Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
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Journal of the ACM (JACM)
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Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
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SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
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As has been pointed out [Schwartz & Sharir, 1983b], various problems of motion planning can be expressed as cylindrical algebraic decompositions [Collins, 1975; Arnon et al., 1984]. The purpose of this note is to discuss a particularly simple such problem, and show what actually happens during the decomposition (as far as we could take it). There is no pretence at originality, except perhaps in the conclusions.