ActiveMath (http://www.activemath.org)
Description: ActiveMath is a learning environment for mathematics. It is a web-server based on java servlets which presents semantic OMDoc content to contemporary web-browsers with good quality. ActiveMath supports the learning experience by modelling the learners' competencies in a learner-model that is fed by tracking the reading and the interactive exercises. The interactive exercises can be rich and multiple-steps exercises and use computer-algebra-systems to evaluate a learner's input. The content items of ActiveMath are annotated with pedagogical and mathematical knowledge which allows the learner to obtain courses prepared on demand on given learning goals. Finally, the semantic OMDoc representation allows copy-and-paste of formulae and search for content items by text, annotations, or formulae.
License: Free and open-source for public educational institution
Live on the KNOPPIX (non-free)
Related presentation: p035
Aldor (http://www.aldor.org)
Description:
Aldor is a computer programming language, like Scheme, Java or C
.
License: Other (BSD like)
Live on the KNOPPIX
Related presentation: p046
Algorithms in real algebraic geometry (interactive book) (http://perso.univ-rennes1.fr/marie-francoise.roy/bpr-posted1.html)
Description: Algorithms in real algebraic geometry, by S. Basu, R. Pollack and M.-F. Roy, is a preliminary test version of an extension of the first edition published by Springer in 2003. This interactive book is based on texmacs, and live examples can be computed within the book through the SARAG maxima library by F. Caruso. The final version is due to be published by Springer.
License: GPL, others
Algorithms in real algebraic geometry (interactive book) non-free documents or executables on DVD
Live on the KNOPPIX (non-free)Related presentation: p003
Arageli (http://www.unn.ru/cs/arageli)
Description: Arageli is a C++ library for doing symbolic computations. It contains arbitrary precision integer and rational numbers, vectors, matrices, polynomials, modular arithmetic, algorithms for number factorization, linear and integer programming etc. Creating new mathematical structures from existing ones (also in other libraries) is easy. Arageli is used in Skeleton, Integizer, Prelinea projects.
License: Free for academic and noncommercial use
Arageli non-free documents or executables on DVD
Related presentation: p029
The Atlas of Lie Groups and Representations (http://atlas.math.umd.edu/)
Description: This is a project to make available information about representations of semi-simple Lie groups over real and p-adic fields. The software is in an early stage of development. Given a general connected complex group G, the software will compute among other things: parameters for the irreducible representations of G with regular integral infinitesimal character, Kazhdan-Lusztig polynomials for representations with regular integral infinitesimal character, .... etc. ( Alfred G. Noel, University of Massachusetts Boston)
License:
Related presentation: p004
axiom (http://www.axiom-developer.org)
Description: Axiom is a computer algebra system with a strongly-typed high-level programming language. Over 1,000 mathematical domains and categories are collected in the library.
License: Modified BSD
Live on the KNOPPIXRelated presentation: p772
BESSELINT (http://www.cs.kuleuven.be/~nines/software/BESSELINT/)
Description:
BESSELINT is a Matlab program to compute integrals of the form
with 
the Bessel function of the first kind and (real) order
. The parameter 
is a real number such that
and the coefficients 
are strictly positive real numbers. In the near
future this will be extended to compute the Laplace transform of a product of
Bessel functions with possibly an additional factor of 
in the
denominator (where 
is a real number).
(Joris Van Deun and Ronald Cools, K.U.Leuven)
License:
Related presentation: p057
CoCoA4 (http://cocoa.dima.unige.it/)
Description: The interactive system CoCoA-4.6 offers facilities for COmputations in COmmutative Algebra: Groebner bases and related operations on ideals and modules, Hilbert functions, factorization of polynomials, and some exact linear algebra. CoCoA-4.6 is well-suited to teaching with its simple and mathematically natural command language, and an extensive online help facility. It is free and runs on most common platforms.
