal Institute of Technology, Stockholm, Sweden
Date: Thu, 3 Sep 1992 16:33:59 GMT

In article <92247.091826J0S@psuvm.psu.edu>, Jack W. Sharer <J0S@psuvm.psu.edu> writes:
|> I'm having to evaluate this integral:
|> 
|>           /\ 0.5
|>          /           N
|>         /      f(x) D (2 pi x + phi) dx
|>        /
|>      \/ -0.5
|> 
|>                        N
|> for N ~ 500 and where D (x) is the N-point Dirichlet kernel:
|> 
|> 
|>                iNx
|>        N      e    - 1
|>       D (x) = --------,  i = sqrt(-1)   (highly oscilatory for large N)
|>                 ix
|>                e  - 1
|> 
|> I'm successfully using a 2000-point Simpson integration, but I cannot
|> begin to evaluate all the needed cases (limited by computer resources).
|> 
|> Could you suggest a change of variable or another technique which
|> would dramatically improve the integration speed?
|> 
|> Thanks, Jack Sharer, Penn State, j0s@psuvm.psu.edu
Try an FFT !
Note that D(x) = 1 + exp(ix) + ...+ exp(i(N-1)x) = exp(-iMx)+...+exp(iMx)
where M=N/2.

So the integral is just the sum of the first N Fourier coeficients of f viewd
as a 1-periodic function. The only thing to do is to pick up N equaly spaced
points on [-1/2 1/2], evaluate f and then add the components of fft(f).
For a non-zero phase parameter phi, just change the variable but don't
forget to extend f. See your implementation of FFT, you might have to
multiply or divide by sqrt(N) depending on whatever normalization was done
in implementing the FFT algorithm.

I tried it in MATLAB. Up to N=2^14 i had an "instant" answer, waited
for 1 sec. with N=2^16 and a few seconds for N=2^17. (And I wasn't useing
a workstation or a fast PC, just a terminal,sharing time with 40 
other users!!!)

The FFT algorithm uses O(N log N) operations, so it is almost as 
fast as possible. It is also very stable to rounding and truncation errors.


Good luck,
Mihai Dorobantu

Dept.for Numerical Analysis and Computer Science
The Royal Institute for Technology, Stockholm - Sweden



Newsgroups: sci.math.num-analysis
From: suresh@papaya.iss.nus.sg (Suresh Thennarangam - Research Scholar)
Subject: Newton Raphsons iteration method
Originator: suresh@papaya
Organization: Institute of Systems Science, NUS, Singapore
Date: Tue, 1 Sep 1992 09:43:00 GMT


Newton-Raphson's method can handle non-linear n-dimensional equations
with reasonable results given a good starting point. What happens
if the system of equations is over-determined ? i.e. M equations in
N unknowns where M > N. 

I used the routine mnewt() from Numerical Recipes ... with SVD as the 
backbone linear equation solver. It always converged when M <= N but 
refused to converge when M > N.

Any comments about this ? Can NR handle M > N at all or does the 
algorithm have to modified to make it work ?


      __
     (_       o_   o  o |_
     __)/(_( _) (_(_ /_)| )_

***************************************************************************
* Suresh Thennarangam               *  EMail: suresh@iss.nus.sg(Internet) *
* Research Scholar                  *         ISSST@NUSVM.BITNET          *
* Institute Of Systems Science      *  Tel:  (065) 772 2588.              *
* National University Of Singapore  *  Facs.: (065) 778 2571          *
* Heng Mui Keng Terrace             *  Telex: ISSNUS RS 39988             *
* Singapore 0511.                   *                                     *
***************************************************************************
Newsgroups: sci.math.num-analysis
From: gordon@cs.uwa.oz.au (Gordon Royle)
Subject: Linear Programming problem - NAG routine E04MBF
Organization: Dept. Computer Science, University of Western Australia.
Date: Wed, 26 Aug 1992 07:25:45 GMT


I have a linear programming problem (in fact an integer programming
problem, but I thought I would experiment with the relaxation first to
get some feel for these things).

It is very simple:

	Minimize	Sum x_i

	subject to	0 <= x_i <= 1
			Ax > j


	where A is a symmetric matrix with all row and column sums
	equal, and j is the all-ones vector.


