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.
Meta.Numerics is a Mono-compatible .NET library for scientific and numerical programming. It includes functionality for matrix algebra (including SVD, non-symmetric eigensystems, and sparse matrices), special functions of real and complex numbers (including Bessel functions and the complex error function), statistics and data analysis (including PCA, logistic and nonlinear regression, statistical tests, and nonuniform random deviates), and signal processing (including arbitrary-length FFTs).
Polymul is a self-contained C++ template library for efficient multiplication of multivariate polynomials. It is intended for low order polynomials of a few variables, but is in principle limited only by the compiler's maximal template recursion depth. Polynomials can be created over any scalar type, such as integers or double precision floating point numbers.
GSL shell offers an interactive user interface that gives access to the GSL collection of mathematical functions. It is based on the powerful and elegant scripting language Lua. GSL shell is not just a wrapper over the C API of GSL, but offers a much more simple and expressive way to use GSL. The objective is to give the user the power to easily access GSL functions without having to write a complete C application. It also has a powerful module to produce plots or almost any kind of graphics based on data or functions.
Date::Calc::XS is a Perl module that is the C/XS part which Date::Calc used to consist of. Date::Calc has become a (pure-Perl) wrapper which tries to load Date::Calc::XS, and failing that, loads Date::Calc::PP (a pure-Perl implementation which is now part of Date::Calc and used to be Date::Pcalc).
Treep is a simple language for doing symbolical computations. It operates on numbers and strings that can be organized in more complex objects. These objects are lists of name-value pairs that are stored in memory as AVL trees. It has about sixty built-in functions to operate on such data and a way to define new functions. Treep syntax very much resembles Lisp. The power of treep is its simplicity and security. Treep is a good tool do process objects and relations between them. For example it is possible to define graphs as a sets of vertices and edges in text file, parse that file, do any computations you like, write modified data to text file. Treep works well on graphs, trees, linked lists, simple hashes. Treep is not good at processing texts, dealing with system input/output.