Because of MATLAB‘s sheer popularity, most open source tools mimic MathWorks’s proprietary language. Octave, which started as a teaching tool in a similar vein as MATLAB, is probably the most widely used. Its language is very compatible with MATLAB and the command-line front end can be customized to mimic MATLAB’s editing window.
Likewise, Scilab is another open source tool, though the language—while perhaps “inspired”—is different from MATLAB’s. However, Scilab does include Scicos, which is used for simulation and modeling. Scicos is unfortunately incompatible with Simulink.
As for statistics, many users prefer a dedicated package like S-PLUS to MATLAB’s matrix-oriented computation. S-PLUS itself is a commercial implementation of the S language. Similar to S is the R language and its open-source implementation.
In terms of symbolic computation like Maple and Mathematica, there are Axiom and Maxima. These packages are useful for solving integrals and the sort.
Thus there are numerous open-source, as well as commercial, packages available for technical computing. As is usually the case, the open-source programs tend to be slower and have fewer features, whereas the commercial applications tend to be fairly expensive.
