Links to Projects. Mathematical Software,
icms2006—developer’s meeting
This document is a collection of links and descriptions of projects related to
icms2006—developer’s meeting.
1. ActiveMath
http://www.activemath.org
License: Free and open-source for public educational institution
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.
2. Aldor
http://www.aldor.org
License: Other (BSD like)
Aldor is a computer programming language, like Scheme, Java or C].
3. Algorithms in real algebraic geometry (interactive book)
http://perso.univ-rennes1.fr/marie-francoise.roy/bpr-posted1.html
License: GPL, others
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 publishedby 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.
4. Arageli
http://www.unn.ru/cs/arageli
License: Free for academic and noncommercial use
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.
5. The Atlas of Lie Groups and Representations
http://atlas.math.umd.edu/
License:This is a project to make available information about representations ofsemi-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, KazhdanLusztig polynomials for representations with regular integral infinitesimalcharacter, .... etc. ( Alfred G. Noel, University of Massachusetts Boston)
6. axiom
http://www.axiom-developer.org
License: Modified BSD
Axiom is a computer algebra system with a strongly-typed high-level programming language. Over 1,000 mathematical domains and categories arecollected in the library.
7. BESSELINT
http://www.cs.kuleuven.be/˜nines/software/BESSELINT/
License:BESSELINT is a Matlab program to compute integrals of the form
Z ∞
0

xm

k
Y

Jνi (ai x)dx

i=1

with Jνi (x) the Bessel function of the P
first kind and (real) order νi . The
parameter m is a real number such that i νi + m > −1 and the coefficients
ai are strictly positive real numbers. In the near future this will be extended
to compute the Laplace transform of a product of Bessel functions withpossibly an additional factor of 1 + dx2 in the denominator (where d is a real
number). (Joris Van Deun and Ronald Cools, K.U.Leuven)
8. CoCoA4
http://cocoa.dima.unige.it/
License: The executables are free
The interactive system CoCoA-4.6 offers facilities for COmputations in COmmutative Algebra: Gröbner 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 isfree and runs on most common platforms.
9. CoCoALib
http://cocoa.dima.unige.it/
License: GPL, others
The C++ library CoCoALib offers data structures and operations for COmputations in COmmuative Algebra, most particularly Gröbner bases. Easeof use through a clean design is paramount (with some concessions to guarantee good performance). The library comes with full documentation andnumerous example programs. A “beta” release is anticipated in late 2006. A
server and interactive system are planned.

10. Computer Algebra Animation
http://www.math.kobe-u.ac.jp/caa
License: GPL
An experimental project for algorithm animations and graphical or interactive user interface in computer algebra with Java and OpenXM.
11. Coq
http://coq.inria.fr
License: LGPL
Coq is a proof assistant.
12. DEpthLAUNAY
http://www.dma.fi.upm.es/mabellanas/delonedepth/
License: QPL
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 fromimage files. ( Manuel Abellanas, Universidad Politecnica de Madrid)
13. Epsilon
http://www-calfor.lip6.fr/˜wang/epsilon
License: Free for academic and noncommercial use
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)
14. GAP
http://www.gap-system.org
License: GPL
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.
15. GAP package Alnuth
http://www.gap-system.org/Packages/alnuth.html
License: GPL
The Alnuth package provides various methods to compute with number fields
which are given by a defining polynomial or by generators. Some of themethods provided in this package are written in GAP code. The other partof the methods is imported from the Computer Algebra System KANT.
16. GCLC/WinGCLC
http://www.matf.bg.ac.yu/˜janicic/gclc/
License: Free for academic and noncommercial use
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 ofgeometrical conjectures, for exporting figures into LaTeX and bitmap format
etc.
17. GEX
http://www.mmrc.iss.ac.cn/gex/
License:
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 hundredsof non-trivial geometry theorems automatically
18. Gfan
http://home.imf.au.dk/ajensen/software/gfan/gfan.html
License: GPL
Gfan is a command line tool for enumerating the reduced Gröbner bases ofa polynomial ideal in n variables. Hereby the Gröbner 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.
19. GiANT: Graphical Algebraic Number Theory
http://giantsystem.sourceforge.net
License: GPL
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.
20. GiNaC
http://www.ginac.de/License: GPL
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.
21. GloptiPoly
http://www.laas.fr/˜henrion/software/gloptipoly
License: GPL, requires Matlab
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)
22. GMP: GNU Multiple Precision Arithmetic Library
http://www.swox.com/gmp
License: LGPL
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 themachine GMP runs on. GMP has a rich set of functions, and the functions
have a regular interface.
23. HOL Light
http://www.cl.cam.ac.uk/users/jrh13/hol-light/index.html
License: Custom BSD-like
HOL Light is a theorem prover for classical higher-order logic. It is a rationalized re-implementation in Objective CAML (OCaml) of Mike Gordon’soriginal HOL system. HOL Light generates proofs using very low-level primitive inference steps, but has numerous higher-level automated rules and agood library of pre-proved mathematics. ( John Harrison.)
24. jReality
http://www.jreality.de
License:jReality is a library that allows for interactive manipulation of scientific dataon 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 PORTAL as wellas file formats like PIXAR’s renderman and SVG.
25. jtem - Java Tools for Experimental Mathematics
http://www.jtem.de
License: GPL
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.
26. Kan/sm1
http://www.openxm.org
License: GPL, LGPL
Kan/sm1 is originally developed for a computer algebra system for the ringof differential operators D. It is designed to be a backend system with apostscript-like small language. It is now used for a controller of OpenXM
communications behind as well as a system for the D.
27. KASH/KANT
http://www.math.tu-berlin.de/˜kant/kash.html
License: Other
KASH/KANT is a computer algebra system specialized for algebraic number
theory and its applications. It offers powerful functions for working withnumber 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.
28. KENZO
http://www-fourier.ujf-grenoble.fr/˜sergerar/Kenzo
License: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.
29. KENZO package for A-infinity structures: ARAIA and CRAIC
http://www.ehu.es/aba/investigation.htm
License: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)
30. KETpic
http://www.kisarazu.ac.jp/˜masa/math/E.html
License: Free for academic and noncomercial use
KETpic is a macro package for Maple, which generates TEXsource codes forclear 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
TEXsource from the indicated web site. (Masayoshi SEKIGUCHI)
31. KNOPPIX/math
http://www.knoppix-math.org
License:KNOPPIX/Math is a project to archive free mathematical software and freemathematical documents and provide them on KNOPPIX.
32. libMpIeee
http://www.mpieee.ua.ac.be
License:libMpIeee is a C++ software library for radix 2n or 10m 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 remainderand square root operations are exactly rounded, involving a relative error ofat 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 tosatisfy the same error bound as the basic operations. The elementary functions are computed with a relative error of at most 1 ULP for round tonearest 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.
33. Linbox
http://www.linalg.org
License: LGPL
LinBox is a C++ template library for exact, high-performance linear algebra
computation.

