Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
On mechanical quantifier elimination for elementary algebra and geometry
Journal of Symbolic Computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
An Improved Projection Operation for Cylindrical Algebraic Decomposition
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Approaches to parallel quantifier elimination
ISSAC '98 Proceedings of the 1998 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
Heuristic search and pruning in polynomial constraints satisfaction
Annals of Mathematics and Artificial Intelligence
Testing Positiveness of Polynomials
Journal of Automated Reasoning
Reachability Analysis of Delta-NotchLateral Inhibition Using Predicate Abstraction
HiPC '02 Proceedings of the 9th International Conference on High Performance Computing
Solving Geometric Problems with Real Quantifier Elimination
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
A generic projection operator for partial cylindrical algebraic decomposition
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
Abstractions for hybrid systems
Formal Methods in System Design
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
Black-box/white-box simplification and applications to quantifier elimination
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Compiler-enforced memory semantics in the SACLIB computer algebra library
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Quantifier elimination for quartics
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Variant quantifier elimination
Journal of Symbolic Computation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
ACM Communications in Computer Algebra
Theoretical Computer Science
A symbiosis of interval constraint propagation and cylindrical algebraic decomposition
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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The Cylindrical Algebraic Decomposition (CAD) method of Collins [5] decomposes r-dimensional Euclidean space into regions over which a given set of polynomials have constant signs. An important component of the CAD method is the projection operation: given a set A of r-variate polynomials, the projection operation produces a set P of (r - 1)-variate polynomials such that a CAD of r-dimensional space for A can be constructed from a CAD of (r-1)-dimensional space for P. In this paper, we present an improvement to the projection operation. By generalizing a lemma on which the proof of the original projection operation is based, we are able to find another projection operation which produces a smaller number of polynomials. Let m be the number of polynomials contained in A, and let n be a bound for the degree of each polynomial in A in the projection variable. The number of polynomials produced by the original projection operation is dominated by m2n3 whereas the number of polynomials produced by our projection operation is dominated by m2n2.