HDTenEightyP/NetNews huggingface dataset:
From: columbus@strident.think.com (Michael Weiss)
Newsgroups: sci.math
Subject: cubic equation feetnote
Date: 19 Nov 92 10:13:21
Organization: Thinking Machines Corporation, Cambridge MA, USA
Distribution: usa
	<1992Nov19.095515.1896@sun0.urz.uni-heidelberg.de>
NNTP-Posting-Host: strident.think.com
In-reply-to: afm@trillian's message of Thu, 19 Nov 92 09:55:15 GMT

Scott Chase has already given a solution to the cubic 
x^3 + bx^2 + cx + d = 0 using trig functions: 

    x = rational_function(cos(1/3 arccos(f))),

                            where f = rational_function(b,c,d,sqrt(-D)),
                            where D is the discriminant = prod (r_i-r_j)^2
                                                          i<j
                            where r_1, r_2, r_3 are the roots; D is of
                               course also a rational function of the coefficients

and Mark Dubinsky has given the solution by radicals, often called Cardan's
formula.  Finally Andreas Mueller has pointed out that when the cubic has
three distinct real roots, we have the famous irreducible case: D is
positive, so we end up taking a cube root of a complex number, which in a
sense means using trig functions anyway (though that point is arguable).

Feetnote:

(1) The ancient Greeks, as is well-known, came up with three problems (or
    constructions) that they were unable to do with ruler and compass: (i)
    duplicating the cube, (ii) trisecting the angle, and (iii) squaring the
    circle.  As many books point out, (i) and (ii) both reduce to cubics,
    and so cannot be done in general with ruler and compass (though a
    rigorous proof requires a little field theory).  I find it entertaining
    to note that, conversely, all cubics reduce essentially to either
    n-plicating the cube (i.e., finding the cube root of a real number n),
    or trisecting an angle!

(2) Cardan was not the discover of Cardan's formula, merely the first to
    publish it.  According to several histories of mathematics, Scipio del
    Ferro was the first discoverer, and Tartaglia later independently
    rediscovered it.

(3) It is an amusing exercise in Galois theory to prove that the
    irreducible case is in fact irreducible-- that is, if a cubic with
    rational coefficients has three distinct real roots, and none of these
    roots are rational, then none of the roots lie in any extension field
    obtained by repeatedly adjoining roots of positive reals.
Newsgroups: sci.math
From: joel@math.toronto.edu (Joel Chan)
Subject: P=NP
Organization: Department of Mathematics, University of Toronto
Distribution: math
Date: Wed, 18 Nov 92 19:55:29 GMT

Professor E.R. Swart of the University of Guelph has written a paper
claiming that he has resolved P=NP.  The title of one of his 3 papers
is called

"A polynomial-time procedure for resolving the graph isomorphism problem."

The others are titled "N=1" and "A polynomial time solution to the
Travelling Salesperson Problem"

For the time being, these files are available in my account.  Look
for them in ~joel/pub/peqnp

The files are compressed, so to print them, your command will be

riemann% zcat <filename>.ps.Z | lpr

All users are welcome to look at these files.  As a courtesy, may I
ask you that you not copy these files in order to preserve disk space.

Thanks

Joel
-- 
Joel Chan, Department of Mathematics	  	 joel@math.toronto.edu
Toronto Blue Jays: 1992 World Series Champions
"History: Those who ignore it are condemned to repeat it.  Math, too."
				    -From the comic strip "Betty"
Newsgroups: sci.math
From: alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz)
Subject: Re: faq?
Organization: University of Waterloo
Date: Tue, 17 Nov 1992 18:26:19 GMT

In article <1992Nov16.224920.16045@athena.cs.uga.edu>,
greg@athena.cs.uga.edu (Greg Whitlock) writes:
> I'm been watching this group for a few weeks and haven't seen a
> faq.  Is there one?  If so, can someone forward me the most 
> recent edition?

