Mathematics Packages:
Octave
GNU 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 using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language.
Octave has extensive tools for solving common numerical linear algebra problems, finding the roots of nonlinear equations, integrating ordinary functions, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations. It is easily extensible and customizable via user-defined functions written in Octave's own language, or using dynamically loaded modules written in C++, C, Fortran, or other languages.
R-Project
R is a language and environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers and colleagues. R can be considered as a different implementation of S. There are some important differences, but much code written for S runs unaltered under R.
R provides a wide variety of statistical (linear and nonlinear modelling, classical statistical tests, time-series analysis, classification, clustering, ...) and graphical techniques, and is highly extensible. The S language is often the vehicle of choice for research in statistical methodology, and R provides an Open Source route to participation in that activity.
bc
bc is an arbitrary precision numeric processing language. Syntax is similar to C, but differs in many substantial areas. It supports interactive execution of statements. bc is a utility included in the POSIX P1003.2/D11 draft standard.
Scilab
Scilab is a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It is developed since 1990 by researchers from INRIA and ENPC. Distributed freely via the Internet since 1994, Scilab is currently being used in educational and industrial environnments around the world.
Scilab includes hundreds of mathematical functions with the possibility to add interactively programs from various languages (C, Fortran...). It has sophisticated data structures (including lists, polynomials, rational functions, linear systems...), an interpreter and a high level programming language.
Yorick
Yorick is an interpreted programming language, designed for postprocessing or steering large scientific simulation codes. Smaller scientific simulations or calculations, such as the flow past an airfoil or the motion of a drumhead, can be written as standalone yorick programs. The language features a compact syntax for many common array operations, so it processes large arrays of numbers very efficiently. Unlike most interpreters, which are several hundred times slower than compiled code for number crunching, yorick can approach to within a factor of four or five of compiled speed for many common tasks. Superficially, yorick code resembles C code, but yorick variables are never explicitly declared and have a dynamic scoping similar to many Lisp dialects. The yorick language is designed to be typed interactively at a keyboard, as well as stored in files for later use. Yorick includes an interactive graphics package, and a binary file package capable of translating to and from the raw numeric formats of all modern computers.
Algae
Algae is an interpreted language for numerical analysis. Algae was developed because we needed a fast and versatile tool, capable of handling large problems. Algae has been applied to interesting dynamics problems in aerospace and related fields for more than a decade.
Yacas
YACAS is an easy to use, general purpose Computer Algebra System, a program for symbolic manipulation of mathematical expressions. It uses its own programming language designed for symbolic as well as arbitrary-precision numerical computations. The system has a library of scripts that implement many of the symbolic algebra operations; new algorithms can be easily added to the library. YACAS comes with extensive documentation (320+ pages) covering the scripting language, the functionality that is already implemented in the system, and the algorithms we used.
Rlab
Rlab is an interactive, interpreted scientific programming environment. Rlab is a very high level language intended to provide fast prototyping and program development, as well as easy data-visualization, and processing. Rlab is not a clone of languages such as those used by tools like Matlab or Matrix-X/Xmath. However, as Rlab focuses on creating a good experimental environment (or laboratory) in which to do matrix math, it can be called ``Matlab-like''; since the programming language possesses similar operators and concepts.
Euler
EULER is a program for quickly and interactively computing with real and complex numbers and matrices, or with intervals, in the style of MatLab, Octave,... It can draw and animate your functions in two and three dimensions.
Maxima
Maxima is a descendant of DOE Macsyma, which had its origins in the late 1960s at MIT. It is the only system based on that effort still publicly available and with an active user community, thanks to its open source nature. Macsyma was the first of a new breed of computer algebra systems, leading the way for programs such as Maple and Mathematica. This particular variant of Macsyma was maintained by William Schelter from 1982 until he passed away in 2001. In 1998 he obtained permission to release the source code under GPL. It was his efforts and skill which have made the survival of Maxima possible, and we are very grateful to him for volunteering his time and skill to keep the original Macsyma code alive and well. Since his passing a group of users and developers has formed to keep Maxima alive and kicking. Maxima itself is reasonably feature complete at this stage, with abilities such as symbolic integration, 3D plotting, and an ODE solver, but there is a lot of work yet to be done in terms of bug fixing, cleanup, and documentation. This is not to say there will be no new features, but there is much work to be done before that stage will be reached, and for now new features are not likely to be our focus.
