| Believe it or not I found an answer to my own question. This is a
lengthy article by very informative. I pulled it from a PC MAGAZINE
article off of "Computer Select" CD-ROM. Hope you folks find this as
helpful as I did. By the way, based on this information I bought
MathCAD. Please feel free to offer feedback about this article.
Joel McKenzie
DTN: 522-2725
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***** Computer Select (Standalone), May 1992 : Doc #13317 *****
Journal: PC Week Feb 17 1992 v9 n7 p81(2)
* Full Text COPYRIGHT Ziff-Davis Publishing Co. 1992.
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Title: Math packages take distinctive approaches: Mathcad 3.0 is more
compact, stable; Mathematica 2.0 has edge in 3-D graphics. (from
MathSoft Inc. amd Wolfram Research Inc., respectively) (Software
Review) (includes related article on testing methodology)
(Evaluation)
Author: Coffee, Peter C.
Abstract: Two Windows-compatible mathematical packages are evaluated and
compared. The products are: Mathcad 3.0, $495, from MathSoft Inc,
Cambridge, MA; and Mathematica 2.0, $995, from Wolfram Research
Inc, Champaign, IL. Mathcad requires MS-DOS and Windows 3.0, and
at least, an 80286-based microcomputer with 2Mbytes of system
memory and 7.2Mbytes of disk memory. Four megabytes of RAM are
recommended. Mathematica needs DOS 3.0 and Windows 3.0 on an
80386SX-based machine with 4Mbytes of RAM and 13Mbytes of disk
space. Six megabytes of RAM and a 16Mbyte swap space on disk are
recommended. Mathematica is recommended as a state-of-the-art
program suited to advanced needs. Mathcad, though less expensive,
is capable of high performance. It is especially recommended for
its ease of use and modest hardware requirements.
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Descriptors..
Company: MathSoft Inc. (Products)
Wolfram Research Inc. (Products).
Product: MathCAD 3.0 (Mathematical software) (evaluation)
Mathematica 2.0 (Mathematical software) (evaluation).
Topic: Mathematical software
Evaluation.
Feature: illustration
table.
Record#: 11 927 125.
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Full Text:
By Peter C. Coffee
Veteran computing professionals will recall, with mixed pride and pain, those
early years when "computing" meant doing mathematics and "automatic
programming" meant using a FORTRAN compiler.
In recent months, mainstream PCs have come to offer a choice of far more
powerful tools for productive, interactive investigation and documentation of
the math that makes the world go 'round.
This review compares two leading-edge mathematical WYSIWYG products with
dramatically different interpretations of how to "do Windows," giving the lie
to those who charge that graphical user interface conventions restrict
creativity in user interface design.
In one corner, MathSoft Inc.'s Mathcad 3.0 is an attractive and functional
Windows-compatible upgrade of a near-WYSIWYG tool for DOS. In the other
corner, Wolfram Research Inc.'s Mathematica 2.0 for Windows finally offers PC
users the same graphical interface provided for this product on other
workstations, replacing a relatively crude interface under DOS and improving
both speed and stability.
Evaluating earlier versions of these products, PC Week Labs unequivocally
recommended Mathcad for those who sought numeric and graphical results from
actual data and Mathematica for those interested mainly in exploring symbolic
relationships -- such as solving equations in terms of variables, without the
limitation of specific examples using actual values. The choice is no longer
so simple.
Expanding beyond literal-minded number-crunching, Mathcad now incorporates
Maple, the symbolic-processing engine developed at Ontario's University of
Waterloo. Maple is not, however, completely integrated with the rest of
Mathcad.
For example, it remains unaware of variable and function definitions the user
has made using Mathcad's other facilities, and the gap between Mathcad and
Maple is sometimes apparent in the form of warning messages when unusual
results are returned.
More seriously, Mathcad's symbolic results (such as indefinite integrals)
lack the "hot-link" interaction that makes the rest of Mathcad such a
powerful and flexible extension of the spreadsheet metaphor.
