正则柱面代数分解
Regular cylindrical algebraic decomposition
摘要：
我们证明了有界半代数集的强良基圆柱代数分解P是正则胞腔剖分，在任何维度上，并且与P的构造方法无关。良基是P上的一个全局条件，适用于许多广泛使用的算法的输出。我们还表明，同样的S维至多3和P的一个强圆柱代数分解，是局部边界单连通的：这是一个纯粹的局部额外条件。
英文摘要：
We show that a strong well-based cylindrical algebraic decomposition P of a bounded semi-algebraic set is a regular cell decomposition, in any dimension and independently of the method by which P is constructed. Being well-based is a global condition on P that holds for the output of many widely used algorithms. We also show the same for S of dimension at most 3 and P a strong cylindrical algebraic decomposition that is locally boundary simply connected: this is a purely local extra condition.
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