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NumPy - fundamental package for scientific computing with Python
NumPy is the fundamental package needed for scientific computing with Python. Numerical Python adds a fast and sophisticated N-dimensional array facility to the Python language. NumPy can also be used as an efficient multi-dimensional container of generic data. Arbitrary data-types can be defined. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases.
SciPy (pronounced "Sigh Pie") is open-source software for mathematics, science, and engineering. The SciPy library is built to work with NumPy arrays, and provides many user-friendly and efficient numerical routines such as routines for numerical integration and optimization.
GNU Octave is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation. Octave Forge is a place for development of its packages; from bioinformatics and fuzzy logic to mechanics and instrument control.
Spyder is a Python development environment with advanced editing, interactive testing, debugging and introspection features. It is especially recommended for scientific computing thanks to NumPy (linear algebra), SciPy (signal and image processing), matplotlib (interactive 2D/3D plotting) and MayaVi’s mlab (interactive 3D visualization) support.
OpenAxiom is an open source Computer Algebra System. It offers an interactive environment, an expressive programming language, a compiler, a large set of mathematical libraries of interest to researchers and practitioners of computational sciences.
ORSA is an interactive tool for scientific grade Celestial Mechanics computations. Asteroids, comets, artificial satellites, Solar and extra-Solar planetary systems can be accurately reproduced, simulated, and analyzed.
A programmable signal generator and RF synthesizer for scientific experiments, especially quantum computing and quantum information processing. It includes hardware, firmware, software, and documentation, all under an open source license.
FreeMat is a free environment for rapid engineering and scientific prototyping and data processing. It is similar to commercial systems such as MATLAB and IDL. It has built in arithmetic for manipulation of all supported data types, N-dimensional array manipulation, 2D and 3D plotting and image display, Visualization, Image manipulation, and as well as parallel programming.