It was posted the 21st of October and the 6th of november. Most FAQ's
can be obtained through anonymous ftp to "rtfm.mit.edu"
in the directory /pub/usenet/<newsgroup>/*

Alex
> 
> thanks
> 
> -greg

-- 
Alex Lopez-Ortiz                              alopez-o@maytag.UWaterloo.ca
Department of Computer Science                      University of Waterloo
Waterloo, Ontario                                                   Canada
From: jcbhrb@nic.cerf.net (Jacob Hirbawi)
Newsgroups: sci.math
Subject: Re: Looking for name of group of order 12...
Date: 22 Nov 92 23:54:15 GMT
Organization: CERFnet

In <a_rubin.722193951@dn66> a_rubin@dsg4.dse.beckman.com (Arthur Rubin) writes:

> In <1992Nov18.194440.4819@tamsun.tamu.edu> rlm7638@tamsun.tamu.edu (Jack McKinney) writes:
> >     Here I go, with yet another group theory question. This one is of
> >etymology. There are five groups of order 12: The cyclic group of order
> >12 (Z_12), the direct product of the cyclic groups of orders 2 and 6
> >(Z_2 x Z_6), The alternating group on 4 objects (A_4), the dihedral
> >group of a 6-sided object (D_6), and then one more. This last one
> >I have always seen written as just 'T'. Can anyone tell me where this
> >name comes from?
> >           T={<a,b>: a^6=e, a^3=b^2, ba=a^5 b}

> I've never seen "T", but it is also [Z_3]Z_4;
> {<a,b>: a^3=b^4=e, ba=a^2 b}
> Z_12        = Z_4 x Z_3
> Z_2 x Z_6   = K_4 x Z_3  (K_4 = Z_2 x Z_2))
> D_6         = S_3 x Z_2 = [Z_3]Z_2 x Z_2
> A_4         = [K_4]Z_3
> "T"         = [Z_3]Z_4

Actually I've seen "T" being used for A_4 -- the group of rotations that leave
a "T"etrahedron invariant. The fifth group in question I usually think of as
a "generalized quaternion" group; I think Coxeter and Moser also use the term
"dicyclic" group. The definition of these groups is given by:

  Q_n = <n,2,2> = {<a,b>, a^n = b^2 = (ab)^2 = c, c^2 = 1}

The order of the group is 4n (Q_1=C_4, Q_2= ordinary quaternions,Q_3 the
fifth group of order 12). These groups are very close to the dihedral groups:

  D_n = (n,2,2) = {<a,b>, a^n = b^2 = (ab)^2 = c, c^1 = 1}

of order 2n. D_4 and Q_2 are also related in another way: they are both 
extensions of the abelian group C_4 by C_2 through the same map from 
C_2 to Aut(C_4). As such these two groups form a group. in this case 
of order 2 with D_4 as the identity element. This probably generalizes 
somehow to other members of the two families.

Jacob Hirbawi
JcbHrb@CERF.net
Newsgroups: sci.math
From: rkaivola@mits.mdata.fi (Risto Kaivola)
Subject: Re: Fermat's Last Theorem and the FAQ
Organization: Microdata Oy
Date: Mon, 23 Nov 1992 21:37:16 GMT

cyeomans@ms.uky.edu (Charles Yeomans) writes:

>In article <rkaivola.722428224@mits> rkaivola@mits.mdata.fi (Risto Kaivola) writes:
>>I haven't seen the FAQ for weeks, and I don't know if it answers my
>>question.  If it does, I apologize for the inconvenience.
>> [deleted]
>>
>>n >=3 upto some fixed constant (quite large, I imagine).  My question
>>is this:  Are there some other trivial cases like this, where we
>>can easily show FLT to be true for infinitely many n?
>>
>Why, yes there are .  I can prove that FLT is true for all n which are
>divisible by 3.  I wonder if this can be generalized.

>Charles Yeomans


I am interested in your proof.  Meanwhile, here is my proof that there
are no odd x,y such that for an even n >=2,
(A)                             (x**n) + (y**n) = (z**n) for an integer z:

Suppose that there exist odd x,y such that the above equation is satisified.
Then, it is clear that the right side of the above equation is divisible by
2, and consequently, that z is divisible by 2.

