TooN is a very efficient numerics library for C++. The main focus of the library is efficient and safe handling of large numbers of small vector matrices and providing as much compile time checking as is possible. The library also works with large vectors and matrices and integrates easily with existing code. In addition to elementary vector and matrix operations, the library also providers linear solvers, matrix decompositions, optimization, and wrappers around LAPACK.
REDUCE is a system for doing algebra by computer that also supports numerical approximation and interfaces to gnuplot to provide graphics. It has a long and distinguished place in the history of computer algebra systems. For comparison, other systems that address some of the same issues but sometimes with rather different emphases are Axiom, Derive, Macsyma (Maxima), Maple, Mathematica, and MuPAD.
EngLab is a cross-compile mathematical platform with a C like syntax intended to be used both by engineers and users with little programming knowledge. It supports programming through small script files but also enables users to easily compile their own functions as shared objects and use them through the program's main interface.
SciDAVis is an interactive application aimed at data analysis and publication-quality plotting. It combines a shallow learning curve and an intuitive, easy-to-use graphical user interface with powerful features such as scriptability and extensibility. It is similar in its field of application to proprietary Windows applications like Origin and SigmaPlot, as well as free applications like QtiPlot, Labplot, and Gnuplot. What sets SciDAVis apart from the above is its emphasis on providing a friendly and open environment (in the software as well as the project) for new and experienced users alike, and particularly in providing good documentation on all levels.
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.
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.