The goal of Hilbert II, which is in the tradition of Hilbert's program, is the creation of a system that enables a working mathematician to put theorems and proofs (in the formal language of predicate calculus) into it. These proofs are automatically verified by a proof checker. Because this system is not centrally administered and enables references to any location on the Internet, a world wide mathematical knowledge base could be built. It also contains information in "common mathematical language".
Frink is a calculating tool and programming language designed to help you in the real world. It tracks units of measurement throughout all calculations and ensures that answers are correct. It converts between systems of measurement, and has a huge library of physical data. It is both a simple calculator for quick calculations and a full-fledged programming language for large tasks. It draws high-quality graphics, handles conversions between time zones, currencies, and historical values of the U.S. dollar and the British pound, translates between several languages, does date/time math, and more.
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.
The Shared Scientific Toolbox is a library that facilitates development of efficient, modular, and robust scientific/distributed computing applications in Java. It features multidimensional arrays with extensive linear algebra and FFT support, an asynchronous, scalable networking layer, and advanced class loading, message passing, and statistics packages.
PBZIP2 is a parallel implementation of the bzip2 block-sorting file compressor that uses pthreads and achieves near-linear speedup on SMP machines. The output of this version is fully compatible with bzip2 1.0.2 or newer (ie: anything compressed with PBZIP2 can be decompressed with bzip2).
GiNaC (GiNaC is Not a CAS (Computer Algebra System)) is a C++ library for symbolic calculations. It is designed to allow the creation of integrated systems that embed symbolic manipulations together with more established areas of computer science (like computation-intense numeric applications, graphical interfaces, etc.). Contrary to other CASes it does not try to provide extensive algebraic capabilities and a simple programming language but instead accepts a given language (C++) and extends it by a set of algebraic capabilities.
MayaVi is a free, cross platform, easy-to-use scientific data visualizer. It provides a powerful GUI to ease the visualization process. It is written in Python and uses the Visualization Toolkit (VTK) for the graphics. MayaVi can be scripted from other Python programs and also from the interactive Python interpreter. MayaVi includes the VTK Pipeline browser. The VTK Pipeline browser is a Python module (vtkPipeline) that enables one to view and configure the objects in the VTK pipeline graphically with a Tkinter-based GUI. The browser should work for any Python script that uses VTK. MayaVi also provides classes to pickle a VTK object and a simple class documentation browser.
TBCI is a C++ library which provides classes for Vectors, Matrices, etc., and defines operations on them such as additions, multiplications, etc. There are many Matrix classes providing specializations for different sparse matrices. They all feature a similar interface. TBCI comes with an extensive set of solvers for linear systems and an interface to lapack libraries. It uses the temporary base class idiom, which avoids unnecessary copying of data by having a notion of real and temporary objects which are treated differently with respect to assignment and copy c'tor.