License: The executables are free
Live on the KNOPPIX
CoCoALib (http://cocoa.dima.unige.it/)
Description: The C++ library CoCoALib offers data structures and operations for COmputations in COmmuative Algebra, most particularly Groebner bases. Ease of use through a clean design is paramount (with some concessions to guarantee good performance). The library comes with full documentation and numerous example programs. A ``beta'' release is anticipated in late 2006. A server and interactive system are planned.
License: GPL, others
Live on the KNOPPIXRelated presentation: p055
Computer Algebra Animation (http://www.math.kobe-u.ac.jp/caa)
Description: An experimental project for algorithm animations and graphical or interactive user interface in computer algebra with Java and OpenXM.
License: GPL
Live on the KNOPPIXRelated presentation: p054
Coq (http://coq.inria.fr)
Description: Coq is a proof assistant.
License: LGPL
Coq documents or executables on DVD
Live on the KNOPPIX
Related presentation: p105
DEpthLAUNAY (http://www.dma.fi.upm.es/mabellanas/delonedepth/)
Description: DEpthLAUNAY is a C++ software developed with CGAL ( http://www.CGAL.org ) that computes the following geometric structures given a finite set of points in the plane: convex hull, convex layers, convex levels, Delaunay triangulation, Delaunay layers, Delaunay levels, and Voronoi diagram. Input points can be randomly generated, introduced interactively or simply aquired from image files. ( Manuel Abellanas, Universidad Politecnica de Madrid)
License: QPL
DEpthLAUNAY non-free documents or executables on DVD
Live on the KNOPPIX (non-free)Related presentation: p034
Epsilon (http://www-calfor.lip6.fr/~wang/epsilon)
Description: Epsilon is a library of functions implemented in Maple and Java for polynomial elimination and triangular decomposition with (geometric) applications. It has 8 modules and contains more than 70 functions, with documentation, examples, and Maple worksheets. (Dongming Wang, Beihang University, China and UPMC-CNRS, France)
License: Free for academic and noncommercial use
GAP (http://www.gap-system.org)
Description: 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.
License: GPL
GAP documents or executables on DVD
Live on the KNOPPIX
GAP package Alnuth (http://www.gap-system.org/Packages/alnuth.html)
Description: The Alnuth package provides various methods to compute with number fields which are given by a defining polynomial or by generators. Some of the methods provided in this package are written in GAP code. The other part of the methods is imported from the Computer Algebra System KANT.
License: GPL
GCLC/WinGCLC (http://www.matf.bg.ac.yu/~janicic/gclc/)
Description: GCLC/WinGCLC is a tool for visualizing and teaching geometry (and not only geometry), and for producing mathematical illustrations. It has support for a range of geometrical constructions and transformations, for symbolic expressions, parametric curves, program loops, for automated proving of geometrical conjectures, for exporting figures into LaTeX and bitmap format etc.
License: Free for academic and noncommercial use
GCLC/WinGCLC non-free documents or executables on DVD
Live on the KNOPPIX (non-free)Related presentation: p002
GEX (http://www.mmrc.iss.ac.cn/gex/)
Description: Geometry Expert (GEX) is a software for dynamic geometric diagram drawing and automated geometry theorem proving and discovering. As a dynamic geometry software, GEX can be used to build dynamic visual models to assist manipulating and teaching various mathematical concepts. As an automated reasoning software, GEX can be used to prove and discover hundreds of non-trivial geometry theorems automatically
License:
GEX non-free documents or executables on DVD
Live on the KNOPPIX (non-free)Gfan (http://home.imf.au.dk/ajensen/software/gfan/gfan.html)
Description: Gfan is a command line tool for enumerating the reduced Groebner bases of a polynomial ideal in n variables. Hereby the Groebner fan, an n-dimensional polyhedral complex, is computed. The tropical variety is a certain subcomplex which can also be computed by the software. Gfan uses Gmp and Cddlib for exact arithmetic and polyhedral computations, respectively.
