Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets

Bertini real is a command line program for numerically decomposing the real portion of a oneor two-dimensional complex irreducible algebraic set in any reasonable number of variables. Using numerical homotopy continuation to solve a series of polynomial systems via regeneration from a witness set, a set of real vertices is computed, along with connection information and associated homotopy functions. The challenge of embedded singular curves is overcome using isosingular deflation. This decomposition captures the topological information and can be used for further computation and refinement.