Bounding the rational LS-category of certain spaces via the Hilbert function

Let (ΛV,d) be the Sullivan model of a pure elliptic space S. We give an algorithm, based on the computation of the Hilbert function of certain ideal, that provides a lower and an upper bound for the rational L.–S. category of S,cat0(ΛV,d). When S has null Euler homotopy characteristic, both bounds are sharp.