34. LiveTeXmacs
ftp://math.cgu.edu.tw/pub/KNOPPIX
License: GPL
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.
35. Logiweb
http://logiweb.eu/
License: GPL
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 maybuild on top of the work of each other. (Klaus Grue, University of Copenhagen)36. Macaulay2
http://www.math.uiuc.edu/Macaulay2
License: GPL
Macaulay2 is a software system to support researches in algebraic geometry
and commutative algebra.
37. Magma
http://magma.maths.usyd.edu.au
License: Commercial
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.
38. Maple
http://www.maplesoft.com
License: Commercial
Maple is a tool for solving mathematical problems and creating interactive
technical applications.
39. Mathematica
http://www.wolfram.com
License: Commercial
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).

40. math-polyglot
http://www.math.kobe-u.ac.jp/math-polyglot
License: GFL, BSD
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 theknoppix-math. The project will be moved to a MediaWiki of knoppix-mathafter the icms2006. (Nobuki Takayama, Kobe University)
41. MATLAB
http://www.mathworks.com
License: Commercial
Matlab is a language for technical computing and an interactive environment.
42. Mizar
http://www.mizar.org
License:Mizar project provides a database for mathematics (7000 definitions, 40000
theorems) as well as the mizar system.
43. MPFR library for multiple precision floating point computation
http://www.mpfr.org
License: LGPLThe 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.
44. Multi Parametric Toolbox
http://control.ee.ethz.ch/˜mpt/
License: GPL, it depends on yalmip(non-free), matlab
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 multiparametric 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.
45. MuPad
http://www.mupad.de
License: Commercial

MuPad is a mathematical expert system mainly symbolic/algebraic computation and numerical calculations with arbitrary accuracy.
46. MuPAD-Combinat
http://mupad-combinat.sourceforge.net
License: GPL, LGPL, requires MuPAD
MuPAD-Combinat is an open-source algebraic combinatorics package for thecomputer 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.
47. NZMATH
http://tnt.math.metro-u.ac.jp/nzmath/
License: BSD
NZMATH is a number theory oriented calculation system based on thescripting 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)
48. Octave
http://www.octave.org
License: GPL
GNU Octave is a high-level language, primarily intended for numerical computations.
49. Oorange
http://www.oorange.de
License: GPL
Oorange is a development environment that was initially designed for experimental mathematics but has become a general Java programming tool. It’smain feature is its interactive programming, also known as rapid prototyping. It also fits into component oriented development.
50. OpenMath
http://www.openmath.org
License: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.
51. OpenXM
http://www.openxm.org
License: BSD, GPL, FFL
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.

52. webOrigami
http://weborigami.score.cs.tsukuba.ac.jp/webOrigami/jsp/
License:Origami assistant on a web.
53. ORMS
http://orms.mfo.de
License: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 softwaresystems, 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 areprovided, 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, astructured key word search, and a full text search in the description of thesoftware 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 (atcontrib-orms@mfo.de).
54. Pari-GP
http://pari.math.u-bordeaux.fr
License: GPL
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.
55. PHCpack
http://www.math.uic.edu/˜jan/download.html
License: GPL, free software
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 jointlywith Andrew Sommese and Charles Wampler. Contributions made by Anton
Leykin, Yusong Wang, Ailing Zhao, and Yan Zhuang. ( Jan Verschelde, UIC.)
56. PHCmaple
http://www.math.uic.edu/˜leykin/PHCmaple
License: GPL
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.

