Cayley factorization

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. A Cayley factorization of a homogeneous bracket polynomial P is a Cayley algebra expression (using only the join and meet operations) which evaluates to P. We give an introduction to both Cayley algebra and bracket algebra for those readers not already familiar with them. The main result of this paper is an algorithm which solves the Cayley factorization problem in the important special case that P is multilinear.