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The Open Source version of the REDUCE algebra system was registered on SourceForge.net on Dec 18, 2008. 
Tony Hearn, who is the main and original author of this software, writes:
In 1963, I began work on a software system that would in time evolve into REDUCE. By 1968, copies had been made available to various researchers throughout the world. Forty years later, there is still an active community of users. In order to encourage further development, I have decided to make the software freely available under a modified BSD license.
This Wiki for the project reducealgebra is quite new. But you might already find some interesting information via the sidebar.
About Reduce
REDUCE is a system for doing algebra by computer, which also supports numerical approximation and interfaces to gnuplot to provide graphics.
The development of the REDUCE computer algebra system was started in the 1960s by Anthony C. Hearn. Since then, many scientists from all over the world have contributed to its development. REDUCE has a long and distinguished place in the history of computer algebra systems. Other systems that address some of the same issues but sometimes with rather different emphasis are Axiom, Derive, Macsyma (Maxima), Maple, Mathematica and MuPAD.
REDUCE is implemented in Standard Lisp expressed in an intuitive imperativestyle notation called RLISP. The latter is used as a basis for REDUCE's userlevel language.
REDUCE primarily runs on either Portable Standard Lisp (PSL) or Codemist Standard Lisp (CSL), both of which are included in the SourceForge distribution. By modern standards, REDUCE is not a large application and should run well on any personal computer.