Computing with Composed Functions

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This project aims to develop the theory, algorithms, and software for solving systems of equations made of composed functions efficiently, by utilizing their composition structure. The project will investigate methods for various symbolic and numeric operations such as multivariate subresultants, Groebner bases, characteristic sets, and Newton iterations that are fundamental to solving systems of equations. Composed functions arise very naturally and frequently in most moderate- to large-scale engineering computations. It is expected that the results of this research will have a broad impact on system solving in science and industry.