Write the above equation as
(B)                           (x**2k) + (y**2k) = (2**(2k))*b
for some k>0 and some b>0.

For any pair of integers x,y we can surely form the sum

                              (x**k) + (y**k)
Because, in this case, x and y are odd, the above sum is even.
Defining 2c to be this sum, we write the equation
(C)                           (x**k) + (y**k) = 2c.

Squaring both sides of the equation (C), and subtracting the resulting
equation from the equation (B), we get the equation

(x**2k) + (y**2k) - (x**2k) -2*(x**k)*(y**k) - (y**2k) = 4*d

                             <=>
                                   (x**k)*(y**k) = -2*d
for some integer d.
But this is impossible, since both x and y are odd.  Therefore,
by the contradiction just obtained, it cannot be the case that both
x and y are odd, which was the thing to be proven.
  Unfortunately, it seems that the above method cannot be generalized.

--
Risto Kaivola
(Internet address:   rkaivola@mits.mdata.fi)
Newsgroups: sci.math
From: adept@hal.gnu.ai.mit.edu (Adept)
Subject: PEANO theorems/axioms anyone???
Organization: MIT Laboratory for Computer Science
Distribution: us
Date: Tue, 17 Nov 1992 18:41:28 GMT

I can't seem to find these anywhere.  If anyone could take a few minutes
to type them up and send them to me I would appreciate it!

		Thanks,

			Adept

Newsgroups: sci.math
From: stpa@nws.e-technik.tu-muenchen.de  (St. Paul)
Subject: Discrete Fields
Organization: TU-Munich
Date: Thu, 19 Nov 1992 15:30:57 GMT

I'm looking for literature on matrix computation on 
discrete fields  (SVD, eigenvalues, QR-decomposition etc. ..).
Newsgroups: sci.math,sci.physics
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: 3-sided coin
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Tue, 17 Nov 92 07:10:17 GMT

In article <1e98b8INN6s@manuel.anu.edu.au> butler@rschp2.anu.edu.au (Brent Butler) writes:
>The solution to this problem is simple.  When a coin is flipped it
>will *come to rest* in a position that represents a minimum in its
>(gravitational) potential energy.  For a real coin this means one
>of its two faces with equal probability - it will never *come to
>rest* on its edge even though it has a finite area because this is
>a metastable state.
>
>Our three sided coin, therefor, should be 1 coin diameter thick. This 
>is where the center of mass is at equal heights in each of the three
>states and so each configuration represents an equally likely
>stable state for the coin to *come to rest* after a toss.

It seems that by *come to rest* you simply mean come to a
lowest-energy state.  While all metastable states should eventually
tunnel to ground states quantum-mechanically at zero temperature, 
"eventually" can be a long time.  (Also, near-ground states will have a
by chance of being occupied at nonzero temperature.)

A more major nitpick is the following: the chance of one of several
macrostates being occupied (lying on one side vs. lying on an edge)
depends on the volue of phase space occupied by the state, not just
the energy.  Someone already noted this and I believe it is a serious
problem for your line of reasoning.

Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: closed forms
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Sun, 22 Nov 92 22:50:43 GMT

In article <1992Nov22.100111.42575@urz.unibas.ch> kullmann@urz.unibas.ch writes:

>Another question that could belong here: How does one proof that there is
>no closed form expression of \int(exp(-x**2))? 

In practice, here's how: "If there was such a closed form, I would have
heard about it.  But I haven't.  So there isn't.  QED."    

:-)
From: kullmann@urz.unibas.ch
Newsgroups: sci.math
Subject: Re: closed forms
Date: 22 Nov 92 10:01:11 MET
Organization: University of Basel, Switzerland

In article <92324.223138YUKQC@CUNYVM.BITNET>, <YUKQC@CUNYVM.BITNET> writes:
> Let S be a set and f1,...,fn be functions over S. I want to know
> which branch of mathematics has dealt with questions of the following kind.
> 
> Given a bunch of recursive equations that purport to define
> a function f, how to decide the existence of, or find, a closed formula
> for f in terms of f1,...,fn (I mean a finite closed formula).
> The recursive equations only contain f1,...,fn.
> 
> Example: Does a closed form of +, -, * exist for a factorial function?
>          Does a closed form of +, -, *, /, sqrt exist for a factorial
>          function over reals?
> 
> References to books are greatly appreciated.
> (What's the answer to the above question anyway?)

