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.
The METSlib QAP solver is a Tabu Search solver for the quadratic assignment problem, a combinatorial optimization problem that arises in many applicative cases. It can be used to find optimal locations for a set of facilities while minimizing the cost of moving commodities between them, to optimize the placement of components on a circuit board, and for many other applications. This software is based on the METSlib framework.
pyPEG is a quick and easy solution for creating a parser in Python programs. pyPEG uses a PEG language in Python data structures to parse, so it can be used dynamically to parse nearly every context free language. The output is a plain Python data structure called pyAST, or, as an alternative, XML.
Evolving Games for Unnatural Intelligence is a Java package for unsupervised machine learning based on Evolutionary Game Theory on directed graphs. It is able to segment data without any previuos information on the number of segments. It has no GUI, but implements generalizations of the original method proposed by Li, Chen, He and Jiang in the arxiv paper "A Novel Clustering Algorithm Based Upon Games on Evolving Network", published on 30 Dec 2008.
clac (Command Line Advanced Calculator) evaluates mathematical expressions input via command line arguments or from stdin and writes the results to stdout. Unlike other command line calculators, clac has infix (natural order) expression syntax, is quite comfortable with complex numbers, defines a great many functions and constants by default, and allows easy definition of new user functions and constants using Python.
Jasymca is an interactive system for solving math problems. It supports arbitrary precision numbers and symbolic variables. Scalars, vectors, and matrices can be built from all datatypes and used in calculations. From the pseudoinverse of symbolic matrices over trigonometric simplifications to symbolic solutions of integrals and systems of equations, the main functionalities of CAS-programs are provided. Additionaly, high performance numerical routines from LAPACK and a plotmodule are implemented. The user interface can be selected from either an Octave/Matlab/SciLab-like language or a GNU-Maxima style. Three versions of Jasymca are provided to cover almost any computer platform: a midlet version for portable devices like cell phones or PDAs; a Java application for desktop PCs, laptops, and workstations; and an applet which can be integrated in Web pages.
jblas is a fast linear algebra library for Java. It is based on BLAS and LAPACK, the de-facto industry standard for matrix computations, and uses state-of-the-art implementations like ATLAS for all its computational routines, making it very fast. It is essentially a lightweight wrapper around the BLAS and LAPACK routines. These packages originated in the Fortran community, which explains their archaic API. On the other hand, modern implementations are hard to beat performance-wise. jblas aims to make this functionality available to Java programmers such that they do not have to worry about writing JNI interfaces and calling conventions of Fortran code.
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.