From: ca@math.berkeley.edu (Computer Algebra Systems)
Newsgroups: sci.math.symbolic
Subject: FAQ - Available Systems
Date: 14 Dec 1998 18:20:14 GMT
Computer Algebra Systems
by Paulo Ney de Souza
Department of Mathematics
University of California
Berkeley CA 94720-3840
This is the list of currently developed and distributed software for
symbolic mathematical applications. Most of the information here is obtained
from the developers and we try to keep it up to date, a not so easy task.
Any errors in the list are mine and I would like to hear about them.
Electronic mail concerning this database and additions to it could be sent to:
ca@math.berkeley.edu
Many new developments have surfaced since the last publication of the list,
specially the advent of real-parallel computation, compilers and use of OpenGL.
All of them technologies that have been around for some time, but did not find
their way on most CAS. After a short stint by Kurt Siegl with his marvelous
version of Maple parallelized by Strands 88 in the beginning of the 90's
we now have parallel functionality in Maple, with a Java based distributed
system, Mathematica, with a Toolkit provided by Roman Maeder, MuPAD and with
Scilab// via PVM calls. MathCode C++ is now able to generate numerical-based
code for Mathematica defined routines, and both Mathematica and MathCAD are
finally making use of OpenGL, MathCAD in a native way and Mathematica via a
3rd party package by Conix3d.
No information is supplied on systems no longer being supported like: AALPAK,
Aljabr, ALTRAN, ANALITIK, CAMAL, Cayley, CC, CCALC, FORMAC, MATHLAB, MathPlus,
Milo, MuMath, Paramacs, SAC, SAINT, ScratchPad, SIN, SMP, TRIGMAN, Theorist,
Vaxima.
We also do NOT list software which is available on the net but for which there
is no support or continuing development, like for example AMP, CLA, ODE, PFSA,
ODE and SOlutions; as well as packages that have been absorbed by other like
CHEVIE, GRAPE, GUAVA and ANU-pq; programs that are only available in
architectures no longer supported like BigNum and Schoonschip; for which no
current contact is available like FLAC, SENAC, Galois, DELiA, and the Parellel
||Maple|| developed by Kurt Siegl on Strand88, or packages with very limited
abilities like Mercury, Calculus and Mathomatic.
A more thorough description and detailed information for each of the systems
below is available on the web site:
http://math.berkeley.edu/CAS
An updated version of this list can also be obtained from the site. No
particular recommendation is made for any of the systems listed in here.
If you want the commercial packages prices, contact the developers.
Programs are classified among General Purpose, Group Theory, Algebra and
Number Theory, Algebraic Geometry, Tensor Analysis and CAS Susbtrates and
listed in alphabetical order inside each class, general purpose systems first.
Magma is listed twice due to the breath of its set of functions.
GENERAL PURPOSE
===============
Axiom::
Type: Commercial
OS: Unix and Win95/NT.
Web: http://www.nag.co.uk/symbolic/AX.html
Version: 2.1
Contact: NAG Ltd
Wilkinson House, Jordan Hill Road
Oxford, UK OX2 8DR
Phone: +44 (0) 1865-511245 Fax: +44 (0) 1865-310139
E-mail: infodesk@nag.co.uk
Comments: General purpose. Object oriented with multiple inheritance
based on algebraic concepts. Powerful type-inferencing
techniques to minimise the need for type declarations.
Hypertext browser and on-line documentation with source code
available for all library functions. High level interactive
language and powerful graphics capability. Design goal:
unlimited extensibility without degradation in performance
or usability. It offers the ability to compile user
extensions to the library and building of stand-alone
packages and to link with Nag Fortran Libraries of
numerical and statistical routines.
Derive::
Type: Commercial
OS: DOS and Win3.1/95/NT
Web: http://www.derive.com/drvset.htm
Version: 4.11
Contact: Soft Warehouse Inc. 3660 Waialae Ave, Suite 304
Honolulu HI 96816-3236 USA
Phone: +1 808 734-5801
E-mail: info@derive.com
Comments: Very robust, gets problems that other larger programs fail
on. Low cost. Runs on the tiny palmtops like HP 95-100 and
on meager machines like the PC XT.
FORM::
Type: Version 1 is public domain, Version 2 is commercial
OS: DOS, MacOS, NeXTStep, OpenVMS, Unix and WinNT
Web: http://www.candiensten.nl
Version: Version 1.1 and Version 2.3.
Contact: Jos Vermaseren E-mail: t68@nikhef.nl
Binary for version 1 are available from
ftp://ftp.nikhef.nl/pub/form/.
Version 2 is commercially distributed by:
CANdiensten
Kruislaan 419
NL-1098 VA Amsterdam
Ph: +31 (0) 20 560 8400 Fax: +31 (0) 20 560 8448
E-mail: info@candiensten.nl
Comments: FORM is designed for the processing of exceptionally
large formulae, pattern matching, computations in
noncommutative algebras and high energy physics.
GNU-calc::
Type: GNU copyleft
OS: Needs Emacs.
