Georgia Institute of Technology College of Sciences

The Macaulay dual space offers information about a polynomial ideal localized at a point such as initial ideal and values of the Hilbertfunction, and can be computed with linear algebra. Unlike Gr\"obner basis methods, it is compatible with floating point arithmetic making it anatural fit for the toolbox of numerical algebraic geometry. I willpresent an algorithm using the Macaulay dual space for computing theregularity index of the local Hilbert function.