symbolic computation program/software What is your recommended symbolic computation program/software for free and commercial respectively?
What are its strength and weakness? For example, efficiency, comprehensiveness, etc
Thanks!
 A: Both Mathematica and Maple are excellent. 
It seems they have added symbolic computation toolbox for scilab (which is free). Since you are linux user, you might want to explore it. I have never personally used it though (I have used scilab itself and it does a good job of being a lilliputian Matlab)
http://packages.ubuntu.com/lucid/scilab-scimax-doc
A: Another very popular free program for symbolic computations is PARI/GP. It is aimed somehow at computations in number theory, but its functionality is not only restricted to this. You can read a little bit about it also in the wikipedia article.
A: I suggest mathHandbook.com
mathHandbook - Online symbolic math software
www.mathHandbook.com 
It is an online symbolic math and computer algebra system.  It can perform exact, numeric, symbolic and graphic computation, e.g. any order of derivative, fractional calculus, solve equation, and user-defined functions, linear regression, symbolic differentation and integration, pattern-match. It is a programming language, in which you can define conditional, case, piecewise, recursive, multi-value functions and procedures, derivatives, integrals and rules. 
 It runs in any computer that supports Java. If you see it online, it can run offline in your computer. It is all of Java applet, Java application and Window application. Run MathHandbook.htm as Java applet, or run MathHandbook.bat as Java application.
A: I recommend sageMath, also Mathematica and Maple
An easy to use is Maxima
You can  to work with sage here: http://www.sagenb.org/, it is not necessary to install !!!
A: I have been using Mathematica since fall 2007. I absolutely love it. It has good palettes included that help you typeset your equations more easily. It also has nice display options for giving presentations. However, if you are just wanting to typeset a paper, LaTeX is probably your best bet. TeXmaker is a very good free mac OS software for LaTeX.
Maple is another very popular computational software; however, I have not used it.
A: I think http://www.hicalc.com is good. This is a smple http://www.hicalc.com/program/24
Hicalc is online platform to calculate expression quickly or create program with a simple, intuitive interface and share them with other people.
You can create program with almost all C# 4.0 syntax such as if, switch, while, for, foreach, etc., store and calculate your program anywhere at any time, share and Search Programs in public library. 
With Hicalc, you can customize any converter and share with other people
A: DataMelt (http://jwork.org/dmelt/) is free program for symbolic computation.
A: I am surprised no one mentioned the Symbolic Math Toolbox which comes with MATLAB.