Web: ftp://prep.ai.mit.edu/pub/gnu/
Version: 2.02
Contact: Free Software Foundation
Comments: It runs inside GNU Emacs and is written entirely in Emacs
Lisp. It does the usual things: arbitrary precision integer,
real, and complex arithmetic (all written in Lisp),
scientific functions, symbolic algebra and calculus,
matrices, graphics, etc, and, can display expressions with
square root signs and integrals by drawing them on the
screen with ASCII characters. It comes with a well written
600 page on-line manual. You can FTP it from any GNU site.
JACAL::
Type: Gnu CopyLeft
OS: DOS, MacOS, OpenVMS, OS/2 and Unix.
Web: http://swissnet.ai.mit.edu/~jaffer/JACAL.html
Version: 1a8
Contact: Aubrey Jaffer, 84 Pleasant St. Wakefield MA 01880, USA.
E-mail: jaffer@ai.mit.edu
Comments: JACAL is a symbolic mathematics system for the simplification
and manipulation of equations and single and multiple valued
algebraic expressions constructed of numbers, variables,
radicals, and algebraic functions, differential, and
holonomic functions. In addition, vectors and matrices of
the above objects are included. It is written in Scheme and
runs where the language is available, an IBM PC version on
floppy for $99 is available directly from Aubrey Jaffer.
Macsyma:: Macsyma was developed at MIT and has spun-off a series of different versions that run on specific machines. From many that existed in the
80-90's there are only two being actively distributed now:
(i) Macsyma::
Type: Commercial
OS: Unix and Win95/98/NT
Web: http://www.macsyma.com/
Version: 421 for Unix and 2.3 for Windows.
Contact: Macsyma Inc, 20 Academy St., Arlington MA 02174-6436
E-mail: info@macsyma.com
Phone: 800-MACSYMA, +1 781 646-4550 Fax: +1 781 646-3161
Comments: General purpose, many diverse capabilities, one of the
oldest around. Includes proprietary improvements from
Symbolics and Macsyma Inc. Descendant of MIT's Macsyma.
Recent major enhancements include new capabilities in ODE's,
Laplace transforms, integrations, inequalities, linear
algebra and partial differential equations.
(ii) Maxima::
Type: Licensed for a fee. Get license from ESTSC before download.
OS: Unix.
Web: ftp://ftp.ma.utexas.edu/pub/maxima/
Version: 5.4
Contact: Bill Schelter E-mail: wfs@math.utexas.edu
Comments: A descendant of the MIT Macsyma family, implemented by
William F. Schelter, from University of Texas, based on
GNU Common Lisp. It is available to ESTSC (DOE) sites.
Get the license from ESTSC below, and then download the
software.
ESTSC - Energy Science & Technology Software Center
P. O. Box 1020 Oak Ridge TN 37831-1020
Phone: +1 423 576-2606, Fax: +1 423 576-6436
E-mail: estsc@adonis.osti.gov
ESTSC acts as a license collector only.
Currently their charge for one machine license is $165 for
universities. Site licenses are also available.
Maple:: Maple has two offsprings in the parallel comoutation arena, description below, and the kernel is available embedded in other products like MATLAB.
(i) Maple::
Type: Commercial
OS: MacOS, Unix and Win95/98/NT.
Web: http://www.maplesoft.com/
Version: 5 release 5.1.
Contact: Waterloo Maple Inc, 57 Erb Street W,
Waterloo, Ontario, Canada N2L 6C2
E-mail: info@maplesoft.com
Phone: +1 519 747-2373 and 800-267-6583 Fax: +1 519 747-5284
Comments: General purpose, source available for most routines.
Graphics and animation. On-screen and printable real-math
notation. A share library, written in the Maple language,
contains many additional routines, packages, and
application worksheets.
Maple's symbolic technology is incorporated into MathCAD
(MathSoft, Inc) and MATLAB (The MathWorks, Inc)
(ii) Distributed Maple::
Type: Free + Maple license.
OS: MacOS, Unix and Win95/98/NT.
Web: http://www.risc.uni-linz.ac.at/software/distmaple/
Version: 1.0.5
Contact: Wolfgang Schreiner
Research Institute for Symbolic Computation (RISC-Linz)
Johannes Kepler University, A-4040 Linz, Austria
Comments: Distributed Maple is a system for writing parallel programs
in the computer algebra system Maple. It allows one to
create concurrent tasks and have them executed by Maple
kernels running on different machines of a network.
(iii) Matlab Symbolic Math Toolbox::
Type: Commercial
OS: Unix, OpenVMS and Win95/NT. MacOS support is being dropped.
Web: http://www.mathworks.com/products/symbolic/
Version: 2.0
Contact: The MathWorks, Inc.
24 Prime Park Way
Natick, MA 01760-1500
Phone: +1 508 653-1415 Fax: +1 508 653-2997
E-mail: info@mathworks.com
Comments: General purpose. Based on the Maple V computational kernel,
with a set of MATLAB M-files designed to make symbolic
computation more easy. The MATLAB Symbolic Math Toolbox
includes the computational functions in the Maple kernel
and the linear algebra package. An Extended Symbolic Math
Toolbox is also available that supports Maple procedure
execution and includes other Maple packages for statistics,
Grobner bases, combinatorial functions, number theory,
Euclidean geometry, Lie symmetries, etc.
