From Null Monomials to Versors in Conformal Geometry
Hongbo Li -- Chinese Academy of Sciences
Although in conformal geometric constructions, starting from points one can construct lines and circles by 3-vectors, 2-planes and 2-spheres by 4-vectors, etc, which are outer products of null vectors representing the incident points involved in the construction, in symbolic geometric computing it is the geometric product of these null vectors that prove to be much more efficient than the graded parts of the geometric product, such as the outer product, the meet product, the inner product, etc. Hence, monomials that are the geometric product of null vectors, called null monomials, turn out to be the basic algebraic terms in symbolic computing. Their geometric interpretations and applications are an important topic of research.