HDTenEightyP/NetNews huggingface dataset:
From: masjpf@gdr.bath.ac.uk (J P Fitch)
Newsgroups: sci.math.symbolic
Subject: MPP implementations of symbolic algebra systems
Date: 4 Sep 92 17:58:26 GMT
Organization: School of Mathematics, University of Bath, UK

We have developed an implementation of Lisp (EuLisp) for the MasPar
array processor and now this appears to be fairly stable we will be
(amongst other things) be looking at doing symbolic algebra on it.
The first project we have in mind involves manipulating distributed
polynomials with a view to Groebner basis computations.
	
The implementation supports a look-alike of Connection Machine Lisp
and of Paralation Lisp (but not *Lisp!).  We have almost finished
developing a server mechanism so that LAN workstation Lisp users can
use parallel datatypes without having to access the array processor
explicitly.
	
I have not seen any reports from Thinko themselves on data-parallel
CA or, that I can recall, in recent SYMSAC proceedings.
	
--Julian Padget
------------------------------------------------------------------------
	School of Mathematical Sciences
	University of Bath
	Bath, BA2 7AY, UK			    jap@maths.bath.ac.uk
------------------------------------------------------------------------
Newsgroups: sci.math.symbolic
From: wongda@eecg.toronto.edu (Daniel Y.H. Wong)
Subject: Re: Maple differntiation
Organization: Dept. of Electrical Engineering, University of Toronto, Canada
Date: 9 Sep 92 13:13:25 GMT


> Maple V does this

> > diff(xy,y);
> > 0


> This is clearly a bug.


Try 

diff(x*y,y);

Maple thinks 'xy' is a variable name.


Daniel.

Newsgroups: sci.math.symbolic
From: Richard J. Gaylord <gaylord@ux1.cso.uiuc.edu>
Subject: Re: Thread question in Mathematica
X-Xxdate: Tue, 8 Sep 92 03:30:54 GMT
X-Useragent: Nuntius v1.1.1d9
Organization: University of Illinois
Date: Tue, 8 Sep 1992 08:29:29 GMT
X-Xxmessage-Id: <A6D1CEEE4B019B13@mm-mac19.mse.uiuc.edu>

Dave Seaman writes

>In article <Bu7pyr.734@mentor.cc.purdue.edu> carlson@math.purdue.edu
(Neil N. Carlson) 
> asks essentially why Thread[{{x1, {y11, y12}}, {x2, {y21, y22}}}]
>gives                 {{x1, x2}, {{y11, y12}, {y21, y22}}}
>and not               {{{x1, y11}, {x2, y21}}, {{x1, y12}, {x2, y22}}}
===============================

perhaps a simple explanation  of Thread will help explain.

Thread[f[{a, b, c,..}, {x, y, z,...}] simply 'pairs off' the
corresponding components of the lists and makes each pairing the
arguments of the function f. 

Thus,
Thread[f[{a, b, c,..}, {x, y, z,...}]  gives {f[a, x], f[b, y],...}

In the posed question, Dave says that neil has 
Thread[{{x1, {y11, y12}}, {x2, {y21, y22}}}]

which is equivalent to
Thread[List[{x1, {y11, y12}}, {x2, {y21, y22}}]

so the  pairings are  List[x1, x2] and List[{y11, y12}, {y21, y22}}] and
the full answer is
{ List[x1, x2], List[{y11, y12}, {y21, y22}}]} 

ie.,   {{x1, x2}, {{y11, y12}, {y21, y22}}}
From: ags@mentor.cc.purdue.edu (Dave Seaman)
Newsgroups: sci.math.symbolic
Subject: Re: Thread question in Mathematica
Date: 7 Sep 92 16:09:32 GMT
Organization: Purdue University Computing Center

In article <Bu7pyr.734@mentor.cc.purdue.edu> carlson@math.purdue.edu (Neil N. Carlson) 
 asks essentially why Thread[{{x1, {y11, y12}}, {x2, {y21, y22}}}]
gives                 {{x1, x2}, {{y11, y12}, {y21, y22}}}
and not               {{{x1, y11}, {x2, y21}}, {{x1, y12}, {x2, y22}}}

