Algebraic Representation, Elimination and Expansion in Automated Geometric Theorem Proving

Cayley algebra and bracket algebra are important approaches to invariant computing in projective and affine geometries, but there are some difficulties in doing algebraic computation. In this paper we show how the principle “breefs” – bracket-oriented representation, elimination and expansion for factored and shortest results, can significantly simplify algebraic computations. We present several typical examples on automated theorem proving in conics and make detailed discussions on the procedure of applying the principle to automated geometric theorem proving.

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