Conference rusure::math

983.0. "hope someone is doing something about this..." by HERON::BUCHANAN (Berlin = Bellona) Thu Dec 01 1988 11:15

The attached will make some feel humble... 

To Distribution List:

From:	NAME: MACHEFSKY                      <MACHEFSKY@RDVAX@BONNET@MRGATE@STATOS@VBO>
Date:	01-Dec-1988
Posted-date: 01-Dec-1988
Precedence: 1
Subject: The riddleiculous wonder of MATHEMATICA
To:	SINAWI@A1NSTC


Riddle: What does the VAX on your desktop have in common with the Casio
	Data Bank calculator-watch on my wrist?


Stephan Wolfram, Eton drop-out, Cal Tech drop-out, Cambridge
graduate, winner of the MacArthur Prize, professor of computer
science, mathematics and physics at the University of Illinois,
founder of Wolfram Research Inc., and inventor of MATHEMATICA, gave a
talk on his invention at Stanford earlier this month. Wolfram,
described to me once as the bete noire of ISVs, was anything but.
Speaking in a mellifluous British accent and with evident mastery of
the full scope of his subject, Wolfram held an overflow, standing room
only audience of several hundred Stanford students, faculty, and
illuminati spell-bound for two hours as he put his baby through its
paces.

MATHEMATICA is a system for doing mathematics by computer. It performs
calculations in all areas of mathematics and was designed to make
algebra, calculus, geometry and other areas of mathematics as
straightforward as the calculator has made simple arithmetic.
MATHEMATICA can perform numerical computation on exact integers of
arbitrary length and floating point numbers of arbitrary precision. It
performs symbolic computation, polynomial operations, rational
function operations, calculus, diffrentiaon and integration, equation
solving, symbolic matrix operations, tensor operations, and list
operations. It can also make grahps of its results in two dimensional,
contour, density, three dimensional, black-and-white, and color
output.

MATHEMATICA has a machine independent back-end kernel and a machine
dependent front-end based on display PostScript. The front-end is
networked to the back-end so the back-end could run, for example, on a
Cray while the front-end display was handled by a bit-mapped
workstation. Of course, the two can also run together on the same
system, which is how Wolfram demoed it, using a MAC-II and a NeXT
Computer that was an unannounced co-star with him. 

He started with very simple arithmetic and ended with very complex
matrix manipulations. In all examples Wolfram would invariably say,
"And now the computer will think about it..." which it never did
because the answer was on the screen before he finished the sentence.
MATHEMATICA is fast. Answers to problems like Sqrt(17) to 200
significant places, 2000!, and find the 1000th prime, were nearly
instantaneous on a MAC-II. The graphics output was truly amazing.
MATHEMATICA can display the results of operations graphically, and on
a suitably fast machine, like the NeXT Computer, the effect was one of
continuous animation in real-time.

MATHEMATICA has a few nice input and output features as well. It can
show its output in C and Fortran language form, so it can be
incorporated in a program using one of those languages, as well as
give its results in TeX input form. Conversely, a program can call in
to it to use one of its functions as a library routine. It can also be
used as a powerful programming language in its own right.

Another amazing function is its support of Live Textbooks and Live
Notebooks. Mathematics texts can be written in MATHEMATICA and the
equations and examples can literally come to life and perform
themselves.  They can also be dynamically changed for ad hoc queries.
Scientists and experimenters can keep their notes and results in a
MATHEMATICA Live Notebook with similar effect.

At this time, versions of MATHEMATICA are available for the Apple
Macintosh, Ardent, Stellar, IBM, NeXT, Silicon Graphics, Sony NEWS,
and SUN-3, SUN-4, and SUN386i systems. Wolfram announced that by the
end of the year versions would also be available for MS-DOS and OS/2.
Wolfram Research Inc., which Wolfram founded with seven other
mathematicians and scientists to develop MATHEMATICA, is a funny kind
of organization. They develop the software but don't want to get their
hands dirty with distribution and support, so they send the code to
the companies that license it, and it is their responsibility to
package and ship it.

Attached below is an article about MATHEMATICA from the "San Francisco
Chronicle", a reproduction of the MATHEMATICA data sheet, and the full
SUN announcement of pricing and availability of MATHEMATICA on SUN
systems.

Oh yes, the answer to the riddle: Neither the VAX on your desktop nor
the Casio Data Bank calculator-watch on my wrist supports MATHEMATICA.

