  The NumericalHilbert package for Macaulay2 includes algorithms for computing
local dual spaces of polynomial ideals, and related local combinatorial data
about its scheme structure. These techniques are numerically stable, and can be
used with floating point arithmetic over the complex numbers. They provide a
viable alternative in this setting to purely symbolic methods such as standard
bases. In particular, these methods can be used to compute initial ideals,
local Hilbert functions and Hilbert regularity.

Commutative Algebra;Symbolic Computation;Algebraic Geometry