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****1/2 SAGE
SAGE is free open source math software that supports research and teaching in algebra, geometry, number theory, cryptography, numerical computation, and related areas. Both the SAGE development model and the technology in SAGE itself is distinguished by an extremely strong emphasis on openness, community, cooperation, and collaboration: we are building the car, not reinventing the wheel. The overall goal of SAGE is to create a viable free open source alternative to Maple, Mathematica, Magma, and MATLAB.
****1/2 Scilab
Scilab is a scientific software package for numerical computations in a user-friendly environment. It features: Elaborate data structures (polynomial, rational and string matrices, lists, multivariable linear systems,...). Sophisticated interpreter and programming language with Matlab-like syntax. Hundreds of built-in math functions (new primitives can easily be added). Stunning graphics (2d, 3d, animation). Open structure (easy interfacing with Fortran and C via online dynamic link). Many built-in libraries: Linear Algebra (including sparse matrices, Kronecker form, ordered Schur,...). Control (Classical, LQG, H-infinity,...). Package for LMI (Linear Matrix Inequalities) optimization. Signal processing. Simulation (various ode's, dassl,...). Optimization (differentiable and non-differentiable, LQ solver). Scicos, an interactive environment for modeling and simulation of dynamical systems. Metanet (network analysis and optimization). Symbolic capabilities through Maple interface. Parallel Scilab.
****1/2 Octave
GNU Octave is a high-level language, primarily intended for numerical computations.
****1/2 K3DSurf
K3DSurf is a program for visualizing and manipulating multidimensional surfaces by using Mathematical equations. It's also a "modeler" for POV-Ray in the area of parametric surfaces. It features 3D, 4D, 5D, and 6D HyperObjects visualization, full support for all functions (like the C language), support for mouse events in the drawing area, animation and morph effects, Povscript and mesh file generation, and support for VRML2 and OBJ files. More than 100 examples are provided.
**** Netlib
An incredibly useful set of libraries for numerical computation.
**** JSci - A science API for Java
JSci is a set of open source Java packages. The aim is to encapsulate scientific methods/principles in the most natural way possible. As such they should greatly aid the development of scientific based software. Features include: abstract math interfaces, linear algebra (support for various matrix types), statistics, wavelets, newtonian mechanics, chart/graph components (AWT and Swing), partial MathML DOM implementation, lots more...
***1/2 Java Algebra System
The Java Algebra System (JAS) is an object oriented, type safe and 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 an jython (Java Python) and jruby (Java Ruby) front end. The focus of JAS is at the moment on commutative and solvable polynomials, Gröbner bases and applications. By the use of Java as implementation language JAS is 64-bit and multi-core cpu ready.
***1/2 Maxima
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. Also has a graphical interface built in wxWidgets called wxMaxima (http://andrejv.github.com/wxmaxima/).
***1/2 Gephi
Gephi is an interactive visualization and exploration platform for all kinds of networks and complex systems, dynamic and hierarchical graphs. Gephi is a tool for people that have to explore and understand graphs. Like Photoshop but for data, the user interacts with the representation, manipulate the structures, shapes and colors to reveal hidden properties. The goal is to help data analysts to make hypothesis, intuitively discover patterns, isolate structure singularities or faults during data sourcing. It is a complementary tool to traditional statistics, as visual thinking with interactive interfaces is now recognized to facilitate reasoning. This is a software for Exploratory Data Analysis, a paradigm appeared in the Visual Analytics field of research.
***1/2 GNU libmatheval
GNU libmatheval is a library (callable from C and Fortran) to parse and evaluate symbolic expressions input as text. It supports expressions in any number of variables of arbitrary names, decimal and symbolic constants, basic unary and binary operators, and elementary mathematical functions. In addition to parsing and evaluation, libmatheval can also compute symbolic derivatives and output expressions to strings.
***1/2 Mathomatic
Mathomatic is a general purpose CAS (Computer Algebra System) and calculator software that can symbolically solve, simplify, combine, and compare algebraic equations, perform complex number and polynomial arithmetic, etc. It does some calculus and handles all elementary algebra, except logarithms.
***1/2 Lybniz
Lybniz is an easy to use mathematical function graph plotter using pyGTK. It is sutable for use as a graphing calculator or in education
*** clados Project
The Clados Project maintains an open source java library capable of implementing geometric algebras (Clifford Algebras) in computer applications designed to simulate physical events and environments.
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