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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.

Armadillo is a C++ linear algebra library (matrix maths) aiming towards a good balance between speed and ease of use. The API is deliberately similar to Matlab's. Integer, floating point, and complex numbers are supported, as well as a subset of trigonometric and statistics functions. Various matrix decompositions are provided through optional integration with LAPACK and ATLAS numerics libraries. A delayed evaluation approach, based on template meta-programming, is used (during compile time) to combine several operations into one and reduce or eliminate the need for temporaries.

R is a language and environment for statistical computing and graphics. It is similar to S, which was developed at Bell Laboratories by John Chambers et al. It provides a wide variety of statistical and graphical techniques (linear and nonlinear modelling, statistical tests, time series analysis, classification, clustering, etc.). R is designed as a true computer language with control-flow constructions for iteration and alternation, and it allows users to add additional functionality by defining new functions. For computationally intensive tasks, Fortran and C code can be linked and called at run time.

FFTW is a fast C FFT library. It includes complex, real, symmetric, multidimensional, and parallel transforms, and can handle arbitrary array sizes efficiently.It is typically faster than other freely available FFT implementations, and is even competitive with vendor-tuned libraries (benchmarks are available at the homepage). To achieve this performance, it uses novel code generation and runtime self optimization techniques (along with many other tricks).

galculator is a GTK 2/GTK 3-based scientific calculator supporting algebraic mode, RPN, and formula entry mode. Features include arithmetic operations plus precedence handling, full keypad support, trigonometric functions, power, square root, natural and common logarithm, constants (e, PI), and inverse and hyperbolic functions. It supports different number bases (decimal, hexadecimal, octal, and binary) and angle bases (radiant, degree, and grad).

JSXGraph is a cross-browser library for interactive geometry, function plotting, and data visualization in a Web browser. It is implemented in JavaScript and uses SVG, VML, or canvas. JSXGraph is easy to embed and has a small footprint: about 120kB if embedded in a Web page. No plugins or further libraries are required.

GNU CLISP is an ANSI Common Lisp implementation with an interpreter, compiler, debugger, object system (CLOS, MOP), sockets, fast bignums, arbitrary precision floats, and a foreign language interface that runs on most Unix variants and Win32.

Botan is a crypto library written in C++. It provides a variety of cryptographic algorithms, including common ones such as AES, MD5, SHA, HMAC, RSA, Diffie-Hellman, DSA, and ECDSA, as well as many others that are more obscure or specialized. It also offers SSL/TLS (client and server), X.509v3 certificates and CRLs, and PKCS #10 certificate requests. A message processing system that uses a filter/pipeline metaphor allows for many common cryptographic tasks to be completed with just a few lines of code. Assembly and SIMD optimizations for common CPUs offers speedups for critical algorithms like AES and SHA-1.

MathGL is a library for making high-quality scientific graphics under Linux and Windows, fast data plotting and handling of large data arrays, working in window and console modes, and easily embedding into other programs. It has more than 40 general types of graphics for 1d, 2d, and 3d data arrays. It can export graphics to raster and vector (EPS or SVG) formats. It has an OpenGL interface and can be used from console programs. It has functions for data handling and MGL language scripting for simplification of data plotting. It has several types of transparency and smoothed lightning, vector fonts and TeX-like formula drawing, an arbitrary curvilinear coordinate system, and many other useful things.

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.

Gmsh is an automatic 3D finite element grid generator with built-in CAD and post-processing facilities. Its design goal is to provide a simple meshing tool with parametric input and advanced visualization capabilities. It is built around four modules: geometry, mesh, solver, and post-processing. The specification of any input to these modules is done either interactively using the graphical user interface (based on FLTK and OpenGL) or in ASCII text files using Gmsh's own scripting language.