------------------------------------------------------------------------------

From the "San Francisco Chronicle"

MATH SOFTWARE WINS MAJOR ENDORSEMENT

                             By Don Clark
                        Chronicle Staff Writer


Some of the biggest names in computing yesterday endorsed new software 
they say could revolutionize mathematics and engineering.

IBM, Apple Computer and Sun Microsystems were among the companies that 
hailed Mathematica, which was developed by 28-year-old scientist, 
Stephen Wolfram.  Apple co-founder Steve Jobs even said he would give 
the program away with the forthcoming machines from his company, Next 
Inc.

"I think it's going to be surprising to all of us how widely this tool 
is going to be used in the next few years," Jobs said at a press 
conference in Santa Clara.  Mathematica in some ways is like a 
calculator that can automate more advanced fields of mathematics like 
algebra, trigonometry and calculus.  Ask it to factor a particular 
equation, for example, and the program produces line after line of 
letters and numbers in perfect mathematical notation.

But the program's functions go much further.  For one thing, it can 
simultaneously produce two-dimensional or three-dimensional graphs and 
simulations that illustrate particular problems or equations.

Moreover, Wolfram and his company have produced a kind of language 
that can be customized and used to make more specialized applications 
programs for specific industries or tasks.  For example, high school 
and college professors already are using it to develop interactive 
textbooks for teaching mathematical concepts.

Steve Christensen, a research scientist at the National Center for 
Supercomputing Applications, said the program allowed him to reproduce 
in just a few hours complex physics equations that had taken him 
several months to develop.  Researchers can also use Mathematica to 
quickly check their computations and make computerized notebooks of 
their own work.

"This idea of notebooks is going to be a very important means of 
communication to others and to yourself," said Dana Scott, a professor 
of computer science at Carnegie Mellon University.

Wolfram's company, Wolfram Research Inc. of Champaign IL will sell an 
initial version of the Mathematica software for Apple's Macintosh 
computers.  The Macintosh SE version costs $495; a version for the 
more powerful Macintosh II is $795.

IBM said it would offer the program on its IBM AIX/RT workstation, 
while Sausalito-based Autodesk Inc. said it would help develop a 
version for IBM-compatible personal computers.

Other versions are expected to be available on Sun and Silicon 
Graphics workstations, and desktop supercomputer from Ardent Computer 
and Stellar Computer.

Wolfram, born in London and educated at Eton, Oxford and Caltech, is 
widely described as a genius in several disciplines.  His research 
specialties have included high-energy physics, cosmology, cryptography 
and fluid dynamics.

He worked with seven other scientists and mathematicians to develop 
the product.  A book he authored on the technology is being published 
by Addison-Wesley Publishing Co.

"There are really no other programs that have the coverage that 
Mathematica has," Wolfram said.  "It covers the whole spectrum - 
numerical computation, algebraic computation, graphics and the ability 
to program."
-----------------------------------------------------------------------------

From the MATHEMATICA data sheet:

FACTS ABOUT MATHEMATICA:


                               GENERAL

PURPOSE:
Numerical, symbolic, and graphical computation; symbolic programming
language.

VERSIONS (as of July 1988):
Apple Macintosh and Macintosh II; Ardent Titan; IBM RT PC, NeXT; Silicon
Graphics Iris 4D; Stellar GS-100; Sun3, 4 and 386i.

MACHINE DEPENDENCE:
Operation of kernel is independent of machine (except for commands
requiring multitasking); front ends are built for specific machines.

MODE OF OPERATION:
Interpreter (transformation rules are complied into internal form).  Open
architecture for connection to external programs.

SIZE OF PROGRAM:
1.5 - 3 megabytes of compiled code, depending on computer system
(150,000 lines of extended C source code).

MEMORY REQUIREMENTS:
At least 1 megabyte of working space; total memory needed depends on
memory management used by operating system.  (On Macintosh requires at
least 2 MB.)



                        NUMERICAL COMPUTATION

NUMBER TYPES:
Exact integers (arbitrary length), rationals, floating point (arbitrary
precision), complex.

MATHMATICAL FUNCTIONS: 
Elementary transcendental, orthogonal polynomials (Legendre,
Gegenbauer, Chebyshev, Hermite, Laguerre, Jocobi), gamma, beta,
polygamma, Riemann zeta, polylogarithm, Lerch, exponential integral,
logarithmic integral, error, Bessel, Airy, Legendre, confluent
hypergeometric, (2)F(1) hypergeometric, elliptic integrals, Jacobi and
Weierstrass functions. All functions evaluated to arbitrary precision
for any complex parameters where they are defined.

