On Computing a Cell Decomposition of a Real Surface Containing Infinitely Many Singularities

Numerical algorithms for decomposing the real points of a complex curve or surface in any number of variables have been developed and implemented in the new software package Bertini real. These algorithms use homotopy continuation to produce a cell decomposition. The previously existing algorithm for surfaces is restricted to the “almost smooth” case, i.e., the given surface must contain only finitely many singular points. We describe the use of isosingular deflation to remove this almost smooth condition and describe an implementation of deflation via Bertini with MATLAB.