We design a homotopy continuation algorithm, that is based on numerically tracking Viro's patchworking method, for finding real zeros of sparse polynomial systems. The algorithm is targeted for polynomial systems with coefficients satisfying certain concavity conditions. It operates entirely over the real numbers and tracks the optimal number of solution paths. In more technical terms; we design an algorithm that correctly counts and finds the real zeros of polynomial systems that are located in the unbounded components of the complement of the underlying A-discriminant amoeba.

翻译：我们设计了一个基于数字跟踪 Viro 的补丁法的同质延续算法, 以寻找稀有多元合成系统的实际零数。 该算法针对多元系统, 其系数能满足某些混凝土条件。 它完全在实际数字上运行, 并跟踪最佳解决方案路径。 用更技术性的术语来说, 我们设计了一个正确计数的算法, 并找到位于A- discriminant amieba 辅助系统未受约束的组件中的多元系统的实际零数 。