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.
FFTW is a fast C FFT library. It includes complex, real, symmetric, multidimensional, and parallel transforms, and can handle arbitrary array sizes efficiently.It is typically faster than other freely available FFT implementations, and is even competitive with vendor-tuned libraries (benchmarks are available at the homepage). To achieve this performance, it uses novel code generation and runtime self optimization techniques (along with many other tricks).
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.
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.
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.
The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing on applying empirical techniques in order to provide portable performance. It provides C and Fortran77 interfaces to a portably efficient BLAS implementation, as well as a few routines from LAPACK.