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Re: Should I get Matlab or Mathematica or ?

In <4c2k9b$8gh at>, doug at (Doug Wellington) writes:
>I am in the market for a math program to do some simulations with.
>I want a general purpose tool that will let me do algebra and
>calculus as well as working with signal processing.  I also have
>interests in fuzzy logic and neural nets, chaos, fractals, etc...
>I have seen a nice package called "Calculus and Mathematica" that
>makes me think Mathematica is a nice expandable program, but then
>I have seem some DSP work that is done with Matlab.  ...[snip]...

I went through this decision as well.  One of my primary uses was to
simulate various pulse detection and equalization schemes - primarily
a numerical task.  I also wanted symbolic capability, however, since I
need to work out the mathematics of these systems before I can simulate
them (transfer functions, etc.).  I asked people who had used each program
and the bottom line seemed to be that those who had chosen Matlab had
done so because it is supposedly faster for numerical calculations,
particularly those involving matrices and vectors.  Those who had
chosen Mathematica had done so because of its intrinsic symbolic nature
and other features such as superior graphing capabilities and expandability
to a wide range of problems, as well as being less costly than Matlab.

I have found the speed issue to be partially true.  If you begin
programming in Mathematica as you would in C or FORTRAN, you will end
up with slow programs.  This is because Mathematica is intrinsically
symbolic in nature and internally breaks down most operations into 
function calls who's evaluations involve alot of overhead.  You can
write efficient programs in Mathematica, however, by minimizing
function calls (including hidden ones like array subscripting), using 
compiled functions where applicable, and making as much use as
possible of the vast array of built-in functions.  Built-in functions
(such as dot product, for example) usually operate many times faster
than the same function coded explicitly.  There are many other things
as well that can be used to improve program efficiency.  It still may
not be quite as fast as Matlab (or even MathCad) for numerical work, but
it is not nearly as bad as one would expect just looking on the surface.
The catch is that it requires a paradigm shift.  I have speeded up
some of my earlier Mathematica programs by as much as 10x by careful
re-coding using techniques I gained after playing with it for a while.

David Rosky
(groskyd at


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