@inproceedings{10.1007/BFb0030287,
    Abstract = {An algorithm is described producing for each formula of the first order theory of algebraically closed fields an equivalent free of quantifiers one. Denote by N a number of polynomials occuring in the formula, by d an upper bound on the degrees of polynomials, by n a number of variables, by a a number of quantifier alternations (in the prefix form). Then the algorithm works within the polynomial in the formula's size and in (Nd)n(2a+2) time. Up to now a bound (Nd)no(n) was known ([5], [7], [15]).},
    Address = {Berlin, Heidelberg},
    Author = {Chistov, A. L. and Grigor'ev, D. Yu.},
    BookTitle = {Mathematical Foundations of Computer Science 1984},
    Editor = {Chytil, M. P. and Koubek, V.},
    ISBN = {978-3-540-38929-3},
    Pages = {17--31},
    Publisher = {Springer Berlin Heidelberg},
    Title = {Complexity of quantifier elimination in the theory of algebraically closed fields},
    Year = {1984},
    date-added = {2020-10-20 12:06:12 +0200},
    date-modified = {2020-10-20 12:06:12 +0200},
    doi = {10.1007/BFb0030287}
}

@inproceedings{10.1007/BFb0030287, Abstract = {An algorithm is described producing for each formula of the first order theory of algebraically closed fields an equivalent free of quantifiers one. Denote by N a number of polynomials occuring in the formula, by d an upper bound on the degrees of polynomials, by n a number of variables, by a a number of quantifier alternations (in the prefix form). Then the algorithm works within the polynomial in the formula's size and in (Nd)n(2a+2) time. Up to now a bound (Nd)no(n) was known ([5], [7], [15]).}, Address = {Berlin, Heidelberg}, Author = {Chistov, A. L. and Grigor'ev, D. Yu.}, BookTitle = {Mathematical Foundations of Computer Science 1984}, Editor = {Chytil, M. P. and Koubek, V.}, ISBN = {978-3-540-38929-3}, Pages = {17--31}, Publisher = {Springer Berlin Heidelberg}, Title = {Complexity of quantifier elimination in the theory of algebraically closed fields}, Year = {1984}, date-added = {2020-10-20 12:06:12 +0200}, date-modified = {2020-10-20 12:06:12 +0200}, doi = {10.1007/BFb0030287} }