License: GPL
Live on the KNOPPIXRelated presentation: p028
GiANT: Graphical Algebraic Number Theory (http://giantsystem.sourceforge.net)
Description: GiANT is a graphical interface for working with number fields. GiANT offers interactive diagrams, drag-and-drop functionality, and typeset formulas. GiANT is written in Java, but uses KASH to perform its computations.
License: GPL
Live on the KNOPPIX
Related presentation: p027
GiNaC (http://www.ginac.de/)
Description: GiNaC looks like a computer algebra system and a library, but the name GiNac is an iterated and recurseive abbreviation for GiNaC is Not a Computer Algebra System.
License: GPL
GiNaC documents or executables on DVD
Live on the KNOPPIX
Related presentation: p110
GloptiPoly (http://www.laas.fr/~henrion/software/gloptipoly)
Description: Matlab/SeDuMi add-on to build and solve convex LMI relaxations of the (generally non-convex) global optimization problem of minimizing a multivariable polynomial function subject to polynomial inequality, equality or integer constraints. (Didier Henrion and Jean-Bernard Lasserre, LAAS-CNRS, Toulouse, France)
License: GPL, requires Matlab
GloptiPoly documents or executables on DVD
Related presentation: p1050
GMP: GNU Multiple Precision Arithmetic Library (http://www.swox.com/gmp)
Description: GMP is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers. There is no practical limit to the precision except the ones implied by the available memory in the machine GMP runs on. GMP has a rich set of functions, and the functions have a regular interface.
License: LGPL
GMP: GNU Multiple Precision Arithmetic Library documents or executables on DVD
Live on the KNOPPIXHOL Light (http://www.cl.cam.ac.uk/users/jrh13/hol-light/index.html)
Description: HOL Light is a theorem prover for classical higher-order logic. It is a rationalized re-implementation in Objective CAML (OCaml) of Mike Gordon's original HOL system. HOL Light generates proofs using very low-level primitive inference steps, but has numerous higher-level automated rules and a good library of pre-proved mathematics. ( John Harrison.)
License: Custom BSD-like
HOL Light documents or executables on DVD
Live on the KNOPPIX
Related presentation: p103
jReality (http://www.jreality.de)
Description: jReality is a library that allows for interactive manipulation of scientific data on a wide variety of platforms. It is written in Java. The output media include software only Java rendering, hardware accelerated OpenGL rendering stereo viewing, immersive virtual reality applications like in the http://www.math.tu-berlin.de/geometrie/f5/portal.shtml as well as file formats like PIXAR's renderman and SVG.
License:
Related presentation: p015
jtem - Java Tools for Experimental Mathematics (http://www.jtem.de)
Description: jtem is a collection of mostly mathematical tools and algorithms implemented in Java. The libraries include a wide range from complex numbers to theta-functions, basic linear algebra and adaptive ODE solvers.
License: GPL
jtem - Java Tools for Experimental Mathematics documents or executables on DVD
Live on the KNOPPIXRelated presentation: p015
Kan/sm1 (http://www.openxm.org)
Description: Kan/sm1 is originally developed for a computer algebra system for the ring of differential operators D. It is designed to be a backend system with a postscript-like small language. It is now used for a controller of OpenXM communications behind as well as a system for the D.
License: GPL, LGPL
Kan/sm1 documents or executables on DVD
Live on the KNOPPIX
KASH/KANT (http://www.math.tu-berlin.de/~kant/kash.html)
Description: KASH/KANT is a computer algebra system specialized for algebraic number theory and its applications. It offers powerful functions for working with number fields, function fields, and local fields, as well as functions for solving Diophantine equations. The KANT shell KASH provides a programming language and an interactive help system.
