Results 141 to 150 of about 40,102 (181)
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation, 1991 The Cylindrical Algebraic Decomposition method (CAD) decomposes Rr into regions over which given polynomials have constant signs. An important application of CAD is quantifier elimination in elementary algebra and geometry.
George E Collins, Hoon Hong
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Enhancements to Lazard's Method for Cylindrical Algebraic Decomposition
Computer Algebra in Scientific Computing, 2020In 1994 Daniel Lazard proposed an improved method for constructing a cylindrical algebraic decomposition (CAD) from a set of polynomials, which recent work has, finally, fully validated. Lazard’s method works for any set of input polynomials, but is less efficient than the method of Brown (2001) which, however, fails for input sets that are not “well ...
Christopher W. Brown, Scott McCallum
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Quantifier elimination by cylindrical algebraic decomposition based on regular chains
Journal of Symbolic Computation, 2016 A quantifier elimination algorithm by cylindrical algebraic decomposition based on regular chains is presented. The main idea is to refine a complex cylindrical tree until the signs of polynomials appearing in the tree are sufficient to distinguish the ...
Changbo Chen, Marc Moreno Maza
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Flexibility index and design of chemical systems by cylindrical algebraic decomposition
Computers and Chemical Engineering, 2021The traditional methods for the solution of flexibility index and design problems are mainly developed by numerical calculation methods. In this work, a new solution approach is proposed for chemical systems described by polynomials to deduce explicit ...
Chenglin Zheng, Fei Zhao, Xi Chen
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Suggesting Variable Order for Cylindrical Algebraic Decomposition via Reinforcement Learning
Neural Information Processing Systems, 2023Cylindrical Algebraic Decomposition (CAD) is one of the pillar algorithms of symbolic computation, and its worst-case complexity is double exponential to the number of variables.
Fuqi Jia +5 more
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ACM Communications in Computer Algebra, 2023
We present some current improvements, implemented in the software package GeoGebra Discovery, that combine symbolic computation and graphics algorithms to faithfully visualize (semi-)algebraic expressions. Our implementation allows fluid animation of set
Christopher W. Brown +2 more
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We present some current improvements, implemented in the software package GeoGebra Discovery, that combine symbolic computation and graphics algorithms to faithfully visualize (semi-)algebraic expressions. Our implementation allows fluid animation of set
Christopher W. Brown +2 more
semanticscholar +1 more source
Flexibility Analysis of High-dimensional Systems via Cylindrical Algebraic Decomposition
Computer Aided Chemical Engineering, 2020In process design, flexibility analysis is an important technique for evaluating the operability of a chemical process. The cylindrical algebraic decomposition (CAD) method has been proposed for flexibility analysis to derive analytical expressions of a ...
Chenglin Zheng, Xi Chen
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A Variant of Non-uniform Cylindrical Algebraic Decomposition for Real Quantifier Elimination
SC-Square@CADEThe Cylindrical Algebraic Decomposition (CAD) method is currently the only complete algorithm used in practice for solving real-algebraic problems. To ameliorate its doubly-exponential complexity, different exploration-guided adaptations try to avoid ...
Jasper Nalbach, Erika 'Abrah'am
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On proving inequalities by cylindrical algebraic decomposition
Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, 2020Summary: Cylindrical algebraic decomposition (CAD) is a basic concept in real algebraic geometry, and it has useful applications to deal with symbolic inequalities. We present a new implementation of CAD in the SageMath computer algebra system.
Marcell János Uray
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Cylindrical Algebraic Decomposition I: The Basic Algorithm
SIAM Journal on Computing, 1984 Given a set of r-variate integral polynomials, a cylindrical algebraic decomposition (cad) of euclidean r-space E r partitions E r into connected subsets compatible with the zeros of the polynomials. By “compatible with the zeros of the polynomials” we mean that on each subset of E r , each of the polynomials either vanishes everywhere or nowhere.
Dennis S Arnon +2 more
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