Computer-aided construction of finite geometric spaces: Automated verification of geometric constraints
The category of noncommutative geometric spaces is a rather new and wide field in geometry that provides a rich source of hard computer applications. In this contribution we give a short summary of the basic notions of geometric spaces. The so-called parallel map that describes a space will play a fundamental role because, in terms of the parallel map, a geometric space can be represented in such a way that geometric conditions/axioms (which form the structure of a space) are expressible by certain equations. To verify a configuration amounts to showing the solvability of a corresponding equation or a system of equations, respectively. This is a computational aspect that opens the whole field naturally to computer applications by means of "automated deduction in geometry," verification of geometric constraints, computer-aided construction of finite geometries. We give motivation why we use specific declarative programming languages for doing all the implementations and computer applications.
geometric constraints noncommutative geometric spaces computer applications