MATLAB (MATrix LABoratory) a numerical computing environment and fourth-generation computing language. MATLAB allows signal processing and communication, image and video processing, control systems, test and measurement, computational finance, and computational biology.
Mathematica is a mathematics software program used to help with science, math, and engineering fields. It can be used for industrial work, or for educational purposes. It allows integration of computation to many different types of fields and work flows.
GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command-line interface (CLI) for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB.