Automated Geometric Theorem Proving, Clifford Bracket Algebra and Clifford Expansions

We report some of our recent progress on using Clifford bracket algebra to simplify automated geometric theorem-proving via the homogeneous model, and on systematic expansions of Clifford expressions with the purpose of finding the shortest expansions. With such simplification and expansion techniques, we are able to finish some pure geometric computation tasks that are too difficult for other algebraic methods to finish even with the aid of a good PC, and we get better results through a readable procedure.

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