Only the top-level lists (two of them, in this case) are seen by
thread. To see what is happening, try the following:

    	template = {{x1, y1}, {x2, y2}}
	subs = {y1 -> {y11,y12}, y2 -> {y21,y22}}
	
and verify that

	Thread[template] /. subs
	
gives the same result as

	Thread[template /. subs]
	
Where template /. subs is the expression you are trying to thread, and

	Thread[template] /. subs 
	
is clearly equivalent to 

	{{x1, x2}, {y1, y2}} /. subs
	
which is

	{{x1, x2}, {{y11, y12}, {y21, y22}}}

-- 
Dave Seaman
ags@seaman.cc.purdue.edu
Organization: Ministry of Education, Computer Center NETNEWS system V2.3
Date: Sunday, 13 Sep 1992 14:55:02 EST
From: <NCKUT057@TWNMOE10.BITNET>
Newsgroups: sci.math.symbolic
Subject: about Symbol

Dear my friend,

   I want define a function like that

       f[x_] := Block [ body ... ]

   and I want the first character of variable x must be "A" and
   this function could test it automatically. Is any one know how
   to do that?

   Thanks

                                                Sincerely yours,
                                                G.J.Cheng
Newsgroups: sci.math.symbolic
From: qmdbms@gsusgi2.gsu.edu (Brian Schott)
Subject: Re: pc applications other than Mma or Maple (for IBM or Apple)
Organization: Georgia State University
Date: Sun, 13 Sep 1992 01:52:56 GMT

stiv@stat.rice.edu (david n stivers) writes:

>Are there any other packages available? 

>Are they any better than these?o

David,
  I personally like Prescience's Theorist available only for the Mac.
It is very user friendly and I think is great for algebra and calculus.

-- 
Brian Schott/Decision Sciences Dept.             qmdbms@gsusgi2.gsu.edu
College of Business Administration                         404-651-4070
Georgia State University                  interests: approx. reasoning,
Atlanta, Georgia USA 30303-3083     (B=)       decision support systems
From: ara@zurich.ai.mit.edu (Allan Adler)
Newsgroups: sci.math.symbolic
Subject: Re: commercial version of IBM's "new scratchpad"
Date: 9 Sep 92 03:29:32 GMT
Distribution: sci.math.symbolic
Organization: M.I.T. Artificial Intelligence Lab.

I played with Scratchpad on an IBM mainframe at the University of Kentucky.
I'm no expert by any means. It is true that its data types reflect those
used by mathematicians. However there is more to a computer algebra
system than data types. I would need to know more about its computing power
compared to the various other packages, commercial and otherwise, that
are available. I would also need to know more about the availability of
source code and the ability to diagnose failures. And taking it on its
own ground, I would need to know how successfully they implement the
data structures of mathematics.

I tend to associate IBM with procrustean software and regard
with great suspicion anything that  they produce until proven otherwise.
I'm willing to be convinced otherwise but I am not willing to pay for
the privelege of doing so (actually, I'm broke so the point is moot).

COmprehensive systems that are based on mathematics are not new. The system
SETL of Jack Schwartz was supposed to be based on set theory. Since set theory
is the foundation of mathematics (I know about categories...let's not get
into that), I would imagine that one can have all kinds of structures in
SETL. But has SETL ever proved useful for any serious computation?


