|
|
Symbolic Algebra
Since the symbolic algebra systems have been well documented elsewhere, I simply provide pointers instead of reviewing them here.Comparative Reviews on Symbolic Algebra Packages
Michael Wester's review (1999) is a detailed review of Axiom, Derive, Macsyma, Maple, Mathematica, Mupad, and Reduce, as well as references and links to other reviews.Wester's review compares the packages on 131 problems, mostly from symbolic algebra.
Steven Christensen's site
lists several comparisons of mathematica on various computers.
Web sites for Symbolic Algebra
Kent State's SymbolicNet
provides a convenient starting point for discovering information
about Symbolic and Algebraic Computation (SAC).
Number Theory Web is a large web site devoted to number theory resources.
Maxima
The Maxima computer algebra system is an updated version of the Macsyma system that was the largest and most capable of the early systems from the 1960s, and under development for over 20 years at MIT, primarily. It is available in neatly installable packages for Windows, Mac, or Linux. It has an active international user community with documentation in several Languages. It fits in the category of general-purpose system, which means that it is most directly comparable with the commercial systems Maple or Mathematica. (see Wikipedia article on Macsyma)Axiom
The Axiom system is another general purpose CAS, whose distinctive feature is its foundational organization on a strongly typed mathematical hierarchy. It is based on an IBM Research project, Scratchpad II.MuPAD
MuPAD is a computer algebra system (CAS) for exact symbolic and numeric computing with arbitrary precision. Its programming language has a Pascal-like syntax and allows imperative, functional, as well as object-oriented programming. It is not free.Jacal
Jacal is an interactive symbolic mathematics program. JACAL can manipulate and simplify equations, scalars, vectors, and matrices of single and multiple valued algebraic expressions containing numbers, variables, radicals, and algebraic differential, and holonomic functions. It is available free under the GPL license.GAP
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.PARI/GP
urlhttp://pari.math.u-bordeaux.fr/ PARI/GP is a computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library.Form
Form: The Form Symbolic Manipulation System is aimed at doing large scale algebraic calculations. It may be used as a complement to comman Computer Algebra Systems for performance-critical tasks.GRTensorII
GRTensorII is a computer algebra 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. It is available in both MapleV and Mathematica versions, and is distributed free of charge.SACLIB
SACLIB is a library of C programs for computer algebra derived from the SAC2 system.NTL - A Library for doing Number Theory
NTL is a 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.Yacas: Yet another computer algebra system
Yacas (Yet Another Computer Algebra System) is a general purpose Computer Algebra System. It uses its own programming language designed for symbolic as well as arbitrary-precision numerical computations. The system has a library of scripts that implement many of the symbolic algebra operations; new algorithms can be easily added to the library.Ginac
The Ginac open framework for symbolic computation within the C++ programming language does not try to define a language of its own as conventional CAS do. Instead, it extends the capabilities of C++ by symbolic manipulations.Sage
Sage is a computer algebra plus mathematical software system. It includes interfaces to Magma, Maple, Mathematica, MATLAB, and MuPAD, and the free programs Axiom, GAP, GP/PARI, Macaulay2, Maxima, Octave, and Singular.SAGE can be used from a web browser. It connects either to a program running on your computer, or to a server elsewhere.
The SAGE notebook can be used to create graphics, typeset mathematical expressions, and to start up and interrupt multiple calculations. The notebook can be used to create and publish collaborative worksheets.
Sage is Python based. It provides a standard, uniform Python programming
interface to all the underlying systems.
Automatic Differentiation Tools
[Luiz Henrique de Figueiredo]:
A good starting point for automatic differentiation tools is:
Argonne National Lab
Copyright 1995-2008 Mathcom Solutions Inc
info@mathcom.com
Updated March 27, 2008