Clifford algebra provides nice algebraic representations for Euclidean geometry
via the homogeneous model, and is suitable for doing geometric reasoning
through
symbolic computation. In this paper, we propose various
symbolic computation techniques in Clifford algebra. The content includes
representation, elimination, expansion and simplification. Simplification
includes
contraction, combination and factorization. We apply the techniques
to automated geometric deduction, and derive the conclusion in completely
factored
form in which every factor is a basic invariant. The efficiency of Clifford
algebra in doing geometric reasoning is reflected in the short and readable
procedure of deriving sincere geometric factorization.
