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REDUCE has a long and distinguished place in the history of computer algebra systems (see the bibliography). 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, but the normal user language is based on Algol-60 and is broadly similar to the Maple user language.
REDUCE primarily runs on either Portable Standard Lisp (PSL) or Codemist Standard Lisp (CSL), both of which are included in the SourceForge distribution. PSL is long-established and compiles to machine code, whereas CSL is newer and compiles to byte code. Hence, PSL is likely to be faster but CSL is available on a wider range of platforms. By modern standards, REDUCE is not a large application and should run well on any personal computer.
Since December 2008, an Open Source version of REDUCE is available on SourceForge.net:
REDLOG implements symbolic algorithms on first-order formulas with respect to user-chosen first-order languages and theories. The available domains include real numbers, integers, complex numbers, p-adic numbers, quantified propositional calculus, term algebras.
GUARDIAN: A REDUCE package for computing with guarded expressions.
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