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The dynamic mathematics software Geonext establishes new ways of teaching and learning mathematics. It offers opportunities of visualisation that can't be realised on paper or blackboard and with traditional construction tools. Geonext enables autonomous and cooperative learning of mathematics in the classroom. It encourages an active discovering approach to mathematical thinking. Geonext can be used at school and at home for free (GPL). Therefore the software can be handed out to students without any copyright problems (GPL). Geonext can be used from elementary school up to calculus at high school and in teacher-training at university in a manifold and flexible way. -Andreas Fehlner fehlner@gmx.de

GGobi is an open source visualization program for exploring high-dimensional data. It provides highly dynamic and interactive graphics such as tours, as well as familiar graphics such as the scatterplot, barchart and parallel coordinates plots. Plots are interactive and linked with brushing and identification.

JEuclid is a complete MathML rendering solution, consisting of: a MathViewer application, command line converters from MathML to other formats, an ant task for autmated conversion, display components for AWT and Swing and a component for Apache Cocoon.

General purpose computer algebra system released under GPLv3. French documentation by Renee De Graeve is for non-commercial use only. The package consists of: - C++ library (libgiac). It is build on C and C++ libraries: PARI, NTL (arithmetic), CoCoA (Groebner basis), GSL (numerics), GMP (big integers), MPFR (bigfloats) and provides algorithms for basic polynomial operations (product, GCD) and symbolic computations (simplifications, limits/series, symbolic integration, summation, ...). The library can be configured to accept Maple or TI syntax to ease the transition for users of these systems. - Command line interpreter (icas or giac). It can be called from texmacs. - FLTK-based GUI (xcas). It is a GUI for symbolic computation with several modules added: 2-d and 3-d graphics, dynamic 2-d and 3-d geometry (exact or numeric), spreadsheet, programming environment.

Givaro is a C++ library for arithmetic and algebraic computations. Its main features are implementations of the basic arithmetic of many mathematical entities: prime fields, extension fields, finite fields, finite rings, polynomials, algebraic numbers, arbitrary precision integers and rationals (via C++ wrappers over gmp). It also provides data structures and templated classes for the manipulation of basic algebraic objects, such as vectors, matrices (dense, sparse, and structured), univariate polynomials, and recursive multivariate polynomials.

GMP is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers. There is no 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. GMP is designed to be as fast as possible, both for small operands and for huge operands. The speed is achieved by using fullwords as the basic arithmetic type, by using fast algorithms, with carefully optimized assembly code for the most common inner loops for a lot of CPUs, and by a general emphasis on speed (instead of simplicity or elegance). GMP is believed to be faster than any other similar library. The advantage for GMP increases with the operand sizes for certain operations, since GMP in many cases has asymptotically faster algorithms.

GLgraph visualize mathematical functions. It can handle 3 unknowns (x,z,t) and can produce a 4D function with 3 space and 1 time dimension.

OpenGL Mathematics (GLM) is a header only C++ mathematics library for graphics software based on the OpenGL Shading Language (GLSL) specification. GLM provides classes and functions designed and implemented with the same naming conventions and functionalities than GLSL so that when a programmer knows GLSL, he knows GLM as well which makes it really easy to use. This project isn't limited to GLSL features. An extension system, based on the GLSL extension conventions, provides extended capabilities: matrix transformations, quaternions, half-based types, random numbers, procedural noise functions, etc... This library works perfectly with OpenGL but it also ensures interoperability with third party libraries and SDKs. It is a good candidate for software rendering (Raytracing / Rasterisation), image processing, physic simulations and any context that requires a simple and convenient mathematics library.

GraphThing is a tool that allows you to create, manipulate and study graphs. These "graphs" are mathematical objects that describe relationships between sets; they are not 2D plots, charts, or anything similar to that.

Gmm++ is a generic C++ template library for sparse, dense and skyline matrices. It is built as a set of generic algorithms (mult, add, copy, sub-matrices, dense and sparse solvers ...) for any interfaced vector type or matrix type. It can be view as a glue library allowing cooperation between several vector and matrix types. However, basic sparse, dense and skyline matrix/vector types are built in Gmm++, hence it can be used as a standalone linear algebra library. Interfacing a vector or matrix type means writing "traits" objects called "linalg_traits", which describe their properties. The library offers predefined dense, sparse and skyline matrix types.