  An ideal of a local polynomial ring can be described by calculating a
standard basis with respect to a local monomial ordering. However standard
basis algorithms are not numerically stable. Instead we can describe the ideal
numerically by finding the space of dual functionals that annihilate it,
reducing the problem to one of linear algebra. There are several known
algorithms for finding the truncated dual up to any specified degree, which is
useful for describing zero-dimensional ideals. We present a stopping criterion
for positive-dimensional cases based on homogenization that guarantees all
generators of the initial monomial ideal are found. This has applications for
calculating Hilbert functions.