(iv) MathCAD::
Type: Commercial
OS: MacOS and Win3.1/95/NT.
Web: http://www.mathsoft.com/mathcad/
Version: Version 8 for Win95/98/NT and Version 6 for Win3.1 and MacOS.
Contact: MathSoft, Inc.
101 Main Street
Cambridge, MA 02142-1521
Phone: +1 617 577-1017, Fax: +1 617 577-8829
E-mail: sales-info@mathsoft.com
Comments: General purpose, good graphics the only one so far to
have OpenGL support.
(v) MathView::
Type: Commercial
OS: MacOS and Win3.1/95/NT.
Web: http://www.maplesoft.com/
Version: 2.5
Contact: Waterloo Maple Inc, 57 Erb Street W,
Waterloo, Ontario, Canada N2L 6C2
E-mail: info@maplesoft.com
Phone: +1 519 747-2373 and 800-267-6583 Fax: +1 519-747-5284
Comments: General purpose, good graphics. Good symbolic algebra
and graphics manipulation for a high-school setting.
(vi) SciLab::
Type: Anonymous FTP
OS: Unix and Win95/NT
Web: http://www-rocq.inria.fr/scilab/scilab.html
Version: 2.4
Contact: Meta2 Project
INRIA-Rocquencourt
Domaine de Voluceau - BP 105
78153 Le Chesnay Cedex France
E-mail: scilab@inria.fr
Comments: Elaborate data structures, sophisticated interpreter and
programming language with MATLAB-like syntax.
Hundreds of built-in math functions (new primitives can
easily be added), stunning graphics (2d, 3d, animation),
an open structure (easy interfacing with Fortran and C via
online dynamic link) and symbolic capabilities through a
Maple interface.
MAS::
Type: Anonymous FTP
OS: NextStep, OS2 and Unix.
Web: http://www.fmi.uni-passau.de/algebra/projects/mas.html
Version: 1.00
Contact: H. Kredel. Computer Algebra Group
University of Passau, Germany
E-mail: mas@alice.fmi.uni-passau.de
Comments: MAS is an experimental computer algebra system combining
imperative programming facilities with algebraic
specification capabilities for design and study of algebraic
algorithms.
Mathematica::
Type: Commercial
OS: MacOS, NeXTStep, OpenVMS, OS/2, Unix and Win95/NT
Web: http://www.wolfram.com/
Version: 3.01 or 3.02 depending on OS.
Contact: Wolfram Research, Inc.
100 Trade Center Drive
Champaign, IL 61820-7237
E-mail: info@wri.com
Phone: 800-441-MATH and +1 217 398-0700 Fax: +1 217 398-0747
Comments: General purpose, Notebook interface, with the whole manual
on-line at http://documents.wolfram.com/.
Packages include: MathTensor for Tensors, NCAlgebra for
Non-Commutative Algebra, Combinatorica for Graph Theory
and MathLink for a 2-way communication with C programs.
The Parallel Computing Toolkit brings parallel computing
support to Mathematica, running on any computer network
(http://www.mathconsult.ch/math/stuff/MSRI98/MSRI98.html),
and MathCode C++ generates optimized C++ code directly from
Mathematica programs, creating stand-alone executables
that can take advantage of the speed of native C++ code
(http://www.wolfram.com/applications/mathcode) at a
stratospheric price! OpenGL support is now provided by
Conix3D Explorer (http://www.conix3d.com/). Student versionss
available for Mac and PC's.
Mock-Mma::
Type: Anonymous FTP
OS: Needs Common LISP.
Web: ftp://peoplesparc.berkeley.edu:/pub
Version: 1.7
Contact: Richard Fateman
Computer Science Division
University of California
Berkeley CA 94720-1776
E-mail: fateman@cs.berkeley.edu
Comments: It is a framework of a parser, display, polynomial
manipulator, and a few other pieces, that allow one to
program other pieces of common-lisp systems for computer
algebra. The pieces supplied are roughly consistent with the
conventions adopted by the Mathematica system.
MuPAD::
Type: Commercial with free personal single-user licenses for
teachers and students.
OS: MacOS, Unix and Win95/NT
Web: http://www.sciface.com/
Version: 1.4.0
Contact: SciFace Software GmbH & Co. KG
Technologiepark 12
D-33100 Paderborn
Germany
Phone: +49 5251-6407-51 Fax: +49 5251-6407-99
E-mail: info@sciface.com
Comments: General purpose, source available for library routines,
graphics support, source code debugger, on-line hypertext
help system. Users can view the library code, implement
their own routines and data types easily and can also
dynamically link C/C++ compiled modules for raw speed
and flexibility. The latest (beta) release 1.4.1 is the
first parallel version of MuPAD.
