Georgia Institute of Technology College of Sciences

An ideal of a local polynomial ring can be described by calculating astandard basis with respect to a local monomial ordering. However if we areonly allowed approximate numerical computations, this process is notnumerically stable. On the other hand we can describe the ideal numericallyby finding the space of dual functionals that annihilate it. There areseveral known algorithms for finding the truncated dual up to any specifieddegree, which is useful for zero-dimensional ideals. I present a stoppingcriterion for positive-dimensional cases based on homogenization thatguarantees all generators of the initial monomial ideal are found. This hasapplications for calculating Hilbert functions.