We design a homotopy continuation algorithm  for finding real zeros of sparse polynomial systems. Our algorithm builds on a well-known geometric deformation process, namely Viro's patchworking method. 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 works for polynomial system with coefficients satisfying certain concavity conditions . More precisely, it requires the given polynomial system to be located in the unbounded components of the complement of the underlying A-discriminant amoeba. A preliminary implementation of an example from the literature suggests practical performance of the algorithm. We plan to work towards a vigorous implementation including a larger scale of examples and a software paper .
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 .
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, that is based on numerically tracking Viro's patchworking method,
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Our algorithm builds on a well-known geometric deformation process, namely Viro's patchworking method.
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. More precisely, it requires the given polynomial system to be located in the unbounded components of the complement of the underlying A-discriminant amoeba. A preliminary implementation of an example from the literature suggests practical performance of the algorithm. We plan to work towards a vigorous implementation including a larger scale of examples and a software paper