Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
On approximations and incidence in cylindrical algebraic decompositions
SIAM Journal on Computing
An improved projection operation for cylindrical algebraic decomposition of three-dimensional space
Journal of Symbolic Computation
An adjacency algorithm for cylindrical algebraic decompositions of three-dimenslonal space
Journal of Symbolic Computation
A polynomial-time algorithm for the topological type of a real algebraic curve
Journal of Symbolic Computation
On mechanical quantifier elimination for elementary algebra and geometry
Journal of Symbolic Computation
A cellular decomposition algorithm for semi-algebraic sets
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Algebraic cell decomposition in NC
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
An adjacency algorithm for cylindrical algebraic decompositions of three-dimenslonal space
Journal of Symbolic Computation
A polynomial-time algorithm for the topological type of a real algebraic curve
Journal of Symbolic Computation
On mechanical quantifier elimination for elementary algebra and geometry
Journal of Symbolic Computation
A bibliography of quantifier elimination for real closed fields
Journal of Symbolic Computation
Quantifier elimination and the sign variation method for real root isolation
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
A parallel implementation of the cylindrical algebraic decomposition algorithm
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Local box adjacency algorithms for cylindrical algebraic decompositions
Journal of Symbolic Computation
Heuristic search and pruning in polynomial constraints satisfaction
Annals of Mathematics and Artificial Intelligence
Towards better simplification of elementary functions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Better simplification of elementary functions through power series
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Adherence is better than adjacency: computing the Riemann index using CAD
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Exact geometric-topological analysis of algebraic surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
An efficient algorithm for the stratification and triangulation of an algebraic surface
Computational Geometry: Theory and Applications
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Let A @? Z [x"1,000, x"r be a finite set. An A-invariant cylindrical algebraic decomposition (cad) is a certain partitlon of r-dlmensional euclidean space E^r into semi-algebralc cells such that the value of each A"i @? A has constant sign (positive, negative, or zero) throug|umt each cell. Two cells are adjacent if their union is connected. Recently a number of mathoda have been given for augmenting Colllns' cad construction algorithm (1975), so that in addition to specifying the cell~ that comprise a cad, it identifies the pairs of adjacent cells. Assuming the availability of such an adjacency algorithm, in this paper we give a modified cad construction algorithm based on the utillzatloa of clusters of cells in a cad (a cluster is a collection of cells whose union is connected). Preliminary observations indicate that the 11ew algorithm can be significantly more efficient in some cases than the original, although in other examples it is somewhat less efficient.