Reduce::
Type: Commercial
OS: Cray Y-MP down to Mac's and PC's and Atari's.
Web: http://www.rrz.uni-koeln.de/REDUCE/
http://www.codemist.tc/reduce/index.html
Version: 3.6
Contact: Anthony C. Hearn, RAND, 1700 Main Street
P. O. Box 2138, Santa Monica CA 90407-2138 U.S.A.
Phone: +1 310 393-0411 Ext. 7681 Fax: +1 310 393-4818
E-mail: reduce@rand.org
Comments: General purpose, LISP based, with source code provided
and extensive library of user contributions.
Risa/Asir::
Type: Anonymous FTP
OS: DOS, MacOS and Unix
Web: ftp://endeavor.fujitsu.co.jp/pub/isis/asir/
Version: 953801
Contact: Taku Takeshima, Research Fellow
Institute for Social Information Science,
Fujitsu Laboratories Limited
140 Miyamoto, Numazu-shi, Shizuoka
410-03 Japan
Phone: +81 559-24-7210, Fax: +81 559-24-6180
E-mail: tak@iias.flab.fujitsu.co.jp and
noro@iias.flab.fujitsu.co.jp
Comments: An experimental sytem developed by Fujitsu, Risa/Asir is a
CAS which provides a programming system Asir with several
subroutine libraries that can also be used as parts of
other programs. Its programming system Asir has a C-like
language, also called `Asir,' its interpreter and a dbx-like
source-line debugger. The source line debugger is very
helpful and may be indispensable for those who want to
implement algorithms for algebraic computation.
GROUP THEORY
============
GAP::
Type: Anonymous FTP (free, but not PD; basically GNU copyleft).
OS: DOS, MacOS, Unix and Windows
Web: http://www-gap.dcs.st-and.ac.uk/~gap
Version: 3.4.4
Contact: E-mail: gap@dcs.st-and.ac.uk
Comments: GAP is a system mainly for computational group theory.
It consists of a small kernel implementing the language,
a large library of functions implementing the algorithms,
a large library of important groups and character tables.
LiE::
Type: Free
OS: Unix
Web: http://www.can.nl/SystemsOverview/Special/GroupTheory/LiE/
/index.html
Version: 2.2
Contact: Arjeh M. Cohen, E-mail: amc@win.tue.nl or
Marc A.A. van Leeuwen , E-mail: maavl@cwi.nl
Comments: Lie group computations. It focuses on the representation
theory of complex semisimple (reductive) Lie groups and
algebras, and on the structure of their Weyl groups and
root systems. One can even run it from the Web without
installing it from:
http://www.can.nl/SystemsOverview/Special/GroupTheory/LiE/form.html
Magma::
Type: Cost recovery.
OS: DOS and Unix.
Web: http://www.maths.usyd.edu.au:/u/magma/index.html
Version: 2.4
Contact: Computational Algebra Group
School of Mathematics
University of Sydney
NSW 2006 Australia
E-mail: magma@maths.usyd.edu.au
Phone: +61 2 9351 3338 Fax: +61 2 9351 4534
Comments: The system is designed to support computation in algebra,
number theory, geometry and algebraic combinatorics. It
has an advanced functional programming language with many
novel features designed for concise and efficient
specification of algebraic algorithms. The kernel has
(coded in) the fundamental algorithms for ring theory
(polynomial rings, matrix rings, integer rings), field
theory (general algebraic number fields -- KANT Version 2,
finite fields, real and complex fields), module theory,
group theory (fp groups, permutation groups, soluble groups
and matrix groups) and algebraic combinatorics (coding
Magnus::
Type: Free
OS: Unix
Web: http://zebra.sci.ccny.cuny.edu/web/aboutmagnus.html
Version: 3.0.0
Contact: E-mail: rgr@groups.sci.ccny.cuny.edu
Comments: Magnus is a system for exploring infinite groups.
Schur::
Type: Commercial
OS: DOS and Unix
Web: http://smc.vnet.net/Schur.html
Version: 5.2
Contact: Steven M. Christensen
P.O. Box 16175
Chapel Hill, NC 27516
Phone/Fax: +1 919 382-5584, E-mail: steve@smc.vnet.net
Comments: Schur is an interactive program for calculating properties
of Lie groups and symmetric functions.
ALGEBRA & NUMBER THEORY
=======================
CoCoA::
Type: Anonymous FTP
OS: MacOS, Unix and Win95
Web: http://ideal.dima.unige.it/main.html
Version: 3.5
Contact: Gianfranco Niesi
Dipartimento di Matematica
Via L. B. Alberti, 4
I-16134 Genova Italy
E-mail: cocoa@dima.unige.it
Comments: Computations in commutative algebra.
