Abstract
An algorithm is designed which tests solvability of a system of k polynomial equations in n variables with degrees d within complexity polynomial in \(n^{d^{3k}}\). If the system is solvable then the algorithm yields one of its solutions. Thus, for fixed d, k the complexity of the algorithm is polynomial.
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Grigoriev, D. (2013). Polynomial Complexity of Solving Systems of Few Algebraic Equations with Small Degrees. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_11
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DOI: https://doi.org/10.1007/978-3-319-02297-0_11
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