Operational Flexibility Analysis of High-Dimensional Systems via Cylindrical Algebraic Decomposition
, 2020 The cylindrical algebraic decomposition (CAD) method has been proposed for flexibility analysis to derive analytical expressions of a feasible region.
Chenglin Zheng +3 more
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Machine Learning to Improve Cylindrical Algebraic Decomposition in Maple
IEEE Workshop on Memetic Computing, 2019 Many algorithms in computer algebra systems can have their performance improved through the careful selection of options that do not affect the correctness of the end result.
M. England, Dorian Florescu
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The Complexity of Cylindrical Algebraic Decomposition with Respect to Polynomial Degree [PDF]
Computer Algebra in Scientific Computing, 2016 Cylindrical algebraic decomposition (CAD) is an important tool for working with polynomial systems, particularly quantifier elimination. However, it has complexity doubly exponential in the number of variables.
M. England, J. Davenport
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Choosing the Variable Ordering for Cylindrical Algebraic Decomposition via Exploiting Chordal Structure [PDF]
International Symposium on Symbolic and Algebraic Computation, 2021 Cylindrical algebraic decomposition (CAD) plays an important role in the field of real algebraic geometry and many other areas. As is well-known, the choice of variable ordering while computing CAD has a great effect on the time and memory use of the ...
Haokun Li +3 more
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Cylindrical Algebraic Sub-Decompositions [PDF]
Mathematics in Computer Science, 2014 26 ...
David J. Wilson +3 more
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Cylindrical algebraic decompositions for boolean combinations [PDF]
Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, 2013 This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae involving them.
Russell J. Bradford +4 more
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Truth table invariant cylindrical algebraic decomposition by regular chains [PDF]
, 2014 A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the ...
Matthew England +11 more
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Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition [PDF]
International Conference on Intelligent Computer Mathematics, 2019 There has been recent interest in the use of machine learning (ML) approaches within mathematical software to make choices that impact on the computing performance without affecting the mathematical correctness of the result.
M. England, Dorian Florescu
semanticscholar +1 more source
Dataset supporting "Using Machine Learning to decide when to Precondition Cylindrical Algebraic Decomposition with Groebner Bases" [PDF]
, 2017 Dataset supporting the paper: Z. Huang, M. England, J.H. Davenport and L.C. Paulson Using Machine Learning to decide when to Precondition Cylindrical Algebraic Decomposition with Groebner Bases. Proceedings of the 18th International Symposium on Symbolic
Paulson, Lawrence C. +5 more
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The complexity of quantifier elimination and cylindrical algebraic decomposition [PDF]
Proceedings of the 2007 international symposium on Symbolic and algebraic computation, 2007 This paper has two parts. In the first part we give a simple and constructive proof that quantifier elimination in real algebra is doubly exponential, even when there is only one free variable and all polynomials in the quantified input are linear.
Christopher W. Brown 0001 +1 more
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