Thing is, the solution of this is obvious - the best thing is to put

		x_i = 1/r		where r is the row sum of A


So, I took a 243 x 243 example of this problem and gave it to 
NAG routine E04MBF.

Funny thing was though - instead of quickly giving me the obvious
solution, it gave a far-from-optimal INTEGRAL feasible point and then
stopped, saying that it had made too many iterations without changing
the trial solution.


Three questions:

	1. Why does it behave like this?

	2. What do I do to make it give the right answer

	and thirdly...

	3. when I get down to actually trying to solve the 
	integer linear program, is there any theory around
	that says that symmetric As etc are particularly hard
	(or better still, particularly easy)


    Cheers

    Gordon
Newsgroups: sci.math.num-analysis
From: jonathan@chpc.utexas.edu (Jonathan Thornburg)
Subject: reviews of symbolic algebra systems (was: Re: 100 digit integer division?)
Followup-To: sci.math.symbolic
Summary: there are several good SAS's; test-drive or read reviews to choose
Keywords: symbolic algebra Macsyma Reduce Maple Mathematica
Organization: U of Texas at Austin / Physics Dept / Center for Relativity
Date: Sun, 30 Aug 92 15:47:24 GMT

In article <SCHULTZ.92Aug29220351@halley.est.3m.com>
schultz@halley.est.3m.com (John C. Schultz) writes:
>Is maple free? anon ftp sites?  All I could find asking ARCHIE was
>maple DOS demo programs.
>
>Also, not to start a flame war, but why use MAPLE V vs Mathematica if
>they both cost money.  Mathematica seems to be the most widely used
>from my viewpoint in a hole :-).

There are four major "full-featured" symbolic algebra systems:
Macsyma, Reduce, Maple, and Mathematica.  All are basically workable,
all cost (widely varying amounts of) money.

IMHO, in some sense the differences between them are comparable
to those between Pascal, C, Fortran, PL/I, and Basic:  They're
all fundamentally equivalent in power, but in practice there are
large differences between them in power, speed, memory use,
correctness, "look and feel", and amount-of-marketing-hype.  The
programming language anlogy is also useful in illuminating the
nature of many of the inter-system flame wars...

For a quite detailed, relatively unbiased, and IMHO very cogent
and well written, review of and comparison betwen these and other
symbolic algebra systems, see Barry Simon's latest review in the
August 1992 "PC Magazine".

Further discussion of the relative merits of various symbolic
algebra systems should probably occur in sci.math.symbolic if at
all; please note the "Follup-To" header line.

- Jonathan Thornburg
  <jonathan@einstein.ph.utexas.edu> or <jonathan@hermes.chpc.utexas.edu>
  University of Texas at Austin / Physics Dept / Center for Relativity
  and (for a few more months) U of British Columbia / {Astronomy,Physics}
From: sundaram@cps.msu.edu (Divya Sundaram)
Newsgroups: sci.math.num-analysis
Subject: Need info on PD Matlab program
Keywords: Lapack, Matlab, C++ Conversion Project
Date: 2 Sep 92 23:58:54 GMT
Distribution: usa
Organization: Michigan State University, College of Engineering
Originator: sundaram@arctic.cps.msu.edu

Hi all,

I am a graduate student in Electrical Engineering (DSP) at Michigan State 
University. I would like to write a C++ program that will provide the 
many important mathmatical functions (a la Matlab).

I had posted (on comp.os.linux) that I was interested in finding out whether
a PD package existed that allowed me to perform a lot of the computations 
that commercial programs like Matlab allow. If not, I stated, I would like 
to implement such a package. In response, a reader sent me the following 
message:

>>> There is indeed a (old) PD version of Matlab.  That is before
>>> it became big and famous and commercial.

