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.
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.
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.
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.
GtkMathView is a GTK widget for rendering MathML documents. It is meant to be a standalone, light-weight component and not a full browser. GTK applications can use the widget as a window for displaying mathematical formulas and doing simple interactions. Among other features, GtkMathView includes support for breaking long mathematical expressions, rendering of stretchy operators, and provides a customizable support for additional fonts.
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.
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).