MathGL is a library for making high-quality scientific graphics under Linux and Windows, fast data plotting and handling of large data arrays, working in window and console modes, and easily embedding into other programs. It has more than 40 general types of graphics for 1d, 2d, and 3d data arrays. It can export graphics to raster and vector (EPS or SVG) formats. It has an OpenGL interface and can be used from console programs. It has functions for data handling and MGL language scripting for simplification of data plotting. It has several types of transparency and smoothed lightning, vector fonts and TeX-like formula drawing, an arbitrary curvilinear coordinate system, and many other useful things.
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.
R is a language and environment for statistical computing and graphics. It is similar to S, which was developed at Bell Laboratories by John Chambers et al. It provides a wide variety of statistical and graphical techniques (linear and nonlinear modelling, statistical tests, time series analysis, classification, clustering, etc.). R is designed as a true computer language with control-flow constructions for iteration and alternation, and it allows users to add additional functionality by defining new functions. For computationally intensive tasks, Fortran and C code can be linked and called at run time.
Mathomatic is a portable, general-purpose computer algebra system (CAS) that can solve, differentiate, simplify, combine, and compare algebraic equations, perform standard, complex number, modular, and polynomial arithmetic, etc. It does some calculus and is very easy to compile/install, learn, and use. The symbolic math application with a simple command-line interface is designed to be a colorful algebra calculator that is reliable, responsive, and convenient to use. The symbolic math library is lightweight and easy to include in other software, due to being written entirely in C with no additional dependencies.
SHOGUN is a machine learning toolbox whose focus is on large scale kernel methods and especially on Support Vector Machines (SVM). It provides a generic SVM object interfacing to several different SVM implementations, all making use of the same underlying, efficient kernel implementations. Apart from SVMs and regression, SHOGUN also features a number of linear methods like Linear Discriminant Analysis (LDA), Linear Programming Machine (LPM), (Kernel) Perceptrons, and algorithms to train hidden Markov models. SHOGUN can be used from within C++, Matlab, R, Octave, and Python.
Class Library for Numbers (CLN) is a library for computations with all kinds of numbers. Its rich set of number classes includes integers, rational numbers, floating-point numbers, complex numbers, modular integers, and univariate polynomials. It implements elementary functions (also with unlimited precision), logical functions, and transcendental functions. It is designed for memory and speed efficiency as well as interoperability.
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.
SCaVis is an environment for scientific computation, data analysis, and data visualization designed for scientists, engineers, and students. The program can be used for function and data plotting in 2D and 3D, histograms, statistical analysis, and symbolic calculations using the Matlab/Octave high-level interpreted language.