Many varieties of interest in algebraic geometry and applications
are given as images of regular maps, i.e. via a parametrization.
Implicitization is the process of converting a parametric description of a
variety into an intrinsic (i.e. implicit) one. Theoretically,
implicitization is done by computing (a Grobner basis for) the kernel of a
ring map, but this can be extremely time-consuming -- even so, one would
often like to know basic information about the image variety. The purpose
of the NumericalImplicitization package is to allow for user-friendly
computation of the basic numerical invariants of a parametrized variety,
such as dimension, degree, and Hilbert function values, especially when
Grobner basis methods take prohibitively long.