Best Numerical Analysis Software for Physics

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Two criteria

1. Freely Available
2. Large support for additional scientific libraries/packages/modules for reuse

http://en.wikipedia.org/wiki/Comparison_of_numerical_analysis_software

Which one would you recommend and why?

 

[SteamKing]

'Numerical analysis software' is a vague term.

What do you want to do with the software?

Are you looking for symbolic math?
Do you want to generate an harmonic analysis?
Are you interested in a statistics package to help analyze experimental data?
Do you need a tool to plot data?

Depending on your ultimate goal, there may be several packages which fit your requirements.

 

[gsal]

hhhmmm...at one time or another, a few years ago, I visited some of the webpages for the software listed in the link...at the end, I simply chose Python (numpy, scipy, matplotlib, pyQt, etc).

As a non-user of the software, a brief homepage visit and maybe a trial usage, I have the following speculative opinions...

Sage is huge, a beast, a conglomerate of many other programs (dozens) unified under a common python interface; needless to say, one would need to really know how to use those other individual programs in order to use them through Sage.

Scilab and Freemat are a-la-matlab kind of programs. Scilab seems rather popular with literature, conferences, etc.

Euler seems for mathematicians, fancy plots, reminds me of Mathematica.

Julia is picking up good, seems designed for good performance, very friendly language but I am not sure what kind of shape is in regards to libraries...I would like Julia to be my programming language of the future...we shall see...keeping an eye on it.

...for now, I am sticking with Python...many libraries not only for data analysis but also for plotting, and even for quick application prototyping, I am talking enabling some of us non-programmer engineers/scientists fairly easily and quickly build basic GUI-based applications (pyqwt, enthought, pyQt, pySide). Besides, once you learn Python, you will also be able to script many other applications that have chosen Python as their scripting language.

Anyway, that's just my non-educated opinion, no need to sue me.

Lastly, do you know anybody in the field that you are looking to get into? Have you asked anyone there what they use?

 

[FactChecker]

You might look into R or Perl Data language (PDL). R is mostly for statistics, but there are add-ins and it is gaining popularity in the research community.
PDL: http://en.wikipedia.org/wiki/Perl_Data_Language
R: http://en.wikipedia.org/wiki/R_(programming_language)
A comparison of languages: http://en.wikipedia.org/wiki/Comparison_of_numerical_analysis_software

 

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Numerical Analysis of

- Einstein Field Equations
- Schrödinger Equations

As a starter and graphs of solutions