Symbolic computation in the homogeneous geometric model with clifford algebra

Authors:
Hongbo Li
Affiliations:
Chinese Academy of Sciences, Beijing, China
Venue:
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Year:
2004

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Abstract

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 it sincere geometric factorization.