Mathematica is a computational software program used widely in scientific, engineering, and mathematical fields and other areas of technical computing.
MATLAB is a numerical computing environment and programming language. Maintained by The MathWorks, MATLAB allows easy matrix manipulation, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs in other languages.
SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more.
Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors.
SMath Studio - is a math program with 'paper'-like interface and numerous computing features. It has an ability to work with systems, matrices, vectors, complex numbers, infinities and fractions.
Maple is a general-purpose commercial computer algebra system. Users can enter mathematics in traditional mathematical notation. Custom user interfaces can also be created. There is support for numeric computations, to arbitrary precision, as well as symbolic computation and...
Python(x,y) is a free scientific and engineering development software for numerical computations, data analysis and data visualization based on Python programming language, Qt graphical user interfaces and .
The project seems no longer developed. Last version, 220.127.116.11, released in June 2015, can be still downloaded from the official website.
FreeMat is an environment for rapid engineering and scientific processing. It is similar to commercial systems such as MATLAB from Mathworks and IDL from Research Systems, but is Open Source.
The project is no longer updated. Last version, 4.2, released in June 2013, can be still downloaded from SourceForge