Solving systems of polynomial inequalities in subexponential time

Authors:
D. Yu. Grigor'ev;N. N. Vorobjov, Jr
Affiliations:
Leningrad Department of Mathematical Steklov Institute of the Academy of Sciences of the USSR, Fontanka embankment, 27, Leningrad, 191011, USSR and Leningrad State University, Universitetskaya emb ...;Leningrad Department of Mathematical Steklov Institute of the Academy of Sciences of the USSR, Fontanka embankment, 27, Leningrad, 191011, USSR and Leningrad State University, Universitetskaya emb ...
Venue:
Journal of Symbolic Computation
Year:
1988

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Abstract

Let the polynomials f"1,..., f"k@? @?[X"1,..., X"n] have degrees deg (f"i) = 0,..., f"k = 0. In the case of a positive answer the algorithm constructs a certain finite set of solutions (which is, in fact, a representative set for the family of components of connectivity of the set of all real solutions of the system). The algorithm runs in time polynomial in M(kd) ^n^2. The previously known upper time bound for this problem was Sh=(A"1+A"2log@?Re@?)Re@?^n.Sc^1^/^3.