Regular cylindrical algebraic decomposition
Algebraic Geometry
2019-08-07 v1 Symbolic Computation
Algebraic Topology
Abstract
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.
Cite
@article{arxiv.1803.04029,
title = {Regular cylindrical algebraic decomposition},
author = {J. H. Davenport and A. F. Locatelli and G. K. Sankaran},
journal= {arXiv preprint arXiv:1803.04029},
year = {2019}
}