English

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.

Keywords

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}
}