Allan Adler
ara@altdorf.ai.mit.edu
From: santas@inf.ethz.ch (Philip Santas)
Newsgroups: sci.math.symbolic
Subject: Re: mma -- creating a generic argument list
Date: 15 Sep 92 13:25:19 GMT
Distribution: na
Organization: Dept. Informatik, Swiss Federal Institute of Technology (ETH), Zurich, CH


In article <1992Sep13.195413.27402@wuecl.wustl.edu> dek2@cec2.wustl.edu (Dean E Kassmann) writes:
>
>what i want is a method for taking a list and converting it to a similar list
>in which to each member is appended the symbol _. ( i.e. {x,y} ---> {x_,y_} )

ToPatterns[list_List]:= Map[Pattern[#,Blank[]]&, list]

>then to take that list and use it as a collection of ordered arguments for use

ToPatSeq[list_List]:= Apply[Sequence, ToPatterns[list]]

>in a global function
>                             g[x_,y_] := stuff

Attributes[trans]=HoldRest;

trans[symbols:{___Symbol},funHead_Symbol,stuff_]:=
   funHead[ToPatSeq[symbols]]:= stuff

>I would appreciate any help on the subject. Thanks in advance.

You may try:

In[5]:= trans[{x,y,z},g,stuff]

In[6]:= ??g
Global`g
g[x_, y_, z_] := stuff

You can arrange the arguments of trans in the way you wish.
Hope this helps.

Philip Santas

  "In an evolving universe those who stand still are really moving backwards"
--------------------------------------------------------------------------------
email: santas@inf.ethz.ch				 Philip Santas
Mail: Dept. Informatik				Department of Computer Science
      ETH-Zentrum			  Swiss Federal Institute of Technology
      CH-8092 Zurich				       Zurich, Switzerland
      Switzerland
Phone: +41-1-2547391
From: karp@are.Berkeley.EDU (Larry Karp)
Newsgroups: sci.math.symbolic
Subject: derive - simple display question
Date: 11 Sep 1992 18:06:26 GMT
Organization: UC Berkeley, Agr & Res Economics
Distribution: world
NNTP-Posting-Host: are.berkeley.edu

Hello, I'm a new user of derive (without a manual) and I have a
simple question.  When I obtain a long expression after computing
something, the display only shows part of the result.  How do I
display the whole thing?  Thanks.
Newsgroups: sci.math
From: claude@bauv106.bauv.unibw-muenchen.de (Claude Frantz (RZ))
Subject: Algorithm for the inversion of large matrices
Keywords: matrix inversion algorithm computer
Organization: Universitaet der Bundeswehr Muenchen (Germany)
Date: Thu, 10 Sep 1992 05:24:06 GMT

Hello !

Can you inform me about algorithms suitable for the inversion of
large matrices, especially using external files on computers ?
Where can I find more information and subroutines ?

Please send me your response via E-Mail.
Many thanks in advance.
Claude
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Proof of God's Existence
Date: 6 Sep 92 00:42:11 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Sep1.235230.8805@massey.ac.nz> news@massey.ac.nz (USENET News System) writes:
>> 
>court offered to debate the existence of God. It happened that a well known
>French mathematician was visiting at the time (possibly Laplace - I'm not
>sure). He claimed to have a mathematical proof.

The philosopher in question was Denis Diderot, and the Mathematician was 
Leonhard Euler, otherwise the story is essentially true.

Later,
Andrew Mullhaupt
Newsgroups: sci.math
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Jokes in papers (was Re: Einstein's Erdos number)
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Wed, 9 Sep 92 17:56:47 GMT

Sorry to be so grumpy, but I wish people would think twice before
posting things they vaguely remember, which are likely to be false. 
Someone asks a question and gets a pile of misinformation with one
correct reply buried in it.  In the famous "Alpha, Beta, Gamma" paper the 
"Alpha" was NOT Ahlfors, the famous author of a book on complex analysis, 
and it was NOT Alfven, the famous plasma physicist.  Jeez!  As Brad Pierce 
correctly noted, it was Alpher.  And it most certainly was not a math paper.
None of these guys are mathematicians, even though Gamow wrote the
great pop math book, "One, Two, Three, Infinity"


Newsgroups: sci.math
From: gillies@m.cs.uiuc.edu (Don Gillies)
Subject: Re: Minimizing waste when cutting fabric.
Keywords: Waste; Fabric
Organization: University of Illinois, Dept. of Comp. Sci., Urbana, IL
Date: Sun, 6 Sep 1992 21:33:43 GMT