FELIX::
Type: Anonymous FTP
OS: DOS, Unix and Win3.1/NT
Web: http://felix.hgb-leipzig.de/
ftp://aix550.informatik.uni-leipzig.de/pub/felix
Version: 3.0
Contact: Joachim Apel and Uwe Klaus, Universit\"at Leipzig,
Augustusplatz 10-11, O-7010 Leipzig, Germany
E-mail: japel@informatik.uni-leipzig.de
klaus@informatik.uni-leizig.de
Comments: FELIX is designed for computations in and with algebraic
structures. The structures implemented so far are commutative
polynomial rings, non-commutative algebras as well as modules
over them. The central method is Buchberger's algorithm and
its generalizations to non-commutative rings, in particular
to free k-algebras and algebras of solvable type. Among the
implemented applications there are syzygy computations and
basic ideal operations. Felix provides a complete
programming language which in standard mode is interpreted
but also on-line compiler and linker are included.
Fermat::
Type: Anonymous FTP
OS: MacOS and Win95/NT
Web: http://www.bway.net/~lewis/
Version: 2.2.1
Contact: Robert H. Lewis
Fordham University
E-mail: rlewis@murray.fordham.edu
Comments: It does arithmetic of arbitrarily long integers and
fractions, symbolic calculations, graphics, and other
numerical calculations, oriented toward polynomial and
matrix algebra over the rationals and finite fields.
Very fast in matrix calculations---much faster than
any of the big systems.
GRB::
Type: Anonymous FTP
OS: DOS and Unix.
Web: ftp://math.vt.edu/pub/green/
Version: 1.0
Contact: E.L. Green
Virginia Polytechnic Institute and State University
Blacksburg, Virginia 24061-0123
E-mail: green@math.vt.edu
Comments: GRB provides a computational basis to do algebraic and
homological manipulations on algebras and modules.
Functionality currently in the package includes computation
of a basis for the algebra, reduced Groebner basis for the
ideal of relations, the Cartan matrix and determinant for
finite dimensional algebras, construction of minimal
projective resolutions and coefficients of the Hilbert and
Poincare' series.
Bergman::
Type: Anonymous FTP
OS: DOS and Unix, with PSL (Portable Standard Lisp).
Web: ftp://ftp.matematik.su.se/pub/src/bergman/
Version: 0.926
Contact: Joergen Backelin E-mail: joeb@matematik.su.se
Department of Mathematics
Stockholm University, 106 91 Stockholm
Comments: Bergman is a Groebner basis calculation program with
homogeneous input (although there are some possibilities
to homogenise/dehomogenise an arbitrary commutative input),
by polynomials in the commutative or the non-commutative
polynomial ring over the rationals or a finite prime field,
in a finite number of variables.
References in: Jan-Erik Roos, Journal of Pure and Applied
Algebra, volume 91, 1994, pages 255-315 - Bergman relevant
pages are 300-302.
Kan::
Type: Anonymous FTP
OS: Linux and Sun Sparc.
Web: http://www.math.kobe-u.ac.jp/KAN
Version: 2.981129
Contact: Nobuki Takayama, Department of Mathematics
Kobe University, Japan
E-mail: kan@math.kobe-u.ac.jp
Comments: Kan is a system for doing algebraic analysis by computer
based on computations of Groebner bases. It does
computations in the rings of polynomials, differential
operators, difference operators and q-difference operators.
Macaulay::
Type: Anonymous FTP
OS: Unix and Windows
Web: http://www.math.uiuc.edu/Macaulay2/
Version: 3.0
Contact: Daniel Grayson Mike Stillman
Department of Mathematics Department of Mathematics
University of Illinois Cornell University
Urbana, IL 61801 Ithaca, NY 14853
Phone: +1 217-333-6209 +1 607-255-7240, 277-1835
E-mail: dan@math.uiuc.edu mike@math.cornell.edu
Comments: Macaulay 2 is a new re-write of the Macaulay system devoted
to supporting research in algebraic geometry and commutative
algebra. The old version, developed by Stillman and Dave
Bayer is still available at:
http://www.math.columbia.edu/~bayer/Macaulay.html
Magma::
Type: Cost recovery.
OS: DOS and Unix.
Web: http://www.maths.usyd.edu.au:/u/magma/index.html
Version: 2.4
Contact: Computational Algebra Group
School of Mathematics
University of Sydney
NSW 2006 Australia
E-mail: magma@maths.usyd.edu.au
Phone: +61 2 9351 3338 Fax: +61 2 9351 4534
Comments: The system is designed to support computation in algebra,
number theory, geometry and algebraic combinatorics. It
has an advanced functional programming language with many
novel features designed for concise and efficient
specification of algebraic algorithms. The kernel has
(coded in) the fundamental algorithms for ring theory
(polynomial rings, matrix rings, integer rings), field
theory (general algebraic number fields -- KANT Version 2,
finite fields, real and complex fields), module theory,
group theory (fp groups, permutation groups, soluble groups
and matrix groups) and algebraic combinatorics (coding
theory and graph theory).
Numbers::
Type: Free but not Public Domain, registration required.
OS: DOS
Web: http://www.infj.ulst.ac.uk/~cccz23/
Version: 202d
Contact: Ivo Duentsch E-mail: I.Duentsch@ulst.ac.uk
Comments: Numbers is a calculator for number theory. It performs
various routines in elementary number theory, some of
which are also usable in algebra or combinatorics.
