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gnuplot plots 2d and 3d graphs, from a data file or with a formula. It has an interactive mode with online help, or it can be used non-interactively. gnuplot does function fitting to data sets, and it does output to many terminals, among which are PostScript, X11 display, PNG, and GIF (via the old gd library).
Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments. It may also be used as a batch-oriented language.
Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high
Sage is mathematical software, very much in the same vein as MATLAB, MAGMA, Maple, and Mathematica. Unlike these systems, every component of Sage is GPL-compatible. The interpretative language of Sage is Python, a mainstream programming language. Use Sage for studying a huge range of mathematics
The GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. The library provides a wide range of mathematical routines such as random number generators, special functions and least-squares fitting. There are over 1000 functions in total with an extensive test suite.
wxMaxima is a cross-platform graphical front-end for the computer algebra system Maxima based on wxWidgets. It provides nice display of mathematical output and easy access to Maxima functions through menus and dialogs.
QtOctave is a front-end for Octave. Octave is a high-level language for numerical computations, like Matlab.
Kig is a program for exploring geometric constructions. It is meant as a better replacement for such free programs as KGeo, KSeg and Dr. Geo and commercial programs like Cabri. Kig is meant as a useful and powerful utility for high school students and teachers.
KmPlot is a mathematical function plotter. It has a powerful parser built in. You can plot different functions simultaneously and combine their function terms to build new functions. KmPlot supports functions with parameters and functions in polar coordinates. Several grid modes are possible. Plots
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.
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