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