ACL2 is a mathematical logic, programming language, and mechanical theorem prover based on the applicative subset of Common Lisp. It is an "industrial-strength" version of the NQTHM or Boyer/Moore theorem prover, and has been used for the formal verification of commercial microprocessors, the Java Virtual Machine, interesting algorithms, and so forth.
ASCIIMathML is a script that converts calculator-style ASCII math notation (and many LaTeX formulas) to Presentation MathML while your Web page loads. It works with HTML and XHTML files in Mozilla/Firefox/Netscape 7+ browsers, as well as in Internet Explorer 6 with MathPlayer. For example, the solutions for the equation 'ax^2+bx+c=0' are expressed in the HTML file as '(-b +- sqrt(b^2 - 4ac))/(2a)', and display as nicely formatted MathML. The script can be easily used in wikiservers and blogs, as a rudimentary MathML editor (with instant preview), and to preview math formulas as they are typed into a Web page input area.
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.
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.
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.
CCruncher is a project for quantifying portfolio credit risk using the copula approach. It is a framework consisting of two elements: a technical document that explains the theory, and a software program that implements it. CCruncher evaluates the portfolio credit risk by sampling the portfolio loss distribution and computing the Expected Loss (EL), Value at Risk (VaR), and Expected Shortfall (ES) statistics. The portfolio losses are obtained simulating the default times of obligors and simulating the EADs and LGDs of their assets.
CONSIDEO MODELER allows you to mindmap a complex problem, analyse it qualitatively to discover levers and bottlenecks, and even to simulate it by automatically building a system dynamics model. One can integrate any external data and setup a customized management cockpit for playing out scenarios. It is useful for organizational problems, project management, financial analysis, production processes, score cards, and much more.
Cadabra is a computer algebra system designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, implicit coordinate dependence, multiple index types, and many more. The input format is a subset of TeX. Both a command-line and a graphical interface are available.