License: Other
Live on the KNOPPIX
Related presentation: p027
KENZO (http://www-fourier.ujf-grenoble.fr/~sergerar/Kenzo)
Description: KENZO program is a Common Lisp Object System (CLOS) whose purpose is to compute various invariants in Algebraic Topology Framework (mainly homology groups). It implements and uses numerous algebraic structures as dg-algebras, simplicial groups, morphisms, reductions, chain complexes, etc. It allows to compute homology groups of sophisticated spaces.
License:
Live on the KNOPPIX (non-free)Related presentation: p009
KENZO package for A-infinity structures: ARAIA and CRAIC (http://www.ehu.es/aba/investigation.htm)
Description: The package component we add to KENZO allows us to compute A-infinity-(co)algebra structures induced on the small module of a reduction if the big dg-module is a (co)algebra. (Ainhoa Berciano Alcaraz)
License:
Live on the KNOPPIX (non-free)Related presentation: p009
KETpic (http://www.kisarazu.ac.jp/~masa/math/E.html)
Description: KETpic is a macro package for Maple, which generates TeX source codes for clear drawings. This supports users to draw every kind of complicated figure easily with the highest accuracy. The current version as well as the latest Maple runs on major OS: Windows, Mac and Linux. One can download the package, various samples, the command reference and a template of TeX source from the indicated web site. (Masayoshi SEKIGUCHI)
License: Free for academic and noncomercial use
KETpic non-free documents or executables on DVD
Related presentation: p047
KNOPPIX/math (http://www.knoppix-math.org)
Description: KNOPPIX/Math is a project to archive free mathematical software and free mathematical documents and provide them on KNOPPIX.
License:
Live on the KNOPPIXRelated presentation: p016
libMpIeee (http://www.mpieee.ua.ac.be)
Description:
libMpIeee is a C++ software library for radix 
or
mixed precision floating-point arithmetic, that is
fully compliant with the IEEE 754/854 standards for floating-point
arithmetic.
This implies, among others, that the basic operations as well as the
remainder and square root operations are exactly rounded, involving a
relative error of at most 0.5 units in the last place (ULP) for round
to nearest and 1 ULP for directed roundings. As required by the IEEE
754/854 standards, libMpIeee also provides denormal numbers, signed
zeroes, signed infinities and NaN (Not-a-Number).
Moreover, the conversions between decimal and binary are implemented
to satisfy the same error bound as the basic operations. The
elementary functions are computed with a relative error of at most 1
ULP for round to nearest and 2 ULP for directed roundings.
More information on the implementation of these elementary functions
can be found in the contribution "Towards reliable software for the
evaluation of a class of special functions" by Annie Cuyt and Stefan
Becuwe.
License:
libMpIeee non-free documents or executables on DVD
Related presentation: p061
Linbox (http://www.linalg.org)
Description: LinBox is a C++ template library for exact, high-performance linear algebra computation.
License: LGPL
Live on the KNOPPIXRelated presentation: p773
LiveTeXmacs (ftp://math.cgu.edu.tw/pub/KNOPPIX)
Description: LiveTeXmacs is a knoppix-based live distribution for mathematical education. Many mathematical software systems (Axiom, Gnuplot, Maxima, Octave, R etc) are integrated in this distribution. In addition to this, it also includes free documentations for calculus, mathematical (2D/3D) visualization and stochastic processes etc, which are made by TeXmacs. Web applications, such as PHP, Python, Apache, SQL and Zope etc, are also supported. Especially, the Web Mathematics Interactive is pre-installed as the web application for Maxima, Gnuplot and more. Pre-installed development environment gives a scalability of the distribution even with very few knowledge about linux.
License: GPL
Logiweb (http://logiweb.eu/)
Description: Logiweb is an infrastructure for publication and archival of machine verified mathematics. It allows users to publish definitions, theories, lemmas, proofs, and computer programs. The system allows proofs to reference previously published material across the Internet so that users in different sites may build on top of the work of each other. (Klaus Grue, University of Copenhagen)
License: GPL
Logiweb documents or executables on DVD
Related presentation: p014
Macaulay2 (http://www.math.uiuc.edu/Macaulay2)
Description: Macaulay2 is a software system to support researches in algebraic geometry and commutative algebra.
