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NumPy adds a flexible multi-dimensional array to Python along with mathematical and structural manipulation routines to allow Python to be used for high-level scientific and engineering code development.
matplotlib is a python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms. matplotlib can be used in python scripts, the python and ipython shells (similar to matlab or mathematica), web application servers, and six graphical user interface toolkits
SciPy is a collection of mathematical routines that builds on the NumPy array extension. It collects a large number of general-purpose scientific and engineering routines. With NumPy + SciPy, you can use Python much as you would use Octave, Scilab, Matlab, or IDL
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. It may also be used as a batch-oriented language.
The GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. The library provides a wide range of mathematical routines such as random number generators, special functions and least-squares fitting. There are over 1000 functions in total with an extensive test suite.
(from the scilab homepage...) Scilab is a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. Scilab is an open source software. Since 1994 it has been distributed freely along with the source code ... [More]
GMP is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers. There is no practical limit to the precision except the ones implied by the available memory in the machine GMP runs on. GMP has a rich set of functions, and the functions have a regular interface.
A mathematical open source library written in C#/.Net, aiming to provide a self contained clean framework for symbolic algebraic and numerical / scientific computations.
OOFEM is an open source multi-physics parallel finite element code with object oriented architecture. The aim of this project is to provide efficient and robust tool for FEM computations as well as to offer highly modular and extensible environment for development.
FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST). We believe that FFTW, which is free software ... [More]