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 Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
An adjacency algorithm for cylindrical algebraic decompositions of three-dimenslonal space
Journal of Symbolic Computation
A cluster-based cylindrical algebraic decomposition algorithm
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
Approaches to parallel quantifier elimination
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On projection in CAD-based quantifier elimination with equational constraint
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Improved projection for CAD's of R3
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
On propagation of equational constraints in CAD-based quantifier elimination
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Improved projection for cylindrical algebraic decomposition
Journal of Symbolic Computation
Local box adjacency algorithms for cylindrical algebraic decompositions
Journal of Symbolic Computation
Testing Positiveness of Polynomials
Journal of Automated Reasoning
On order-invariance of a binomial over a nullifying cell
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Efficient projection orders for CAD
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
On using bi-equational constraints in CAD construction
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Abstractions for hybrid systems
Formal Methods in System Design
On delineability of varieties in CAD-based quantifier elimination with two equational constraints
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Computing cylindrical algebraic decomposition via triangular decomposition
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Automated symbolic reachability analysis: with application to delta-notch signaling automata
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Computation with semialgebraic sets represented by cylindrical algebraic formulas
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Quantifier elimination for quartics
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Cylindrical algebraic decompositions for boolean combinations
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Optimising problem formulation for cylindrical algebraic decomposition
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
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A key component of the cylindrical algebraic decomposition (cad) algorithm of Collins (1975) is the projection operation: the projection of a set A of r-variate polynomials is defined to be a certain set or (r-1)-variate polynomials. Tile zeros of the polynomials in the projection comprise a ''shadow'' of the critical zeros of A. The cad algorithm proceeds by forming successive projections of the input set A, each projection resulting in the elimination of one variable. This paper is concerned with a refinement to the cad algorithm, and to its projection operation in particular. It is shown, using a theorem from complex analytic geometry, that the original projection set for trivariate polynomials that Collins used can be substantially reduced in size, without affecting its essential properties. Observations suggest that the reduction in the projection set size leads to a substantial decrease in the computing time of the cad algorithm.