Abstract
An important problem in computer-aided geometric reasoning is to automatically find geometric interpretations for algebraic expressions. For projective geometry this question can be reduced to the Cayley factorization problem. Before describing this problem, we give a brief introduction to the Cayley algebra for those readers not already familiar with it. The Cayley algebra is essentially the same as the classical Grassmann algebra. This algebra provides projectively invariant algebraic interpretations of synthetic geometric statements. A more thorough exposition may be found in Barnabei et al. (1985), Doubilet et al. (1974), or Rota & Stein (1976).
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