License: GPL
Macaulay2 documents or executables on DVD
Live on the KNOPPIX
Related presentation: p111
Magma (http://magma.maths.usyd.edu.au)
Description: 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.
License: Commercial
Maple (http://www.maplesoft.com)
Description: Maple is a tool for solving mathematical problems and creating interactive technical applications.
License: Commercial
Mathematica (http://www.wolfram.com)
Description: Mathematica is a system for doing mathematics. The cite also provides http://functions.wolfram.com (a data base for special functions) and http://library.wolfram.com (a collection of notebooks).
License: Commercial
math-polyglot (http://www.math.kobe-u.ac.jp/math-polyglot)
Description: This project is started for editing icms2006 --- developer's meeting DVD's. It provides sample codes for mathematical software systems in our DVD's. Samples are grouped with mathematical problems. This project also provides inputs for testing and checking if the installation is properly done to the knoppix-math. The project will be moved to a MediaWiki of knoppix-math after the icms2006. (Nobuki Takayama, Kobe University)
License: GFL, BSD
math-polyglot documents or executables on DVD
Live on the KNOPPIXMATLAB (http://www.mathworks.com)
Description: Matlab is a language for technical computing and an interactive environment.
License: Commercial
Mizar (http://www.mizar.org)
Description: Mizar project provides a database for mathematics (7000 definitions, 40000 theorems) as well as the mizar system.
License:
MPFR library for multiple precision floating point computation (http://www.mpfr.org)
Description: The MPFR library is a C library for multiple-precision floating-point computations with exact rounding (also called correct rounding). It is based on the GMP multiple-precision library. The main goal of MPFR is to provide a library for multiple-precision floating-point computation which is both efficient and has a well-defined semantics.
License: LGPL
MPFR library for multiple precision floating point computation documents or executables on DVD
Live on the KNOPPIXMulti Parametric Toolbox (http://control.ee.ethz.ch/~mpt/)
Description: The Multi-Parametric Toolbox (MPT) is a free Matlab toolbox for design, analysis and deployment of optimal controllers for constrained linear, nonlinear and hybrid systems. Efficiency of the code is guaranteed by the extensive library of algorithms from the field of computational geometry and multi-parametric optimization. The toolbox offers a broad spectrum of algorithms compiled in a user friendly and accessible format: starting from different performance objectives (linear, quadratic, minimum time) to the handling of systems with persistent additive and polytopic uncertainties. Users can add custom constraints, such as polytopic, contraction, or collision avoidance constraints, or create custom objective functions. Resulting optimal control laws can either be embedded into your applications in a form of a C code, or deployed to target platforms using Real Time Workshop.
License: GPL, it depends on yalmip(yalmip free license), matlab
Multi Parametric Toolbox non-free documents or executables on DVD
Related presentation: p039
MuPad (http://www.mupad.de)
Description: MuPad is a mathematical expert system mainly symbolic/algebraic computation and numerical calculations with arbitrary accuracy.
License: Commercial
MuPAD-Combinat (http://mupad-combinat.sourceforge.net)
Description: MuPAD-Combinat is an open-source algebraic combinatorics package for the computer algebra system MuPAD http://www.mupad.de/ . Its main purpose is to provide an extensible toolbox for computer exploration, and foster code sharing between researchers in this area. The core of the package is integrated in the official library of MuPAD since version 2.5.0.
License: GPL, LGPL, requires MuPAD
MuPAD-Combinat documents or executables on DVD
Related presentation: p026
NZMATH (http://tnt.math.metro-u.ac.jp/nzmath/)
Description: NZMATH is a number theory oriented calculation system based on the scripting language Python. It is currently providing the Python library package named nzmath, which contains modules for primality testings, factorization, polynomial, matrix, elliptic curves, etc. ( MATSUI Tetsushi, Tokyo Metropolitan University)
License: BSD
Live on the KNOPPIX
Related presentation: p019
Octave (http://www.octave.org)
Description: GNU Octave is a high-level language, primarily intended for numerical computations.