JACAL
JACAL is an interactive symbolic mathematics program. JACAL can manipulate and simplify equations, scalars, vectors, and matrices of single and multiple valued algebraic expressions containing numbers, variables, radicals, and algebraic differential, and holonomic functions.
gTybalt
Symbolic calculations, carried out by computer algebra systems, have become an integral part in the daily work of scientists. The advance in algorithms and computer technology has led to remarkable progress in several areas of natural sciences. gTybalt was developed as a tool for certain kind of calculations. The characteristics of these calculations are: First of all, these tend to be "long" calculations, e.g. the system needs to process large amounts of data and efficiency in performance is a priority. Secondly, the algorithms for the solution of the problem are usually developed and implemented by the scientists themselves. This requires support from the computer algebra system for a programming language which allows to implement complex algorithms for abstract mathematical entities. In other words, it requires support of object oriented programming techniques from the system. On the other hand, these calculations usually do not require that the computer algebra system provides sophisticated tools for all branches of mathematics. Thirdly, despite the fact that these calculations process large amounts of data, the time needed for the implementation of the algorithms usually outweights the actual running time of the program. Therefore convenient development tools are also important.
Symaxx
Symaxx/2 is a graphical frontend for Maxima.
Singluar
SINGULAR is a Computer Algebra System for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry, and singularity theory.
HartMath
HartMath is an experimental computer algebra system written in Java.
GiNaC
The name GiNaC is an iterated and recursive abbreviation for GiNaC is Not a CAS, where CAS stands for Computer Algebra System. It has been developed to become a replacement engine for xloops which is up to now powered by the Maple CAS. Its design is revolutionary in a sense that contrary to other CAS it does not try to provide extensive algebraic capabilities and a simple programming language but instead accepts a given language (C++) and extends it by a set of algebraic capabilities.
XLoops
Aim of this project is to provide a package that completely evaluates massive one- and two-loop Feynman diagrams to make calculations in high energy physics easier.
PARI-GP
PARI-GP is a software package for computer-aided number theory. It consists of a C library, libpari (with optional assembler cores for some popular architectures), and of the programmable interactive gp calculator. While you can write your own libpari-based programs, many people just start up a gp session, or have gp execute their scripts.
GRASS
GRASS GIS (Geographic Resources Analysis Support System) is an open source, Free Software Geographical Information System (GIS) with raster, topological vector, image processing, and graphics production functionality that operates on various platforms through a graphical user interface and shell in X-Windows. It is released under GNU General Public License (GPL).
Macaulay 2
Macaulay 2 is a software system devoted to supporting research in algebraic geometry and commutative algebra, whose development has been funded by the National Science Foundation.
NumExp
NumExp is a family of open-source applications for numeric computation. When it was created, the idea was to make a powerfull tool like Mathematica. Now, we know this is almost impossible without more open-source hackers. Meanwhile, we are trying to make, at least, an useful tool!
GtkGraph
GtkGraph is a simple graphing calculator written for X Windows using the Gtk+ widget set. It is intended as a replacement for a standalone graphing calculator, which typically costs over $80 USD, and has a tiny monochrome display driven by a CPU running at around 6 MHz with no FPU. GtkGraph can plot functions and solve arithmetic expressions using double precision arithmetic.
surf
surf is a tool to visualize some real algebraic geometry: plane algebraic curves, algebraic surfaces and hyperplane sections of surfaces. surf is script driven and has (optionally) a nifty GUI using the Gtk widget set.