INTEGER FUNCTIONS:
Modulus, gcd, lcm, factors, divisors, nth prime, totient, Mobius, divisor
function, Jacobi symbol, lattice reduction, factorial, multinomial
coefficient, Bernoulli, Euler, Stirling numbers, partition.

NUMERICAL MATRIX OPERATIONS:
Inverse, determinant, null space, eigenvalues, eigenvectors, singular value
decomposition, pseudoinverse.

DATA ANALYSIS:
Generalized least-squares fit, Fourier transform.

NUMERICAL OPERATIONS ON FUNCTIONS:
Integration, summation, product, root finding, minimization.



                         SYMBOLIC COMPUTATION


POLYNOMIAL OPERATIONS:
Expansion, factoring, gcd, resultant, decomposition.  Operations can also
be performed modulo a prime.

RATIONAL FUNCTION OPERATIONS:
Common denominator, partial fractions.

CALCULUS:
Partial and total differentiation, integration (Risch-based method plus
pattern matching), power series, limits.

EQUATION SOLVING:
Analytic solutions to linear and polynomial equations and systems of
equations, when possible (Grobner basis reduction method).

SYMBOLIC MATRIX OPERATIONS:
Inverse, determinant, null space, eigenvalues, eigenvectors.

TENSOR OPERATIONS:
Generalized inner product, generalized outer product, generalized
transpose.

LIST OPERATIONS:
Subsequence extraction, removal and replacement, union, intersection,
complement, sort, flatten, partition, permutations.  Mathematical
functions can be used on lists.

                               GRAPHICS


TYPES OF GRAPHICS:
Two-dimensional, contour, density, three-dimensional.  Black-and-white
and color.

GRAPHICS REPRESENTATIONS:
Symbolic form, PostScript page description language.  (Front ends for
many versions of Mathematica include PostScript interpreters.) 
Mathematica for the Macintosh supports encapsulated color PostScript.

FUNCTION PLOTTING:
Adaptive evaluation point algorithm, default scaling to find "region of
tnterest", options for curve color and style, axes.  Single functions,
multiple functions, parametric curves.

THREE-DIMENTIONAL GRAPHICS:
Resolution independent, full hidden surface removal, including
intersecting surfaces.

SURFACE RENDERING:
Wire frame or shaded (simulated illumination or user specified).

GRAPHICS PRIMITIVES:
Two dimensions: point, line, rectangle, polygon, cell array, text, gray
level, color, point size, line thickness, line dashing.  Three dimensions:
point, line, polygon, gray level, color, point size, line thickness, polygon
back face and edge renderings.

                           BASIC STRUCTURE


FUNDAMENTAL DATA TYPE:
Tree-structured expressions.  Leaves are symbols, numbers, strings, or
special raw data.

FUNDAMENTAL OPERATION:
Evaluation using built-in code or user-defined transformation rules and
programs.

EVALUATION STRATEGY:
Infinite level, depth-first with one-level lookahead.

ASSIGNMENTS:
Immediate and delayed, for symbols or arbitrary expressions, including
patterns.  Rules attached to arbitrary symbols.

PATTERN OBJECTS:
Arbitrary expressions, arbitrary sequences of expressions, expressions
with specific heads, arbitrary repetitions of patterns.

PATTERN MATCHING:
Syntactic, allowing for associativity, commutativity and optional
arguments,  (Algebraic pattern matching is also supported).

FUNCTION REPRESENTATION:
Transformation rules for patterns.  Pure functions are supported. 

SCOPING MECHANISMS:
Dynamic scoping for values, static scoping for names.  Package mechanism
with private and exportable names.  Aliases supported.

PROCEDURAL PROGRAMMING structures:
Blocks; do, while, and for loops; functional fixed point, conditionals,
switch, goto, non-local return, error condition handling.

STRUCTURAL OPERATIONS:
Function application to specified levels or parts in expressions; nested
and accumulated function application; expression part extraction and
replacement; operator transformations.

                          EXTERNAL INTERFACE


OUTPUT FORMS:
Mathematical, Mathematica input, C input, Fortran input, TEX input, outline,
tabular.

EXPRESSION OUTPUT:
Two-dimensional mathematical form with linebreaking.  Fully user
extensible.

CHARACTER STRINGS:
ASCII international character set.  Regular expression matching.

DATA INPUT:
From files, programs, or interactively.  Expressions, strings and numbers
(in Mathematica or Fortran format).

