Reduce is a computer algebra system first published
in 1969 (!). This means the software has survived
40 (!) years. Main and original author
is Anthony C. Hearn.
It is written in Portable Standard Lisp
(thus does not work in Common Lisp). It uses an
'algebraic' syntax. The necessary Lisp to run it
is available, too. Lots of work has been put into
REDUCE over the years.
http://reduce-algebra.sourceforge.net/
Tony Hearns REDUCE
http://reduce-algebra.com/
REDUCE: the First Forty Years
http://reduce-algebra.com/reduce40.pdf
Short REDUCE overview
http://reduce-algebra.com/info-package.htm