57. polymake
http://www.math.tu-berlin.de/polymake/License: GPLpolymake 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, especiallyfor visualisation. It can be used interactively as well as driven by perl scripts
or C++ programs. (Ewgenij Gawrilow, Technische Universität Berlin, andMichael Joswig, Technische Universität Darmstadt)
58. ProofPowerhttp://www.lemma-one.com/ProofPower/index/index.html
License: GPL
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 powerfulstrongly-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 verificationof safety-critical avionics control systems. Libraries of discrete and continuous mathematics have been and continue to be developed to support theseapplications and for their intrinsic interest.
59. QaoS - Querying Algebraic Objects System
http://www.math.tu-berlin.de/˜kant/database.html
License: BSD like
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).
60. R
http://www.r-project.org
License: GPL
R is a system for statistical computing and graphics.
61. Risa/Asir
http://www.math.kobe-u.ac.jp/AsirLicense: Other(FFL, BSD)
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 (bfunction).
62. SAGE: Software for Algebra and Geometry Experimentation
http://sage.scipy.org/sage
License: GPL

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.
63. SARAG
http://perso.univ-rennes1.fr/marie-francoise.roy/bpr-posted1.html
License: GPL
SARAG(Some Algorithms in Real Algebraic Geometry) is a software librarythat implements some algorithms in real algebraic geometry written in thefree computer algebra system Maxima. SARAG has two main applications:extending the capabilities of Maxima and being part of the interactive versionof the book “Algorithms in Real Algebraic Geometry” by S. Basu, R. Pollack,
M.-F. Roy, which can be now freely downloaded.
64. sgpviz
http://www.gap-system.org/Packages/sgpviz.html
License:The GAP package sgpviz is a package designed to visualize finite semigroups
through their D-classes or Cayley graphs, as well as to make friendlier theusage of GAP when dealing with finite semigroups.
65. Singular
http://www.singular.uni-kl.de
License: GPL, others
Singular is a Computer Algebra System for polynomial computations withemphasis 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 noncommutative G-algebras (in the subsystem Plural). Large variety of algorithms, including those based on Gröbner and standard bases, have powerfulimplementations in Singular.
66. Strong Noether Position
http://www-calfor.lip6.fr/˜hashemi/Noether
License:We introduce the notion of a homogeneous ideal in Strong Noether Position (SNP); a new definition for the notion of generic coordinates for someproblems. 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 whethera 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)
67. Surface Evolver
http://www.susqu.edu/facstaff/b/brakke/evolver/
License:The Surface Evolver is an interactive program for the study of surfaces
shaped by surface tension and other energies, and subject to various con-

straints. 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 inseveral file formats.
68. surfex
http://www.surfex.algebraicsurface.net
License: Freeware
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 familiesof 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.
69. SYNAPS
http://www-sop.inria.fr/galaad/logiciels/synaps
License: GPL
SYNAPS (SYmbolic Numeric APplications) is a C++ library devoted tosymbolic 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 forunivariate and multivariate polynomials, including generalized normal formor subdivision solvers, tools for the manipulatiion of algebraic numbers, forthe construction of resultants, ...
70. TC
ftp://tnt.math.metro-u.ac.jp/pub/math-packs/tc/
License: GPL
TC (Tiny C) is an interpreter of multi-precision C language suitable forfloating-point calculations of several thousands digits which often appear
in computational algebraic number theory. Furthermore TC ver.4, which isequipped 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)
71. TeXmacs
http://www.texmacs.org
License: GPL
GNU TeXmacs is a free wysiwyw editing platform for scientists.

72. Virtual Math Laboratories
http://www.jreality.de
License: GPL
Virtual Math Labs is a collection of educational and scientific java web start
applications. The library of mathematical experiments shows topics fromvaries areas, e.g. dynamical systems, polyhedral surfaces, calculus, and curves
and surfaces.
About this document
This document, edited by Masayuki Noro and Nobuki Takayama, is distributed under the GNU Free Documentation License Version 1.2. June27, 2006.
List of contributors of this document:
Ainhoa Berciano Alcaraz, Alfred Gerard Noel, Amir Hashemi, Anders
Nedergaard Jensen, Anton Leykin, Bernard Mourrain, Chu-ching Huang,
Colin Jones, Dongming Wang, Ewgenij Gawrilow, Fabrizio Caruso, Francois Descouens, Fukuda Takashi, Gert Martin Greuel, Jan Verschelde,Jean B. Lasserre, John Abbott, John Harrison, Joris Van Deun, Klaus
Ebbe Grue, MATSUI Tetsushi, Manuel Abellanas, Manuel Delgado, MarieFrancoise Roy, Markus Schmies, Masayoshi SEKIGUCHI, Masayuki Noro,
Nobuki Takayama, Oliver Labs, Predrag Janicic, Rob Arthan, SebastianPauli, Sergey Lyalin, Stefan Becuwe, Viktor Levandovskyy, Xiaoshan
Gao, Xin Li, Paul Libbrecht,