The E Equational Theorem Prover
E is a a purely equational theorem prover for clausal logic. That means it is a program that you can stuff a mathematical specification (in clausal logic with equality) and a hypothesis into, and which will then run forever, using up all of your machines resources. Very occasionally it will find a proof for the hypothesis and tell you so ;-).
TISEAN
TISEAN is free a software project for the analysis of time series with methods based on the theory of nonlinear deterministic dynamical systems, or chaos theory, if you prefer.
Plotting Software
Gnuplot
gnuplot is a command-driven interactive function plotting program. It can be used to plot functions and data points in both two- and three-dimensional plots in many different formats, and will accommodate many of the needs of today's scientists for graphic data representation. gnuplot is copyrighted, but freely distributable; you don't have to pay for it.
NCAR
The NCAR Command Language (NCL) is a programming language designed specifically for the access, analysis, and visualization of data. NCL can be run in interactive mode, where each line is interpreted as it is entered at your workstation, or it can be run in batch mode as an interpreter of complete scripts.
Gri
Gri is a language for scientific graphics programming. The word "language" is important: Gri is command-driven, not point/click. Some users consider Gri similar to LaTeX, since both provide extensive power as a reward for tolerating a learning curve. Gri can make x-y graphs, contour graphs, and image graphs, in PostScript and (someday) SVG formats. Control is provided over all aspects of drawing, e.g. line widths, colors, and fonts. A TeX-like syntax provides common mathematical symbols.
PLplot
PLplot is a library of functions that are useful for making scientific plots. PLplot can be used from within compiled languages such as C, C++, FORTRAN and Java, and interactively from interpreted languages such as Octave, Python, Perl and Tcl. The PLplot library can be used to create standard x-y plots, semilog plots, log-log plots, contour plots, 3D surface plots, mesh plots, bar charts and pie charts. Multiple graphs (of the same or different sizes) may be placed on a single page with multiple lines in each graph.
PGPLOT
The PGPLOT Graphics Subroutine Library is a Fortran- or C-callable, device-independent graphics package for making simple scientific graphs. It is intended for making graphical images of publication quality with minimum effort on the part of the user. For most applications, the program can be device-independent, and the output can be directed to the appropriate device at run time.
plotutils
The GNU plotutils package contains software for both programmers and technical users. Its centerpiece is libplot, a powerful C/C++ function library for exporting 2-D vector graphics in many file formats, both vector and raster. It can also do vector graphics animations.
SciGraphica
SciGraphica is a scientific application for data analysis and technical graphics. It pretends to be a clone of the popular commercial (and expensive) application "Microcal Origin". It fully supplies plotting features for 2D, 3D and polar charts. The aim is to obtain a fully-featured, cross-plattform, user-friendly, self-growing scientific application. It is free and open-source, released under the GPL license.
Grace
Grace is a WYSIWYG 2D plotting tool for the X Window System and M*tif.
Ptplot
Ptplot 5.2 is a 2D data plotter and histogram tool implemented in Java. Ptplot can be used as a standalone applet or application, or it can be embedded in your own applet or application.
DISLIN
DISLIN is a high-level plotting library for displaying data as curves, polar plots, bar graphs, pie charts, 3D-color plots, surfaces, contours and maps.
ImLib3D
ImLib3D is an open source C++ library for 3D (volumetric) image processing. It contains most basic image processing algorithms, and some more sophisticated ones. It comes with an optional viewer that features multiplanar views, animations, vector field views and 3D (OpenGL) multiplanar. All image processing operators can be interactively called from the viewer as well as from the UNIX command-line. ImLib3D's goal is to provide a standard and easy to use platform for volumetric image processing research. Focus has been put on simplicity for the developer. ImLib3D has been carefully designed, using modern, standards conforming C++. It intensively uses the Standard C++ Library, including strings, containers, and iterators.