License: GPL
Octave documents or executables on DVD
Live on the KNOPPIX
Oorange (http://www.oorange.de)
Description: Oorange is a development environment that was initially designed for experimental mathematics but has become a general Java programming tool. It's main feature is its interactive programming, also known as rapid prototyping. It also fits into component oriented development.
License: GPL
Oorange documents or executables on DVD
Live on the KNOPPIXRelated presentation: p015
OpenMath (http://www.openmath.org)
Description: OpenMath is an emerging standard for representing mathematical objects with their semantics, allowing them to be exchanged between computer programs, stored in databases, or published on the worldwide web.
License:
OpenXM (http://www.openxm.org)
Description: OpenXM is an infrastructure for communications among mathematical software systems. The project has proposed protocols OpenXM RFC 100, 101, 102, 103, 104. The OpenXM package is a collection of software systems supporting OpenXM protocols. The current distribution contains asir, sm1, Macaulay 2, PHCpack, gnuplot, polymake, cdd, ntl, pari, supports for Maple, Mathematica, OpenMath, and some small sized systems.
License: BSD, GPL, FFL
OpenXM documents or executables on DVD
Live on the KNOPPIXwebOrigami (http://weborigami.score.cs.tsukuba.ac.jp/webOrigami/jsp/)
Description: Origami assistant on a web.
License:
Related presentation: p049
ORMS (http://orms.mfo.de)
Description: The Oberwolfach References on Mathematical Software (ORMS) project is a web-interfaced collection of information and links on mathematical software, see http://orms.mfo.de . It presents carefully selected software, including general purpose software systems, teaching software, and more specialized packages up to specific implementations on particular mathematical research problems. Each software package is presented by a short description of its mathematical features, information on basic properties like license type and distribution media are provided, and links to syntax examples, possible demo versions and manuals are given. The ORMS offers a choice of retrieval functions, for example, searching via browsing through a mathematical classification scheme, a structured key word search, and a full text search in the description of the software systems. The success of this project will rely on the co-operation of experienced users from different areas of mathematical software. We therefore encourage discussion (at orms@mfo.de) and we will be grateful to contributions (at contrib-orms@mfo.de).
License:
Pari-GP (http://pari.math.u-bordeaux.fr)
Description: The PARI system is a package which is capable of doing formal computations on recursive types at high speed. It is primarily aimed at number theorists, but is useful to anyone whose primary need is speed. The functionality of PARI is available through a sophisticated programmable calculator, named GP, which also implements many features of high level languages.
License: GPL
Pari-GP documents or executables on DVD
Live on the KNOPPIX
PHCpack (http://www.math.uic.edu/~jan/download.html)
Description: PHCpack is a package for Polynomial Homotopy Continuation. Version 1 was archived by ACM TOMS as Algorithm 795. Currently it is a platform for ``numerical algebraic geometry'' providing algorithms developed jointly with Andrew Sommese and Charles Wampler. Contributions made by Anton Leykin, Yusong Wang, Ailing Zhao, and Yan Zhuang. ( Jan Verschelde, UIC.)
License: GPL, free software
PHCpack documents or executables on DVD
Live on the KNOPPIXPHCmaple (http://www.math.uic.edu/~leykin/PHCmaple)
Description: This Maple package provides a convenient interface to the functions of PHCpack, a collection of numerical algorithms for solving polynomial systems using polynomial homotopy continuation.
