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.
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.
CCMATH is a mathematics library, coded in C, that contains functions for linear algebra, numerical integration, geometry and trigonometry, curve fitting, roots and optimization, Fourier analysis, simulation generation, statistics, special functions, sorts and searches, time series models, complex arithmetic, and high precision computations.
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.
Gnofract 4D is a Gnome-based program to draw fractals. What sets it apart from other fractal programs (and makes it "4D") is the way that it treats the Mandelbrot and Julia sets as different views of the same four-dimensional fractal object. It contains a Fractint-compatible formula compiler, allowing it to draw an unlimited number of fractal types, using numerous coloring options.
C-XSC 2.0 is a C++ class library for eXtended Scientific Computing. It provides real, complex, interval, complex-interval, and multi-precision data types. There are also vector and matrix classes corresponding to these scalar types. The interval data types are very useful for verified numerical computations.
KSEG is a program for exploring Euclidean geometry, similar to Geometer's Sketchpad. It features points, lines, transformations, measurements, calculations, simple editable recursive Constructions (similar to macros), adaptively sampled loci, and selection groups. Several languages are supported. KSEG is very fast, stable, and has an efficient and consistent UI. It uses Qt and does not require KDE.
The GNU Triangulated Surface Library (GTS) provides a set of useful functions to deal with 3D surfaces meshed with interconnected triangles. It features metric operations (area, volume, curvature, etc.), 2D Delaunay and constrained Delaunay triangulations, robust geometric predicates and set operations on surfaces (union, intersection, etc.), surface refinement and coarsening (multiresolution models), and bounding-boxes trees for collision/intersection detection.
GiNaC (GiNaC is Not a CAS (Computer Algebra System)) is a C++ library for symbolic calculations. It is designed to allow the creation of integrated systems that embed symbolic manipulations together with more established areas of computer science (like computation-intense numeric applications, graphical interfaces, etc.). Contrary to other CASes it does not try to provide extensive algebraic capabilities and a simple programming language but instead accepts a given language (C++) and extends it by a set of algebraic capabilities.
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.