  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 $\mathbb P^n$) passing through multiple
points in general position. To do the above we formulate and prove new theorem,
which allows to show non-specialty of linear system by splitting it into
non-special (and simpler) systems. As a result we give new bounds for multiple
point Seshadri constants on $\PP^2$.
