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Free math programs

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I'm learning how to use MatLab & Maple. But I wonder if there is a really good, free alternative to these programs.

 

What do you think of SciLab & GNU Octave (vs. MatLab) ?

 

...or Maxima (vs. Maple or Mathematica) ?

I use Mathematica, but that is not free.

 

There are free programs out there. What is best will probably depend on what you want to do. GAP is good for group theory for example.

 

There is a list here.

 

 

I have not used any of them other than Mathematica.

One of my friends loves Maxima, I've never used it that much.

 

I quite like octave as a matlab replacement, but I don't do that much with matrices atm so don't use it much...

 

For everyday statistical analysis, graph plotting, fitting (minimising) etc... I use GNU R, and think EVERYONE should because IT RULES!

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I'm mostly working with ODEs, PDEs and dynamical systems.

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