Projective geometric theorem proving with Grassmann–Cayley algebra

Abstract

Grassmann–Cayley algebra was invented by Grassmann and Cayley in the nineteenth century [A1K]. It is an algebra equipped with two products: the exterior product (outer product), and the dual of the exterior product called the meet product. Geometri-cally, this algebra provides an invariant language for the synthetic projective geometry on the incidence relations among points, lines and other “flat” objects. The algebra of invariants associated with this algebra is the so-called bracket algebra, or the algebra of determinants [White 1975].