Scilab vs Mathlab vs Mathematica ?

[ker2x]

Hi !

I'm willing to experiment mathematic software for : fractal, image processing, simulation, and ... "that kind of stuff".

I tried Scilab (free software !) but i just "don't get it". i was never able to do something interesting with it.
Matlab ... couldn't tried it and very expensive.
Mathematica ... look much more user friendly, and there is a "cheap" (~295€) for "personnal use" complete version (home edition).

Overall, Wolfram (mathematica) provide a lot of information, tools, tutorials, ... and look like the "best" to me (because of the documentation and interface).
And it look like the "best" to continue to learn more and more and more mathematic, by providing the right tool.

Any user of one of the software (or all?) could share their experiences please ?

I love math, but i lack a lot of knowledge (i stopped school too early ... *sigh*), of course i know complex numbers (fractal is full of it), trigonometry, some linear algebra, differential equation (not so much), ... and i keep learning math by following courses at http://www.khanacademy.org/ (free and awesome!) but i'm tired of mixing both math and programming (fortran, java, c, ...) and i'd like to focus on math while still being able to generate and/or process image, or (simple) fluid dynamic simulation.

I'm afraid to do a mistake by buying a software (or spending a lot of time to understand the very unfriendly scilab) for nothing.

Well ... mmm ... help ? 

[ker2x]

I'm sorry for being so confused.

I try again again with some simple questions (it's a good start, huh ?) :
- I want to focus on math (not programming) and make (fantastic) fractal (and optionally compute the life, universe, ... and everything!).
- Is it a good idea to buy Mathematica home edition for 295€ ?
- Should i save 295€ and try (again) scilab ?
- what about mathlab ?

thank you 

[ker2x]

I'm exploring http://demonstrations.wolfram.com/ ... is there something that this software can't do ? 

[hobold]

I only ever used Maple, not the other computer algebra packages you mentioned. This kind of software can be very powerful, but it does not turn everyone into a mathematician. The software can and will do the tedious job of manipulating formulas, meticulously, fast, and with far fewer errors than almost any human. But the computer never knows the _meaning_ of those formulas. That is the task of the human user of the software. It's not the machine that gains enlightening insights, it's the person in front of it.

I am not trying to tell you that you suck. I am trying to prepare you for a bit of disappointment ... unless you are very serious and use the computer algebra tool as a means for learning. Computer algebra systems are not a shortcut to mathematical knowledge, but they can be great tools for exploration. Mathematics is much more tangible these days than ever before in history.

[ker2x]

I only ever used Maple, not the other computer algebra packages you mentioned. This kind of software can be very powerful, but it does not turn everyone into a mathematician. The software can and will do the tedious job of manipulating formulas, meticulously, fast, and with far fewer errors than almost any human. But the computer never knows the _meaning_ of those formulas. That is the task of the human user of the software. It's not the machine that gains enlightening insights, it's the person in front of it.

I am not trying to tell you that you suck. I am trying to prepare you for a bit of disappointment ... unless you are very serious and use the computer algebra tool as a means for learning. Computer algebra systems are not a shortcut to mathematical knowledge, but they can be great tools for exploration. Mathematics is much more tangible these days than ever before in history.

Thank you for your reply.
I'm testing the Trial of Mathematica 7. Just reading some basic tutorials.  I like it.

I want to use it as a "tool" that help to understand, not as a teaching book.
A good exemple is :
i own the NonLinear workbook ( http://www.amazon.com/Nonlinear-Workbook-Fractals-Algorithms-Expression/dp/9812818537/ref=sr_1_3?ie=UTF8&s=books&qid=1276697352&sr=1-3 ) which is awesome.
I try to understand what they say (usually, i don't understand), i read some reference and documentation to understand the concept they use in the this book. Once i understood enough of the required concept to understand a chapter, i go back to the book, and read again.

Then, i want to experiment.
Writing a program you barely understand is very difficult. programming often require that you master (or really understand) the concept you use.
I don't want to focus on "how can i implement this problem in <choose a langage>", i want to know "what can i do with this math concept" and "what happen if i change this or that".

Focus on mathematic, not programming. that's it.

[ker2x]

I'm still not sure if it is easier than programming in Fortran ...

My monte carlo method to evaluate (and display) Pi

Code:

sampleSize = 100.;
data = RandomReal[{-1, 1}, {sampleSize, 2}];
result = {};
For[ i = 1, i < Length[data], i++, 
   AppendTo[result, 
   4. * Count[data [[;; i]], {x_, y_} /; x^2 + y^2 < 1] / i ]
  ];

Show[ListPlot[result, Joined -> True], 
 Plot[\[Pi], {x, 0, sampleSize}], 
 PlotRange -> {{0, sampleSize}, {2, 4}}]

[ker2x]

Ha, this screenshot is easier to understand

[ker2x]

Just found "Maxima" (  http://maxima.sourceforge.net/ ) which is a free opensource alternative to Mathematica. (if i understood correctly, it's not a "clone" as the original Maxima (Macsyma)  is older (1960) than Mathematica)

A big difference between scilab and Mathematica (and Maximan, Maple, ...) is that :
- Scilab : Numerical software
- Maxima, mathematica, Maple, ...  : Symbolic software

[hobold]

Numerical software focuses on manipulating datasets of concrete numbers. Usually it comes with a library of ready-made methods to compute specific results. If all goes well, you don't have to worry much about the finite precision or the finite processing speed of the available computing machinery. I.e. the software package "knows" how to do stuff accurately and quickly even when the input is millions or billions of numbers.

Computer algebra systems focus on manipulating abstract mathematical formulas that do not necessarily contain concrete numbers. In fact, they can manipulate formulas that don't contain numbers at all, but merely number-like entities.

I guess one could say that numerical software is for people who know what problems they want to solve, while computer algebra systems is for people who don't know yet what problems they are looking for.


Programming in FORTRAN would be numerical computation without the library of ready-made methods, and without a consistent user interface. Programming your own computer algebra system would be like ... madness. :-)