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
An improved projection operation for cylindrical algebraic decomposition of three-dimensional space
Journal of Symbolic Computation
Quantifier elimination: Optimal solution for two classical examples
Journal of Symbolic Computation
An improvement of the projection operator in cylindrical algebraic decomposition
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Improved projection for cylindrical algebraic decomposition
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
A generic projection operator for partial cylindrical algebraic decomposition
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
An improved projection operation for cylindrical algebraic decomposition (computer algebra, geometry, algorithms)
Problem #9: an ellipse problem
ACM SIGSAM Bulletin
Adherence is better than adjacency: computing the Riemann index using CAD
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Implementing the cylindrical algebraic decomposition within the Coq system
Mathematical Structures in Computer Science
The complexity of quantifier elimination and cylindrical algebraic decomposition
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Symbolic optimization of algebraic functions
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
Combined Decision Techniques for the Existential Theory of the Reals
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Computing cylindrical algebraic decomposition via triangular decomposition
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Proceedings of the 2009 conference on Symbolic numeric computation
Automatic verification of the adequacy of models for families of geometric objects
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
Efficient preprocessing methods for quantifier elimination
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Speeding up cylindrical algebraic decomposition by gröbner bases
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
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
The strategy challenge in SMT solving
Automated Reasoning and Mathematics
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We introduce an efficient algorithm for determining a suitable projection order for performing cylindrical algebraic decomposition. Our algorithm is motivated by a statistical analysis of comprehensive test set computations. This analysis introduces several measures on both the projection sets and the entire computation, which turn out to be highly correlated. The statistical data also shows that the orders generated by our algorithm are significantly close to optimal.