Another question that could belong here: How does one proof that there is
no closed form expression of \int(exp(-x**2))? 

--
Peter 

Newsgroups: sci.math.num-analysis
From: patton@phy.uab.edu (David Patton)
Subject: errata sheet for NR book?
Followup-To: patton@phy.uab.edu
Reply-To: patton@phy.uab.edu
Organization: University of Alabama at Birmingham
Date: Thu, 19 Nov 1992 18:02:19 GMT

Has anyone compiled an errata sheet for Numerical Recipes (the Art of ...)
like the one available for Goldstein's mechanics book.  If anyone
can direct me toward one, I would be most gracious.

Thanks.

David Clay Patton                                  patton@phy.uab.edu
Physics Department
University of Alabama at Birmingham
Birmingham, Al 35294




Newsgroups: sci.math.num-analysis
From: batra@boulder.Colorado.EDU (sajeev batra)
Subject: question: how to show that a set of linear inequalities is consistent?
Organization: University of Colorado, Boulder
Date: 18 Nov 92 08:59:05 GMT

hi,

I have a large set of  linear inequalities (with about a 20 unknowns)
and I am about to use linear programming to solve for them.
Is there an algorithm that will tell me that my set is consistent or
inconsistent?  Also, I need to know specifically which inequalities
contradict each other.  How do I go about doing this?  Any suggestions?
Please post or email.

Thank YoO,
sajeev
batra@cs.colorado.edu

Newsgroups: sci.math.num-analysis
From: geo@netcom.com (George Pontis)
Subject: Amateur needs source for Marquardt-Levenburg fit
Keywords: Marquardt Levenburg
Organization: Netcom - Online Communication Services  (408 241-9760 guest) 
Distribution: usa
Date: Thu, 19 Nov 1992 04:21:02 GMT

Dear Net ...
I'm faced with a SW consulting project requiring a Marquardt-Levenburg method
of fitting data to a 4 parameter equation, as used in a biochemistry system.
Having little experience with this sort of thing, I've equipped myself with
"Numerical Recipes" and "C curve fitting and modelling for Scientists and
Engineers". Both these books have sample source code for such an algorithm.
I've also asked netlib for info on the subject "marquardt".

My question: Are there other references that I should be looking at or 
better examples of code ? Any other tips for the novitiate ?

Thanks for any and all comments.

George
-- 
George Pontis ( geo@netcom.COM )
From: patton@phy.uab.edu (David Patton)
Newsgroups: sci.math.num-analysis
Subject: netlib
Keywords: X interface
Date: 16 Nov 92 15:25:05 GMT
Reply-To: patton@phy.uab.edu
Followup-To: patton@phy.uab.edu
Organization: University of Alabama at Birmingham


Here is a nice tool.  I find it extremely helpful.

# 
# 
#         xnetlib 3.0 -- an X interface to netlib
# 
#         Xnetlib is a new version of netlib recently developed at the
#         University of Tennessee and Oak Ridge National Laboratory.
#         Unlike netlib, which uses electronic mail to process requests
#         for mathematical software, xnetlib uses an X Window graphical
#         user interface and a socket-based connection between the user's
#         machine and the xnetlib server machine to process software
#         requests.  Xnetlib is available to anyone who has access to the
#         TCP/IP Internet.



Actually, I think the latest version is 3.2

To get it send email 


To:       netlib@ornl.gov
Subject:  send xnetlib



And leave the body blank.


