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Re: V9 !!!

There are two answers to this. One is for Mathematica to have greater
"hierarchical density" or "hierarchical depth", i.e., provide lower level
routines from which higher level routines are built. Then students might
work at the lower levels and "applied production mathematicians" might work
at the top levels. But Mathematica does not do a lot of this, which might be
considered one of its weaknesses. It is too "top-level" oriented. However,
it does provide basic routines from which one can implement lower level

So the second answer is to provide third party applications that expand the
"hierarchical density" for specific mathematical or technical fields. WRI
could not reasonable do this for all technical fields. Do you want a million
commands in Mathematica? And WRI people might not even be the best people to
do this - they can't be elegant experts in everything. Teachers might want
really good additions for teaching undergraduate math, and a graduate
student or researcher might want an extensive application for a specific
area. But neither of them would want every possible application.

That is why those who say that Mathematica users should never buy a third
party application are absolutely wrong. Documented Mathematica applications
for communication and collaboration are one of its most powerful features -
still much underused and only fitfully supported by WRI itself.

David Park
djmpark at 

From: Murray Eisenberg [mailto:murray at] 

However, I've always had mixed feelings as Mathematica has grown to build in
more and more mathematical functions. At times this has taken the edge off
what was a valuable exercise for my undergraduate students: defining more
complicated functions -- e.g., div in vector analysis or nullSpace in linear
algebra -- that forced students to understand the precise underlying
definitions and algorithms. And it tended to take away a sense of power and
accomplishment when students could start by defining the simplest kind of
function, such as performing a single elementary row operation, and
step-by-step building ever more complicated functions, culminating in
something relatively sophisticated, such as finding the orthogonal
projection of a vector upon the span of a given set of vectors, and even
going further, such as using the latter to find the least-squares solution
to an overdetermined linear system.

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