>>> There are some others working on a PD Matlab, I think.
>>> Write a posting on sci.math.num-analysis.
>>> The modern approach is to do it in C++, so the Matlab project
>>> often coincides with the project of machine-translation
>>> of Lapack into C++.
>>> 
>>> [stuff deleted]
>>> 
>>> You may want to look at
>>> 1. netlib/c/free-c
>>> 2. there is a alpha library in pub on terminator.cc.umich.edu
>>> 	The library is lib.tar.Z.  If you are not fluently setup to

I was inspired by the example of Linus Torvalds, who (with a lot of help)
"created" a new implementation of Linux (available freely) for the 80386
AT machines. Along the way, he learnt a lot, and helped provide a valuable
tool for the rest of us poor students 8->. 

Along the same lines, I would like to write or work on such a package. I
would appreciate any ideas and pointers on this subject. I would also love 
to get in touch with people working on the Lapack to C++ conversion project
or the PD Matlab project.

Thanks,

Later
Divya
(sundaram@cps.msu.edu)
Newsgroups: sci.math.num-analysis
From: emc@doe.carleton.ca (Eli Chiprout)
Subject: Re: A Tailor's Problem
Organization: Dept. of Electronics, Carleton University
Date: Tue, 1 Sep 1992 18:21:42 GMT

In <1992Sep1.190730.1@vmsa.technion.ac.il> chr09tk@vmsa.technion.ac.il writes:
>We are given a roll of cloth of a given width and unlimited length. We are also
>given a finite set of polygons (pieces of clothing). We want to cut out the
>polygons using a minimal length of the cloth. Devise an algorithm that will get
>us as close as possible to the minimum (within reasonable time). 

Sounds like the travelling salesman again -- NP complete at best.

--
Eli Chiprout
Dept. of Electronics, Carleton University
Ottawa, Ontario, Canada
emc@doe.carleton.ca
From: bardo@ief-paris-sud.fr (Bardo Muller)
Newsgroups: sci.math.num-analysis
Subject: IMPLICIT method for ODE set wanted
Keywords: implicit method ode
Date: 1 Sep 92 17:13:04 GMT
Reply-To: bardo@ief-paris-sud.fr
Followup-To: sci.math.num-analysis
Organization: Universite de Paris

Dear netters,

is there any (simple ?!) code known which uses
an implicit method for the solution of a system of 
first order ODE's.

The result of each integration step should therefore 
be separable (for each dependent variable) in

1) 	(time-dependent) "factors" relating them only to the 
 	present (or next) values of the independent variables.

2)	(time-dependent) "histories" relating them to 
	previous calculated values.

Any comments welcome...

Bardo
___________________________________________________________________________
| Bardo MULLER                          | phone  : [33] [1] 69 41 78 50    |
| Institut d'Electronique Fondamentale  | fax    : [33] [1] 60 19 25 93    |
| Bat. 220 Universite Paris Sud         | e-mail : bardo@ief-paris-sud.fr  |
| 91405 ORSAY CEDEX FRANCE              |             THE NET WORKS !      |
|_______________________________________|__________________________________|
Newsgroups: sci.math.num-analysis
From: berg@a1.arc.umn.edu (Brian Berg)
Subject: re: Genetic Algorithm
Reply-To: berg@a1.arc.umn.edu
Organization: AHPCRC, University of Minnesota
Date: Fri, 28 Aug 1992 22:56:35 GMT

The genetic algorithm described in the July 1992 Scientific American Amateur
Scientist column is available by anonymous ftp from um.cc.umich.edu
Then:

cd LJ1J
binary
get SA2.C.Z
bye

uncompress SA2.C
mv SA2.C sa2.c

The author provides a sample makefile for compilation.  The code is well
documented, but not user friendly.

Have fun,
Brian Berg
berg@a1.arc.umn.edu
Xref: sparky sci.math.num-analysis:2555 sci.math.stat:1756 sci.math:10599
From: hougen@uirvlh.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math.num-analysis,sci.math.stat,sci.math
Subject: Re: Least Squares with Inequality Constraints?
Keywords: least squares, inequality constraints
Date: 25 Aug 92 22:04:54 GMT
Distribution: inet
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: uirvlh.csl.uiuc.edu

As an addendum to my note, I should point out that I had a similar
question some time ago.  Several people sent responses which I later
posted.  Currently, I am using a nonnegative least squares program
provided to me by another person.  It has the desirable properties
that it usually finds a solution in a small number of iterations and I
think it even keeps the partial results from one iteration to the next
so that only one column/row of the matrix has to be updated on each
iteration.  It is pretty fast.  

