  Let $R=k[x_1,\dots,x_n]$ be a ring of polynomials over a field $k$ of
characteristic $p>0$. There is an algorithm due to Lyubeznik for deciding the
vanishing of local cohomology modules $H^i_I(R)$ where $I\subset R$ is an
ideal. This algorithm has not been implemented because its complexity grows
very rapidly with the growth of $p$ which makes it impractical. In this paper
we produce a modification of this algorithm that consumes a modest amount of
memory.