The problem you are describing is known as the "2-dimensional
bin-packing problem," or "stock cutting problem".  The basic
assumption is that the rectangles cannot be rotated (i.e. perhaps
because there is a pattern on the fabric).  Several algorithms were
developed for it in the late 1970's and early 1980's, vis:

%Z     25
%X A
%A Daniel D. Sleator
%T A 2.5 Times Optimal Algorithm for Packing in Two Dimensions
%J Information Processing Letters
%D 12 February 1980
%V 10 1
%P 37 40
%K bin packing
%K best
%K 2-d

%Z     39
%X A
%A E. G. Coffman
%A M. R. Garey
%A D. S. Johnson
%A R. E. Tarjan
%T Performance Bounds for Level-Oriented Two-Dimensional Packing Algorithms
%J SIAM Journal on Computing
%D 1980
%V 9
%P 808 826
%K 2-d
%K bin packing

%Z     141
%X I
%A E. G. Coffman, Jr.
%A M. R. Garey
%A D. S. Johnson
%T Approximation Algorithms for Bin-Packing - An Updated Survey
%B Algorithm Design for Computer System Design
%E G. Ausiello, M. Luccertini, P. Serafini
%I Springer Verlag
%C Berlin
%P 49 106
%D 1984
%K survey
%K bin packing

There is also an algorithm that is asymptotically 5/4 + C times
optimal (with C very large, like 11), which was published around that
time in either SIAM J. on Computing or CACM, but I don't have the
reference handy.

Don Gillies - gillies@cs.uiuc.edu - University of Illinois at Urbana-Champaign


--
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.math
Subject: Re: Chess Problem
Date: 15 Sep 92 23:36:52 GMT
Organization: U of Cambridge, England

In article <BuML8A.9Ds@mentor.cc.purdue.edu>, hrubin@pop.stat.purdue.edu (Herman Rubin) writes:

> >As I see it, white has a choice of two stratgies:
> >1. Run the pawn down and queen it without a king defense.
> >2. Move the king toward the pawn and defend it. Then advance the two in tandem.
> 
> >(strategies where the king and pawn move toward each other may save time, but
> >they work just as well as strategy 2).
> 
> These are not all the strategies, nor is strategy 2, as stated, adequate.
> The "standard" result for the 8x8 board, which uses nothing about the size
> of the board, is that if white has the opposition in front of the pawn, but
> not on the side until one gets to the 6th rank, white wins, but otherwise 
> it is a draw.  This would reduce the probability of winning.
> 
> But there is another strategy, frequently possible, and that is for white to
> keep the black king from the pawn.  Now this might not be possible to do 
> indefinitely and also advance the pawn, but enough of this might be possible.

Hmm. With probability 1-o(1) the difference between the distances WK-P and BK-P
is not small (say, at least log(board-size)). If the black king is at least
3 moves or thereabouts closer to the pawn than is the white king, Black can just
rush up and eat the pawn. If the white king is at least 5 moves or thereabouts
closer to the pawn than is the black king, White can just rush up and get between
the Black king and the pawn; if he can do this a square or more in front of the
pawn (again, probability -> 1) he doesn't need to worry about the opposition
because he has a move in hand.

This is what I meant in my earlier posting when I said that all the interesting
chess only happens with probability o(1).

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
Newsgroups: sci.math

In sci.math, hussein@bora.inria.fr (Hussein Yahia) writes:
[Concerning Donaldson/Freedman theory]

> Could someone give me a list of references leading to a proof of that theorem
> for somebody like me who is just at the level of Volumes 1-2 of Spivak's 
> Course on Differential Geometry and Hirsh's Differential Topology (Springer
> Verlag) ?

Well, a reasonable place to start is (a) Donaldson and Kronheimer's book
"The geometry of four manifolds" and (b) Freedman and Quinn's book
"The topology of four manifolds". (Sorry if the titles are inaccurate
but my copies are at home). You will get hopelessly stuck :-) but
the authors are considerate enough to give good overviews of what
is happening and to explain (implicitly) what is required of the reader.
(And the references are pretty good).
You can then work back from there to fill in your knowledge, but be warned,
there's a lot to get familiar with! 

