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GraphViz
[222 users on Ohloh]
Graph visualization is a way of representing structural information as diagrams of abstract graphs and networks. Automatic graph drawing has many important applications in software engineering, database and web design, networking, and in visual interfaces for many other domains.

Graphviz is open source graph visualization software. It has several main graph layout programs. See the gallery for some sample layouts. It also has web and interactive graphical interfaces, and auxiliary tools, l...

gnuplot
[72 users on Ohloh]
gnuplot plots 2d and 3d graphs, from a data file or with a formula. It has an interactive mode with online help, or it can be used non-interactively. gnuplot does function fitting to data sets, and it does output to many terminals, among which are PostScript, X11 display, PNG, and GIF (via the old gd library).
R
[53 users on Ohloh]
R is a language and environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers and colleagues. R can be considered as a different implementation of S. There are some important differences, but much code written for S runs unaltered under R.

R provides a wide variety of statistical (linear and nonlinear modelling, classical st...

GNU Octave
[40 users on Ohloh]
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.
CLISP - an ANSI Common Lisp
[34 users on Ohloh]
GNU CLISP is an ANSI Common Lisp implementation with an interpreter, compiler, debugger, object system (CLOS, MOP), sockets, fast bignums, arbitrary precision floats, and foreign language interface which runs on most UNIXes and Win32.
SciPy
[33 users on Ohloh]
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
mcrypt
[29 users on Ohloh]
mcrypt is a program for encrypting files or streams. It is intended to be a replacement for the old UNIX crypt. It uses well-known and well-tested algorithms like BLOWFISH, AES, ARCFOUR, CAST-128, and more in several modes of operation. It also has a compatibility mode with the old UNIX crypt program and the des program found in Solaris.
Anjuta DevStudio
[22 users on Ohloh]
Anjuta is a versatile Integrated Development Environment (IDE) for C and C++ in GNU/Linux. It has been written for GTK/GNOME, and features a number of advanced programming facilities. These include project management, application wizards, an onboard interactive debugger, and a powerful source editor with source browsing and syntax highlighting.
Maxima -- GPL CAS based on DOE-MACSYMA
[22 users on Ohloh]
Maxima is a Common Lisp implementation of MIT's Macsyma system for computer based algebra. It features plotting over the network via netmath, computations over the network, extensive testing on a large array of problems, a source level debugger for maxima code, ease of extension in fundamentally new ways, access to Common Lisp and portability to many systems.
Bullet Physics Engine
[19 users on Ohloh]
Bullet is a 3D Collision Detection and Rigid Body Dynamics Library for games and animation.
Free for commercial use, including Playstation 3, open source under the ZLib License.
Discrete and continuous collision detection, integrated into Blender 3D, and COLLADA 1.4 Physics import.

It is highly optimized for x86 SIMD SSE, Cell SPE and CUDA.

Open Dynamics Engine
[17 users on Ohloh]
ODE is an open source, high performance library for simulating rigid body dynamics. It is fully featured, stable, mature and platform independent with an easy to use C/C++ API. It has advanced joint types and integrated collision detection with friction. ODE is useful for simulating vehicles, objects in virtual reality environments and virtual creatures. It is currently used in many computer games, 3D authoring tools and simulation tools.
Sage: Open Source Mathematics Software
[16 users on Ohloh]
Tags: algebra math mathematics python science programming
Sage is mathematical software, very much in the same vein as Matlab, MAGMA, Maple, and Mathematica. Unlike these systems, every component of Sage is GPL-compatible. The interpretaive language of Sage is Python, a mainstream programming language. Use Sage for studying a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra.

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GMP
[11 users on Ohloh]
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.
GSL - GNU Scientific Library
[11 users on Ohloh]
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.

ScUtil
[11 users on Ohloh]
Hundreds of functions of a variety of topics, from statistics to string parsing, module utilities to network tools.

Everyone's pet library accumulates features over time. My erlang library got big, fast. I often find myself giving functions from it out to other people, and a lot of my other libraries are dependant on ScUtil in various ways, so I figured what the hell, let's give it away.

This library is believed to be efficiently implemented at all points. Efficiency tips are, howeve...

Math.NET
[10 users on Ohloh]
A mathematical open source library written in C#/.Net, aiming to provide a self contained clean framework for symbolic algebraic and numerical / scientific computations.
Eigen
[10 users on Ohloh]
Eigen is a C++ template library for linear algebra (vectors, matrices, and related algorithms).
* It supports tiny, dense, and sparse matrices (the latter is still experimental), fully integrated with one another.
* It takes full advantage of expression templates to provide a great API. For example, m.row(i)+=m.row(j) just works.
* Expression templates are also the basis for many optimizations: automatic determination of which temporaries to remove, and ...
SymPy
[9 users on Ohloh]
Tags: mathematics
SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python and does not require any external libraries, except optionally for plotting support.
Kig
[6 users on Ohloh]
Kig is a program for exploring geometric constructions. It is meant as a better replacement for such free programs as KGeo, KSeg and Dr. Geo and commercial programs like Cabri. Kig is meant as a useful and powerful utility for high school students and teachers.
Scilab
[6 users on Ohloh]
(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 via the Internet. It is currently used in educational and industrial environments around the world. Scilab is now the responsibility of the Scilab Consortium, launched in May 2003. There are cur...