PARI/GP::
Type: Anonymous FTP
OS: DOS, MacOS and Unix
Web: ftp://megrez.ceremab.u-bordeaux.fr/pub/pari/
Version: 2.0.12
Contact: E-mail: pari@ceremab.u-bordeaux.fr
Comments: Number theoretical computations, source available, key
routines are in assembler, ASCII and Xwindows graphics.
Complete package for algebraic number theory computations
including handling of ideals, prime ideals, prime ideal
factorization, p-adic factorization, etc ...
SIMATH::
Type: Anonymous FTP
OS: Unix
Web: http://emmy.math.uni-sb.de/~simath/index.html
Version: 4.0
Contact: SIMATH-Gruppe, Lehrstuhl Prof. Dr. H.G. Zimmer,
FB 9 Mathematik, Universitaet des Saarlandes,
D-W-6600 Saarbruecken, Germany.
Phone: 0681 302-2206.
E-mail: simath@math.uni-sb.de
Comments: SIMATH is written in C, contains an interactive
calculator (simcalc) and many C-functions over
algebraic structures such as arbitrary long integers,
rational numbers, floating point numbers, poly-
nomials, Galoisfields, matrices, elliptic curves,
algebraic number fields, modular integers, finite fields,
Groebner basis, etc...
SINGULAR::
Type: Anonymous FTP
OS: MacOS, Unix and Win95/NT.
Web: http://www.mathematik.uni-kl.de/~zca/Singular/
Version: 1.2.2
Contact: E-mail: singular@mathematik.uni-kl.de
Comments: SINGULAR is a system for polynomial computations with
special emphasis on the needs of commutative algebra,
algebraic geometry, and singularity theory
ALGEBRAIC GEOMETRY
==================
CASA::
Type: Anonymous FTP
OS: Unix
Web: http://www.risc.uni-linz.ac.at/software/casa/casa.html
Version: 2.3
Contact: E-mail: alggeo@risc.uni-linz.ac.at
Comments: The Maple package CASA is designed for performing
computations and reasoning about geometric objects in
classical algebraic geometry, in particular affine and
projective algebraic geometry over an algebraically closed
computable field of characteristic 0, like the rational
numbers Q or any of its finite algebraic extensions.
GANITH::
Type: Person to person distribution, contact the author.
OS: Unix
Web: http://king.ticam.utexas.edu/CCV/projects/shastra/toolkits/ganith.html
ftp://ftp.cs.purdue.edu/pub/shastra/bin
Contact: Chandrajit Bajaj
Department of Computer Science, Purdue University
West Lafayette, IN 47907
E-mail: bajaj@cs.purdue.edu
Comments: GANITH is an algebraic geometry toolkit, for the computation and visualization of solutions to systems of algebraic
equations.
Example applications of this for geometric modeling and
computer graphics are algebraic curve and surface
display, curve-curve intersections, surface-surface
intersections, global and local parameterizations,
implicitization.
GANITH also incorporates techniques for interpolation and
least-squares approximation (multivariate data fitting)
with algebraic curves and surfaces.
TENSOR ANALYSIS
===============
Cartan::
Type: Commercial
OS: Needs Mathematica 2.2 or greater.
Web: http://www.scup.no/books/en/cartan/index.html
Version: 1.2
Contact: Harald H. Soleng E-mail: harald.soleng@nr.no
Comments: An easy-to-use tensor component package. The program employs
the powerful formalism of rigid frames (e.g., orthonormal
frames or vielbeins) and can return results both in the
rigid frame and in the coordinate basis. Tensors such as
Riemann, Ricci, Weyl, Einstein, Lanczos, and Cotton-York
are predefined. It is also possible to extend the program
by adding your own functions and variables.
FeynCalc::
Type: Commercial
OS: Needs Mathematica 3.0 or greater
Web: http://www.mertig.com/
Version: 3.0.5.1
Contact: Mertig Research & Consulting
Oosterpark 77/78 1092 AT Amsterdam
Phone: +31 (0) 20 4602 677, Fax: +31 (0) 20 4602 692
E-mail: rolf@mertig.com
Comments: A Mathematica 3.0 package for algebraic calculations in
high-energy physics including Feynman diagram calculations.
GRG::
Type: Anonymous FTP
OS: DOS and Unix
Web: ftp://ftp.maths.qmw.ac.uk/pub/grg3.2/
Version: 3.2r2
Contact: Vadim V. Zhytnikov E-mail: vvzhy@td.lpi.ac.ru
Comments: GRG is the computer algebra system designed for calculations
in differential geometry and field theory. It is based on
REDUCE but has its own simple input language. Works with
tensors, spinors, vectors, differential forms; knows the
covariant properties of the objects: one can raise and lower
indices, compute covariant and Lie derivatives, perform
coordinate and frame transformations etc. GRG has more
than 150 built-in standard field-theory and geometrical
quantities and formulas for their computation providing ready
solutions to many standard problems.