GLgraph
GLgraph visualize mathematical functions. It can handle 3 unknowns (x,z,t) and can produce a 4D function with 3 space and 1 time dimension.
MayaVi
MayaVi is a free, easy to use scientific data visualizer. It is written in Python and uses the amazing Visualization Toolkit (VTK) for the graphics. It provides a GUI written using Tkinter. MayaVi is free and distributed under the conditions of the BSD license. It is also cross platform and should run on any platform where both Python and VTK are available (which is almost any *nix, Mac OSX or Windows).
Graphviz
Graph Drawing Programs from AT&T Research and Lucent Bell Labs
Numerical Libraries
GNU Scientific Library
The GNU Scientific Library (GSL) is a numerical library for C and C++ programmers. It is free software under the GNU General Public License.
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.
SAML
The "Simple Algebraic Math Library" is a C library for computer algebra, together with some application programs: a desktop calculator, a spreadsheet (sort of) and a program to factorize integers.
Numerical Python
Numerical Python adds a fast, compact, multidimensional array language facility to Python.
VTK
The Visualization ToolKit (VTK) is an open source, freely available software system for 3D computer graphics, image processing, and visualization used by thousands of researchers and developers around the world. VTK consists of a C++ class library, and several interpreted interface layers including Tcl/Tk, Java, and Python. VTK supports a wide variety of visualization algorithms including scalar, vector, tensor, texture, and volumetric methods; and advanced modeling techniques such as implicit modelling, polygon reduction, mesh smoothing, cutting, contouring, and Delaunay triangulation. In addition, dozens of imaging algorithms have been directly integrated to allow the user to mix 2D imaging / 3D graphics algorithms and data. The design and implementation of the library has been strongly influenced by object-oriented principles.
PDL
PDL (``Perl Data Language'') gives standard Perl the ability to compactly store and speedily manipulate the large N-dimensional data arrays which are the bread and butter of scientific computing.
LAPACK
LAPACK is written in Fortran77 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision.
PARI-GP
PARI-GP is a software package for computer-aided number theory. It consists of a C library, libpari (with optional assembler cores for some popular architectures), and of the programmable interactive gp calculator. While you can write your own libpari-based programs, many people just start up a gp session, or have gp execute their scripts.
Python Number Crunching
This page lists a number of packages related to numerics, number crunching, signal processing, financial modeling, linear programming, statistics, data structures, date-time processing, random number generation, and crypto.
LINPACK
LINPACK is a collection of Fortran subroutines that analyze and solve linear equations and linear least-squares problems. The package solves linear systems whose matrices are general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square. In addition, the package computes the QR and singular value decompositions of rectangular matrices and applies them to least-squares problems. LINPACK uses column-oriented algorithms to increase efficiency by preserving locality of reference.
LINPACK was designed for supercomputers in use in the 1970s and early 1980s. LINPACK has been largely superceded by LAPACK, which has been designed to run efficiently on shared-memory, vector supercomputers.
ATLAS
ATLAS stands for Automatically Tuned Linear Algebra Software. ATLAS is both a research project and a software package. This FAQ describes the software package. ATLAS's purpose is to provide portably optimal linear algebra software. The current version provides a complete BLAS API (for both C and Fortran77), and a very small subset of the LAPACK API. For all supported operations, ATLAS achieves performance on par with machine-specific tuned libraries.
CLN
CLN is a library for computations with all kinds of numbers. It has a rich set of number classes... [see web page]
Colt
This distribution provides an infrastructure for scalable scientific and technical computing in Java. It is particularly useful in the domain of High Energy Physics at CERN: It contains, among others, efficient and usable data structures and algorithms for Off-line and On-line Data Analysis, Linear Algebra, Multi-dimensional arrays, Statistics, Histogramming, Monte Carlo Simulation, Parallel & Concurrent Programming. It summons some of the best concepts, designs and implementations thought up over time by the community, ports or improves them and introduces new approaches where need arises. In overlapping areas, it is competitive or superior to toolkits such as STL, Root, HTL, CLHEP, TNT, GSL, C-RAND / WIN-RAND, (all C/C++) as well as IBM Array, JDK 1.2 Collections framework, JGL (all Java), in terms of performance (!), functionality and (re)usability.
