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3D-XplorMath
The primary goal of 3D-XplorMath is to allow users with little or no programming experience to see, with minimal effort, concrete visual representations of many different categories of mathematical objects and processes. To accomplish this, objects from each category are described internally by well-designed, parameterized data structures, and for each category a variety of rendering methods is provided to permit visualization of objects of the category in ways that are appropriate for various purposes. Each of the hundreds of built-in objects known to the program is assigned carefully chosen defaults so that, when the object is selected from a menu, the program can immediately construct a standard example of the object and render it in an optimized view. The user may then use various menus and dialogs to alter the parameters describing the shape and coloration of the object, change the viewpoint from which it is seen, select different rendering methods, etc. Moreover, as its name suggests, the program can display objects such as surfaces, space curves and polyhedra using various stereo techniques. In addition to the many built-in objects known to the program, a user can create "user-defined" objects by entering formulas using standard mathematical notation. Visualizations created by the program can be saved in jpeg and other graphic formats and the data defining 3D objects can be exported to other 3D programs (e.g., Bryce or POV-Ray) in formats such as .obj and .inc. Both built-in and user-defined objects can depend on parameters, and the program can create morphing animations by moving along a path in the parameter space, and these animations can then be saved as QuickTime movies. Each of the built-in objects has associated to it a so-called ATO (About This Object) file that provides documentation for the object. An early and more developed version of the program, written in Object Pascal, runs under the Macintosh Operating System and a Java-based cross-platform version is now also available.
More informationAxiom
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.
More informationePix
ePiX, a collection of batch-oriented utilities for *nix, creates mathematically accurate line figures, plots, and movies using easy-to-learn syntax. LaTeX and dvips comprise the typographical rendering engine, while ImageMagick is used to create bitmapped images and animations. The user interface resembles that of LaTeX itself: You prepare a short scene description in a text editor, then compile'' the input file into a picture. Default output formats are eepic (a plain text enhancement to the LaTeX picture environment), eps, pdf, png, and mng.
More informationMagma
Magma is a large, well-supported software package designed to solve computationally hard problems in algebra, number theory, geometry and combinatorics. It provides a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatoric and geometric objects.
More informationPLTMG
PLTMG is a package for solving elliptic partial differential equations in general regions of the plane. It is based on continuous piecewise linear triangular finite elements, and features adaptive local mesh refinement, multigraph iteration, and pseudo-arclength continuation options for parameter dependencies. It also provides options for solving several classes of optimal control and obstacle problems. The package includes an initial mesh generator and several graphics packages. Support for the Bank-Holst parallel adaptive meshing strategy is also provided. PLTMG is provided as Fortran (and a little C) source code, in both single and double precision versions. The code has interfaces to X-Windows, MPI, and Michael Holst's OpenGL image viewer SG. The X-Windows, MPI, and SG interfaces require libraries that are NOT provided as part of the PLTMG package.
More informationpolymake
polymake is an object-oriented system for experimental discrete mathematics. The typical working cycle of a polymake user starts with the construction of an object of interest, auch as a convex polytope, a finite simplicial complex, a graph, etc. It is then possible to ask the system for some of the object's properties or for some form of visualization. Further steps might include more elaborate constructions based on previously defined objects. Each class of polymake objects comes with a set of rules which describe how a new property of an object can be derived from previously known ones. It is a key feature that the user can extend or modify the set of rules, add further properties or even new classes of objects (with entirely new rule bases). The functions provided include: several convex hull algorithms, face lattices of convex polytopes, Voronoi diagrams and Delaunay decompositions (in arbitrary dimensions), simplicial homology (with integer coefficients), simplicial cup and cap products, intersection forms of triangulated 4-manifolds. Several forms of (interactive) visualization via interfaces to Geomview, JavaView and other programs.
More informationSage
SAGE is a framework for number theory, algebra, and geometry computation. It is open source and freely available under the terms of the GNU General Public License (GPL). SAGE is a Python library with a customized interpreter. It is written in Python, C++, and C (via Pyrex). Python (http://www.python.org) is an open source object-oriented interpreted language, with a large number of libraries, e.g., for numerical analysis, which are available to users of SAGE. Python can also be accessed in library mode from C/C++ programs. SAGE provides an interface to several important open source libraries, including Cremona’s MWRANK library for computing with elliptic curves, the PARI library (pari.math.u-bordeaux.fr) for number theory, Shoup’s number theory library NTL (http://www.shoup.net/ntl/), SINGULAR (http://www.singular.uni-kl.de) for commutative algebra, GAP (http://www.gap-system.org) for group theory and combinatorics, and maxima (http://maxima.sourceforge.net) for symbolic computation and calculus.
More informationSINGULAR
SINGULAR is a Computer Algebra system for polynomial computations in commutative algebra, algebraic geometry, and singularity theory. SINGULAR's main computational objects are ideals and modules over a large variety of baserings. The baserings are polynomial rings over a field (e.g., finite fields, the rationals, floats, algebraic extensions, transcendental extensions), or localizations thereof, or quotient rings with respect to an ideal. SINGULAR features fast and general implementations for computing Groebner and standard bases, including e.g. Buchberger's algorithm and Mora's Tangent Cone algorithm. Furthermore, it provides polynomial factorizations, resultant, characteristic set and gcd computations, syzygy and free-resolution computations, and many more related functionalities. Based on an easy-to-use interactive shell and a C-like programming language, SINGULAR's internal functionality is augmented and user-extendible by libraries written in the SINGULAR programming language. A general and efficient implementation of communication links allows SINGULAR to make its functionality available to other programs.
More informationSYNAPS
SYNAPS (Symbolic and Numeric APplicationS) is a library developed in C++. The aim of this open source project is to provide a coherent and efficient library for symbolic and numeric computation. It implements data-structures and classes for the manipulation of basic objects, such as (dense, sparse, structured) vectors, matrices, univariate and multivariate polynomials. It also provides fundamental methods such as algebraic number manipulation tools, different types of univariate and multivariate polynomial root solvers, resultant computations, ...
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