Titlebook: Quantifier Elimination and Cylindrical Algebraic Decomposition; Bob F. Caviness,Jeremy R. Johnson Conference proceedings 1998 Springer-Ver

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Characterizations of the Macaulay Matrix and Their Algorithmic Impact,gar (1992a, 1992b, 1992c) made it a central tool in their study of the complexity of quantifier elimination. They developed algorithms which have better complexities than Collins’ quantifier elimination algorithm based on the CAD (Collins 1975), but until now Collins’ CAD is much faster in practice.

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Computation of Variant Resultants, were introduced in (Hong 1993d) while devising quantifier elimination algorithms for a certain fragment of the elementary theory of the reals, where the input formulas are required to contain at least one quadratic polynomial equation. Hong (1993d) also gave a method for computing these two variant

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A New Algorithm to Find a Point in Every Cell Defined by a Family of Polynomials, .. We present a new algorithm which computes a point in each connected component of each non-empty sign condition over .,…,.. The output is the set of points together with the sign condition at each point. The algorithm uses .(./.).. arithmetic operations in A. The algorithm is nearly optimal in th

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A Combinatorial Algorithm Solving Some Quantifier Elimination Problems,rt and Heintz 1988) that the general problem of quantifier elimination cannot be solved in polynomial time. Therefore the only way to attack this problem is to consider specific cases where efficient algorithms can be applied. By efficient we do not mean “polynomial time”. Instead we are looking for

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,Quantifier Elimination by Cylindrical Algebraic Decomposition — Twenty Years of Progress,de to the method which, together with a very large increase in available computational power, have made it possible to solve in seconds or minutes some interesting problems. In the following we survey these improvements and present some of these problems with their solutions.

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Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition,ntence of the theory is true or false. Since many important and difficult mathematical problems can be expressed in this theory, any computationally feasible quantifier elimination algorithm would be of utmost significance.

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Partial Cylindrical Algebraic Decomposition for Quantifier Elimination,ant method of clustering for reducing the required computation and McCallum (1984) introduced an improved projection operation which is also very effective in reducing the amount of computation. In this paper we introduce yet another method for reducing the amount of computation which we will call ..

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