Using only the multigraded betti numbers of a $\ZZ^r$graded module $M$, this function identifies a subset of the multigraded regularity of a module $M$ over the coordinate ring $S$ of a product of projective spaces, in the sense of Maclagan and Smith. It assumes that the local cohomology groups $H^0_B(M)$ and $H^1_B(M)$ vanish, where $B$ is the irrelevant ideal of $S$.






The output is often but not always {partialRegularities M}.
In general regularityBound will not give the minimal elements of $\operatorname{reg} M$ but will be faster than computing cohomology.
The object regularityBound is a method function.