An algorithm to bound the regularity and nonemptiness of linear systems in Pn

The main goal of this paper is to present a new algorithm bounding the regularity and “alpha” (the lowest degree of existing hypersurface) of a linear system of hypersurfaces in Pn passing through multiple points in a general position. To do the above we formulate and prove a new theorem, which allows us to show the non-speciality of a linear system by splitting it into non-special and simpler systems. As a result we give new bounds for multiple point Seshadri constants on P2.