NumericalImplicitization for Macaulay2

Algebra Seminar
Friday, September 30, 2016 - 3:05pm for 1 hour (actually 50 minutes)
Skiles 005
Justin Chen – UC Berkeley
Anton Leykin

Please Note: 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.