FILES OUTPUT:
Expressions, definitions.  Supports splicing at specific points in external
files.

EXTERNAL PROGRAM COMMUNICATION (multitasking operating systems only):
Pipes treated indistinguishably from files.  Data exchanged through
standard input-output channels, or through calls to specific functions in
external programs.

FRONT END COMMUNICATION:
Based on packet exchange through bidirectional pipes.  Compression and
error correction supported.


                         MACINTOSH FRONT END


BASIC OBJECTS:
Hierarchically-structured notebooks, supporting mixture of text,
Mathematica input, and graphics (PostScript, Bitmap, or PICT).

TEXT:
Multi-font, multi-color editing, with style sheets; search and replace by
content or keywords.

GRAPHICAL INPUT:
Converts PICTs from other programs into encapsulated PostScript. 
Graphical coordinate selection in all types of graphics.

GRAPHICAL OUTPUT:
PostScript-based, output in black-and-white or color to screen and
printers.  Sequences can be animated.  Can be transferred to other
programs in bitmap, PICT or encapsulated PostScript form.  Can be printed
at arbitrary size in poster mode.

HELP:
Context sensitive, available for menu items, dialog boxes, Mathematica
names, and objects on screen.


------------------------------------------------------------------------------
SUN Prodcut Announcement:


Date: Tue, 8 Nov 88 11:35:58 PST
From: warner%sunncal@sun.com (Eric Warner--Palo Alto Sales Office)
Message-Id: <8811081935.AA13590@sunncal.sun.com>
To: sun-news@jessica.stanford.edu
Subject: Mathamatica on sun's
 
*********There is also a new equation editor from Arbor Text!***********
 
 
			    07-October-88
 
			SunMathematica LIVES!!!
 
 
The Product:
 
SunMathematica is the SUN version of Mathematica from Wolfram Research,
Inc.  It is a software tool for anyone who uses mathematics in their
work.  SunMathematica can perform numerical computations to any degree
of precision, solve problems in algebra and calculus, and incorporates
a powerful symbolic programming language.  This product also produces
KILLER GRAPHICS!  Just wait until you see the THREE DIMENSIONAL COLOR PLOTS
both in SunView and in NeWS!
 
Some Facts:
 
	~ SunMathematica runs on ALL three SUN PRODUCT LINES!
             Sun-3, Sun-4, and yes, Sun-386i!!!
 
	~ SunMathematica runs in SunView, NeWS, and X11!
	  (Note: X11 is not a currently supported Sun product.)
 
	~ SunMathematica will be supported via your favorite 1-800-USA-4SUN
	     telephone support group!
 
	~ SunMathematica has a super, easy-to-use install script!
 
	~ All three versions of SunMathematica are distributed on
	    the SAME TAPE!
 
	~ SunMathematica runs on BOTH OS 3.5 and OS 4.0!
 
	~ A copy of the book MATHEMATICA by Stephen Wolfram will
	    be sent with EVERY LICENSE!  (a $29.95 value)
 
 
The Schedule:
 
	BETA Test Period:   Oct 21 thru Dec 2
 
	PILOT Release:	    Oct 27
 
	Major Announcement:  SunMathematica will be formally announced
			     at the EDUCOM show in Washington DC, the
			     week of October 23rd.
 
	FCS Release:        Dec 30
 
 
The Prices:
 
	Qty	Commercial License	Educational License
 
	 1	    $   1,800		    $     995
 
	10	    $   9,990		    $   6,240
 
	25	    $  22,500		    $  14,500
 
	50	    $  40,000		    $  25,000
 
       100	    $  69,500		    $  43,400
 
       250	    $ 149,000		    $  93,000
 
       500	    $ 249,000		    $ 155,600
 
 
 
Order Information:
 
	Pilot 1/4" : MAT-1.1-34-34R-5-P
	FCS   1/4" : MAT-1.1-34-34R-5
 
   Note: The 1/4" release kits will contain all three versions of the
	 the software; Sun-3, Sun-4, and Sun-386i.
 
	 Also, if ordering Pilot, be sure to list both numbers on your
	 sales order to ensure automatic upgrade when FCS is available.
 
 
The Caveats:
 
	~ Sun-386i floppies will not be available for the Pilot release.
 
	~ SunMathematica is 'node locked', you will need to call in with
	  the name and hostid number of each machine you wish to run on.
	  The Sun 800 number will direct your call to someone who can
	  provide the password code over the phone.
 
 
 
			     -------END------