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Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields.
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Quantifier elimination for real closed fields by cylindrical algebraic decomposition
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Real quantifier elimination is doubly exponential
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B. Caviness and J. Johnson · 1998
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An improved projection operation for cylindrical algebraic decomposition
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S. McCallum · 1999
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Improved projection for cylindrical algebraic decomposition
C.W. Brown · 2001
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A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
J.C. Faugère · 2002
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QEPCAD B: A program for computing with semi-algebraic sets using CADs
C.W. Brown · 2003
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A survey on pattern recognition applications of support vector machines
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An introduction to variable and feature selection
I. Guyon and A. Elisseeff · 2003
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N.H. Arai, T. Matsuzaki, H. Iwane, and H. Anai · 2014
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Truth table invariant cylindrical algebraic decomposition by regular chains
R. Bradford, C. Chen, J.H. Davenport, M. England, M. Moreno Maza, and D. Wilson · 2014
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Machine learning for first-order theorem proving
J.P. Bridge, S.B. Holden, and L.C. Paulson · 2014
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An incremental algorithm for computing cylindrical algebraic decompositions
C. Chen and M. Moreno Maza · 2014
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Real quantifier elimination in the RegularChains library
C. Chen and M. Moreno Maza · 2014
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Problem formulation for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
M. England, R. Bradford, C. Chen, J.H. Davenport, M. Moreno Maza, and D. Wilson · 2014
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Companion to the tutorial: Cylindrical algebraic decomposition, presented at ISSAC ’04
C.W. Brown · 2004
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Efficient projection orders for CAD
A. Dolzmann, A. Seidl, and T. Sturm · 2004
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B. Schölkopf, K. Tsuda, and J.-P. Vert · 2004
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A support vector method for multivariate performance measures
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Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
M. England, R. Bradford, J.H. Davenport, and D. Wilson · 2014
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Using the Regular Chains Library to build cylindrical algebraic decompositions by projecting and lifting
M. England, D. Wilson, R. Bradford, and J.H. Davenport · 2014
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The SymbolicData project: Towards a computer algebra social network
H.G. Graebe, A. Nareike, and S. Johanning · 2014
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Constructing fewer open cells by gcd computation in CAD projection
J. Han, L. Dai, and B. Xia · 2014
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Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition
Z. Huang, M. England, D. Wilson, J.H. Davenport, L. Paulson, and J. Bridge · 2014
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A survey on decision tree algorithm for classification
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Cylindrical algebraic sub-decompositions
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Using the distribution of cells by dimension in a cylindrical algebraic decomposition
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Open non-uniform cylindrical algebraic decompositions
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Constructing a single cell in cylindrical algebraic decomposition
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Improving the use of equational constraints in cylindrical algebraic decomposition
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Detection of Hopf bifurcations in chemical reaction networks using convex coordinates
H. Errami, M. Eiswirth, D. Grigoriev, W.M. Seiler, T. Sturm, and A. Weber · 2015
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The SDEval benchmarking toolkit
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𝖲𝖢 2 \mathsf{SC}^{2} : Satisfiability checking meets symbolic computation
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Truth table invariant cylindrical algebraic decomposition
R. Bradford, J.H. Davenport, M. England, S. McCallum, and D. Wilson · 2016
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Quantifier elimination by cylindrical algebraic decomposition based on regular chains
C. Chen and M. Moreno Maza · 2016
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Need polynomial systems be doubly exponential?
J.H. Davenport and M. England · 2016
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The complexity of cylindrical algebraic decomposition with respect to polynomial degree
M. England and J.H. Davenport · 2016
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Real quantifier elimination for the synthesis of optimal numerical algorithms (Case study: Square root computation)
M. Erascu and H. Hong · 2016
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Using machine learning to decide when to precondition cylindrical algebraic decomposition with Groebner bases
Z. Huang, M. England, J.H. Davenport, and L. Paulson · 2016
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Efficient subformula orders for real quantifier elimination of non-prenex formulas
M. Kobayashi, H. Iwane, T. Matsuzaki, and H. Anai · 2016
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On using Lazard’s projection in CAD construction
S. McCallum and H. Hong · 2016
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Automated economic reasoning with quantifier elimination
C.B. Mulligan · 2016
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Cylindrical algebraic decomposition using local projections
A. Strzeboński · 2016
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A case study on the parametric occurrence of multiple steady states
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Symbolic versus numerical computation and visualization of parameter regions for multistationarity of biological networks
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Analytical solutions for the minimum weight design of trusses by cylindrical algebraic decomposition
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