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  operates entirely over the real numbers and tracks the optimal number of solution paths. In exchange, the algorithm is not universally applicable - it only works for polynomial systems with coefficients satisfying certain concavity conditions .
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 .
A
is targeted for polynomial systems with coefficients satisfying certain concavity conditions. It
R
exchange, the algorithm is not universally applicable - it only works for polynomial systems with coefficients satisfying certain concavity conditions
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