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(formerly Encyclopedic directory) Computational Algebra
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Algebra

Algebra (from the Arabic "al-jabr" meaning "reunion", "connection" or "completion") is a branch of mathematics which may be defined as a generalization and extension of arithmetic. The process of "balancing and restoration" is important in algebra. It is the process of equaling both sides of any given equation. Basically, "whatever you do to one side of the equation, you do to the other". Also in Algebra: the distributive law which is used to properly factor out and solve equations. The field may be roughly divided in

elementary algebra, where the properties of operations on the real number system are recorded, symbols are used as "place holders" to denote constants and variables, and the rules governing mathematical expressions and equations involving these symbols are studied,
abstract algebra, where algebraic structures such as groups, rings and as fieldss are axiomatically defined and investigated.
The specific properties of vector spaces are studied in linear algebra.
universal algebra, where those properties common to all algebraic structures are studied.
computer algebra, where algorithms for the symbolic manipulation of mathematical objects are collected

The word algebra is also used for various algebraic structures:

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Computer Algebra Nederland (CAN)
Coordinates the use of computer algebra in education and research. Research reports, newsletters and historical material.
http://www.can.nl/

SymbolicNet
Information centre for symbolic mathematical computation. Links to research and software.
http://www.SymbolicNet.org/

Groebner Bases
Definitions and examples, with Java applet.
http://www.geocities.com/CapeCanaveral/Hall/3131/g_bases.html

SIGSAM
ACM Special Interest Group in Symbolic and Algebraic Manipulation. Site has details of meetings, reports and other links.
http://www.acm.org/sigsam/

Journal of Symbolic Computation
Editors' site. Abstracts, contents, calls for papers and author information.
http://www4.ncsu.edu:8030/~hong/jsc.htm

Communications in Computer Algebra
The ACM SIGSAM Bulletin. Some tables of contents and sample articles.
http://www.apmaths.uwo.ca/~rcorless/sigsam/

GROEBNER: A Package for Calculating GrÃ¶bner Bases
A REDUCE package by H. Melenk and W. Neun, Konrad--Zuse--Zentrum, Berlin.
http://www.uni-koeln.de/REDUCE/3.6/doc/groebner/

Computer Algebra Site
Of the Hungarian Academy of Sciences. General- and special-purpose systems and substrates.
http://compalg.inf.elte.hu/compalg/coindex.html

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