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).
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.
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.
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.
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.
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.