Math
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Cadabra is a computer algebra system (CAS) designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor computer algebra, tensor polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, implicit coordinate dependence, multiple index types and many more. The input format is a subset of TeX. Both a command-line and a graphical interface are available. Designed for field-theory problems, with handling of anti-commuting and non-commuting objects without special notations for their products, gamma matrix algebra, Fierz identities, Dirac conjugation, vielbeine, flat and curved, covariant and contravariant indices, implicit dependence of tensors on coordinates, partial and covariant derivatives...
Cadabra: a field-theory motivated approach to computer algebra
Axiom is a general purpose Computer Algebra system. It is useful for research and development of mathematical algorithms. It defines a strongly typed, mathematically correct type hierarchy. It has a programming language and a built-in compiler.
Axiom Computer Algebra System
Above image created with the old float version of Fermat. Fermat is a computer algebra system for Macintosh, Windows, Linux, and Unix by me, Robert H. Lewis of Fordham University, that does arithmetic of arbitrarily long integers and fractions, multivariate polynomials, symbolic calculations, matrices over polynomial rings, graphics, and other numerical calculations. It is extremely fast and extremely economical of space. The main version that I care most about is oriented toward polynomial and matrix algebra over the rationals Q and finite fields. On the Mac side, there is are versions for OS X and old versions for OS 9.
Fermat, Computer Algebra System
Main Page - wxMaxima
About wxMaxima is a document based interface for the computer algebra system Maxima . wxMaxima uses wxWidgets and runs natively on Windows, X11 and Mac OS X. wxMaxima provides menus and dialogs for many common maxima commands, autocompletion, inline plots and simple animations. wxMaxima is distributed under the GPL license .
Yorick Home @ Sourceforge
What is Yorick? Yorick is an interpreted programming language for scientific simulations or calculations, postprocessing or steering large simulation codes, interactive scientific graphics, and reading, writing, or translating large files of numbers. 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. Yorick is written in ANSI C and runs on most operating systems (*nix systems, Windows, MacOS). For a short overview, see the Linux Gazette and Unix review articles. Yorick has a compact syntax, similar to C, but with array operators.parce que les mathématiques peuvent être un vrai plaisir! K3DSurf est un programme qui permet la visualisation et la manipulation de modèles mathématiques dans l'espace de trois, quatre, cinq et six dimensions. K3DSurf supporte les équations Paramétriques et les Isosurfaces. Animation en temps réel(rotation) et morphe (avec l'introduction d'une nouvelle variable t_temps). L'animation et l'effet morphe peuvent aussi être asservis par des contrôles qui affectent la CPU et le pas t_temps.
K3DSurf : 3d surface generator
ParaView is an open-source, multi-platform data analysis and visualization application. ParaView users can quickly build visualizations to analyze their data using qualitative and quantitative techniques. The data exploration can be done interactively in 3D or programmatically using ParaView's batch processing capabilities. ParaView was developed to analyze extremely large datasets using distributed memory computing resources. It can be run on supercomputers to analyze datasets of terascale as well as on laptops for smaller data.
ParaView
This is the GTK+ based version of EULER for Unix / Linux systems. It has been ported to GTK+ by Eric Boucharé (bouchare dot eric at wanadoo dot fr) on the base of Dr Rene Grothmann 's X11 version. Euler was started by Dr Grothmann. He also maintains a version for Windows systems. 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.
Euler
Maxima, a Computer Algebra System
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 precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions. The Maxima source code can be compiled on many systems, including Windows, Linux, and MacOS X. The source code for all systems and precompiled binaries for Windows and Linux are available at the SourceForge file manager .
REDUCE Computer Algebra System
REDUCE is an interactive system for general algebraic computations of interest to mathematicians, scientists and engineers. It has been produced by a collaborative effort involving many contributors . Its capabilities include: