APAtools (http://) , [IMA talk or demo]
Description: A Maple/Matlab toolbox for approximate polynomial algebra. The toolbox includes software for computing the approximate GCD, approximate factorization, dual basis and multiplicity identification, as well as numerical elimination in solving polynomial systems.
License: No public download
ATLAS (http://math-atlas.sourceforge.net/)
Description: ATLAS (automatically tuned linear algebra software) provides highly optimized linear algebra kernels for arbitrary cache-based architectures. (It is used by PHoM below.)
License: An original license. Partly LGPL for alpha processors
Apt-get: aptget install atlas3-base-dev atlas3-doc
Bertini (http://www.nd.edu/~sommese/bertini) , [IMA talk or demo]
Description: Bertini is a software package for computation in numerical algebraic geometry.
License: Original (No redistribution, only for education or research, ...)
CoCoA4 (http://cocoa.dima.unige.it/) , [IMA talk or demo]
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
download, install instruction, tutorial, manual, Live on the KNOPPIX
CoCoALib (http://cocoa.dima.unige.it/) , [IMA talk or demo]
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 KNOPPIXCRACK (http://lie.math.brocku.ca/crack/src/) , [IMA talk or demo]
Description: This is a package for solving systems of equations (algebraic and differential) interactively and automatically. It is especially suited for larger overdetermined systems. Crack needs REDUCE but can also be used online http://lie.math.brocku.ca/crack/demo/ . Running under Parallel-REDUCE on clusters (Intel, AMD64, Cray) it can perform parallel computations.
License: freely downloadable
tutorial, applications/examples,diffalg (http://www-sop.inria.fr/cafe/Evelyne.Hubert/diffalg/) , [IMA talk or demo]
Description: The diffalg package is for systems of polynomial differential equations and inequations.
License: Unknown. Downloading is free. Require Maple.
manual,D-modules for Macaulay2 (http://www.ima.umn.edu/~leykin/Dmodules) , [IMA talk or demo]
Description: The package D-modules for Macaulay 2 implements the majority of the now classical algorithms in the computational D-module theory. Based on the ability of Macaulay 2 engine to compute Grobner bases in the Weyl algebra, the package provides, in particular, tools to work with holonomic D-modules such as the algorithms for b-functions, localized modules, restriction, etc. Amongst the applications there are computation of the local cohomology modules, polynomial and rational solutions, and A-hypergeometric systems.
License: GPL. Require Macaulay2
manual, Live on the KNOPPIX
4ti2 (http://www.4ti2.de) , [IMA talk or demo]
Description: Computation of Hilbert bases, Graver bases, toric Groebner bases.
License: GPL (from the next version 1.3)
Live on the KNOPPIXGambit (http://econweb.tamu.edu/gambit/) , [IMA talk or demo]
Description: Gambit is a library of game theory software and tools for the construction and analysis of finite extensive and strategic games.
License: GPL
download, tutorial, manual, Live on the KNOPPIXApt-get: apt-get install gambit gambit-doc
Gfan (http://home.imf.au.dk/ajensen/software/gfan/gfan.html) , [IMA talk or demo]
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
tutorial, manual, Live on the KNOPPIXHOM4PS (http://www.csulb.edu/~tgao/RESEARCH/Software.htm) , [IMA talk or demo]
Description: Solving equations by the polyhedral homotopy continuation method.
License: GPL
Live on the KNOPPIXHomLab (http://www.nd.edu/~cwample1/HomLab/main.html) , [IMA talk or demo]
Description: Solving systems of algebraic equations by the homotopy continuation method.
License: HomLab original license, downloading is free after a registration. Require MATLAB.
download, install instruction,HybridRif (http://) , [IMA talk or demo]
Description: Symbolic-Numeric completion of differential systems by homotopy continuation.
License: No public downloading
KNOPPIX/math (http://www.knoppix-math.org) , [IMA talk or demo]
Description: KNOPPIX/Math is a project to archive free mathematical software and free mathematical documents and provide them on KNOPPIX.
License:
download, Live on the KNOPPIXKronecker (http://www.math.uvsq.fr/~lecerf/software/kronecker) , [IMA talk or demo]
Description: System for solving systems of polynomial equations and inequations.
License: Unknown. Downloading is free. Require Magma
download, manual,Macaulay2 (http://www.math.uiuc.edu/Macaulay2) , [IMA talk or demo]
Description: Macaulay2 is a software system to support researches in algebraic geometry and commutative algebra.
License: GPL
download, tutorial, manual, Live on the KNOPPIX
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
applications/examples,Maple (http://www.maplesoft.com) , [IMA talk or demo]
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 knoppix/math 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.
License: GFL, BSD
Live on the KNOPPIXMATLAB (http://www.mathworks.com)
Description: Matlab is a language for technical computing and an interactive environment.
License: Commercial
MixedVol (http://www.csulb.edu/~tgao/RESEARCH/Software.htm) , [IMA talk or demo]
Description: Package to evaluate mixed volumes.
License: GPL
Live on the KNOPPIXMultroot (http://www.neiu.edu/~zzeng/multroot.htm) , [IMA talk or demo]
Description: Computing polynomial roots and multiplicities.
License:
Octave (http://www.octave.org)
Description: GNU Octave is a high-level language, primarily intended for numerical computations.
License: GPL
download, manual, Live on the KNOPPIX
Apt-get: apt-get install octave octave-forge octave-sp octave2.1-htmldoc octave2.1-doc
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:
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
download, tutorial, Live on the KNOPPIXPHCmaple (http://www.ima.umn.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
PHoM (http://www.is.titech.ac.jp/~kojima/PHoM/index.html) , [IMA talk or demo]
Description: A software package for a polyhedral homotopy continuation method of finding all isolated solutions of a system of n polynomial equations f(x) = 0.
License: GPL
Live on the KNOPPIXRifsimp (http://www.cecm.sfu.ca/~wittkopf/rif.html) , [IMA talk or demo]
Description: Simplification package for overdetermined polynomially nonlinear PDE or ODE systems
License: Unknown. Downloading is free and is also a Maple package. Require Maple.
Live on the KNOPPIXRisa/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)
Live on the KNOPPIX
SAGE: Software for Algebra and Geometry Experimentation (http://sage.scipy.org/sage) , [IMA talk or demo]
Description: The mathematics software system SAGE comes with GAP, PARI, Singular, and Maxima, and provides interfaces to KASH/KANT, Macaulay2, Gnuplot, Octave, Magma, Mathematica, and Maple. It uses Python for the interactive interpreted language. It includes functions for algebraic number theory, basic algebraic geometry, elliptic curves, modular forms, linear algebra and Z-modules, and inherits functionality from the systems it includes.
License: GPL
download, tutorial, manual, Live on the KNOPPIX
SALSA (http://fgbrs.lip6.fr/salsa/Software/) , [IMA talk or demo]
Description: SALSA Software contains recent algorithms for computing certified solutions of systems of polynomial equalities, inequalities and inequations. It consists of FGb, RS, RAGlib, DV.
License: Unknown. Downloading is free.
download,SDPT3 (http://www.math.nus.edu.sg/~mattohkc/sdpt3.html)
Description: A software for semidefinite-quadratic-linear programming. (It is used by SOStools.)
License: Unknown. Downloading is free. Require MATLAB
SeDuMi (http://sedumi.mcmaster.ca/)
Description: Software for optimization over symmetric cones. (It is used by SOStools.)
License: GPL. Require Matlab.
Singular (http://www.singular.uni-kl.de) , [IMA talk or demo]
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
download, tutorial, manual, Live on the KNOPPIX
SOSTOOLS (http://www.cds.caltech.edu/sostools/) , [IMA talk or demo]
Description: It solves sums of squares (SOS) optimization programs.
License: GPL. Require MATLAB and (SeDuMi or SDPT3) package
manual,SparsePOP (http://www.is.titech.ac.jp/~kojima/SparsePOP) , [IMA talk or demo]
Description: SparesPOP is an implementation of a sparse semidefinite programming (SDP) relaxation method.
License: Unknown. Downloading is free. Require Matlab and SeDuMi.
SYNAPS (http://www-sop.inria.fr/galaad/logiciels/synaps) , [IMA talk or demo]
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
install instruction, manual, Live on the KNOPPIX