Sage is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages, within a common Python-based interface. See http://sagemath.org for more information.

Maxima is a system for the manipulation of symbolic and numeric expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices, and tensors. Maxima yields high-precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions. See http://maxima.sourceforge.net for more information.

R is a language and environment for statistical computing and graphics, similar to the S language and environment. It provides a wide variety of statistical (linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering, ...) and graphical techniques, and is highly extensible. The S language is often the vehicle of choice for research in statistical methodology, and R provides an open-source route to this. See http://www.r-project.org for more information.

KAlgebra is a MathML-based graph calculator, that ships with KDE Education project. See http://edu.kde.org/kalgebra/ for more information.

Qalculate! is not your regular software replication of the cheapest available calculator. Qalculate! aims to make full use of the superior interface, power and flexibility of modern computers. The center of attention in Qalculate! is the expression entry. Instead of entering each number in a mathematical expression separately, you can directly write the whole expression and later modify it. The interpretation of expressions is flexible and fault tolerant, and if you nevertheless do something wrong, Qalculate! will tell you so. Not fully solvable expressions are however not errors. Qalculate! will simplify as far as it can and answer with an expression. In addition to numbers and arithmetic operators, an expression may contain any combination of variables, units, and functions. See http://qalculate.sourceforge.net/ for more information.

Python is a remarkably powerful dynamic programming language that is used in a wide variety of application domains. There are several Python packages to scientific programming.

Python is distributed under Python Software Foundation license (GPL compatible). See the official website for more information.

Scilab is an free software, cross-platform numerical computational package and a high-level, numerically oriented programming language.

Scilab is distributed under CeCILL license (GPL compatible). See http://www.scilab.org/ for more information.

GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB. See http://www.gnu.org/software/octave/ for more information.

Lua is a fast and lightweight scripting language, with a simple procedural syntax. There are several libraries in Lua aimed at math and science.

See http://www.lua.org/ for more information.

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