BLD-GA is a Common Lisp geometric algebra library. It uses BLD-GEN for arithmetic functions re-defined as generic functions, with methods for scalars and certain geometric algebra objects. If BLD-GENSYM is loaded, symbolic scalars and coefficients can be used.
"Efficient Implementation of Geometric Algebra" http://staff.science.uva.nl/~fontijne/phd.html
...and the books:
"Geometric Algebra For Computer Science" http://www.geometricalgebra.net/
"Geometric Algebra for Physicists" http://www.mrao.cam.ac.uk/~cjld1/pages/book.htm
"New Foundations for Classical Mechanics" http://geocalc.clas.asu.edu/html/NFCM.html
Gaigen: http://www.science.uva.nl/ga/gaigen/ Gaigen 2: http://staff.science.uva.nl/~fontijne/gaigen2.html