## 19 Search Results

### 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 information### Cinderella

Cinderella is a software system for doing geometry on a computer. The new version Cinderella.2 also includes physics simulations and algorithmic elements.

More information### CoCoA

CoCoA is a system for Computations in Commutative Algebra. It is able to perform simple and sophisticated operations on multivaraiate polynomials and on various data related to them (ideals, modules, matrices, rational functions). For example, it can readily compute Grobner bases, syzygies and minimal free resolution, intersection, division, the radical of an ideal, the ideal of zero-dimensional schemes, Poincare' series and Hilbert functions, factorization of polynomials, toric ideals. The capabilities of CoCoA and the flexibility of its use are further enhanced by the dedicated high-level programming language. For convenience, the system offers a textual interface, an Emacs mode, and a graphical user interface common to most platforms.

More information### Convex

Convex is a Maple package for convex geometry. It can deal with rational polytopes, cones and other polyhedra of arbitrary dimension. Polyhedral complexes and fans are also supported, as well as computations in face lattices. The integration into Maple makes Convex particularly suited for "applied" problems where polyhedra arise together with other mathematical structures.

More information### GAP

GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more. GAP is developed by international cooperation. The system, including source, is distributed freely under the terms of the GNU General Public License. You can study and easily modify or extend GAP for your special use. The current version is GAP 4, the older version GAP 3 is still available.

More information### HiFlow³

HiFlow³ is a multi-purpose finite element software providing powerful tools for efficient and accurate solution of a wide range of problems modeled by partial differential equations. Based on object-oriented concepts and the full capabilities of C++ the HiFlow³ project follows a modular and generic approach for building efficient parallel numerical solvers. It provides highly capable modules dealing with the mesh setup, finite element spaces, degrees of freedom, linear algebra routines, numerical solvers, and output data for visualization. Parallelism – as the basis for high performance simulations on modern computing systems – is introduced on two levels: coarse-grained parallelism by means of distributed grids and distributed data structures, and fine-grained parallelism by means of platform-optimized linear algebra back-ends.

More information### HSL

HSL (formerly the Harwell Subroutine Library) is a collection of ISO Fortran codes for large scale scientific computation, written by members of the Numerical Analysis Group and other experts.

More information### ISAAC

ISAAC (Integrated Solution Algorithm for Arbitrary Configurations) is a compressible Euler/Navier-Stokes computational fluid dynamics code. ISAAC includes the capability of calculating the Euler equations for inviscid flow or the Navier-Stokes equations for viscous flows. ISAAC uses a domain decomposition structure to accomodate complex physical configurations. ISAAC can calculate either steady-state or time dependent flow. ISAAC was designed to test turbulence models. Various two equation turbulence models, explicit algebraic Reynolds stress models, and full differential Reynolds stress models are implemented in ISAAC. Several test cases are documented in the User's Guide.

More information### 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.

More information### Maple

Maple is an environment for scientific and engineering problem-solving, mathematical exploration, data visualization and technical authoring.

More information### Normaliz

Normaliz is a tool for computations in affine monoids, vector configurations, lattice polytopes, and rational cones. Its input data can be specified in terms of a system of generators or vertices or a system of linear homogeneous Diophantine equations, inequalities and congruences or a binomial ideal. Normaliz computes the dual cone of a rational cone (in other words, given generators, Normaliz computes the defining hyperplanes, and vice versa), a placing (or lexicographic) triangulation of a vector configuration (resulting in a triangulation of the cone generated by it), the Hilbert basis of a rational cone, the lattice points of a lattice polytope, the normalization of an affine monoid, the Hilbert (or Ehrhart) series and the Hilbert (or Ehrhart) (quasi) polynomial under a Z-grading (for example, for rational polytopes), NEW: generalized (or weighted) Ehrhart series and Lebesgue integrals of polynomials over rational polytopes via NmzIntegrate, a description of the cone and lattice under consideration by a system of inequalities, equations and congruences

More information### 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.

More information### polymake

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 information### rbMIT

The rbMIT © MIT software package implements in Matlab® all the general reduced basis algorithms. The rbMIT © MIT software package is intended to serve both (as Matlab® source) "Developers" — numerical analysts and computational tool-builders — who wish to further develop the methodology, and (as Matlab® "executables") "Users" — computational engineers and educators — who wish to rapidly apply the methodology to new applications. The rbMIT software package was awarded with the Springer Computational Science and Engineering Prize in 2009.

More information### Regina

Regina is a suite of mathematical software for 3-manifold topologists. It focuses upon the study of 3-manifold triangulations and includes support for normal surfaces and angle structures.

More information### Sage

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 information### SINGULAR

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 information### SymPy

SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python and does not require any external libraries.

More information### SYNAPS

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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