Diagrammatic reasoning in projective geometry

Institut de recherche en informatique de Toulouse y Abstract The heart of our thesis is that matrices of incidence can be used for mechanical theorem proving in projective geometry. To every geometrical statement of projective geometry is associated a matrix of incidence whose normal form is computed after successive identiications of rows and columns. Our main result is that the geometrical statement implies such or such property (incidence between a point and a line) if and only if the normal form of the associated matrix contains a 1 at such or such entry.