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RE: Re: Useful Dumb User Questi
 To: mathgroup at smc.vnet.net
 Subject: [mg9069] RE: [mg9027] Re: Useful Dumb User Questi
 From: Ersek_Ted%PAX1A at mr.nawcad.navy.mil
 Date: Thu, 9 Oct 1997 01:42:48 0400
 Sender: ownerwrimathgroup at wolfram.com
I appreciate that sort of discussion. I would be possible to write a
front end with a nice interface (graphical, whatever you want)
which however restricts the input to simple expressions. That is,
only input would be accepted with intuitive meaning such that a
beginning user could solve his/her problems.
I understand WRI will soon release a "Teacher's Edition"
intended for the preuniversity instructor. This version might be something
like what you are talking about. For one thing it will probably assume a
variables have no complex part (as apposed to what ver. 3.0 assumes).

However, I consider another problem more dangerous for the evolution
of the Mathematica dinosaur: It fails to be reliable. I am horrified
by the bugs in version 3.0 some of which have been reported in this
newsgroup in the last months. Suppose your work requires the evaluation
of finite integrals, and Mathematica comes up with obviously wrong
answers?

It is just not practical to expect a large piece of application software to
be flawless.
In some areas it would take centuries to test all necessary cases.
There may even be areas where the number of cases is infinite.
Remember when the AT&T phone system crashed a few years ago because of a
software bug.
Even microprocessors have bugs. Recall the famous FDIV bug in the Pentium.
You can be sure that no recent microprocessors have been tested 100%.
It just isn't practical.
If you are doing very important work, you have to verify your results by an
independent method.
Would you rather use tables to do your integrals?
Don't count on GradshteynRyzhik to help you, because it also has mistakes.
Maybe your integration skills are good enough to do them all by hand.
If you throw away your computer and do it all by hand you won't do much
better.
Even the best mathematicians make mistakes.
Recall the flaw in A. Wiley's Proof of Fermat's Last Theorem.

I have come to the conclusion that I can only use Mathematica safely
with the well defined elementary functions like Differentiate, Together,
Cancel,
Apart  all the stuff I could easily program by myself if I had the time.

Ideally, one would like a formal proof of Mathematica's claims.
This being too much (really ? I don't know.), it would be nice
to be able to get some sort of information what the more complex
functions of Mathematica were doing in a special situation.
I don't think you want to see how Mma solves an integral. It uses a very
complex and advanced Risch algorithm. I understand the algorithm takes a
very convoluted path to solve integrals
a college freshman could do. I herd it does it this way because the same
algorithm can be used to solve a great variety of integrals.
I understand a lot of symbolic calculations in Mma are done with methods
that are very advanced and far from intuitive. I sure don't want to see how
it got an answer.

I know that I am asking in fact for a more complicated system,
one which would be even more difficult to understand and to program.

Another issue is efficiency. Recent posts indicate that in some cases
Mathematica 3.0 is slower than 2.2.
So you want the program to be more complicated, and also more efficient.
That can only be done if the present algorithms are poorly written. WRI
has a lot of bright people writting these programs, and I doubt the
algorithms are poorly written.
 In Mathematica, there are many ways to solve a problem, and it is not
obvious to the
user why one way should be more efficient than the other.
Mma is a very flexible system. The learning curve can be overcome with some
effort. However, one of the great things about Mma is that a brand new user
can solve a lot of hard math problems with very little learning curve. As
the user gets more familiar with Mma they can do more problems.
Ted Ersek
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