Unlike numeric and graphical results, which update automatically, symbolic
results are not recomputed when they are revised. Symbolic operations take
place only when requested from the menu.
Mathcad's new Symbolic menu provides easy access to Maple functions, though,
and many users will find it a useful and satisfactory extension of Mathcad's
core capabilities.
Mathematica, meanwhile, offers far more flexibility than Mathcad in areas
such as visualization of mathematical functions through surface plots and
other three-dimensional graphics. Engineers and artists benefit from linking
Mathematica with "solid lithography" manufacturing systems to produce
prototypes of objects directly from their mathematical descriptions.
While Mathematica works directly with sequential and named list arguments,
defining each variable's range and giving the number of points to plot,
Mathcad's 3-D graphics are annoyingly restrictive. It can generate a surface
plot only from a matrix argument, sometimes forcing the user to remap
function arguments onto the domain of non-negative integers (the legal
subscripts for an array).
Once a 3-D plot was produced, PC Week Labs preferred the interactive
convenience of Mathcad's simple dialog-box settings for rotation, tilt and
vertical magnification in viewing the resulting surface from different
angles.
Mathematica more awkwardly invokes these and all other variations through a
verbose syntax of optional arguments to its enormous vocabulary of commands.
These two approaches demonstrate a basic difference between the evaluated
products.
PC Week Labs found that Mathcad makes it easier to "rough in" a result,
moving quickly from an early approximation to a polished final analysis.
Users benefit from the program's exceptionally interactive editing tools,
which can quickly zero in on the components of a mathematical expression,
revising or replacing terms and immediately demonstrating the results.
Mathematica is more like a programming language with built-in output
formatting. The program produces an extraordinary range of answers, but it
does less than Mathcad to help users discover the most useful questions to
ask. It is also much easier to make unnoticed input errors when formatting
in Mathematica's line-oriented FORTRAN style than it is with the cues
provided in Mathcad's textbook-style formatting of expressions as they are
entered.
Interpretation of output is easier in Mathcad, as well. The program makes
far better use of Windows' text-formatting and graphics capabilities to draw,
for example, proper radical signs and brackets around multiline and nested
expressions. Mathematica's algebraic output employs a BASIC-style notation
-- for example,"Sqrt[]" rather than a radical sign -- and a more awkward,
line-oriented output format that looks as if it is coming out of a teletype,
in jarring contrast to its beautifully shaded and labeled graphics.
Neither product demonstrated a performance edge during PC Week Labs' tests.
Each demonstrated its own strengths and weaknesses.
Mathematica proved to be roughly twice as fast as Mathcad in performing
first-time factorization of a 40-digit integer, but subsequent recalculations
in Mathcad showed negligible delay. Mathematica's executions, though
sometimes initially quicker, did not become any faster with repetition. (See
chart, below.)
PC Week Labs found that symbolic operations in Mathcad appeared to be cached,
minimizing the time required to revalidate results -- an important
consideration given the absence of the hot-link updates necessary to maintain
automatic consistency.
Mathcad performed roughly twice as fast as Mathematica in producing a simple
two-dimensional, trigonometric plot -- although the times were only 1 and 2.1
seconds, respectively, on a 33MHz 486-based Dell System 433E with 12M bytes
of RAM augmented by Windows' virtual memory.
It took more effort to set up the test plot in Mathcad, which requires formal
definition of variables, but Mathcad made it much easier than Mathematica to
experiment with the graph once it was produced. The horizontal and vertical
ranges of the plot, for example, could be adjusted by directly editing the
axis labels. Axis styles, such as logarithmic or linear and numbered or
unnumbered, were easily adjusted from within a complex but intuitively
designed dialog box.
In contrast, Mathematica's graphs are strictly output -- "formatted cells,"
in Mathematica parlance -- with no direct editing capabilities other than the
tricky and potentially destabilizing option of unformatting the cell, editing
the resulting on-screen display of PostScript code, then reinvoking the
PostScript interpreter to display the results. This is not for the
fainthearted, as the simple two-dimensional plot used in PC Week Labs' tests
involved more than 15 screens of cryptic PostScript commands.