GRTensor::
Type: Anonymous FTP
OS: Needs Maple V or Mathematica
Web: http://www.astro.queensu.ca/~grtensor/GRHome.html
Version: 1.7 for MapleV and 1.2 for Mathematica.
Contact: Kayll Lake & Peter Musgrave
Department of Physics
Queens university
Kingston, Ontario, Canada K7L 3N6
E-mail: lake@bill.phy.queensu.ca
Comments: GRTensorII is a package for performing calculations in the
general area of differential geometry. Its purpose is the
calculation of tensor components on curved spacetimes
specified in terms of a metric or set of basis vectors.
MathTensor::
Type: Commercial
OS: Needs Mathematica 1.2, 2.0 or greater.
Web: http://smc.vnet.net/MathTensor.html
Version: 2.1.5
Contact: MathSolutions, Inc., P. O. Box 16175
Chapel Hill, NC 27516, USA
Phone/Fax: +1 919 967-9853
E-mail: mathtensor@wolfram.com
Comments: Elementary and advanced tensor analysis and differential
forms. Adds more than 250 functions and objects to
Mathematica.
RedTen::
Type: Free for non-commercial use.
OS: Needs Reduce.
Web: http://www.scar.utoronto.ca/~harper/redten.html
Version: 4.1
Contact: John Harper E-mail: harper@manitou.astro.utoronto.ca
Comments: REDTEN is a symbolic algebra package for REDUCE which
provides tensor and tensor-like objects and manipulation
functions for work in General Relativity.
Ricci::
Type: Anonymous FTP
OS: Needs Mathematica 2.0 or greater.
Web: http://www.math.washington.edu/~lee/Ricci/
Version: 1.32
Contact: John M. Lee
Department of Mathematics
University of Washington
Seattle, WA 98195-4350
Phone: +1 206 543-1735 Fax: +1 206 543-0397
E-mail: lee@math.washington.edu
Comments: Mathematica package for doing tensor computations in
differential geometry, including coordinate-free tensor
operations as well as indexed tensors with dummy indices
and the summation convention.
TTC::
Type: Anonymous FTP
OS: Unix and Windows
Web: http://baldufa.upc.es/ttc/
Version: 4.0
Contact: A. Balfagsn, P. Castellvm and X. Jain
E-mail: ttc@baldufa.upc.es
Comments: TC (Tools of Tensor Calculus) is a Mathematica package for
doing tensor and exterior calculus on differentiable
manifolds
CAS Substrates
==============
Apfloat::
Type: Anonymous FTP
OS: Needs a C++ compiler.
Web: http://www.hut.fi/~mtommila/apfloat/
Version: 1.50
Contact: Mikko Tommila E-mail: Mikko.Tommila@hut.fi
Comments: Apfloat is a high performance arbitrary precision package.
It uses Number Theoretic Transforms and can be compiled
with most C++ compilers, however gcc is recommended. It has
assembler optimizations for 486, Pentium, Alpha and MIPS
processors.
GNU MP::
Type: Anonymous FTP
OS: DOS and Unix with optmized assembly for many CPU's.
Web: ftp://ftp.prep.ai.mit.edu/pub/gnu/gmp-2.0.2.tar.gz
Version: 2.0.2
Contact: E-mail: bug-gmp@prep.ai.mit.edu
Comments: GNU MP is a library for arbitrary precision arithmetic,
operating on signed integers, rational numbers, and
floating point numbers. It has a rich set of functions,
and the functions have a regular interface. GNU MP is
designed to be as fast as possible, both for small
operands and for huge operands. The speed is achieved by
using fullwords as the basic arithmetic type, by using
fast algorithms, by carefully optimized assembly code for
the most common inner loops for a lots of CPUs, and by a
general emphasis on speed (instead of simplicity or
elegance).
KASH/KANT::
Type: Anonymous FTP
OS: DOS, OS/2, Unix and Win3.1/95
Web: http://www.math.TU-Berlin.DE/~kant/
Version: KANT - Version 4 and KASH - Version 2.0
Contact: KANT Group
Prof. Dr. M. E. Pohst / Dr. Johannes Graf v. Schmettow
Mathematisches Institut, Heinrich-Heine-Universit\"at
Universit\"atsstr. 1, D-4000 D\"usseldorf 1
E-mail: kant@math.tu-berlin.de
Comments: KANT (Computational Algebraic Number Theory) is a
subroutine package for algorithms from geometry of
numbers and algebraic number theory. KANT Version 1 was
written in Fortran 77, has been superseded by Version 2
built for the Cayley Platform and written in C.
KANT Version 4 was the base for Magma and KASH is the
friendly shell to use the primitives.
LiDIA::
Type: Free for non-commercial purposes. Anonymous FTP
OS: MacOS, OS/2, Unix and WinNT
Web: http://www.informatik.th-darmstadt.de/TI/LiDIA/
Version: 1.3.1
Contact: LiDIA Group
Darmstadt University of Technology
Karolinenplatz 5
64289 Darmstadt Germany
E-mail: lidia@cdc.informatik.th-darmstadt.de
Comments: LiDIA is a C++ library for computational number theory
which provides a collection of highly optimized
implementations of various multiprecision data types and
time-intensive algorithms.
