Quickly Computing Isotopy Type for Exponential Sums over Circuits (Extended Abstract)

Fewnomial Theory [Kho91] has established bounds on the number of connected components (a.k.a. pieces) of a broad class of real analytic sets as a function of a particular kind of input complexity, e.g., the number of distinct exponent vectors among a generating set for the underlying ideal. Here, we pursue the algorithmic side: We show how to efficiently compute the exact isotopy type of certain (possibly singular) real zero sets, instead of just estimating their number of pieces. While we focus on the circuit case, our results form the foundation for an approach to the general case that we will pursue later.