David Clay Patton                                  patton@phy.uab.edu
Physics Department
University of Alabama at Birmingham
Birmingham, Al 35294
From: actize@garnet.berkeley.edu ()
Newsgroups: sci.math.num-analysis
Subject: calling Fortran libraries with C
Date: 23 Nov 1992 00:49:23 GMT
Organization: University of California, Berkeley
Distribution: ba
NNTP-Posting-Host: garnet.berkeley.edu
Keywords: Fortran, C

I program in C, and most of our mathematical libraries are in Fortran 77.
Our online documentation describes a few things, such as 
1.	Fortran calls by address
2.	The order of array storage is different.

Does anybody have experience with this, and advice ?

David
actize@garnet.berkeley.edu
Newsgroups: sci.math.num-analysis
From: schoen@ghost.dsi.unimi.it
Subject: Re: question: how to show that a set of linear inequalities is consistent?
Organization: Computer Science Dep. - Milan University
Date: Thu, 19 Nov 1992 10:50:23 GMT

jwg@sparcman.cray.com (John Gregory) writes:
>|> 
>|> I have a large set of  linear inequalities (with about a 20 unknowns)
>|> and I am about to use linear programming to solve for them.


>|> Is there an algorithm that will tell me that my set is consistent or
>|> inconsistent?  

[...]
>This question really is not as well-posed as you may think.  If a group
>of inequalities is inconsistent (infeasible), there may be many ways of
>removing a few to give a feasible set.  It's not likely you can point at
>one or two and say "those are the culprits". 

Notice that the problem of finding a MINIMUM number of inequalities to remove in
order to restore feasibility is NP-complete.

-- 
| Fabio Schoen (assoc .prof. of Op.Res.)        e-mail:                     |
| Dipartimento di Scienze della Informazione    schoen@ghost.dsi.unimi.it   |
| via Comelico 39/41 - I20135 Milano ITALY                                  |
| fax: +39 (2) 55006.276 or 373                 Tel: +39 (2) 55006.319      |
Organization: Middle East Technical University - Computer Center
Date: Wednesday, 11 Nov 1992 11:20:09 TUR
From: <NBAC@TRMETU.BITNET>
Newsgroups: sci.math.num-analysis
Subject: Looking for solver for Differential Algebraic Systems

Hello netters,

I am looking for a powerful solver for differential algebraic systems.
If you know where I can get it, please e-mail to me directly.

A10824 at trmetu

Olcay Oymak
From: schell@gauss.ece.psu.edu (Stephan Schell)
Newsgroups: sci.math.num-analysis
Subject: min ||AX - XB|| s.t. X is unitary ?
Date: 21 Nov 92 00:07:33 GMT
Distribution: sci
Organization: Dept. of Elec. and Comp. Eng., Pennsylvania State University, USA

In the course of solving a least-squares problem I have worked
the thing down to a stumbling block: how does one solve
	min ||AX - XB||
subject to the constraint that X be unitary?  A is a complex
matrix; B is upper triangular and Toeplitz, if that helps at all.
It doesn't matter to me if the matrix norm is Frobenius or 2-norm.
Solutions and/or references to the literature would be most welcome.

Thanks,
--
------------------------------------------------------------------
Dr. Stephan V. Schell                   schell@gauss.ece.psu.edu
121 Electrical Engineering East
Dept. of Electrical and Computer Engineering
The Pennsylvania State University
University Park, PA 16802               (814) 863-8102
Newsgroups: sci.math.num-analysis
From: thng@atri.curtin.edu.au (Ian Li-Jin Thng)
Subject: Help ! Mathematica and Maple Road test
Reply-To: thng@atri.curtin.edu.au
Organization: Australian Telecommunication Research Institute
Date: Wed, 18 Nov 92 17:37:28 GMT

G'day all math netters,

Would really appreciate on any information regarding the strengths
and weaknesses of two very popular symbolic math packages - Maple
and Mathematica. I'm not too sure which to go for but as far as the
brochures are concerned , both seems to be pretty impressive. 

Basically : 

I'm looking for something which provides an extensive repertoire (sp?)
of well known functions and algos. Ie, comes with numerous math packages
for linear algebra, matrix manipulation and inversion , complex number,
non-linear as well as linear optimizations - you know - stuffs like that

Basically - I'm sick and tired of programming in Fortran with NAG . Also
running out of cash to upkeep NAG annually. Would like a math package that 
have functions equivalent or similar to NAG routines so that I can chuck 
Fortran and Nag away. I can use both UNIX and DOS based Windows 3.1 
environments.
  
