Cactus is a general, modular, parallel environment for solving systems of partial differential equations. The code has been developed over many years by a large international collaboration of numerical relativity and computational science research groups and can be used to provide a portable platform for solving any system of partial differential equations.
Calc is arbitrary precision arithmetic system that uses a C-like language. It's useful as a calculator, an algorithm prototype, and as a mathematical research tool. More importantly, calc provides a machine-independent means of computation. Calc comes with a rich set of builtin mathematical and programmatic functions.
distributed.net is a loosely knit group of computer users from all of the world that is taking up challenges requiring lots of computing power (most notably the RC5, DES, and OGR cracking contests). It is simple to participate in the challenges by downloading and running their client software (which uses idle CPU time to complete its tasks).
Genius is an arbitrary precision integer and multiple precision floating point calculator. It includes its own programming language similar in some aspects to C, bc, or Pascal. It can deal with rational numbers and complex numbers. It has matrix support as well. It uses the gmp library so it is very fast for calculations of large numbers. It has a command line and a GNOME interface. The GNOME interface supports plotting functions and 3D surfaces.
GLE (Graphics Layout Engine) is a graphics scripting language designed for creating publication quality figures (e.g., a chart, plot, graph, or diagram). GLE supports various chart types (including function plot, histogram, bar chart, scatter plot, contour plot, color map, and surface plot) through a simple but flexible set of graphing commands. More complex output can be created by relying on GLE's scripting language, which is full featured with subroutines, variables, and logic control. GLE relies on LaTeX for text output and supports mathematical formulae in graphs and figures.
GNU TeXmacs is a free wysiwyw (what you see is what you want) editing platform with special features for scientists. The software aims to provide a unified and user friendly framework for editing structured documents with different types of content: text, mathematics, graphics, interactive content. TeXmacs can also be used as an interface to many external systems for computer algebra, numerical analysis, and statistics. New presentation styles can be written by the user and new features can be added to the editor using Scheme.
Groups, Algorithms, and Programming (GAP) is a system for computational discrete algebra with particular emphasis on computational group theory and related areas. It provides a Pascal-like interpreted language, data types for many algebraic objects, a function library, and large libraries of data.
Isabelle is a popular generic theorem prover developed at Cambridge University and TU Munich. Existing logics like Isabelle/HOL provide a theorem proving environment ready to use for sizable applications. Isabelle may also serve as framework for rapid prototyping of deductive systems. It comes with a large library including Isabelle/HOL (classical higher-order logic), Isabelle/HOLCF (Scott's Logic for Computable Functions with HOL), Isabelle/FOL (classical and intuitionistic first-order logic), and Isabelle/ZF (Zermelo-Fraenkel set theory on top of FOL).
GTL can be seen as an extension of the Standard Template Library STL to graphs and fundamental graph algorithms. It is a platform independent and extendible C++ library, and is a useful aid to any software designer. It contains the classes needed to work with graphs, nodes, and edges, and some fundamental algorithms as building blocks for more complex graph algorithms. Customized algorithms can be developed by experienced programmers.