License: GPL
PHCmaple documents or executables on DVD
Related presentation: p041
polymake (http://www.math.tu-berlin.de/polymake/)
Description: polymake is a modular, object-oriented tool for experimental discrete geometry. The main applications are dealing with polytopes and polyhedra, polyhedral surfaces, and finite simplicial complexes. It offers an unified interface to a wide variety of free software packages from the field, especially for visualisation. It can be used interactively as well as driven by perl scripts or C++ programs. (Ewgenij Gawrilow, Technische Universit\"at Berlin, and Michael Joswig, Technische Universit\"at Darmstadt)
License: GPL
polymake documents or executables on DVD
Live on the KNOPPIX
Related presentation: p024
ProofPower (http://www.lemma-one.com/ProofPower/index/index.html)
Description: ProofPower is a tool for specification and proof in Higher-Order Logic (HOL) and in the Z Notation, based on a re-engineering of Mike Gordon's original HOL system. Like other systems in the LCF tradition, it uses a powerful strongly-typed functional programming language (Standard ML) to ensure logical correctness by reducing all proof steps to primitive inferences rules and to provide a rich and extensible repertoire of automated derived inference rules and decision procedures. Its is used commercially for the verification of safety-critical avionics control systems. Libraries of discrete and continuous mathematics have been and continue to be developed to support these applications and for their intrinsic interest.
License: GPL
ProofPower documents or executables on DVD
Related presentation: p104
QaoS - Querying Algebraic Objects System (http://www.math.tu-berlin.de/~kant/database.html)
Description: QaoS (Querying Algebraic Objects System) is a stand-alone solution for access to the KANT databases of algebraic and transcendental field extensions. QaoS transfers information via the hypertext transport protocol (HTTP). It can be accessed through a web interface and various computer algebra systems (GAP 4, KASH 2.56, KASH 3, Maple, and SAGE).
License: BSD like
R (http://www.r-project.org)
Description: R is a system for statistical computing and graphics.
License: GPL
R documents or executables on DVD
Live on the KNOPPIX
Risa/Asir (http://www.math.kobe-u.ac.jp/Asir)
Description: Risa/Asir is a computer algebra system. Here is a list of some commands: fctr (factorization), gr, nd_gr_trace (Groebner basis), primadec (primary ideal decomposition), af (factorization over algebraic numbers), ifplot (plot of implicit functions), ox_* (OpenXM communication functions), generic_bfct (b-function).
License: Other(FFL, BSD)
Risa/Asir non-free documents or executables on DVD
Live on the KNOPPIX
SAGE: Software for Algebra and Geometry Experimentation (http://sage.scipy.org/sage)
Description: The Python-based computer algebra system SAGE comes with the systems GAP, PARI, Singular. and provides interfaces KASH/KANT, Gnuplot, Octave, Magma, Mathematica, and Maple. It includes functions for basic algebraic geometry, elliptic curves over the rational numbers, modular forms, linear algebra and Z-modules, and noncommutative algebra.
License: GPL
Live on the KNOPPIX
SARAG (http://perso.univ-rennes1.fr/marie-francoise.roy/bpr-posted1.html)
Description: SARAG(Some Algorithms in Real Algebraic Geometry) is a software library that implements some algorithms in real algebraic geometry written in the free computer algebra system Maxima. SARAG has two main applications: extending the capabilities of Maxima and being part of the interactive version of the book ``Algorithms in Real Algebraic Geometry'' by S. Basu, R. Pollack, M.-F. Roy, which can be now freely downloaded.
License: GPL
SARAG documents or executables on DVD
Live on the KNOPPIXRelated presentation: p003
sgpviz (http://www.gap-system.org/Packages/sgpviz.html)
Description:
The GAP package 
-classes
or Cayley graphs, as well as to make friendlier the usage of
GAP when dealing with finite semigroups.
License:
Live on the KNOPPIXRelated presentation: p022
Singular (http://www.singular.uni-kl.de)
Description: Singular is a Computer Algebra System for polynomial computations with emphasis on the special needs of commutative algebra, algebraic geometry, and singularity theory. Singular's main computational objects are ideals and modules over a large variety of rings, including local rings and non-commutative G-algebras (in the subsystem Plural). Large variety of algorithms, including those based on Groebner and standard bases, have powerful implementations in Singular.