Programming Languages
Lush
Lush is an object-oriented programming language designed for researchers, experimenters, and engineers interested in large-scale numerical and graphic applications. Lush is designed to be used in situations where one would want to combine the flexibility of a high-level, loosely-typed interpreted language, with the efficiency of a strongly-typed, natively-compiled language, and with the easy integration of code written in C, C++, or other languages.
Nickle
Nickle is a programming language based prototyping environment with powerful programming and scripting capabilities. Nickle supports a variety of datatypes, especially arbitrary precision numbers. The programming language vaguely resembles C. Some things in C which do not translate easily are different, some design choices have been made differently, and a very few features are simply missing.
Nickle provides the functionality of UNIX bc, dc and expr in much-improved form. It is also an ideal environment for prototyping complex algorithms. Nickle's scripting capabilities make it a nice replacement for spreadsheets in some applications, and its numeric features nicely complement the limited numeric functionality of text-oriented languages such as AWK and PERL.
Open Dynamics Engine
ODE is a free, industrial quality library for simulating articulated rigid body dynamics - for example ground vehicles, legged creatures, and moving objects in VR environments. It is fast, flexible, robust and platform independent, with advanced joints, contact with friction, and built-in collision detection.
Blitz++
Blitz++ is a C++ class library for scientific computing which provides performance on par with Fortran 77/90. It uses template techniques to achieve high performance. The current versions provide dense arrays and vectors, random number generators, and small vectors and matrices.
FFTW
FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine and sine transforms, the DCT and DST). We believe that FFTW, which is free software, should become the FFT library of choice for most applications.
Our benchmarks, performed on on a variety of platforms, show that FFTW's performance is typically superior to that of other publicly available FFT software, and is even competitive with vendor-tuned codes. In contrast to vendor-tuned codes, however, FFTW's performance is portable: the same program will perform well on most architectures without modification. Hence the name, "FFTW," which stands for the somewhat whimsical title of "Fastest Fourier Transform in the West."
GMP
GNU MP is a library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers. It has a rich set of functions, and the functions have a regular interface.
NURBS++
Non-Uniform Rational B-Splines (NURBS) curves and surface are parametric functions which can represent any type of curves or surfaces. This C++ library hides the basic mathematics of NURBS. This allows the user to focus on the more challenging parts of their projects. The library also offers a lot of features to help generate NURBS from data points.
SciPy
SciPy is an open source library of scientific tools for Python. SciPy supplements the popular Numeric module, gathering a variety of high level science and engineering modules together as a single package.
SciPy includes modules for graphics and plotting, optimization, integration, special functions, signal and image processing, genetic algorithms, ODE solvers, and others.
Sites of Interest
The Linux Lab Project
The Linux lab project is intended to help people with development of data collection and process control software for LINUX. It should be in understood as software and knowledge pool for interested people and application developers dealing with this stuff in educational or industrial environment.
Programming Systems on GNU/Linux
This page deals with links to tutorials, documents, and Linux implementations for installing Linux on a PC, getting started with Linux, and then going a step further -- to optimise your PC for processing power, using multiple processors (Symmetric Muliti Processing - SMP); making a cheap, upgradeable, Supercomputing Linux cluster and finally links to software to do parallel programming on Linux.
Scientific Applications on Linux
SAL (Scientific Applications on Linux) is a collection of information and links to software that will be of interest to scientists and engineers. The broad coverage of Linux applications will also benefit the whole Linux/Unix community. There are currently 3,070 entries in SAL.
Netlib
Netlib is a collection of mathematical software, papers, and databases.
FSF Free Software Directory - Mathematics
[Collection of GPL'd and other Free Software]
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