Solving a problem in algebraic geometry with numerical algorithms involves the embedding of the problem in a family of problems with the same structure. The solver then proceeds from an easier to solve instance in the family to the general, given problem. As polynomial homotopy methods to solve polynomial systems have progressed from computing approximations for isolated solutions into the manipulation of positive solution sets, the technology (both hardware and software) has evolved as well. Cloud computing offers the user both algorithms and computers, which has implications for what we currently view as solving a problem. Via a web interface we can export all functionality of phcpy and we introduce numerical algebraic geometry.
This is joint work with Nathan Bliss, Jasmine Otto, and Jeff Sommars.
Computer Algebra in Scientific Computing (CASC), 18-21 September 2017, Beijing, China.