License: GPL, others
Singular documents or executables on DVD
Live on the KNOPPIX
Strong Noether Position (http://www-calfor.lip6.fr/~hashemi/Noether)
Description: We introduce the notion of a homogeneous ideal in Strong Noether Position (SNP); a new definition for the notion of generic coordinates for some problems. This definition is simple to check, because one can test it for the initial ideal of the ideal with respect to the degree reverse lexicographic ordering. It is explicit, because we can provide an algorithm to decide whether a monomial ideal is in SNP or not. We propose some methods to compute the Castelnuovo-Mumford regularity of an ideal which one of them is more efficient than that of [Bermejo-Gimenez, 2005]. ( Amir Hashemi)
License:
Related presentation: p060
Surface Evolver (http://www.susqu.edu/facstaff/b/brakke/evolver/)
Description: The Surface Evolver is an interactive program for the study of surfaces shaped by surface tension and other energies, and subject to various constraints. A surface is implemented as a simplicial complex (a union of triangles) and is evolved toward minimal energy by a gradient descent method. The Evolver can handle arbitrary topology. Graphical output is available in several file formats.
License:
Surface Evolver documents or executables on DVD
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surfex (http://www.surfex.algebraicsurface.net)
Description: surfex is a tool for interactive high quality real algebraic surface visualization. It is mainly an intuitive interface which combines the strenghts of several visualization tools; at the moment, these include surf, javaview, and convert. One of the main features of surfex is the interactive visualization of families of algebraic varieties: The user can introduce parameters into some implicit equations and then play with these parameters via sliders. E.g., this allows one to visualize deformations of surface singularities. All the pictures can easily be exported, either as an animation which shows the whole deformation process, or as a snapshot of a single variety. The user can specify the quality of the output which can range from very high quality for printed publications to lower quality for websites. We also implemented a library for the computer algebra system Singular, called surfex.lib, which enhances the quality of the visualization of surfex using pre-computation of the singular locus etc.
License: Freeware
surfex documents or executables on DVD
Live on the KNOPPIXRelated presentation: p117
SYNAPS (http://www-sop.inria.fr/galaad/logiciels/synaps)
Description: SYNAPS (SYmbolic Numeric APplications) is a C++ library devoted to symbolic and numeric computations. It provides data-structures for the manipulation of basic algebraic objects, such as vectors, matrices (dense, sparse, structured), univariate and multivariate polynomials. It contains solvers for univariate and multivariate polynomials, including generalized normal form or subdivision solvers, tools for the manipulatiion of algebraic numbers, for the construction of resultants, ...
License: GPL
Live on the KNOPPIXRelated presentation: p112
TC (ftp://tnt.math.metro-u.ac.jp/pub/math-packs/tc/)
Description: TC (Tiny C) is an interpreter of multi-precision C language suitable for floating-point calculations of several thousands digits which often appear in computational algebraic number theory. Furthermore TC ver.4, which is equipped with PARI library and turned TCP ver.1, provides frequently used PARI library functions by C-like functions which are easy to call from TC. (Takashi Fukuda)
License: GPL
TC documents or executables on DVD
Live on the KNOPPIX
Related presentation: p501
TeXmacs (http://www.texmacs.org)
Description: GNU TeXmacs is a free wysiwyw editing platform for scientists.
License: GPL
TeXmacs documents or executables on DVD
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Virtual Math Laboratories (http://www.jreality.de)
Description: Virtual Math Labs is a collection of educational and scientific java web start applications. The library of mathematical experiments shows topics from varies areas, e.g. dynamical systems, polyhedral surfaces, calculus, and curves and surfaces.
License: GPL
Related presentation: p015