In general terms you will need a fairly solid background in differential
geometry and analysis for Donaldson theory (I've found that Kobayashi/Nomizu's
"Differential Geometry" and Griffiths/Harris's "Algebraic Geometry" are
helpful references [though I'm not sure I'd want to learn from them.....] and
Lawson's "Spin Geometry" has the avowed aim of helping the reader understand
Donaldson theory. [oh, and is a good book!]). For Freedman's stuff, you 
need to understand geometric topology....I seem to remember review articles
in the AMS Bulletins being very useful, but I can't offhand remember any 
references.

Oh, alternatively, you could go and study at Oxford for a year :-)

Hope this is useful,
		    Simon.

Newsgroups: sci.math
From: qszhan@radon.berkeley.edu
Subject: test
Originator: qszhan@radon.berkeley.edu
Organization: UCB
Date: Tue, 8 Sep 1992 05:21:15 GMT

This is a test.
Newsgroups: sci.math
From: shoham@ll.mit.edu (Daniel Shoham)
Subject: Re: Chess Problem
Organization: MIT Lincoln Laboratory
Date: Sat, 12 Sep 92 10:53:58 GMT

In article <BuGA8t.DL8@cmptrc.lonestar.org> carter@cmptrc.lonestar.org (Carter Bennett) writes:
>rairan@ecf.toronto.edu (RAI Ranjan) writes:
>>Chess Problem:
>> Eight rooks are placed at random on a chessboard.  
>> What is the probability that no two rooks can attack one another?

After n rooks that cannot attack each other are placed, a total of n rows and
n coulmns are now defended (i.e. a further rook may not be placed there). n
rows + n coulmns represent 16*n-n^2 squares (remembering not to double-count
the squares that are defended twice). This leaves (64-16*n+n^2=[8-n]^2) squares
available for the next rook to be placed in without being attacked out of
(64-n) empty squares. The probability that the next rook, when placed randomly
would in fact be placed in one of those available squares is thus:
P(n) = (8-n)^2/(64-n) 

So, 
P(8 rooks) = P(0)*P(1)*...*P(7)

             8^2   7^2   6^2     1^2
           = --- * --- * --- ... ---
             64    63    62      57

             (8!)^2
           = ------
             64!/56!

           =~ 9.1E-6

Or about 1 in a hundreed thousands.

Dan Shoham
shoham@ll.mit.edu
From: rhubner@vax.path.ox.ac.uk
Newsgroups: sci.math.stat
Subject: test for random association
Date: 14 Sep 92 22:16:04 GMT
Organization: Oxford University Molecular Biology Data Centre
Nntp-Posting-User: rhubner

Hi everybody,

 I'm writing up a "D.Phil." in Zoology here at Oxford and I'm stuck with the
following stat problem about chromosomes that join together. 

The background:
1) mice have usually 2n=40 (which means 20 pairs of chromosomes)
   -> these chromosomes look [schematically] like this:

          *
      a  / \

2) some populations 'fuse' the chromosomes of two pairs 
   -> looks like this and is written as Rb(a.b) 

     a   \ /          Rb = Robertsonian fusion or centric translocation
          %           % = **, but now they segregate as one chromosome
     b   / \

3) a maximum of 9 fusions (2n=22) is known from some populations
  (leaving one pair and the sex chromosomes unfused)
  
    ex: Rb(a.b), (c.d), (e.f), (g.h), (i.j), (k.l), (m.n), (o.p), (q.r)
        with s,t, X,Y unfused

4) the same chromosome combination can be found in mice with 1 fusion (2n=38)
   or mice with more fusions (2n=36-22)
 
     ex: 2n=34; Rb(a.b), (c.d), (e.f) 
         2n=26; Rb(a.s), (c.t), (e.f), (g.h), (i.j), (k.l), (m.n)
                                ^^^^^
5) fusions are not independent, because they are sampled without replacement 
   from the initial pool (N) of 20 different chromosomes; this reduces the 
   number of free partners after each subsequent fusion
    -> the number of different combinations [written C(N,k)] for a chromosome 
       set with a given number of fusions (k) is thus

                          N!
         C(N,k) =  ------------------          k=1,2,...9
                   2^k * k! * (N-2k)!

