Characteristic Sets and Gröbner Bases in Geometry Theorem Proving

Publisher Summary This chapter discusses how Grobner basis method can be used to prove geometry theorems. One of the important applications of the Grobner basis method is to decide ideal membership for polynomial ideals. The computation of the Grobner basis is very sensitive to the variable ordering. The chapter discusses the relationship between geometry and algebra to show that the Cartesian product of the field of real numbers is not the only realistic geometry. There are two approaches for defining geometry. These are the algebraic approach and the axiomatic geometry approach. For each model of a theory of geometry, one can prove the existence of a number system inherent to that model. The chapter discusses possible formulations on the algebraic formulation of certain geometry statements and related issues. The discussion is confined to a metric geometry whose associated field E is algebraically closed.