Small graphs in Mathematica could be viewed quickly as raw PostScript code by
selecting the proper menu command. A 3-D plot on a 32-by-32-point grid,
however, appeared to be too much to describe: When PC Week Labs attempted on
two occasions to view the associated PostScript code, there was no activity
for more than 3 minutes, and the system appeared to hang up.
Although Mathcad drew the same 3-D plot more quickly, setting up the plot
required more effort and mathematical expertise to accommodate for the
program's matrix-argument restrictions.
In advanced symbolic operations, results were likewise mixed. Mathematica
took one-third the amount of time required by Mathcad to produce an
indefinite integral, but Mathcad took only one-sixth as long as Mathematica
to compute a sixth-order Taylor series for a transcendental product.
Mathematica's edge proved to be more pronounced in the symbolic solution of
high-order polynomials, with Mathcad taking 20 times as long to solve a
seventh-order polynomial -- and diverting part of its answer to the Windows
clipboard as a "special to Maple" result. A serious limitation was Mathcad's
inability to solve simultaneous equations in symbolic terms, which
Mathematica did with ease.
Offsetting this weakness, Mathcad's excellent editing tools made it
straightforward to perform the necessary partial solutions and substitutions
by hand.
Mathematica is by far the more resource-intensive product of the two
evaluated, requiring more than 11M bytes of RAM compared with less than 0.5M
bytes for Mathcad.
During PC Week Labs' tests, Mathematica refused to run on the 12M-byte test
machine unless Windows' disk-swapping feature was enabled. Mathematica also
crashed, taking Windows with it, when loaded along with other large
applications, even when its status bar indicated several megabytes of free
memory.
One of these episodes was such a shock to the system that a warm boot hung
before completion, leaving the power switch as the only option.
Mathematica's copy-protection mechanism was also unreliable on some machines,
forcing PC Week Labs to re-enter an 18-digit password each time the program
was started. By contrast, Mathcad was completely straightforward to install
and use. Unlike Mathematica, which required frequent reference to both
machine-specific manuals and a bulky, textbook-style language reference,
Mathcad's one user manual provided concise and easily located information on
all program functions.
Mathematica's superb PostScript integration and symbolic processing power
show the state of the art in computer-based tools for the most advanced
needs. Mathcad, however, demonstrates the advantage that comes from aiming
at greater ease of use and more modest hardware requirements while still
meeting nearly as high a standard of capabilities and performance.
Mathcad 3.0
MathSoft Inc.
Cambridge, Mass.
(800) 628-4223; (617) 577-1017
Privately held
Year established: 1985
Number of employees: 60
Net revenue (fiscal 1991): $6.2 million
Product line: software
Technical Support: (800) 624-4223 9 a.m. to 5:30 p.m. ET Monday through
Friday free, unlimited support Source: Information supplied by company
Mathematica 2.0
Wolfram Research Inc.
Champaign, Ill.
(800) 441-6284 (217) 398-0700
Privately held
Year established: 1987
Number of employees: 130
Net revenue: Not disclosed
Product line: software
Technical Support: (217) 398-6500 8:30 a.m. to 5 p.m. CT Monday through
Friday free, unlimited support CompuServe on-line forum Source: Information
supplied by company
PC Week Labs tested MathSoft Inc.'s Mathcad 3.0 and Wolfram Research Inc.'s
Mathematica 2.0 as the only active applications under Microsoft's Windows
3.0, running in 386 enhanced mode on a 33MHz 486-based Dell System 433E
equipped with 12M bytes of total RAM and a 10M-byte swap file.
Each product's user interface provides a document-style view of the user's
session, and each was used to build a document containing benchmark
calculations (see chart, Page 84).
In some cases, times given for Mathcad do not adequately reflect the
additional effort required to set up variables or to recast equations to
accommodate that product's more limited treatment of some types of
calculation. These differences are reflected in the Analyst's Scoreboard,
however. -- P.C.C.
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