The question: How to test for random association given that the probability of
a fusion in a certain context should be quite different? (Some people think
that I should just take  1/C(N,2) as the expected value, but I believe they are
wrong). Furthermore, because I may not be absolutely sure about the sequence of
fusions in a particular population, is there any other way to test for random
association here? Does somebody know about analogue systems (lottery?) and
point out where the solution may have been published? Or is this a totally 
uncommon and 'desperate' situation?

Thanks for any hint!
     Roland                                             [rhubner@ox.path.ac.uk]


              ....        .... 
             '    )._._._(    `^^^^^^^^^^^^^^^`.
            (    (        )    )               .\
             \.   \ 0  0 /   ./         .      )\\
               `._/\    /\_.'    )     (      /  \\
                  ==&__&==  `_| / _._._.(   _/    \\
                     ""     /__|      /_._./       `*****
                                                    
            ***********************************************
            * Roland Huebner, Dept. Zoology, Univ. Oxford *
            * South Parks Road, OX1 3PS, Oxford, England  *
            ***********************************************
From: pbond@spitws100.sbil.co.uk (Philip Bond)
Newsgroups: sci.math.stat
Subject: Re: Testing for Normality
Date: 15 Sep 92 09:22:14 GMT
Reply-To: pbond@spitws100.sbil.co.uk
Organization: Salomon Brothers, Ltd.

Normality Testing.

If you have a lot of samples, a straightforward and powerful test of normality
that does not require the use of tables is the method of moments. Compute
the moments of the distribution ( it is probably sufficient to compute the
first four moments but you can go higher if you so choose ). The normal
distribution has the property that :-

	if m == mean , v is the variance of the distribution then

	define mn = the nth moment ie : E[ (x-m)^n ]

	where E is the expectation, ^ means "to the power of "

	we have the following handy result :-

	mn = 0 if n is odd

	mn = (n-1)(n-3)...3.1.v^n  for n even.

Furthermore, this property is unique to the normal distribution.

Application :-

	compute the mean and variance of the sample distribution, then
compute 1/n*sum( x-m)^n ) where x is the random variable ( I am assuming
large n ; you need to adjust this to get an unbiased estimator for small 
n : use 1/Num Degrees of Freedom ).

Then see if the 3rd , 5th etc. moments are small or vanishing, and whether the
 4th, 6th ... follow the formula above. This is a pretty good test of
normality. It will differentiate between normal and lognormal samples
even for quite small sample sizes ( say, 30-50 observations ).

All my own humble opinion of course. 

Hope this helps, Phil.
From: jose@math.duke.edu (Greg Lawler)
Newsgroups: sci.math.stat
Subject: Re: FULL HOUSE
Summary: interesting probability
Date: 13 Sep 92 19:21:02 GMT

In article <1992Sep13.143329.24796@wuecl.wustl.edu>, ppc1@cec1.wustl.edu (Peter Pui Tak Chiu) writes:
> 
> hi everyone,
> 
> i am trying to find the probability of getting a hand of full house from a
> shuffled deck of 52 cards.
> 
> theoretically, the probability (i think) is:
> 
>         (13 * 4C2) * (12 * 4C3)
>         -----------------------  =  0.001440576
>                  52C5
> 
> but i wrote a c program to calculate this probability and the results turn
> out to be very different.



You're simulation is incorrect.  In your program your
are dealing from an infinite deck.  (in particular,
if the first card you deal is a king, then the
probability the second card is a king is 1/13
instead of 3/51 as it should be).

According to my calculations the probability of
getting a full house from an infinite deck of cards
is .00420....

This is the probability that you are simulating,

(Infinite decks do not arise a lot, but sometimes at
blackjack tables they deal from a large number of
decks in order to beat card counters.)


Greg Lawler
Newsgroups: sci.math.stat