Is there anyone out there whose used both and can answer my queries ?

Better still, if there is an FTp site where I can get comprehensive infos 
on these two packages , please do tell me about it too !  Here's how to 
contact me :

 

------------------------------------------------------------------------------
                 Ian Thng  - Forever Trying to be Young  
                 Email:thng@atri.curtin.edu.au
                 Adaptive Signal Processing Laboratory
                 Australian Telecommunications Research Institute
                 Curtin University of Technology
                 Ph :  +61-9-3513270
                 Fax : +61-9-3513244 
                 Bothered with seat belts ? Ride a Harley Mate !
------------------------------------------------------------------------------


A thousand thanx in advance to anyone who can help !!!




Newsgroups: sci.math.num-analysis
From: chasman@athena.mit.edu (David Chasman)
Subject: BLAS SUMMARY ( where to get ?)
Organization: Massachusetts Institute of Technology
Date: Mon, 16 Nov 1992 21:34:59 GMT

Does anyone out there have an ascii, postscript , or latex summary of 
the fortran blas calls - the papers available from netlib aren't so 
great as a reference source.  Ideally, I'd like something like the info
pages from the RS-6000 online documentation .   Thanks for any help.
--David Chasman
From: pa@verano.sba.ca.us (Pierre Asselin)
Newsgroups: sci.math.num-analysis
Subject: Re: contour plot
Date: 21 Nov 92 06:34:08 GMT
Organization: None.  Santa Barbara, CA

In <1992Nov20.140344.22437@seq.uncwil.edu> bgoffe@seq.uncwil.edu (Bill Goffe) writes:

>luk@ohstpy.mps.ohio-state.edu writes:

>I'm not positive it does what you want, but the public domain Gnuplot 3.2
>does 3d plots and the manual says it does contours.

Yes it does, but only for data on a regular grid (I have version 3.0,
patch 1) It's also an interactive program, as opposed to a subroutine.
The TOMS algorithm I mentioned in another post handles arbitrary data
--it triangulates the x-y plane.

(Gnuplot IS handy to have!)
-- 

--Pierre Asselin, Santa Barbara, California
  pa@verano.sba.ca.us
Newsgroups: sci.math.num-analysis
From: stpa@nws.e-technik.tu-muenchen.de (St. Paul	)
Subject: Discrete Fields
Organization: TU-Munich
Date: Thu, 19 Nov 1992 16:03:34 GMT

I'm looking for literature on matrix algorithms on
discrete fields (SVD, eigenvalues, QR-decomposition...)
From: luk@ohstpy.mps.ohio-state.edu
Newsgroups: sci.math.num-analysis
Subject: contour plot
Date: 19 Nov 92 20:06:01 EST

I am looking for a routine for contour plot, given discrete numerical data 
f(x,y) on a rectangular region.  Can anyone help

luk

Newsgroups: sci.math.num-analysis
From: bgoffe@seq.uncwil.edu (Bill Goffe)
Subject: Re: contour plot
Organization: Univ. of North Carolina @ Wilmington
Date: Fri, 20 Nov 1992 14:03:44 GMT

luk@ohstpy.mps.ohio-state.edu writes:

>I am looking for a routine for contour plot, given discrete numerical data 
>f(x,y) on a rectangular region.  Can anyone help

I'm not positive it does what you want, but the public domain Gnuplot 3.2
does 3d plots and the manual says it does contours. I've used it for 2d
plots and have been quite pleased. It has a variety of output options and
has been ported to a number of different platforms (DOS, X, Next...).

DOS executables can be found at oak.oakland.edu in pub/msdos/plot/gnuplt32.
zip (note the lack of 'o' in gnuplt). The official repository is dartvax.
dartmouth.edu (they don't have DOS executables there, but do have the
source code).

Good luck,
Bill Goffe
bgoffe@seq.uncwil.edu
Newsgroups: sci.math.num-analysis