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.
Asymptote is a powerful descriptive 2D and 3D vector graphics language for technical drawing, inspired by MetaPost but with an improved C++-like syntax. It provides for figures the same high-quality level of typesetting that LaTeX does for scientific text. Asymptote is a programming language as opposed to just a graphics program. It can exploit the best features of script (command-driven) and graphical user interface (GUI) methods. High-level graphics commands are implemented in the language itself, allowing them to be easily tailored to specific applications.
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.
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.
Social Networks Visualizer (SocNetV) is a flexible and user-friendly tool for the analysis and visualization of Social Networks. It lets you construct mathematical graphs with a few clicks on a virtual canvas, load networks of various formats (GraphViz, GraphML, Adjacency, Pajek, UCINET, etc), or create a network by crawling all links in a Web page. The application can compute basic network properties, such as density, diameter, and distances (shortest path lengths), as well as more advanced structural statistics, such as node and network centralities (i.e. closeness, betweenness, graph), clustering coefficient, etc.
The Java Algebra System (JAS) is an object oriented, type safe, multi-threaded approach to computer algebra. JAS provides a well designed software library using generic types for algebraic computations implemented in the Java programming language. The library can be used as any other Java software package, or it can be used interactively or interpreted through a Jython or JRuby front end. The focus at the moment is on commutative and solvable polynomials, power-series, multivariate polynomial factorization, Gröbner bases, and applications.
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.
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.