NTL::
Type: Anonymous FTP
OS: Unix and Win95/NT
Web: http://www.cs.wisc.edu/~shoup/ntl
Version: 3.1
Contact: Victor Shoup
IBM Research-Zurich, Saeumerstr. 4
8803 Rueschlikon Switzerland
Tel: +41 1 724 8909
E-mail: sho@zurich.ibm.com
Comments: NTL is a high-performance, portable C++ library providing
data structures and algorithms for manipulating signed,
arbitrary length integers, and for vectors, matrices, and
polynomials over the integers and over finite fields
SACLIB::
Type: Anonymous FTP, registration required.
OS: Unix.
Web: ftp://ftp.risc.uni-linz.ac.at/pub/
Version: 1.1
Contact: SACLIB Maintenance
Research Institute for Symbolic Computation
Johannes Kepler University
4020 Linz Austria
E-mail: saclib@risc.uni-linz.ac.at
Comments: SACLIB is a library of C programs for computer algebra
derived from the SAC2 system, and incorporating many
improvements. It contains programs for list processing,
infinite precision arithmetic (integer, rational and
modular), operations on multivariate polynomials, polynomial
real root isolation and refinement, and operations with real
algebraic numbers and polynomials having algebraic number
coefficients. Improved and extended versions of SACLIB, and
several SACLIB application packages, are already in advanced
stages of development. These include arbitarary precision
floating point and interval arithmetic, improved greatest
common divisor and factorization algorithms for polynomials,
isolation and refinement of complex roots of polynomials,
Groebner basis computation and quantifier elimination.
A shell ISAC is available for SACLIb and the first package,
Groebner, is also available at
http://www.risc.uni-linz.ac.at/software/Groebner/
UBASIC::
Type: Anonymous FTP
OS: DOS and WinNT
Web: ftp://rkmath.rikkyo.ac.jp/pub/ubibm/ or
http://www.rkmath.rikkyo.ac.jp/~kida/ubasic.htm
Version: 8.8c
Contact: Yuji Kida E-mail: kida@rkmath.rikkyo.ac.jp
Comments: BASIC-like environment for number theory. In the collection
of programs written for it one can find:
MALM (Collection of UBASIC Number Theory Programs) by
Donald E. G. Malm (Department of Mathematical Sciences,
Oakland University, Rochester, MI 48309-4401,
malm@vela.acs.oakland.edu, Phone: 313-370-3425) which
includes Baillie-Wagstaff Lucas pseudoprime test, Algorithm
for Chinese remainder, Elliptic curve method to factorize n,
Fermat's method of factoring, General periodic continued
fraction to quadratic routine, Evaluates Carmichael's
function & D. H. Lehmer's method of solving x^2 = q (mod p).
Other programs include PPMPQS (Prime factorization program
for numbers over 80 digits (ubmpqs32.zip)) which comes with
the distribution, and many others as well. Available by
anonymous FTP from http://wuarchive.wustl.edu/edu/math/
/software/msdos/number.theory/malm/
Weyl::
Type: Anonymous FTP
OS: Needs Common LISP.
Web: ftp://ftp.cs.cornell.edu:/pub/simlab/release
Version: 4.309
Contact: Richard Zippel E-mail: rz@cs.cornell.edu
Comments: Intended to be incorporated in larger, more specialized
systems. Available as part of SimLab from
ftp.cs.cornell.edu:/pub/simlab/release
Zen::
Type: Anonymous FTP
OS: OS/2 and Unix
Web: http://ultralix.polytechnique.fr/~zen/
Version: 1.0b
Contact: Florent Chabaud and Reynald Lercier
E-mail: zen@lix.polytechnique.fr
Comments: A toolbox for fast computations in finite extensions of
finite rings.
Table of Systems per OS:
========================
DOS MacOS NeXTStep OpenVMS OS/2 Unix Win3.1 Win95 WinNT WinCE
Axiom x x x
Bergman x x
BigNum
CoCoA x x x
Derive x x x x
Distr. Maple x x x x
FELIX x x x x
FORM x x x x x x
Fermat x x x
GANITH x
GAP x x x x x
GNU MP x x
GRB x x
GRG x x
JACAL x x x x x
KASH/KANT x x x x x
Kan x
LiDIA x x x x
LiE x
MAS x x x
Macaulay x x x x
Macsyma x x x
Magma x x
Magnus x
Maple x x x x
MathCAD x x x x
MathView x x x x
Mathematica x x x x x x x
Maxima x
MuPAD x x x x
NTL x x x
Numbers x
PARI/GP x x x
Reduce x x x x x x
Risa/Asir x x x
SACLIB x
SIMATH x
SINGULAR x x x x
Schur x x
SciLab x x x
TTC x x x
UBASIC x x
Zen x x
DOS MacOS NeXTStep OpenVMS OS/2 Unix Win3.1 Win95 WinNT WinCE