Quickly Computing Isotopy Type for Exponential Sums over Circuits (Extended Abstract)
Frédéric Bihan, Erika Croy, Weixun Deng, Kaitlyn Phillipson, Robert J. Rennie, J. Maurice Rojas · ACM communications in computer algebra · 2023
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.