Unfortunately, the program I am using only handles the case where all
of the variables are required to be positive and I would like to let
some of the variables range over the reals.  I would really like to
get my hands on the algorithm of Stoer '71 as it appears to be very
good.  Is this available anywhere?  At this point, I don't care too
much whether it is free or not.  However, because I have a *very*
large number of equations (e.g 10,000) in a *very* large number of
unknowns (e.g. 30), the interface should be such that I don't have to
type in all the data by hand (as that would be impossible).

Darrell
Newsgroups: sci.math.num-analysis
From: pwm@netnews.jhuapl.edu (Miller Phil F1E x8335 )
Subject: Advice wanted for using C++ in Numerical Analysis
Summary: Help with object oriented Numerical Analysis
Keywords: object oriented design
Organization: JHU/Applied Physics Laboratory
Date: Wed, 26 Aug 1992 04:24:35 GMT

This question is not meant to start a language war.  I want to learn C++
and object oriented programming, so I can see if it will help me with
my work in mathematical modeling.  I have been exposed to C++ and object
oriented programming, and I would like to see a discussion on how they
benefit the numerical analyst. 

 Also I would like some advice on the best way to learn
C++ and object oriented programming with numerical
simulation in mind.

Again, I do not want to start a language war.  I currently program in 
FORTRAN since it is the only language I know.  However, I want to learn
C++ and develop object oriented numerical code.  Therefore, I would like
to hear from those who may have already taken this step.

I welcome a discussion on the net, or email responses to pwm@macaw.jhuapl.edu.
I will summarize if there is interest.

Sincerely,
Phil Miller
pwm@macaw.jhuapl.edu
 



Newsgroups: sci.math.num-analysis
From: sjreeves@eng.auburn.edu (Stan Reeves)
Subject: MATLAB archives?
Organization: Auburn University Engineering
Date: Fri, 4 Sep 1992 13:29:53 GMT


Does anyone know of the existence of any Matlab m-file archives for
scientific programming?

--
Stan Reeves
Auburn University, Department of Electrical Engineering, Auburn, AL  36849
INTERNET: sjreeves@eng.auburn.edu
Newsgroups: sci.math.num-analysis
From: art@playfair.Stanford.EDU (Art Owen)
Subject: Public Domain CG (thanks)
Organization: Stanford University
Date: Fri, 28 Aug 92 21:39:43 GMT

Thanks to all those who replied.  The suggestions were mostly
for things available on netlib:
 SLAP, a Sparse Linear Algebra Package 
 hints from c/free-c
 dcg.shar in c
 NSPCG (in FORTRAN)

The other suggestion is to hand code based on the description
in Numerical Recipes.

Art Owen
Newsgroups: sci.math.num-analysis,comp.lang.fortran
From: ppc1@cec2.wustl.edu (Peter Pui Tak Chiu)
Subject: Probability
Organization: Washington University, St. Louis Mo.
Date: Sat, 29 Aug 1992 13:52:55 GMT



Hi everyone!


Some of my friends and I have been discussing a question and
we came up w/ an answer and would like to verify if its correctness.

Please give any comments freely!!!

Thanks...

Question:

Assume there are m kinds of balls in an infinitely large pool
(i.e. there are infinitely many balls)
and the distributions of different kinds of balls are equal.
Find the probability of getting all kinds of balls if n balls
are picked.

Solution:

First group the n balls you picked into m groups according to
their kinds using m-1 sticks.  So the number of possible
arrangements for the sticks and balls is (n+m-1)C(m-1).

Then we are to find the number of possible arrangements of:
(m balls of different kinds) + (n-m balls of whatever kinds) + (m-1 sticks)
since the m balls are fixed (to satisfy the constraint that there
exists at least one ball of each kind) and what we are trying to
find is the number of arrangements of n-m balls and m-1 sticks.
So, the possible arrangements is:    ((n-m)+(m-1))C(m-1) = (n-1)C(m-1)

Therefore, the probability is:    (n-1)C(m-1)
				---------------
                                 (n+m-1)C(m-1)
Newsgroups: sci.math.num-analysis