I'd like to know the equivalents of Mathematica and MATLAB on Ubuntu, since both are costly.
Octave provides a lot of the functionality of Matlab, and can run some Matlab programs. Sage is the open source "equivalent" of Mathematica. 


I use QT Octave as GNU Octave does not have a nice GUI. Though most of the commands work out pretty well, some functions may not work as expected in MATLAB 


You can also give R a try. It is an opensource, free, programming environment. It has both powerful visualization capabilities, power numerical libraries, and everything you would expect from a functional programming language (well, except a compiler). 


Reduce, Maxima, Sage, Axiom (in three variations), and others, all are free and will provide you computer algebra on Linux. 


I would suggest python with appropriate libraries as a good option. It is not quite a replacement, since the python language is not as specialised for mathematics as matlab/mathematica syntax, but it combines a relatively good syntax for interactive mathematics with a fullycapable programming language. You will want to install the packages:



Freemat is a good alternative. It can handle most of the Matlab mscripts. 


Both Mathematica and Matlab are very bloated as they try to do too much and be sort of a silver bullet. As I said, they try. Most open source libraries and tools however, focus on a particular problem or domain area and do it the best and fastest way, while making sure that they import and export to appropriate formats so you can work with several different tools and pass your data from one to another. You will likely receive much more useful response to your question by specifying the specific domain you want to work in, or the specific type of tools you need as opposed to trying to find a clone of something like Matlab, which I wouldn't use even if it was free. 


I would suggest installing Cantor , which supports four different environments (Maxima, R, SAGE and KAlgebra). It has a very simple interface and it is easy to use. 

