Re: Mathematica Vs. Matlab

From: Andrey Grozin (grozin_at_lxplus021.cern.ch)
Date: 08/17/04 

Date: 17 Aug 2004 05:43:02 +0200

I completely agree with prof. Fateman: you are trying to compare programs
wich have so little in common that any comparison is practically meaningless.

1. Computer Algebra Systems (CASs) are programs which operate with formulas.
Mathematica is a powerful CAS (though quite expensive). Other CASs are, e.g.,
Maple, REDUCE, MuPAD (it can be legally obtained for free at some circumstances,
but it is not free software). There are also quite powerful free CASs: Maxima
and Axiom. In all of these systems, it is possible to do some numerical
calculations (e.g., to evaluate the formula you have derived at some numerical
values of all parameters). But it is a very bad idea to do large-scale numerical
work in such systems: performance will suffer. In some special cases (e.g.,
numerical calculations with very high precision, impossible at the double-
precision level), you can use Mathematica to do what you need, but there are
other, faster ways to do such things.

2. There are a number of programs to do numerical calculations with usual
double-precision numbers. One example is Matlab; there are similar free programs,
e.g., Octave, Scilab, R, ... Matlab is very good and fast in doing numerical
linear algebra: if you want to solve a system of 100 linear equations whose
coefficients are all numbers, use Matlab; if coefficients contain letters
(symbolic quantities) and you want the solution as formulas, use Mathematica
or some other CAS. Matlab can do a limited amount of formula manipulations
using its "symbolic toolkit", which is an interface to a cut-down Maple. It's a
pain to use this interface: if you want Maple, just use Maple (it's an excellent
CAS).

To summarize:
1. If you want to work with formulas, use Mathematica or some other CAS;
2. If you want to do calculations with double-precision floating numbers
   fast, use Matlab or some similar program;
3. If you don't know what you want, don't post here.

Andrey Grozin,
leading researcher, Budker Institute of Nuclear Physics

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